Step-by-step explanation:
[tex]\tan^2\alpha-\sin^2\alpha=\sin^2\alpha\tan^2\alpha\\\\LS=\left(\dfrac{\sin\alpha}{\cos\alpha}\right)^2-\sin^2\alpha=\dfrac{\sin^2\alpha}{\cos^2\alpha}-\dfrac{\sin^2\alpha\cos^2\alpha}{\cos^2\alpha}\\\\=\dfrac{\sin^2\alpha-\sin^2\alpha\cos^2\alpha}{\cos^2\alpha}=\dfrac{\sin^2\alpha(1-\cos^2\alpha)}{\cos^2\alpha}=\dfrac{\sin^2\alpha\sin^2\alpha}{\cos^2\alpha}\\\\=\sin^2\alpha\cdot\dfrac{\sin^2\alpha}{\cos^2\alpha}=\sin^2\alpha\left(\dfrac{\sin\alpha}{\cos\alpha}\right)^2=\sin^2\alpha\tan^2\alpha=RS[/tex]
Used:
[tex]\tan x=\dfrac{\sin x}{\cos x}\\\\\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\sin^2\alpha+\cos^2\alpha=1\to \sin^2\alpha=1-\cos^2\alpha\\\\\text{distributive property}\ a(b+c)=ab+ac[/tex]
50 points for detailed answer and explanation.
Answer:
∛x² + ∛xy + ∛y²Step-by-step explanation:
Use of formula:
a³ - b³ = (a - b)(a² + ab + b²)Simplify as follows:
(x - y) / (∛x - ∛y) = (∛x³ - ∛y³) / (∛x - ∛y) =(∛x - ∛y)(∛x² + ∛xy + ∛y²) / (∛x - ∛y) =∛x² + ∛xy + ∛y²What is the decimal equivalent of 1/9?
Answer:
0.111111...….
Step-by-step explanation:
Answer:
0.1111111111111(repeating)
Step-by-step explanation:
what is the total surface area?
Answer:
136
Step-by-step explanation:
9*4=36+100=136
A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 4.5, 6.75, 10.125, 15.1875.
What is the multiplicative rate of change of the exponential function represented in the table?
1.5
2.25
3.0
4.5
Answer:
its 3.0
Step-by-step explanation:
ik bc i took the test
The rate of change for the given function is 2.25. Therefore, option B is the correct answer.
What is rate of change of a function?The rate of change, or the slope, is calculated as Δy/Δx , or (y2−y1)/(x2−x1). The slope-intercept equation of a line is y=mx+b , where m is the slope and b is the initial value.
From the given table, we have (1, 4.5), (2, 6.75), (3, 10.125) and (4, 15.1875).
Using coordinate points (1, 4.5) and (2, 6.75), we get
Rate of change = (6.75-4.5)/(2-1)
= 2.25
Therefore, option B is the correct answer.
Learn more about the rate of change here:
https://brainly.com/question/8223651.
#SPJ6
5. A tree is broken at a height of 5 m from the ground
and its top touches the ground at a distance of
12 m from the base of the tree. Find the original
height of the tree.
The original height of the tree is 60 m
Answer:
Step-by-step explanation:
the base of the triangle that the fallen tree makes up is 12 and the up right is 5 the tree top is the hypotenuse of this triangle :)
treeTop= [tex]\sqrt{12^2+5^{2} } }[/tex]
treeTop = [tex]\sqrt{169}[/tex]
treeTop = 13
13+5 = treeHeight
18 = treeHeight
The total number of students in the seventh grade is 9 more than 4 times as many students as are in the art class. There are 101 students in the seventh grade. Write and solve an equation to find the number of students in the art class. Let x represent the number of students in the art class.
Answer:
9 + 4x = 101
Step-by-step explanation:
9 + 4x = 101 Equation
( +9 - 9 ) + 4x = ( 101 - 9 ) Subract 9 on both sides
4x = 92 Simplify
x = 23 Divide 4 on both sides
23 people in art class
Edgar argues that reflecting the following image over the x -axis and
then over the line y = x is the same as reflecting the same image over the
line y = -x. Prove whether Edgar is correct or not.
у
10
7
6
5
4
3
2
1
0
-6-5-4-3-2-1 0
-1
1
9
7
2
3
8
-10-9-8
10
-2
-3
-4
-5
-7
-8
-9
-10
Answer: He is not correct. The resulting will be in a different quadrant.
Step-by-step explanation: This would be much easier to answer with a screen shot of the image.
For example, if the original image is in quadrant 1, the first reflection over the x-axis places the new image in quadrant 4, "upside-down" and the second reflection over the y=x line places the new image in quadrant 2 and "oblique" to the original.
Reflecting the original over the y=-x line places the new image in quadrant 3.
The cost price of a car is $60 000. If the marked price is set so as to make a profit of 15%, find the
marked price.
Answer:
marked price = $69,000
Step-by-step explanation:
cost price = $60,000
profit
= 15%
= 15% × cost price
= 15/100 × $60,000
= $9000
marked price
= cost price + profit
= $60,000 + $9000
= $69,000
I need help pls help me answer this ASAP!!!
Help please!!!!!!!!!!!!!
Answer:
position 1 5 8 12 19 25
term -8 8 20 36 64 88
Step-by-step explanation:
(n - 1) is position ( n ∈ N)
d is the distance between the numbers in the sequence
a1 is the first number in the sequence
we have the fuction: a(n) = a1 + (n - 1)d
see in the table, with position = 1, term = -8 => a1 + d = -8
position = 25, term = 88 => a1 + 25d = 88
=> we have: a1 + d = -8
a1 + 25d = 88
=> a1 = -12
d = 4
=> a(n) = -12 + 4(n - 1)
=> term = 8, position = (8 + 12)/4 = 5
position = 8, term = -12 + 4.8 = 20
term = 36, position = (36 + 12)/4 = 12
position = 19, term = -12 + 4.19 = 64
Answer:
The required table is:
Position 1 5 8 12 19 25
Term -8 8 20 36 64 88
Step-by-step explanation:
The general formula for arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]
where n is the nth term, a₁ is the first term and d is the difference.
Looking at the table, we know that
a₁ = -8 and
a₂₅ = 88
We can find the common difference d:
[tex]a_n=a_1+(n-1)d\\n=25, a_1=-8, a_{25}=88\\a_{25}=a_1+(25-1)d\\88=-8+24(d)\\88+8=24\:d\\96=24\:d\\d=\frac{96}{24}\\d=4[/tex]
So, we have d = 4
Now we can fill the remaining table.
We have to find position n, when term (a_n) is 8
[tex]a_n=a_1+(n-1)d\\8=-8+(n-1)4\\8=-8+4n-4\\8=-12+4n\\8+12=4n\\20=4n\\n=\frac{20}{4}\\n=5[/tex]
So, when term is 8, position is 5
We have to find term a_n when position n is 8
[tex]a_n=a_1+(n-1)d\\a_8=-8+(8-1)4\\a_8=-8+7(4)\\a_8=-8+28\\a_8=20[/tex]
So, when position is 8 term is 20
We have to find position n, when term (a_n) is 36
[tex]a_n=a_1+(n-1)d\\36=-8+(n-1)4\\8=-8+4n-4\\8=-12+4n\\36+12=4n\\48=4n\\n=\frac{48}{4}\\n=12[/tex]
So, when term is 36, position is 12
We have to find term a_n when position n is 19
[tex]a_n=a_1+(n-1)d\\a_{19}=-8+(19-1)4\\a_{19}=-8+18(4)\\a_{19}=-8+72\\a_{19}=64[/tex]
when position is 19 term is 64
So, the required table is:
Position 1 5 8 12 19 25
Term -8 8 20 36 64 88
1,000,000,000,000,000,000,000+1,111,111,111
Answer:
1,000,000,000,000,001,111,111
A client pays for a moving company to move 25 boxes. If the moving
company charges $12.50 per box and a base fee of $199.95 to each
client, what is the total amount the client pays?
Answer:
$512.45
Step-by-step explanation:
total amount = base fee + per box charge
total amount = $199.95 + $12.50 * 25
total amount = $199.95 + $312.50
total amount = $512.45
Acar is traveling at 65 miles per hour. What happens to the number of miles when the number of hours changes?
When the number of hours increases the number of miles decreases
When the number of hours increases the number of miles increases.
When the number of hours decreases the number of miles increases.
When the number of hours decreases the number of miles stays the same.
Please help me ASAP! I’m giving Brainliest to the first correct answer! Please also show working out if possible - Thanks :))
There are oranges that are ¥90 and apples that are ¥150.
When you buy a total of 15 of them, your total cost is ¥1890.
How many oranges and apples did you buy?
Step-by-step explanation:
If 15 oranges were bought,
the total cost would be 15 * ¥90 = ¥1350.
¥1890 - ¥1350 = ¥540.
For every orange that switches to an apple,
the cost increases by ¥150 - ¥90 = ¥60.
Number of apples = ¥540 / ¥60 = 9.
Therefore there are 6 oranges and 9 apples.
Answer:
6 oranges and 9 apples.
Step-by-step explanation:
Let the number of oranges be x then the number of apples = 15 - x.
So 90x + 150(15 - x) = 1890
90x - 150x + 2250 = 1890
-60x = -360
x = 6
and number of apples = 15 - 6
So it's 6 oranges and 9 apples.
What is the rule used to reflect the triangle ABC to its image?
A. Reflect over y = -x
B. Reflect over y = x
C. Reflect over the x axis
D. Reflect over the y-axis
Answer:
The rule used to reflect Δ ABC to its image is Reflect over y = x ⇒ B
Step-by-step explanation:
If the point (x, y) reflected across the x-axis , then its image is (x, -y) If the point (x, y) reflected across the y-axis , then its image is (-x, y) If the point (x, y) reflected across the line y = x , then its image is (y, x) If the point (x, y) reflected across the line y = -x , then its image is (-y, -x)From the given figure
∵ The coordinates of point A are (-4.5, 6)
∵ The coordinates of point A' are (6, -4.5)
→ The coordinates are switched ⇒ 3rd rule
∴ Point A is reflected over the line y = x
∴ Δ ABC is reflected over the line y = x
∴ The rule used to reflect Δ ABC to its image is Reflect over y = x
Note: Point B' on the graph should be C' and point C' should be B' (correct it)
Which equation can be used to determine the percent of the diagram that one section represents?
1/10=1/100=1%
1/10=10/100=10%
1/100=1/10=1%
1/100=10/10=10#
Answer:
First one
Step-by-step explanation:
In a class of 40 children there are 12 who have a dog, 15 who have a pet cat, and 13 children who have no pet. What percentage of this class have a dog as a pet?
Answer:
The percent of children that have a dog is 30%
Step-by-step explanation:
Find the slope of the line.
-1
3
-10
-11
12
4
3
2 0 1
9 10
The slope is
Turn
-1
Step-by-step explanation:
because looking at the graph it is negative, and it goes down one over one
One die is tossed and then another die is tossed. How many outcomes are possible for the two dice?
Answer:
i think its 36!
Step-by-step explanation:
6 x 6+36
PLEASE HELP!!1
Four intersecting lines, t, v, u, and w, are shown in the diagram.
===============================================
Explanation:
Line w and line t are parallel if and only if the corresponding angles (4x+60) and (9x) are congruent.
9x = 4x+60
9x-4x = 60
5x = 60
x = 60/5
x = 12
If x = 12, then
9x = 9*12 = 108
4x+60 = 4*12+60 = 48+60 = 108
Both corresponding angles would be 108 degrees if x = 12. So this confirms we have the right x value.
On average, at least 25,000
pieces of luggage are lost or misdirected
each day by United States airlines. Of
these, 98% are located by the airlines
within 5 days. From a given day’s lost
luggage, at least how many pieces of
luggage are still lost after 5 days?
WRITE AND SOLVE AN INEQUALITY!!!!!! (people just solve without an inequality!)
98% of 25,000 is 24,500.
So from this, we can make the inequality:
25,000 - 500x
x = 5 days.
May I have brainliest please? :)
Answer:
500
Step-by-step explanation:
At least means 25000 and bigger. But 25000 is included in the inequality.
You should write an inequality to to represent the number of pieces of luggage
x ≥ 25000
100% - 98% = 2%
2% of all luggage lost is never found. Multiply both sides of x ≥ 25000 by 2%
2 percent x ≥ 25000 * 2%
2 percent x ≥ 500
Note that 2 percent is not an algebraic variable. 2% is. 2% = 2/100, but that is not what you want on the left.
The function y=3.75x+2.5 represents the cost y(in dollars) of a taxi ride of x miles.
A) Identify the independent and dependent variables.
B) Find the maximum number of miles you could travel if you only had 20 dollars.
Answer:
happy new year
Step-by-step explanation:
i am your biggest fan I am your teacher you fill
Describe the graph of heating curve and water. In terms of time heat is added vs temperature !!!!!!!!!! PLEASE HELP !!!!!!!! EXPLANATION NEEDED CORRECTLY !!!!!!!!
Daryl biked for 12 minutes and traveled 1.6 miles. If He kept the same pace, how far would he travel in 3.5 hours? please show work if possible!!!!
Answer:
27.999999993 or 27.9 or 28 (rounded) miles.
Step-by-step explanation:
Find out how many miles he goes every minute.
(1.6 ÷ 12 = 0.13 recurring (0.1333333333)
3.5 hours = (60 × 3) + 30 = 210 minutes
Multiply 0.13 recurring (0.1333333333) by 210 mins.
210 × 0.13 recurring (above number) = 27.999999993 (You can round this up to the nearest whole number), which is 28 if the question asks you to but as it uses 1.6 miles, you can leave it as 27.9 or even leave the long decimal if you're not entirely sure.
Hope this helps. :)
2/3 is what % of 1/4
Answer: 266.66%
Step-by-step explanation:
(2/3)/(1/4) = (2/3)(4/1) = 8/3 = 2 2/3 = 2.6666 = 266.66%
PLZ HELP this is the question
Answer:
I think is D
I'm not that sure but hope it helps
(5c^2 - 3c +9) - (2c^2 + 8c - 3)
Help me I don't know this answer
. Alex bought a new bike last weekend. It was $185 and he had to pay tax at a rate of 8%. How
much tax did he pay?
Answer:
$14.80
Step-by-step explanation:
Original bike price: $185
Tax: 8% OR 0.08 as a DECIMAL
To find your answer, multiply the bike price by the DECIMAL (number) tax amount:
185 x 0.08
= 14.8
Therefore, Alex paid $14.80 in tax.
Answer: $14.80
Step-by-step explanation:
We know: The bike is $185, and the tax is 8% of the product.
So we multiply them together.
185 * 8 / 100 = 14.8
or
185 * 0.08 = 14.8
The tax will be $14.80.
The other way to solve this question is by cross multiply.
[tex]\ \frac{x}{185} = \frac{8}{100}\[/tex]
But what you get would still be the same as just multiply it directly.
185*5/100 = 14.8
Not an efficient way of doing things :(
WHICH OF THE FOLLOWING IS THE SLOPE AND Y INTERCEPT?
Answer:
the correct answer is Slope = 45 and y intercept = 175
Step-by-step explanation: