The customer would need to use more than 12.5 megabytes for Plan B to be a better deal. (Option 1) more than 12.5 megabytes).
To determine when Plan B would be a better deal than Plan A, we need to compare the charges for both plans based on the number of megabytes used.
Plan A is represented by the linear function y = 10x, where x represents the total number of megabytes used, and y represents the charge for the plan.
Plan B is represented by the linear function y = 4x + 75, where x represents the total number of megabytes used, and y represents the charge for the plan.
To find the point at which Plan B becomes a better deal, we need to find the x-value where the charge for Plan B is less than the charge for Plan A.
In other words, we need to find the x-value that satisfies the inequality:
4x + 75 < 10x
To solve this inequality, we subtract 4x from both sides:
75 < 6x
Then, we divide both sides by 6:
12.5 < x
Therefore, the customer would need to use more than 12.5 megabytes for Plan B to be a better deal.
This means that option 1) "more than 12.5 megabytes" is the correct answer.
For any value of x greater than 12.5, the charge for Plan B will be less than the charge for Plan A, making it a better deal for the customer.
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please answer i am stuck
(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).
In 2011 the assets are about $669.6 billion
(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).
In 2016 the assets are about $931.5 billion.
(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).
In 2019 the assets are about $1135.4 billion.
How to estimate the cost of the assets in 2011?Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:
[tex]A(x)=324e^{0.066x}[/tex]
where:
A(x) is in billions of dollars.x = 7 corresponds to the year 2007.For the year 2011, the cost (in billions of dollars) is given by;
x = (2011 - 2007) + 7
x = 4 + 7
x = 11 years.
Next, we would substitute 11 for x in the exponential function:
[tex]A(11)=324e^{0.066 \times 11}[/tex]
A(11) = $669.6 billions.
Part b.
For the year 2016, the cost (in billions of dollars) is given by;
x = (2016 - 2007) + 7
x = 9 + 7
x = 16 years.
Next, we would substitute 16 for x in the exponential function:
[tex]A(16)=324e^{0.066 \times 16}[/tex]
A(16) = $931.5 billions.
Part c.
For the year 2019, the cost (in billions of dollars) is given by;
x = (2019 - 2007) + 7
x = 12 + 7
x = 19 years.
Next, we would substitute 19 for x in the exponential function:
[tex]A(19)=324e^{0.066 \times 19}[/tex]
A(19) = $1135.4 billions.
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Let p(x) = a1x^2 + b1x +c1 and q(x) = a2x^2 + b2x + c2 be polynomials in P2. Define an inner product in P2 as follows {p,q} = 5a1a2 + 4b1b2 + 3c1c2.
Given p(x) =5x^2 + (-1)x + (-3) and q(x) = 2x^2 + (4)x +(-3). Evaluate the following expressions
1. p(x) - q(x) = 3x^2 - 5x
2. {p - q, p-q} = 145
3. llp-qll = sqrt({p-q,p-q}) = sqrt(145)
For part 1, I know the answer and how to get it.
For part 2, I know the answer but I'm not sure how to get to it
Answer:
Step-by-step explanation:
To evaluate the expression {p - q, p - q}, which represents the inner product of the polynomial (p - q) with itself, you can follow these steps:
Given p(x) = 5x^2 - x - 3 and q(x) = 2x^2 + 4x - 3.
Subtract q(x) from p(x) to get (p - q):
(p - q)(x) = (5x^2 - x - 3) - (2x^2 + 4x - 3)
= 5x^2 - x - 3 - 2x^2 - 4x + 3
= (5x^2 - 2x^2) + (-x - 4x) + (-3 + 3)
= 3x^2 - 5x
Now, calculate the inner product of (p - q) with itself using the given inner product formula:
{p - q, p - q} = 5(a1)(a2) + 4(b1)(b2) + 3(c1)(c2)
= 5(3)(3) + 4(-5)(-5) + 3(0)(0)
= 45 + 100 + 0
= 145
Therefore, the value of {p - q, p - q} is 145.
if the graph of f(x) =3^x shifted 6 units to the right, what is the equation of the new graph
Use the marginal tax rate chart to answer the question. Tax Bracket Marginal Tax Rate $0–$10,275 10% $10,276–$41,175 12% $41,176–$89,075 22% $89,076–$170,050 24% $170,051–$215,950 32% $215,951–$539,900 35% > $539,901 37% Determine the effective tax rate for a taxable income of $175,000. Round the final answer to the nearest hundredth.
Answer:
the effective tax rate for a taxable income of $175,000 is approximately 21.02%.
Step-by-step explanation:
Let's break down the income into the corresponding tax brackets:
The first $10,275 is taxed at a rate of 10%.
Tax on this portion: $10,275 * 0.10 = $1,027.50
The income between $10,276 and $41,175 is taxed at a rate of 12%.
Tax on this portion: ($41,175 - $10,276) * 0.12 = $3,710.88
The income between $41,176 and $89,075 is taxed at a rate of 22%.
Tax on this portion: ($89,075 - $41,176) * 0.22 = $10,656.98
The income between $89,076 and $170,050 is taxed at a rate of 24%.
Tax on this portion: ($170,050 - $89,076) * 0.24 = $19,862.88
The income between $170,051 and $175,000 is taxed at a rate of 32%.
Tax on this portion: ($175,000 - $170,051) * 0.32 = $1,577.44
Now, sum up all the taxes paid:
$1,027.50 + $3,710.88 + $10,656.98 + $19,862.88 + $1,577.44 = $36,836.68
The effective tax rate is calculated by dividing the total tax paid by the taxable income:
Effective tax rate = Total tax paid / Taxable income
Effective tax rate = $36,836.68 / $175,000 = 0.21024 (rounded to the nearest hundredth)
Given that √x + √y=138 and x-y=1656, find x.
The value of x is 5625 when √x + √y=138 and x-y=1656.
To solve for x using the given equations, we will use the method of substitution. Let's go through the steps:
Start with the equation √x + √y = 138.
We want to express y in terms of x, so solve for y in terms of x by isolating √y:
√y = 138 - √x
Square both sides of the equation to eliminate the square root:
(√y)² = (138 - √x)²
y = (138 - √x)²
Now, substitute the expression for y in the second equation x - y = 1656:
x - (138 - √x)² = 1656
Expand the squared term:
x - (138² - 2 * 138 * √x + (√x)²) = 1656
Simplify the equation further:
x - (19044 - 276 * √x + x) = 1656
Combine like terms and rearrange the equation:
-19044 + 276 * √x = 1656
Move the constant term to the other side:
276 * √x = 20700
Divide both sides of the equation by 276 to solve for √x:
√x = 20700 / 276
√x = 75
Square both sides to solve for x:
x = (√x)²
x = 75²
x = 5625
Therefore, the value of x is 5625.
By substituting this value of x back into the original equations, we can verify that √x + √y = 138 and x - y = 1656 hold true.
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Alonso brings
$
21
$21dollar sign, 21 to the market to buy eggs and avocados. He gets eggs that cost
$
2.50
$2.50dollar sign, 2, point, 50. Then, he notices that the store only sells avocados in bags of
3
33 for
$
5
$5dollar sign, 5. He wants to buy as many avocados as he can with his remaining money.
Let
�
BB represent the number of bags of avocados that Alonso buys.
Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.
Alonso has $21.00 to spend on eggs and avocados. He buys eggs that cost $2.50, which leaves him with $18.50. Since the store only sells avocados in bags of 3, he will need to find the cost per bag in order to calculate how many bags he can buy.
First, divide the cost of 3 avocados by 3 to find the cost per avocado. $5.00 ÷ 3 = $1.67 per avocado.
Next, divide the money Alonso has left by the cost per avocado to find how many avocados he can buy.
$18.50 ÷ $1.67 per avocado = 11.08 avocados.
Since avocados only come in bags of 3, Alonso needs to round down to the nearest whole bag. He can buy 11 avocados, which is 3.67 bags.
Thus, he will buy 3 bags of avocados.Let's test our answer to make sure that Alonso has spent all his money:
$2.50 for eggs3 bags of avocados for $5.00 per bag, which is 9 bags of avocados altogether. 9 bags × $5.00 per bag = $45.00 spent on avocados.
Total spent:
$2.50 + $45.00 = $47.50
Total money had:
$21.00
Remaining money:
$0.00
Since Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.
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A man goes 10m North and turns left and covers 6m. He again turns left and walks 5m. Which direction is he in from starting point?
The man is in the south direction from the starting point.
Let's visualize the movements of the man step by step:
The man starts by going 10 meters north.
He then turns left (which means he is now facing west) and covers 6 meters in that direction.
Next, he turns left again (which means he is now facing south) and walks 5 meters.
To determine the final direction of the man from the starting point, we can consider the net effect of his movements.
Starting from the north, he moved 10 meters in that direction. Then, he turned left twice, which corresponds to a 180-degree turn, effectively changing his direction by 180 degrees.
Since he initially faced north and then made a 180-degree turn, he is now facing south. Therefore, the direction he is in from the starting point is "south."
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Deepak wrote out the steps to his solution of the equation StartFraction 5 Over 2 minus 3 x minus 5 plus 4 x equals negative StartFraction 7 Over 4 EndFraction – 3x – 5 + 4x = –.
The solution to the given equation is x = -1/4.To solve the equation, let's break down the steps as outlined by Deepak:
Combine like terms: Starting with the left side of the equation, combine the x terms and the constant terms separately. On the left side, we have -3x and 4x, which can be combined to give x. Similarly, we have -5 and 5, which cancel each other out, leaving us with zero.
Simplify both sides: Now, the equation becomes x = -7/4 - 3x.
Move all the x terms to one side: To isolate the x term on one side, we can add 3x to both sides of the equation. This gives us 4x + 3x = -7/4.
Combine like terms: On the left side, we have 4x and 3x, which can be added to give 7x. The equation now becomes 7x = -7/4.
Solve for x: To solve for x, we divide both sides of the equation by 7. This yields x = -1/4.
Therefore, the solution to the given equation is x = -1/4.
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On January 1, 2022, ABC Company was established (trading firm engaged in buying and selling of laptop computers ), with an initial owner’s equity of P1,000,000. The company has an inventory 10 laptops each costing P50,000. In addition, it purchased a delivery equipment amounting to P250,000 (five years depreciation, straight line). The rest of the assets were in the form of cash.
At the end of 2022, operations showed that 5 laptops were sold at P50,000 each, 50% cash, 50% to be received in March of P2022. Aside from depreciation, a total of P50,000 (paid in cash) was incurred as operating expenses. Taxes are 50% of operating income to be paid in the same year of operations, if there are any. (Tax will not be deducted if there is an operating loss).
Construct the following :
a.) Balance sheet as of January 1, 2022 and December 31, 2022.
b.) Income Statement for the year ended Dec. 31, 2022 .
c.) Statement of Cash Flows for the year ended Dec. 31, 2022.
a) Balance Sheet as of January 1, 2022: Total Assets: P1,750,000
b) Income Statement for the year ended December 31, 2022: Net Income: Operating Income - Tax Expense
c) Statement of Cash Flows for the year ended December 31, 2022: None (Assuming no financing activities are mentioned in the information)
a) Balance Sheet as of January 1, 2022:
Assets:
Cash: P1,000,000
Inventory (10 laptops * P50,000): P500,000
Delivery Equipment (less depreciation): P250,000
Total Assets: P1,750,000
Liabilities:
None (Assuming no liabilities are mentioned in the given information)
Owner's Equity: P1,750,000
Balance Sheet as of December 31, 2022:
Assets:
Cash: (Assuming no cash transactions are mentioned in the information)
Accounts Receivable (50% of P50,000): P25,000
Inventory (5 laptops * P50,000): P250,000
Delivery Equipment (less depreciation): P200,000
Total Assets: P475,000
Liabilities:
Accounts Payable (50% of P50,000): P25,000
Income Tax Payable: (50% of Operating Income)
Total Liabilities: P25,000 + Income Tax Payable
Owner's Equity: (Initial Owner's Equity + Net Income)
b) Income Statement for the year ended December 31, 2022:
Sales Revenue: 5 laptops * P50,000 = P250,000
Operating Expenses: P50,000
Operating Income: Sales Revenue - Operating Expenses
Tax Expense: (50% of Operating Income)
Net Income: Operating Income - Tax Expense
c) Statement of Cash Flows for the year ended December 31, 2022:
Cash Flows from Operating Activities:
Cash received from sales: (50% of P250,000)
Cash paid for operating expenses: P50,000
Tax payments: (50% of Tax Expense)
Cash Flows from Investing Activities:
Purchase of delivery equipment: P250,000
Cash Flows from Financing Activities:
None (Assuming no financing activities are mentioned in the information)
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Evalute 3n² - 8n - 9, given n(n - 3) = 10.
Answer:
19 or 26
Step-by-step explanation:
You want the value of 3n² -8n -9, given that n(n -3) = 10.
Values of nWe recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.
Expression in nThe value of 3n² -8n -9 will be one of ...
(3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2
or
(3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5
The expression 3n² -8n -9 will be either 19 or 26.
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22. Ms. Hernandez has $150 to spend on parking and admission to the zoo. The parking will cost $3, and
admission tickets will cost $10.40 per person, including tax. Write and solve an equation that can be
used to determine the number of people that she can bring to the zoo, including herself.
SHOW ALL WORK
23.A car travels 50+ miles in of an hour. What is the average speed, in miles per hour, of the car?
SHOW ALL WORK
Answer:
Step-by-step explanation:
Let's represent the number of people that Ms. Hernandez can bring to the zoo as "x". Each person will require an admission ticket, which costs $10.40 per person. Additionally, there is a parking fee of $3.
The total cost of admission tickets and parking is given as $150. We can set up the equation as follows:
10.40x + 3 = 150
To solve for x, we need to isolate the variable:
10.40x = 150 - 3
10.40x = 147
Now, divide both sides of the equation by 10.40 to solve for x:
x = 147 / 10.40
Using a calculator, we find:
x ≈ 14.13
Since we can't have a fractional number of people, we need to round down to the nearest whole number since we can't bring a fraction of a person. Therefore, Ms. Hernandez can bring 14 people to the zoo, including herself.
The average speed of a car is calculated by dividing the total distance traveled by the total time taken. In this case, the car travels 50+ miles in "of an hour".
To calculate the average speed in miles per hour, we need to determine the value of "of an hour". If the value is given as a fraction, we need to convert it to a decimal.
Assuming "of an hour" is 1/2 (0.5), the average speed can be calculated as:
Average speed = Total distance / Total time
Average speed = 50+ miles / (1/2) hour
To divide by a fraction, we can multiply by its reciprocal:
Average speed = 50+ miles * (2/1) hour
Average speed = 100+ miles per hour
Therefore, the average speed of the car is 100+ miles per hour.
what is (0.3)0 in binominal distribution
Answer:
When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).
So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.
Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows.
Step 1: m = StartFraction 13 minus 25 Over negative 4 minus (negative 7) EndFraction = StartFraction negative 12 Over 3 EndFraction = negative 4. Step 2: y = negative 4 x + b. 25 = negative 4 (negative 7) + b. 25 = 28 + b. 25 minus 28 = 28 + b minus 28. b = negative 3. Step 3: y = negative 3 x minus 4
What was Brooke’s error?
She found the incorrect slope in step 1.
She mixed up the x- and y-coordinates when she plugged in the point in step 2.
She found the incorrect y-intercept in step 2.
She mixed up the slope and y-intercept when she wrote the equation in step 3
Answer:
she mixed up the slope and y- intercept in step 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
she correctly calculated the slope as m = - 4 and the y- intercept b = - 3
thus equation she should have is
y = - 4x - 3
Brooke's error was that she found the incorrect slope in step 1.
The slope formula is: m = (y₂ - y₁) / (x₂ - x₁)
Using the given points: m = (13 - 25) / (-4 - (-7)) m = -12 / 3 m = -4
So, the slope is -4, not -12/3 as Brooke calculated in step 1.
The correct equation for the line passing through the points (-7, 25) and (-4, 13) is: y = -4x - 3 (as found in step 3)
The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers?
Answer:
Step-by-step explanation:
Let's break down the given information step by step to solve the problem:
The sum of three numbers x, y, and z is 165: x + y + z = 165.
When the smallest number x is multiplied by 7, the result is n: 7x = n.
The value n is obtained by subtracting 9 from the largest number y: y - 9 = n.
The value n is also obtained by adding 9 to the third number z: z + 9 = n.
We can use this information to form a system of equations:
Equation 1: x + y + z = 165
Equation 2: 7x = n
Equation 3: y - 9 = n
Equation 4: z + 9 = n
To find the product of the three numbers, we need to determine the values of x, y, z, and n.
First, let's solve for n using Equation 2:
7x = n
Now, let's substitute the value of n into Equations 3 and 4:
Equation 3: y - 9 = 7x
Equation 4: z + 9 = 7x
We can rearrange Equation 3 to express y in terms of x:
y = 7x + 9
Now, we can substitute the value of y in Equation 1:
x + (7x + 9) + z = 165
Simplifying:
8x + z = 156
Now, we have two equations:
Equation 4: z + 9 = 7x
8x + z = 156
We can solve this system of equations to find the values of x and z:
From Equation 4, we have z = 7x - 9.
Substituting z in Equation 8x + z = 156:
8x + (7x - 9) = 156
15x - 9 = 156
15x = 165
x = 11
Substituting x = 11 in Equation 4:
z + 9 = 7(11)
z + 9 = 77
z = 68
Now, we have the values of x = 11, y = 7x + 9 = 7(11) + 9 = 86, and z = 68.
The product of the three numbers x, y, and z is:
Product = x * y * z = 11 * 86 * 68 = 64648.
Therefore, the product of the three numbers is 64648.
Complete the following number sequence. 2, 4, 7, __, 16, __, 29, __
The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.
To complete the given number sequence, let's analyze the pattern and identify the missing terms.
Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:
The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.
Using this pattern, we can determine the missing terms as follows:
To obtain the third term, we add 2 to the second term:
7 + 2 = 9
To find the fifth term, we add 3 to the fourth term:
16 + 3 = 19
To determine the seventh term, we add 4 to the sixth term:
__ + 4 = 23
Therefore, the missing terms in the sequence are 9, 19, and 23.
By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.
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A student is applying to the University of Florida (UF) and Florida State (FSU).
There is a 40% chance of being accepted at FSU. If the student is accepted at FSU, the probability of being accepted at UF is 60%. If the student is not accepted at FSU there is an 90% chance of non-acceptance at UF.
Of the students not accepted at UF, what is the probability they are accepted at FSU?
Answer:
Let's denote:
- A as the event "student is accepted at FSU"
- B as the event "student is accepted at UF"
We have the following probabilities given:
- P(A) = 0.4 (probability of being accepted at FSU)
- P(B|A) = 0.6 (probability of being accepted at UF given acceptance at FSU)
- P(B'|A') = 0.9 (probability of not being accepted at UF given non-acceptance at FSU), where B' is the complement of B (not being accepted at UF) and A' is the complement of A (not being accepted at FSU).
We want to find P(A|B'), or the probability of being accepted at FSU given non-acceptance at UF.
To calculate this, we can use Bayes' Theorem, which states that:
P(A|B') = P(B'|A) * P(A) / P(B')
We can calculate P(B'|A), the probability of non-acceptance at UF given acceptance at FSU, by using the fact that the sum of probabilities of complementary events equals 1:
P(B'|A) = 1 - P(B|A) = 1 - 0.6 = 0.4
Next, we need to find P(B'), the total probability of non-acceptance at UF. We can use the law of total probability to calculate this:
P(B') = P(B'|A) * P(A) + P(B'|A') * P(A')
P(B') = 0.4 * 0.4 + 0.9 * 0.6 = 0.16 + 0.54 = 0.7
Finally, we can substitute these values into Bayes' theorem:
P(A|B') = P(B'|A) * P(A) / P(B') = 0.4 * 0.4 / 0.7 ≈ 0.229
Therefore, the probability that a student is accepted at FSU given that they are not accepted at UF is approximately 22.9%.
Which expressions represent the statement divided the difference of 27 and 3 by there difference of 16 and 4
The expression that represents the statement "Divide the difference of 27 and 3 by the difference of 16 and 4" is (27 - 3) / (16 - 4), which simplifies to 2.
The statement "Divide the difference of 27 and 3 by the difference of 16 and 4" can be represented using algebraic expressions.
To find the difference between two numbers, we subtract one from the other. So, the difference of 27 and 3 is 27 - 3, which can be expressed as (27 - 3). Similarly, the difference of 16 and 4 is 16 - 4, which can be expressed as (16 - 4).
Now, we need to divide the difference of 27 and 3 by the difference of 16 and 4. We can use the division operator (/) to represent the division operation.
Therefore, the expression that represents the given statement is:
(27 - 3) / (16 - 4)
Simplifying this expression further, we have:
24 / 12
The difference of 27 and 3 is 24, and the difference of 16 and 4 is 12. So, the expression simplifies to:
2
Hence, the expression (27 - 3) / (16 - 4) is equivalent to 2.
In summary, the expression that represents the statement "Divide the difference of 27 and 3 by the difference of 16 and 4" is (27 - 3) / (16 - 4), which simplifies to 2.
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find the ratio for cos
The value of cos E in the triangle is √2/2
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Trigonometric ratio is only applied in right triangles.
Some of the trigonometric functions are ;
sinθ = opp/hyp
cosθ = adj/hyp
tanθ = opp/adj
In the triangle taking reference from angle E, 5 is the opposite and 5 is the adjascent and 5√2 is the hypotenuse.
Therefore;
cos E = 5/5√2
cos E = 1/√2
rationalizing the value;
cos E = √2/2
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Determine the equation of the hyperbola with foci... 100pts
Answer:
[tex]\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1[/tex]
Step-by-step explanation:
To write the equation of the hyperbola with foci (7, -8) and (-19, -8), and vertices (-1, -8) and (-11, -8), we first need to determine the orientation of the hyperbola.
As the y-values of the foci are the same, the foci are located horizontally from the center of the hyperbola, and therefore the hyperbola is horizontal (opening left and right).
The standard equation for a horizontal hyperbola is:
[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]
where:
center = (h, k)vertices = (h±a, k)foci = (h±c, k) where c² = a² + b²The center of a hyperbola is the midpoint of the vertices.
Given that the vertices are (-1, -8) and (-11, -8), we can use the midpoint formula to find the coordinates of the center:
[tex](h,k)=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)[/tex]
[tex](h, k)=\left(\dfrac{-1-11}{2},\dfrac{-8-8}{2}\right)[/tex]
[tex](h, k)=\left(-6,-8\right)[/tex]
The value of "a" is the distance between the center of the hyperbola and each vertex. To find the value of a, calculate the distance between the x-coordinates:
[tex]a=-1-(-6)=5[/tex]
[tex]a=-6-(-11)=5[/tex]
The value of "c" is the distance between the center of the hyperbola and each focus. Given that the foci are (7, -8) and (-19, -8), and the center is (-6, -8), to find the value of c, calculate the distance between the x-coordinates:
[tex]c = 7-(-6)=13[/tex]
[tex]c = -6-(-19)=13[/tex]
Now we have determined the values of a and c, we can use c² = a² + b² to find the value of b:
[tex]c^2 = a^2 + b^2[/tex]
[tex]13^2 = 5^2 + b^2[/tex]
[tex]169 = 25 + b^2[/tex]
[tex]b^2=144[/tex]
[tex]b=12[/tex]
Finally, substitute the found values of a, b, h and k into the standard equation of a hyperbola:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]
[tex]\dfrac{(x-(-6))^2}{5^2}-\dfrac{(y-(-8))^2}{12^2}=1[/tex]
[tex]\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1[/tex]
Therefore, the equation of the hyperbola with foci (7, -8) and (-19, -8), and vertices (-1, -8) and (-11, -8) is:
[tex]\boxed{\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1}[/tex]
The numbers on two consecutively numbered gym lockers have a sum of 129,
What are the locker numbers?
Answer:
64 and 65
Step-by-step explanation:
Let the two lockers be x and (x+1) since they are consecutive
The sum is 129 so,
x + (x+1) = 129
2x + 1 = 129
2x = 128
x = 64
x + 1 = 65
The locker numbers are 64 and 65
Please calculate the volume of a solid oblique pyramid with a triangular base, given that the base has a length of 8 inches and a height of 6 inches, and the height of the pyramid is 10 inches. Round your answer to the nearest cubic inch.
Answer: 74
Step-by-step explanation:
The volume of the pyramid can be found using the formula:
Volume = (1/3) x Base Area x Height
To find the base area, we need to find the area of the triangular base. The area of a triangle can be found using the formula:
Area = (1/2) x Base x Height
Substituting the given values, we have:
Area = (1/2) x 8 x 6 = 24 square inches
To find the height of the pyramid, we can use the Pythagorean theorem. The slant height and one-half of the base form a right triangle, so we have:
Height^2 = (Slant Height)^2 - (1/2 x Base)^2
Height^2 = 10^2 - 4^2
Height^2 = 84
Height = √84 ≈ 9.165 inches
Now we can substitute the values into the formula for the volume:
Volume = (1/3) x Base Area x Height
Volume = (1/3) x 24 x 9.165
Volume ≈ 73.96 cubic inches
Therefore, the volume of the pyramid is approximately 73.96 cubic inches.Step-by-step explanation:
I need help with a question
The function for which f(x) is equal to f⁻¹(x) is: C. [tex]f(x) = \frac{x+1}{x-1}[/tex]
What is an inverse function?In this exercise, you are required to determine the inverse of the function f(x) with an equivalent inverse function f⁻¹(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;
[tex]f(x) = y = \frac{x+6}{x-6} \\\\x=\frac{y+6}{y-6}[/tex]
x(y - 6) = y + 6
y = xy - 6x - 6
f⁻¹(x) = (-6x - 6)/(x - 1) ⇒ Not equal.
Option B.
[tex]f(x) = y = \frac{x+2}{x-2} \\\\x=\frac{y+2}{y-2}[/tex]
x(y - 2) = y + 2
y = xy - 2x - 2
f⁻¹(x) = (-2x - 2)/(x - 1) ⇒ Not equal.
Option C.
[tex]f(x) = y = \frac{x+1}{x-1} \\\\x=\frac{y+1}{y-1}[/tex]
x(y - 1) = y + 1
y - xy = x + 1
f⁻¹(x) = (x + 1)/(x - 1) ⇒ equal.
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–5 < 2x – 1 < 3 solve?? help aap
Answer:
Step-by-step explanation:
To solve the inequality -5 < 2x - 1 < 3, we will break it down into two separate inequalities and solve each one individually.
First, let's solve the left inequality:
-5 < 2x - 1
Add 1 to both sides:
-5 + 1 < 2x - 1 + 1
-4 < 2x
Divide both sides by 2 (remembering to reverse the inequality when dividing by a negative number):
-4/2 < 2x/2
-2 < x
Now, let's solve the right inequality:
2x - 1 < 3
Add 1 to both sides:
2x - 1 + 1 < 3 + 1
2x < 4
Divide both sides by 2:
2x/2 < 4/2
x < 2
So, the solutions to the inequalities are:
-2 < x < 2
This means that x is greater than -2 and less than 2.
HURRY PLEASEEE
A cylinder has a volume of 400 feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.14 for π and a round to the nearest hundredth. radius ≈ type your answer… ft
Answer:
the radius of the cylinder is approximately 2.26 feet.
Step-by-step explanation:
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Given that the volume is 400 feet, the height is 25 feet, and using π ≈ 3.14, we can rearrange the formula to solve for the radius:
400 = 3.14 * radius^2 * 25
Divide both sides of the equation by (3.14 * 25):
400 / (3.14 * 25) = radius^2
Simplifying:
400 / 78.5 ≈ radius^2
5.09 ≈ radius^2
To find the radius, we take the square root of both sides:
√5.09 ≈ √(radius^2)
2.26 ≈ radius
Rounding to the nearest hundredth, the radius of the cylinder is approximately 2.26 feet.
Answer:
Step-by-step explanation:
Volume Formula for a cylinder is V=πr²h
Substitute the following: 400 = 3.14(r²)(25)
r=[tex]\sqrt{\frac{V}{\pi h} }[/tex]
r=[tex]\sqrt{\frac{400}{\pi 25} }[/tex]
r≈2.25676ft
The measurement of the side of a square floor tile is 9 inches, with a possible error of
1/32 inch.
a) Use differentials to find the possible propagated error (in square inches) in computing the area of the square. ± .5625 in^2 Correct: Your answer is correct.
b) Approximate the percent error in computing the area of the square. (Round your answer to three decimal places.)
please answer i am stuck
Answer:
x intercept : -1
y intercept : 3
Step-by-step explanation:
We have 3x - y = -3 ---eq(1)
The x intercept is the value of x when y = 0 in eq(1),
⇒ 3x - 0 = -3
⇒ x = -3/3
⇒ x = -1
The y intercept is the value of y when x = 0 in eq(1),
⇒ 3(0) - y = -3
⇒ -y = -3
⇒ y = 3
how to find surfes area
Remember to use the appropriate units for measurements when calculating surface area.
To find the surface area of an object, you need to calculate the total area of all its exposed surfaces. The method for finding the surface area will vary depending on the shape of the object. Here are some common shapes and their respective formulas:
1. Cube: The surface area of a cube can be found by multiplying the length of one side by itself and then multiplying by 6 since a cube has six equal faces. The formula is: SA = 6s^2, where s is the length of a side.
2. Rectangular Prism: A rectangular prism has six faces, each of which is a rectangle. To find the surface area, calculate the area of each face and add them up. The formula is: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.
3. Cylinder: The surface area of a cylinder includes the area of two circular bases and the area of the curved side. The formula is: SA = 2πr^2 + 2πrh, where r is the radius and h is the height.
4. Sphere: The surface area of a sphere can be found using the formula: SA = 4πr^2, where r is the radius.
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Percents - Modeling Uncategorized Problems
The Nature of Mathematics: page 312 # 1-5, 29, 31, 35, 47 and 54; page 319-320 # 4, 9, 23
In Problems 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, and 21, change the
given form into the two missing forms.
Textbook-
1. Fraction
3. Fraction
5. Fraction
1/3
Write each ront
Decimal
0.75
Decimal
Decimal
Percent
Percent
40%
Percent
2.
Fraction
4. Fraction
Decimal
Decimal
Percent
0.02
Percent
100%
Answer:
Step-by-step explanation:
Converting between Fraction, Decimal, and Percent:
Fraction to Decimal: Divide the numerator by the denominator. The result is the decimal form.
Example: 1/4 = 1 ÷ 4 = 0.25
Decimal to Fraction: Write the decimal as a fraction by placing the decimal value over the appropriate power of 10.
Example: 0.75 = 75/100 = 3/4
Fraction to Percent: Divide the numerator by the denominator and multiply by 100.
Example: 1/3 = (1 ÷ 3) × 100 = 33.33...%
Percent to Fraction: Write the percent as a fraction with a denominator of 100 and simplify if necessary.
Example: 40% = 40/100 = 2/5
Decimal to Percent: Multiply the decimal by 100 and add the percent symbol (%).
Example: 0.75 = 0.75 × 100 = 75%
Percent to Decimal: Divide the percent by 100.
Example: 40% = 40 ÷ 100 = 0.4
93-(15x10)+(160:16) =
Answer:
Step-by-step explanation:
Let's calculate the expression step by step:
93 - (15 × 10) + (160 ÷ 16)
First, we perform the multiplication:
93 - 150 + (160 ÷ 16)
Next, we perform the division:
93 - 150 + 10
Finally, we perform the subtraction and addition:
-57 + 10
The result is:
-47
Therefore, 93 - (15 × 10) + (160 ÷ 16) equals -47.
If R = {(x, y) : x and y are integers and x^2 + y^2 = 64} is a relation, then find R.
Answer:
R = {(0, 8), (0, -8), (8, 0), (-8, 0), (6, ±2), (-6, ±2), (2, ±6), (-2, ±6)}
Step-by-step explanation:
Since [tex](\pm8)^2+0^2=64[/tex], [tex]0^2+(\pm 8)^2=64[/tex], [tex](\pm 6)^2+2^2=64[/tex], and [tex]6^2+(\pm 2)^2=64[/tex], then those are your integer solutions to find R.