Find the area if the trapezoid. THANK YOU!

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

these are 2 similar triangles (all 3 pairs of corresponding angles are equal in their pair, and the lengths of corresponding sides have the same ratio in every pair of corresponding sides and other lengths).

and they are also right-angled triangles.

so, what else do we know about them ?

PQ = 18

RT = 6

ST = QT + 9

therefore

QT = ST - 9

and

QR = QT + RT = ST - 9 + 6 = ST - 3

due to the principles of cumulative triangles

PQ/ST = QR/RT = 18/ST = (ST - 3)/6

108/ST = (ST - 3)

108 = (ST - 3)ST = ST² - 3ST

ST² - 3ST - 108 = 0

we can the write

x² - 3x - 108 = 0

and the solution for such a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -3

c = -108

x = (3 ± sqrt(9 - 4×1×-108))/2 = (3 ± sqrt(441))/2 =

= (3 ± 21)/2

x1 = (3+21)/2 = 24/2 = 12

x2 = (3-21)/2 = -18/2 = -9

a negative solution for real lengths is not valid, so we know

x = ST = 12

so,

QR = ST - 3 = 12 - 3 = 9

and then

QT = QR - RT = 9 - 6 = 3

Answer:

[tex] (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656{x}^{} + 46656 [/tex]

Step-by-step explanation:

we want to solve the following binomial:

[tex](x + 6 {)}^{6} [/tex]

There is a handy way to expand powers of binomials which is known as binomial theorem . and it describes the algebraic expansion of powers of a binomial. binomial theorem is given by

[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0 }^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

comparing (x+6)⁶ to (a+b)ⁿ , we get

now substitute them on the formula which yields:

[tex] \displaystyle (x + 6 {)}^{6} = \sum _{k = 0 }^{n} \binom{6}{k} {x}^{6 - k} \cdot {6}^{k} [/tex]

converting the summation notation into sum yields:

[tex] \displaystyle (x + 6 {)}^{6} = \binom{6}{0} {x}^{6 - 0} \cdot {6}^{0} + \binom{6}{1} {x}^{6 - 1} \cdot {6}^{1} + \binom{6}{2} {x}^{6 - 2} \cdot {6}^{2} + \binom{6}{3} {x}^{6 - 3} \cdot {6}^{3} + \binom{6}{4} {x}^{6 - 4} \cdot {6}^{4} + \binom{6}{5} {x}^{6 - 5} \cdot {6}^{5} + \binom{6}{6} {x}^{6 - 6} \cdot {6}^{6} \\ \implies(x + 6 {)}^{6} = \binom{6}{0} {x}^{6 } \cdot 1 + \binom{6}{1} {x}^{5} \cdot {6} + \binom{6}{2} {x}^{4} \cdot 36+ \binom{6}{3} {x}^{3} \cdot 216 + \binom{6}{4} {x}^{2} \cdot 1296+ \binom{6}{5} {x}^{} \cdot 7776+ \binom{6}{6} {x}^{0} \cdot 46656 \\ \implies(x + 6 {)}^{6} = 1 \cdot {x}^{6 } \cdot 1 + 6 \cdot{x}^{5} \cdot {6} + 15 \cdot {x}^{4} \cdot 36+ 20 \cdot {x}^{3} \cdot 216 + 15 \cdot{x}^{2} \cdot 1296+ 6 \cdot {x}^{} \cdot 7776+ 1 \cdot {x}^{0} \cdot 46656 \\ \implies \boxed{ (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656 {x}^{} + 46656 }[/tex]

and we're done!

Answer:

That is true!

[tex]1,200 * 11 = 13,200[/tex]

Let me know if you need more help with multiplication. I may be able to help.

Have a great day.

Answer:

62.86

Step-by-step explanation:

Add the cost of things without sales tax:

32.5+ (13×2)=58.5

Convert percent to decimal:

8/100=0.08

Multiply cost without sales tax by sales tax to get the amount added to the cost:

0.08×58.2=4.656

Add cost and sales tax amount to get total payment:

4.656+58.5=62.856

Round the total payment to the nearest hundredth place:

62.86

Answer:

b = 25°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

b + 110° + 45° = 180°

b + 155° = 180° ( subtract 155° from both sides )

b = 25°

Answer:

length = 44 ft.

Step-by-step explanation:

A = lw

[tex]880 = 20l\\[/tex]

Solving for l gives us l = 44 ft.

Answer:

False

Step-by-step explanation:

45/100 × 72 = 32.4

45/72 × 100 = 62.5

62.5 ≠ 32.4

Answer:

false

Step-by-step explanation:

45/100x72=32.4%

45/72X100=62.5%

Step-by-step explanation:

every triangle inscribed into a circle with the baseline being a diameter of the circle must be a right-angled triangle.

therefore,

angle XVY = 90°.

for VY we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the line opposite of the 90° angle, in our case XY).

XY = 2×ZY = 2×17 = 34.

so,

34² = 30² + VY²

VY² = 34² - 30² = 1156 - 900 = 256

VY = 16

Answer:

can you provide an image?

Step-by-step explanation:

Answer:

Ans is -1

Step-by-step explanation:

Hope the picture will help you..

Answer:

find the product of (4m-n) and (3m-2n)

Answer:

[tex]\frac{7\pi }{4}[/tex] radians

Step-by-step explanation:

to convert degrees to radians

radians = degrees × [tex]\frac{\pi }{180}[/tex] , then

radian measure = 315° × [tex]\frac{\pi }{180}[/tex] ( cancel 315 and 180 by 45 )

                          = 7 × [tex]\frac{\pi }{4}[/tex]

                         = [tex]\frac{7\pi }{4}[/tex]

315 degrees is equal to 5.49779 radians.

To convert degrees to radians, you need to multiply the degree measure by the conversion factor of π/180.

Let's convert 315 degrees to radians:

315 degrees × (π/180)

315×3.14 /180

= 5.49779 radians

Therefore, 315 degrees is equal to 5.49779 radians.

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Each ticket could have cost up to $31.

What is the discount?

A discount is a reduction in the price of an item or service. It is often offered as an incentive to encourage customers to purchase or use a particular product or service. The discount amount may be a percentage of the total price, a fixed dollar amount, or a combination of both.

Let the cost of each ticket be $x. Then the total cost for 5 tickets would be 5x. After applying the $30 group discount, the total cost would be 5x - $30.

We know that the total cost was under $125, so we can set up the inequality:

5x - $30 < $125

Simplifying this inequality, we get:

5x < $155

Dividing both sides by 5, we get:

x < $31

Hence, each ticket could have cost up to $31.

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Answer: 1. [tex]x=-2[/tex]; 2. [tex]x=\frac{11}{9}[/tex]

Step-by-step explanation :

1.

[tex]6-5x=16\\6-5x-6=16-6\\-5x=10\\\frac{-5x}{-5}=\frac{10}{-5}\\x=-2[/tex]

2.

[tex]4-9x=-7\\4-9x-4=-7-4\\-9x=-11\\\frac{-9x}{-9}=\frac{-11}{-9}\\x=\frac{11}{9}[/tex]

Answer:

Q1)   x =2         Q2)     x = 11/9

Step-by-step explanation:

Q1)   6 - 5x = 16                  check : -5(2) = -10

-6         -6                     6 -- 10 =  6+ 10 = 16

-5x = 10                         Q2)   4 - 9x = -7

-x = -2                                    -4           -4  

x = 2                                      -9x = - 11

--------------                               -x = -11 /9    ----->  x = 11/9

Answer:

sixt

Step-by-step explanation:

thats easy the sin should be six

Answer:

First cone: 29.32

Steps:

1. 3.14(2^2)7/3

2. 3.14(4)7/3

3. 12.56(7/3)

4. 12.56(2.3

5. 29.32

Second cone: 1526.81

Divide 18 in half and so same steps as above to get the answer! :)

Have a great day!!

Please rate and mark brainliest!!

Answer:

Cone 1 = 29.32mi || Cone 2 = 1526.81

Step-by-step explanation:

Step 1) Apply formula (volume of cone)

V= 1/3 * π * r^2 * h [OR] V= π * r^2 * h/3

Step 2) Insert numbers. (cone 1)

V= π * 2^2 * 7/3

Step 3) Insert numbers. (cone 2)

V= π * 9^2 * 18/3 (r=9 because r=1/2 base diameter of circle, 18/2=9)

Step 4) Plug and solve.

Step 5) CHECK YOUR ANSWER BEFORE SUBMISSION. Do it a few times just to make sure it checks out, and then continue!

Answer:

I believe the answer is 135 square feet.

Step-by-step explanation:

so 10x12=120. 10x3=30 and you divide the triangle by 2 so 30/2=15. 120+15=135

well, we don't know the cost of the carpet, however hmmm we know the cost of the carpet is 4 bucks per ft², which means we need to know how many ft² the Randall family is going to use in the first place hmmmm, Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ a=12\\ b=15\\ h=10 \end{cases}\implies \begin{array}{llll} A=\cfrac{10(12+15)}{2} \\\\\\ A=\cfrac{10(27)}{2}\implies A=135~ft^2 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{per~ft^2}{(4)}~~\stackrel{area~in~ft^2}{(135)}\implies \stackrel{\$}{540}\impliedby \textit{total cost}[/tex]

Answer:

2

Step-by-step explanation:

amplitude = distance from undisturbed position/centre line to trough or peak

Answer:

2

Step-by-step explanation:

amplitutde measures the height of the waves.

Step-by-step explanation:

please mark me as brainlest

ans

[tex] \frac{3x}{x + 4} [/tex]

Answer:

Emma began her journey at 7:30 a.m., at 8 a.m. she was 20 miles away, she stayed for an hour and a half, she left at 10 a.m., she was 7.5 miles from her house at 11:45, she traveled 80 miles total

Step-by-step explanation:

please let me know what you don't understand here. because this is really simple.

the distance from home is increasing and then decreasing when she is traveling.

the rate of distance per time would give us even the speed with which she was traveling.

when there is no change in the distance over time, that means she was "stationary" - either at home or at her grandmother's place.

so, let's answer the questions :

(a)

movement started at 7:30am (that is when she began her journey).

(b)

20 miles

you pick 8am on the time scale and move straight up until you hit the curve. and then you check what value is at that point all the way to the left on the distance scale : 20.

(c)

from 8:30am to 10am = 1.5 hours.

we see this by the interval on the time scale for which the curve is totally flat (a horizontal line) = no change in distance from home during that time.

(d)

at 10am

that is when the curve indicates the begin of a change in the distance to home.

(e)

7.5 miles.

this is the point marked by a star on the graph.

down on the time scale this point shows 11:45am, and on the left side in the distance scale it shows 7.5 miles (the middle between 5 and 10 miles).

so, at that time she was still 7.5 miles away from home.

(f)

she traveled 40 miles to her grandmother (the left part of the curve from 0 distance until it turns flat), and then 40 miles back home (the right part of the curve from 40 distance all the way down to 0).

so, in total she traveled

40 + 40 = 80 miles

Answer:

c

Step-by-step explanation:

40 cubic units

divide the shape into 2 pieces first.

4 × 4 ×2 = 32

4×2 = 8

32 + 8 = 40

the idea being that, each cube in the stack, is a 1x1x1 = 1 unit³, now if that's so, then, Check the picture below.

The distance between the two buildings is 844.23 feet apart, we go this answer by simply applying the SOH CAH TOA method

Given Data

Applying the SOH CAH TOA Approach we have

Tan  θ = Opp/Adj

Substituting our given data we have

Tan 35 = 400/x

0.4738 = 400/x

make x subject of the formula we have

x = 400/0.4738

x = 844.23 feet

learn more about trigonometry here:

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8x^5 y^8 z^9 ur welcome

Answer:

[tex]64x^6y^{12}z^{14}[/tex]

Step-by-step explanation:

[tex]\left(8x^3y^6z^7\right)^2[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]

[tex]\left(8x^3y^6z^7\right)^2=8^2\left(x^3\right)^2\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]=8^2\left(x^3\right)^2\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]8^2=64[/tex]

[tex]=64\left(x^3\right)^2\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]=64x^6\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]=64x^6y^{12}\left(z^7\right)^2[/tex]

[tex]=64x^6y^{12}z^{14}[/tex]

~lenvy~

Answer:

66

Step-by-step explanation:

Lacrosse: 33

Tennis: 33

0.25 x 132 = 33

Basket ball:?

33 + 33 + b = 132

66 + b = 132

132 - 66 = 66

b = 66

Have a great day!

Please rate and mark brainliest!!

Answer:

D.  66

Step-by-step explanation:

Total number of students = 132

If 25% of 132 students play tennis:

⇒ 0.25 × 132 = 33

So 33 students play tennis

Number of students who play basketball is: total number of students minus students play tennis minus students play lacrosse:

= basketball = 132 - 33 - 33 = 66

Considering the confidence interval given, the likely difference is given by:

[tex]\frac{0.064 + (-0.014)}{2} = 0.025[/tex]

Given an interval (a,b), the point estimate is the mean of the bounds, that is:

p = (a + b)/2.

In this problem, the interval is (-0.014, 0.064), hence the expression for the likely difference is given by:

[tex]\frac{0.064 + (-0.014)}{2} = 0.025[/tex]

More can be learned about confidence intervals at https://brainly.com/question/25890103

The solution to the problem is correct and the correct option from the given options is B.

A log function is a way to find how much a number must be raised in order to get the desired number.

[tex]a^c =b[/tex]

can be written as

[tex]\rm{log_ab=c[/tex]

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

The given logarithmic problem can be solved in the following manner, therefore,

[tex]\rm log_210\ log_48\ log_{10}4\\\\[/tex]

Using the logarithmic properties, we can write,

[tex]=\rm \dfrac{log10}{log2}\cdot \dfrac{log8}{log4}\cdot \dfrac{log4}{log10}\\\\[/tex]

Now cancelling out the values we will get,

[tex]=\rm \dfrac{log2^3}{log2}\\\\=\rm \dfrac{3log2}{log2}\\\\= 3[/tex]

Thus, the solution to the problem is correct and the correct option from the given options is B.

Learn more about Logarithm:

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Answer:

B

Step-by-step explanation:

on edge

Answer: ∠A=144°

Step-by-step explanation:

∠A and ∠B are alternate exterior angles. Alternate exterior angles are congruent to each other. That means ∠A=∠B. Since we are given the measures of ∠A and ∠B, all we have to do is set them equal to each other.

10x+24=6x+72          [subtract both sides by 6x]

4x+24=72                  [subtract both sides by 24]

4x=48                         [divide both sides by 4]

x=12

Now that we found x, we need to plug it into ∠A.

10(12)+24=120+24=144

We know that ∠A=144°.