Answers
The values in the expression is as follows:
a = 2
b = 0
c = -1
How to solve an expression?The expression can be solve using the exponential law. Therefore,
g = 2³ × 3 × 7²
h = 2 × 3 × 7³
Therefore, let's solve the following:
g/h = 2ᵃ × 3ᵇ × 7ⁿ
Therefore,
g = 2³ × 3 × 7² = 2 × 2 × 2 × 3 × 7 × 7
h = 2 × 3 × 7 × 7 × 7
Hence,
g / h = 2 × 2 × 2 × 3 × 7 × 7 / 2 × 3 × 7 × 7 × 7
Hence,
g / h = 2 × 2 / 7
g . h = 2² × 3° × 7⁻¹
Hence,
a = 2
b = 0
c = -1
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Related Questions
PLEASE HELP ME
How are conditional probability and independent events related?
Select the correct phrase or notation from each drop-down menu to complete the explanation.
The notation P(A|B) reads the probability of Event
choose... (A occurring given that Event B has occurred) or (B occurring given that Event A had occurred)
. If two events are independent, then the probability of one event occurring
Choose... (affects the probability of the other event occurring) or (Does not affect the probability of the other event occurring)
. Events A and B are independent if
Choose... P(A|B)= P(A), P(B|A)= P(B), P(A|B)= P(B|A)
.
Answers
Conditional probability, denoted as P(A|B), represents the probability of event A occurring given that event B has occurred. If events A and B are independent, P(A|B) = P(A) and P(B|A) = P(B).
The notation P(A|B) reads the probability of Event (A occurring given that Event B has occurred). If two events are independent, then the probability of one event occurring (does not affect the probability of the other event occurring). Events A and B are independent if (P(A|B) = P(A), P(B|A) = P(B), P(A|B) = P(B|A)).
To understand the relationship between conditional probability and independent events, let's consider two events A and B. The conditional probability P(A|B) represents the probability of event A occurring given that event B has already occurred. It measures the likelihood of event A happening under the condition that event B has already taken place.
On the other hand, if two events A and B are independent, it means that the occurrence or non-occurrence of one event has no effect on the probability of the other event happening. In other words, the probability of event A happening is not influenced by the occurrence or non-occurrence of event B, and vice versa.
Mathematically, if events A and B are independent, it implies that P(A|B) = P(A) and P(B|A) = P(B). This means that the probability of event A occurring is the same whether or not event B has occurred, and the probability of event B occurring is the same whether or not event A has occurred.
Therefore, the concepts of conditional probability and independent events are related in the sense that if two events are independent, the conditional probabilities P(A|B) and P(B|A) become equal to the unconditional probabilities P(A) and P(B) respectively.
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Which table shows positive correlation? A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 15, 12, 14, 11, 18. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 11, 13, 15, 17, 19. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 18, 16, 14, 12, 11.
Answers
The second table with x and y values (1, 2, 3, 4, 5) and (11, 13, 15, 17, 19) shows a positive correlation.
To determine which table shows a positive correlation, we need to examine the relationship between the values in the x and y columns. Positive correlation means that as the values in one column increase, the values in the other column also tend to increase.
Let's analyze each table:
Table 1:
x: 1, 2, 3, 4, 5
y: 15, 12, 14, 11, 18
In this table, as the values in the x column increase, the values in the y column are not consistently increasing or decreasing. For example, when x increases from 1 to 2, y decreases from 15 to 12. Therefore, this table does not show a positive correlation.
Table 2:
x: 1, 2, 3, 4, 5
y: 11, 13, 15, 17, 19
In this table, as the values in the x column increase, the values in the y column also consistently increase. For example, when x increases from 1 to 2, y increases from 11 to 13. This pattern continues for all the rows. Therefore, this table shows a positive correlation.
Table 3:
x: 1, 2, 3, 4, 5
y: 18, 16, 14, 12, 11
In this table, as the values in the x column increase, the values in the y column consistently decrease. For example, when x increases from 1 to 2, y decreases from 18 to 16. This pattern continues for all the rows. Therefore, this table does not show a positive correlation.
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PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=
Answers
= 20x^2 - 16
(g - f)(x) = (4x - 4) - (5x)
= (-1x) - 4
= -x -4
(g + f)(2) = (4(2) - 4) + (5(2))
= 4 + 10
= 14
40 POINTS: PLEASE HELP!! urgent! using half-angle identities questions
Answers
Answer:
try gauth. math! Take a photo of each question and upload the photo to see if it works
A cargo truck traveled 261 miles in 4 hours. About what speed was the truck averaging on this trip?
a.
65 mph
c.
55 mph
b.
1044 mph
Answers
Answer:
To find the average speed of the truck, we can divide the total distance travelled by the total time taken.
Average speed = Total distance / Total time
In this case, the truck travelled 261 miles in 4 hours.
Average speed = 261 miles / 4 hours
Average speed = 65.25 mph (rounded to two decimal places)
Therefore, the truck was averaging approximately 65 mph on this trip.
The correct option is (a) 65 mph.
Ki Tae uses 54 meters of fencing to make a 6-sided outdoor dog pen. Two of the sides of the dog pen are each 15 meters long. The remaining 4 sides each have the same length.
Answers
Ki Tae used 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides are each 15 meters long, while the remaining four sides are each 6 meters long.
Let's solve the problem step by step. We know that Ki Tae used a total of 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides have a length of 15 meters each.
Let's denote the length of the remaining four sides as "x."
Since the dog pen has six sides, we can set up an equation based on the total length of the fencing:
15 + 15 + x + x + x + x = 54
Simplifying the equation, we have:
30 + 4x = 54
Subtracting 30 from both sides, we get:
4x = 24
Dividing both sides by 4, we find:
x = 6
Therefore, each of the remaining four sides has a length of 6 meters.
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Brianna wants to purchase a vehicle. She has $15,670 saved for a down payment. Chevrolet has a 33% off sale on their Silverado. The Silverado Brianna wants costs $57,999. If she takes advantage of the sale and applies her down payment, how much will Brianna owe on her new vehicle?
Answers
Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.
To solve this problemWe need to follow these steps:
Calculate the discount on the Silverado:
Discount = 33% of $57,999
Discount = 0.33 * $57,999
Discount = $19,079.67
Subtract the discount from the original price of the Silverado:
Price after discount = $57,999 - $19,079.67
Price after discount = $38,919.33
Subtract Brianna's down payment from the price after discount:
Amount owed = Price after discount - Down payment
Amount owed = $38,919.33 - $15,670
Amount owed = $23,249.33
So, Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.
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A parabola can be drawn given a focus of... 100 pts
Answers
Answer:
[tex](y+1)^2=8(x+3)[/tex]
Step-by-step explanation:
The focus of a parabola is a fixed point located inside the curve. It is equidistant from the vertex and the directrix.
The directrix is a line that is located outside the curve. As the directrix on the given graph is a vertical line, the parabola is horizontal (sideways). The directrix is located to the left of the focus, which means the parabola opens to the right.
The axis of symmetry is perpendicular to the directrix and passes through the focus. So the axis of symmetry in this case is y = -1.
The vertex is the turning point of the parabola. It is located on the axis of symmetry, and is halfway between the focus and the directrix. Therefore, the y-coordinate of the vertex is y = -1. Given the focus is (-1, -1) and the directrix is x = -5, the vertex is (-3, -1).
The standard equation of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)Directrix: x = (h - p)Axis of symmetry: y = kAs the vertex is (-3, -1), then h = -3 and k = -1.
Use the formula for the focus to find the value of p:
[tex]\begin{aligned}(h+p, k)&=(-1,-1)\\(-3+p, -1)&=(-1, -1)\\\implies -3+p&=-1\\p&=2\end{aligned}[/tex]
To write an equation for the parabola based on the given focus and directrix, substitute the values of h, k and p into the standard equation :
[tex](y-(-1))^2=4(2)(x-(-3))[/tex]
[tex](y+1)^2=8(x+3)[/tex]
Therefore, the equation of the parabola is:
[tex]\boxed{(y+1)^2=8(x+3)}[/tex]
The equation of the parabola with focus (-1, -1) and directrix x = -5 is (x + 1)² = 16(y + 1).
What is the equation of the parabola?The equation of a parabola with a focus at (-1, -1) and a directrix of x = -5 can be written in standard form as:
(x - h)² = 4p(y - k)
Where (h, k) represents the vertex of the parabola and p is the distance between the vertex and the focus (or directrix).
In this case, the x-coordinate of the focus (-1, -1) is h = -1, and the y-coordinate is k = -1. The directrix is a vertical line x = -5, which means the parabola opens to the right.
Step 1: Determine the value of p
The distance between the vertex and the directrix is given by the absolute difference of their x-coordinates. In this case, p = |-5 - (-1)| = |-5 + 1| = 4.
Step 2: Write the equation
Substituting the values into the standard form equation, we have:
(x - h)² = 4p(y - k)
(x - (-1))² = 4(4)(y - (-1))
(x + 1)² = 16(y + 1)
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D
Drag the expressions to the correct locations on the image. Not all expressions will be used.
Consider this quotient.
(2³ - 8z + 6) ÷ (2² - 2x + 1)
Use long division to rewrite the quotient in an equivalent form as q(z) +
2³ - 8z + 6
2² - 2x + 1
where g(z) is the quotient, r(2) is the remainder, and b(z) is the divisor.
-5z + 4
Reset
H
Next
-11x + 12
x + 2
Answers
The solution to the polynomial division in quotient and remainder form is: (x + 2) + (-5x + 4)/(x² - 2x + 1)
How to carry out Long Division of Polynomials?The polynomials we want to divide are:
x³ - 8x + 6 by x² - 2x + 1 and as such we can write it as:
x + 2
x² - 2x + 1|x³ - 8x + 6
- x³ - 2x² + x
2x² - 9x + 6
- 2x² - 4x + 2
-5x + 4
Thus, the solution expressed in quotient and remainder form is:
(x + 2) + (-5x + 4)/(x² - 2x + 1)
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A comet follows a hyperbolic path in which the sun is located at one of its foci. If the equation... 100 pts
Answers
Answer:
164 million km
Step-by-step explanation:
If the hyperbola models the comet's path, and the sun is located at one of its foci, the closest distance the comet reaches to the sun is the distance between a vertex and its corresponding focus.
Therefore, we need to find the vertices and foci of the given hyperbola.
Given equation:
[tex]\dfrac{x^2}{60516}-\dfrac{y^2}{107584}=1[/tex]
As the x²-term of the given equation is positive, the hyperbola is horizontal (opening left and right).
The general formula for a horizontal hyperbola (opening left and right) is:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Standard equation of a horizontal hyperbola}\\\\$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center.\\ \phantom{ww}$\bullet$ $(h\pm a, k)$ are the vertices.\\\phantom{ww}$\bullet$ $(h\pm c, k)$ are the foci where $c^2=a^2+b^2.$\\\phantom{ww}$\bullet$ $y=\pm \dfrac{b}{a}(x-h)+k$ are the asymptotes.\\\end{minipage}}[/tex]
Comparing the given equation with the standard equation:
h = 0k = ka² = 60516 ⇒ a = 246b² = 107584 ⇒ b = 328To find the loci, we first need to find the value of c:
[tex]\begin{aligned}c^2&=a^2+b^2\\c^2&=60516 +107584\\c^2&=168100\\c&=410\end{aligned}[/tex]
The formula for the loci is (h±c, k). Therefore:
[tex]\begin{aligned}\textsf{Loci}&=(h \pm c, k)\\&=(0 \pm 410, 0)\\&=(-410,0)\;\;\textsf{and}\;\;(410,0)\end{aligned}[/tex]
The formula for the vertices is (h±a, k). Therefore:
[tex]\begin{aligned}\textsf{Vertices}&=(h \pm a, k)\\&=(0 \pm 246, 0)\\&=(-246,0)\;\;\textsf{and}\;\;(246,0)\end{aligned}[/tex]
From the given diagram, the vertex and focus have positive x-values. Therefore, the vertex is (246, 0) and the focus is (410, 0).
We need to find the distance between (246, 0) and (410, 0). To do this, simply subtract the x-value of the vertex from the x-value of the focus:
[tex]410-246=164[/tex]
Therefore, the closest distance the comet reaches to the sun is 164 million km.
. Julio compró ropa por un costo de $5000, por la cual dejó el 20% de apartado. ¿Con cuánto dinero termina de pagar la ropa?
Answers
Julio bought clothes for $5000 with a 20% down payment, which amounts to $1000. Hence, he ends up paying $4000 for the clothes.
Julio's clothing purchase involved a total cost of $5000. To secure the purchase, he made a down payment of 20% of the total cost. To calculate the down payment, we multiply the total cost by the down payment percentage:
Down payment = 20% * $5000
Down payment = 0.20 * $5000
Down payment = $1000
The down payment amount is $1000. To determine the final amount that Julio ends up paying for the clothes, we need to subtract the down payment from the total cost:
Total cost - Down payment = $5000 - $1000
Total cost - Down payment = $4000
Therefore, Julio ends up paying $4000 for the clothes.
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The question probable may be:
Julio bought clothes for a cost of $5000, for which he left a 20% down payment. How much money does he end up paying for the clothes?
A village P is 12 km from village Q. It takes 3 hours 20 minutes to travel from Q to P and back to Q by a boat. If the boat travels at a speed of 6 km/h from P to Q and (6 + x) km/h back to P, find the value of x.
Answers
Answer:
Hope this helps and have a nice day
Step-by-step explanation:
To find the value of x, we can use the formula:
Time = Distance / Speed
Let's calculate the time taken to travel from Q to P and back to Q.
From Q to P:
Distance = 12 km
Speed = 6 km/h
Time taken from Q to P = Distance / Speed = 12 km / 6 km/h = 2 hours
From P to Q:
Distance = 12 km
Speed = (6 + x) km/h
Time taken from P to Q = Distance / Speed = 12 km / (6 + x) km/h
Given that the total time taken for the round trip is 3 hours 20 minutes, we can convert it to hours:
Total time = 3 hours + (20 minutes / 60) hours = 3 + (1/3) hours = 10/3 hours
According to the problem, the total time is the sum of the time from Q to P and from P to Q:
Total time = Time taken from Q to P + Time taken from P to Q
Substituting the values:
10/3 hours = 2 hours + 12 km / (6 + x) km/h
Simplifying the equation:
10/3 = 2 + 12 / (6 + x)
Multiply both sides by (6 + x) to eliminate the denominator:
10(6 + x) = 2(6 + x) + 12
60 + 10x = 12 + 2x + 12
Collecting like terms:
8x = 24
Dividing both sides by 8:
x = 3
Therefore, the value of x is 3.
Answer:
x = 3
Step-by-step explanation:
speed = distance / time
time = distance / speed
Total time from P to Q to P:
T = 3h 20min
P to Q :
s = 6 km/h
d = 12 km
t = d/s
= 12/6
t = 2 h
time remaining t₁ = T - t
= 3h 20min - 2h
= 1 hr 20 min
= 60 + 20 min
= 80 min
t₁ = 80/60 hr
Q to P:
d₁ = 12km
t₁ = 80/60 hr
s₁ = d/t₁
[tex]= \frac{12}{\frac{80}{60} }\\ \\= \frac{12*60}{80}[/tex]
= 9
s₁ = 9 km/h
From question, s₁ = (6 + x)km/h
⇒ 6 + x = 9
⇒ x = 3
Find the value of x.
Answers
subtract (9x^2+4x) from ( -4x^2-7)
Answers
Answer: -13x² - 4x - 7
Step-by-step explanation:
We will subtract (9x² + 4x) from (-4x² - 7).
Given:
-4x² - 7 - (9x² + 4x)
Distribute the negative:
-4x² - 7 - 9x² - 4x
Reorder terms by degree:
-4x² - 9x² - 4x - 7
Combine like terms:
-13x² - 4x - 7
simplify each expression 4(x+2)+(8+2x)
Answers
The simplified form of the expression for 4( x + 2 ) + ( 8 + 2x ) is 6x + 16.
What is the simplified form of the expression?Given the expresion in the equestion:
4( x + 2 ) + ( 8 + 2x )
To simplify the expression 4( x + 2 ) + ( 8 + 2x ), first, apply distributive property by distributing 4 to the terms ( x + 2 ):
4( x + 2 ) + ( 8 + 2x )
4 × x + 4 × 2 + 8 + 2x
4x + 8 + 8 + 2x
Collect and add like terms:
4x + 2x + 8 + 8
Add 4x and 2x
6x + 8 + 8
Add the constants 8 + 8
6x + 16
Therefore, the simplified form is 6x + 16.
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Purchasing a Car
Now you have to decide how to save enough money to purchase a used car in three years. You have the
$1000 that you saved up and you plan to continue working. According to your estimates, you can save an
additional $60 per month to put towards the car purchase. After conducting some research at the banks,
you have decided on two options (see below). You need to figure out which option will yield the most
money after the three years.
Option #1-CD for 3 years
Interest rate of 3% compounded monthly.
No money can be added to the CD.
However you can save your money on the side.
Option # 2-CD for 1 year
Interest rate of 2% compounded quarterly.
You can add money at the end of each year.
You will renew it each year for 3 years.
Work Shown:
Answers
Answer:
Step-by-step explanation:
To determine which option will yield the most money after three years, let's calculate the final amount for each option.
Option #1 - CD for 3 years:
Principal (initial investment) = $1000
Interest rate = 3% per year (compounded monthly)
No additional money can be added
To calculate the final amount, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Final amount
P = Principal (initial investment)
r = Interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
For Option #1:
P = $1000
r = 3% = 0.03 (as a decimal)
n = 12 (compounded monthly)
t = 3 years
A = $1000 * (1 + 0.03/12)^(12*3)
Calculating the final amount for Option #1, we get:
A = $1000 * (1 + 0.0025)^(36)
A ≈ $1000 * (1.0025)^(36)
A ≈ $1000 * 1.0916768
A ≈ $1091.68
Option #2 - CD for 1 year:
Principal (initial investment) = $1000
Interest rate = 2% per year (compounded quarterly)
Money can be added at the end of each year
To calculate the final amount, we need to consider the annual additions and compounding at the end of each year.
First Year:
P = $1000
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1000 * (1 + 0.02/4)^(4*1)
A ≈ $1000 * (1.005)^(4)
A ≈ $1000 * 1.0202
A ≈ $1020.20
At the end of the first year, the total amount is $1020.20.
Second Year:
Now we add an additional $60 to the previous amount:
P = $1020.20 + $60 = $1080.20
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1080.20 * (1 + 0.02/4)^(4*1)
A ≈ $1080.20 * (1.005)^(4)
A ≈ $1080.20 * 1.0202
A ≈ $1101.59
At the end of the second year, the total amount is $1101.59.
Third Year:
Again, we add $60 to the previous amount:
P = $1101.59 + $60 = $1161.59
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1161.59 * (1 + 0.02/4)^(4*1)
A ≈ $1161.59 * (1.005)^(4)
A ≈ $1161.59 * 1.0202
A ≈ $1185.39
At the end of the third year, the total amount is $1185.39.
Comparing the final amounts:
Option #1: $1091.68
Option #2: $1185.39
Therefore, Option #2 - CD for 1 year with an interest rate of 2% compounded quarterly and the ability to add money at the end of each year will yield the most money after three years.
Verify that the given point is on the curve. Find the lines that are a. tangent and b. normal to the curve at the given point.
Answers
The point (2, 7π / 2) does not belong to the implicit curve 8 · x · y + π · sin y = 55π and tangent and normal lines cannot be determined.
Does a point given belong to an implicit curve?
In this question we find the definition of an implicit curve, in which we must determine if point (2, 7π / 2) belongs to the curve. First, we check that point:
8 · x · y + π · sin y = 55π
8 · 2 · (7π / 2) + π · sin (7π / 2) = 55π
56π + 0.191π = 55π
56.191π = 55π
56.191 = 55 (CRASH!)
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Identify an equation in point-slope form for the line parallel to y = 3/4x - 4 that passes through (-1, 7).
Answers
Answer:
A) [tex]y-7=\frac{3}{4}(x+1)[/tex]
Step-by-step explanation:
[tex]y-y_1=m(x-x_1)\\y-7=\frac{3}{4}(x-(-1))\\y-7=\frac{3}{4}(x+1)[/tex]
Parallel lines must have the same slope, and then plugging in [tex](x_1,y_1)=(-1,7)[/tex], we easily get our equation.
Answer:
the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to use the same slope. The given line has a slope of 3/4.
Using the point-slope form of a line, which is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line, we can substitute the values (-1, 7) for (x₁, y₁) and 3/4 for m:
y - 7 = (3/4)(x - (-1))
Simplifying further:
y - 7 = (3/4)(x + 1)
Multiplying through by 4 to eliminate the fraction:
4(y - 7) = 3(x + 1)
Expanding:
4y - 28 = 3x + 3
Rearranging the equation to put it in standard form:
3x - 4y = -31
So, the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.
This year, the number of raffle tickets sold for a school's extracurricular activities fundraiser is 848. It is estimated that the number of raffle tickets sold will increase by 5% each year. Find the total number of raffle tickets sold at the end of 9 years.
Select the correct answer below:
9,158
9,351
9,818
10,666
Answers
This year, the number of raffle tickets sold for a school's extracurricular activities fundraiser is 848. It is estimated that the number of raffle tickets sold will increase by 5% each year.
The total number of raffle tickets sold at the end of 9 years is approximately 9,818.
To find the total number of raffle tickets sold at the end of 9 years, we need to calculate the number of tickets sold each year and sum them up.
Starting with the initial number of tickets sold, which is 848, we will increase this number by 5% each year for a total of 9 years.
Year 1: 848 + (5% of 848) = 848 + 42.4 = 890.4
Year 2: 890.4 + (5% of 890.4) = 890.4 + 44.52 = 934.92
Year 3: 934.92 + (5% of 934.92) = 934.92 + 46.746 = 981.666
Year 9: Ticket sales at the end of 9 years = Number of tickets sold in Year 8 + (5% of Year 8 sales)
Year 9: Total = 1,399.585 + 69.97925 = 1,469.56425 ≈ 1,469.56
The total number of raffle tickets sold at the end of 9 years is approximately 1,469.56.
The correct option is 9,818.
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what percent of 41.12 is 10.28 ?
Answers
41.12 divided by 4 = 10.28
10.28 x 4 = 41.12
Use the perimeter formula to find the perimeter of the rectangle.
a vertical rectangle with one side length labeled 11 inches and another side length labeled 9 inches
40 inches
31 inches
22 inches
18 inches
Answers
Answer:
Perimeter = 40 inches
Step-by-step explanation:
The formula for the perimeter of a rectangle is given by:
P = 2l + 2w, where,
P is the perimeter,l is the length,and w is the width.Thus, we can allow the 11-inch side to represent the length and the 9-inch side to represent the width and plug in 11 for l and 9 for w in the perimeter formula to find P, the perimeter of the rectangle:
P = 2(11) + 2(9)
P = 22 + 18
P = 40
Thus, the perimeter of the rectangle is 40 inches.
10. A triangular prism is shown.
a. Find the area of the base.
b. Find the volume of the prism.
d
5 cm
10 cm
3 cm
8 cm
5 cm
Answers
Answer:
Step-by-step explanation:
Let f(x) = 4x² - 2x +11
The slope of the tangent line to the graph of f(x) at the point (3, 41)
Slope =
M=
B=
Answers
Answer:
f(x) = 4x² - 2x + 11
f'(x) = 8x - 2
m = f'(3) = 8(3) - 2 = 24 - 2 = 22
41 = 22(3) + b
41 = 66 + b
b = -25
y = 22x - 25
Yuri’s sister Karina is 12 years old. In the equation below, y represents Yuri’s age in years.
12 = 3 y minus 2
Which statement accurately relates their ages?
Yuri is 3 years younger than twice Karina’s age.
Yuri is 2 years younger than triple Karina’s age
Karina is 3 years younger than twice Yuri’s age.
Karina is 2 years younger than triple Yuri’s age.
Answers
Yuri is 2 years younger than triple Karina’s age
Answer:
yo
Step-by-step explanation:
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Previous Activity
N
Which would prove that AABC~ AXYZ? Select two
options.
OBA-BC-A
=
YX
YZ XZ
OBA = BC₁
YX
YZ
O
AC
XZ
=
=
BA
XX.
YX
AC
BC
BA = AE = 8C
YX
YZ
XZ
OBC=BA ₁ <=
XY
ZX
Next Activity
Answers
The two options that would prove that ΔABC ~ ΔXYZ include the following:
A. BA/YX = BC/YZ = AC/XZ
C. AC/XZ = BA/YX, ∠A≅∠X
What are the properties of similar triangles?In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent angles and similar triangles:
BA/YX = BC/YZ = AC/XZ (ΔABC ≅ ΔXYZ)
Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following congruent angles and similar sides:
AC/XZ = BA/YX, ∠A≅∠X
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Q.14 In the figure given below, let the lines 1, and 1, be parallel and t is transversal. Find
the value of x.
Answers
Answer:
The consecutive interior angles are supplementary, so we have:
3x + 20 + 2x = 180
5x + 20 = 180
5x = 160, so x = 32
Find the focus of the parabola defined by the equation 100 points.
Answers
Answer : Focus is (0,3)
To find the focus of the parabola defined by the equation (y - 3)² = -8(x - 2), we can compare it with the standard form of a parabolic equation: (y - k)² = 4a(x - h).
In the given equation, we have:
(y - 3)² = -8(x - 2)
Comparing it with the standard form, we can determine the values of h, k, and a:
h = 2
k = 3
4a = -8
Solving for a, we get:
4a = -8
a = -8/4
a = -2
Therefore, the vertex of the parabola is (h, k) = (2, 3), and the value of 'a' is -2.
The focus of the parabola can be found using the formula:
F = (h + a, k)
Substituting the values, we get:
F = (2 + (-2), 3)
F = (0, 3)
Therefore, the focus of the parabola defined by the equation (y - 3)² = -8(x - 2) is at the point (0, 3).
Answer:
Focus = (0, 3)
Step-by-step explanation:
The focus is a fixed point located inside the curve of the parabola.
To find the focus of the given parabola, we first need to find the vertex (h, k) and the focal length "p".
The standard equation for a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.
Given equation:
[tex](y-3)^2=-8(x-2)[/tex]
Compare the given equation to the standard equation to determine the values of h, k and p:
h = 2k = 34p = -8 ⇒ p = -2The formula for the focus is (h+p, k).
Substituting the values of h, p and k into the formula, we get:
[tex]\begin{aligned}\textsf{Focus}&=(h+p,k)\\&=(2-2,3)\\&=(0,3)\end{aligned}[/tex]
Therefore, the focus of the parabola is (0, 3).
Solve the inequality.
x
_ -3 >2
4
Answers
The solution to the inequality[tex](x/4) - 3 > 2 is x > 20.[/tex]
To solve the inequality [tex](x/4) - 3 > 2,[/tex]we'll follow these steps:
Step 1: Eliminate the fraction by multiplying both sides of the inequality by the denominator, which is 4 in this case. This step allows us to get rid of the fraction and simplify the inequality.
[tex](x/4) - 3 > 2[/tex]
Multiply both sides by 4:
[tex]4 * [(x/4) - 3] > 4 * 2[/tex]
This simplifies to:
x - 12 > 8
Step 2: Isolate the variable on one side of the inequality by adding 12 to both sides:
x - 12 + 12 > 8 + 12
This simplifies to:
x > 20
So, the solution to the inequality is x > 20. This means that any value of x greater than 20 will satisfy the inequality.
To represent this solution graphically, we can plot the number line and shade the region to the right of 20, indicating that any value greater than 20 is a valid solution.
---------------------------------
-∞ 20 +∞
--------------------------
●=================
---------------------------------
In the number line above, the shaded region represents the solution x > 20. Any value to the right of 20, including 20 itself, will satisfy the original inequality.
In summary, the solution to the inequality [tex](x/4) - 3 > 2 is x > 20.[/tex]
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find the surface area of the composite figure 12cm x 2cm x 10cm x 3cm x 6cm x 8cm SA=
Answers
Answer:
If you are in Acellus trust me the answer is 394
Step-by-step explanation:
SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )
SA = 48 + 40 + 48 + 48 + 18 + 192
SA = 394 square cm.
Cecilia se compra un libro con la cuarta parte de su dinero y un cómic con la mitad del dinero que le quedaba. Al salir de la librería se da cuenta que le sobraron $8. ¿Cuál es la ecuación para conocer la cantidad de dinero que tenía en un inicio?
Answers
The equation to determine the initial amount of money Cecilia had is x = 0.
Let's denote the initial amount of money Cecilia had as "x" dollars.
According to the given information, Cecilia spent one-fourth (1/4) of her money on a book, which is (1/4)x dollars. After buying the book, she had (x - (1/4)x) dollars left.
Next, Cecilia spent half (1/2) of the remaining money on a comic, which is ((1/2)x - 8) dollars. After buying the comic, she had ((x - (1/4)x) - ((1/2)x - 8)) dollars remaining.
Since she had $8 left, we can set up the equation:
((x - (1/4)x) - ((1/2)x - 8)) = 8
To simplify the equation, we can first combine like terms:
(x - (1/4)x - (1/2)x + 8) = 8
Now, let's solve the equation step by step:
(x - (1/4)x - (1/2)x + 8) = 8
Multiplying the fractions by their common denominator, which is 4, we get:
(4x - x - 2x + 32) = 32
Simplifying further:
(x + 32) = 32
Subtracting 32 from both sides:
x = 0
Therefore, the equation to determine the initial amount of money Cecilia had is x = 0.
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