Use the law of cosines to find the length of a

15. 70° because a right angle is 90° and we have the angle of ADB which is 20°. So 90°-20°=70°.

16. 70° because angle PSQ is 60° and angle QSR is 10°. So 60°+10°=70°.

17. 55° because it says it in the explanation. I assume this is a typo and they meant to ask the measurement of ADC and in that case it would be 130° because angle ADB is 75° and angle BDC is 55°. 75°+55°=130°.

18. 40° because angle PSQ is a right angle which means it's 90°. So 130°-90°=40°.

19. 140° because angle ADB is 120° and angle BDC is 20° so 120°+20°=140°.

20. 125° because again it's in the explanation. But if it's a typo and they meant what is the measurement of PSQ then it is 50° because PSR is 125° and QSR is 75° so 125°-75°=50°.

Hope this helps! :)

Answer:

Step-by-step explanation:

d

Answer:

(a-3)(a+3) is the answer

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {55}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] {a}^{2} - 9[/tex]

Substituting the value "[tex]a = 8[/tex]" in the above expression, we have

➺ [tex] \: {8}^{2} - 9[/tex]

➺ [tex] \: (8 \times 8) - 9[/tex]

➺ [tex] \: 64 - 9[/tex]

➺ [tex] \: 55[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

the answers are in the picture

Answer:

y=3    x=1

Step-by-step explanation:

Answer:

above one is correct. I think so

Answer:

Step-by-step explanation:

By using the property of similar triangles,

"Corresponding sides of two similar triangles are proportional"

If ΔSMA ~ ΔPOD

[tex]\frac{SM}{PO}=\frac{MA}{OD}=\frac{SA}{PD}[/tex]

[tex]\frac{6}{10}=\frac{5}{10}=\frac{5}{12}[/tex]

[tex]\frac{3}{5}=\frac{1}{2}=\frac{5}{12}[/tex]

Since, ratios of corresponding sides are not equal,

Therefore, the given triangles are not similar.

Answer:

A.

Step-by-step explanation:

we are going from a large shape to a smaller shape. the proof is that the side lengths go down from 7m to 0.5m. so, it is a reduction.

and the scaling factor s ? what do we need to multiply the original side lengths with to get the new ones ?

7 × s = 0.5 = 1/2

s = (1/2)/7 = (1/2)/(7/1) = (1×1)/(2×7) = 1/14

=> answer A is correct

The dilation from the figure on the left to the figure on the right is a reduction.  

Reduction scale factor 1/14.

The correct option is A.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

We have given that two figures.

The dilation from the figure on the left to the figure on the right is a reduction.

And the scale factor is,

= actual / scale

= 1/(7 / 0.5)

= 1/14

Therefore, the scale factor is 1/14.

To learn more about the scale factor;

https://brainly.com/question/29464385

#SPJ2

Step-by-step explanation:

123,546,789 > 123,456,789

Answer:

The value of sin theta is 5/13

Step-by-step explanation:

In the second quadrant, sin is positive and cos is negative

Cos theta = -12/13 = adjacent/hypotenuse

Sin theta = opposite/hypotenuse

opposite = sqrt(hyp² - adj²) = sqrt (13² - 12²) = sqrt (169 - 144) = sqrt (25) = 5

Sin theta = opposite/hypotenuse = 5/13

Answer:

[tex]10\frac{7}{18}[/tex]

Step-by-step explanation:

First revert it to improper fraction.

[tex]\frac{13}{2} +\frac{35}{9} \\\\[/tex]

Now put them to a common denominator.

[tex]\frac{187}{18}[/tex]

=> [tex]10\frac{7}{18}[/tex]

Answer:

Step-by-step explanation:

If the function is

[tex]y=x^2-4x[/tex], then its derivative is

y' = 2x - 4. This is equal to 0 where

2x - 4 = 0 and

2x = 4 so

x = 2. When x = 2 in the original equation:

[tex]y =2^2-4(2)[/tex] so

y = -4. So the coordinate is (2, -4). On to the next one:

If the function is

[tex]y=25x +\frac{1}{x}[/tex] then its derivative is

[tex]y'=25-\frac{1}{x^2}[/tex]. This is equal to 0 where

[tex]25-\frac{1}{x^2}=0[/tex] and

[tex]-\frac{1}{x^2}=-25[/tex] or, in simpler terms:

[tex]\frac{1}{x^2}=\frac{25}{1}[/tex] so

[tex]25x^2=1[/tex] and

[tex]x^2=\frac{1}{25}[/tex] so

x = ±[tex]\sqrt{\frac{1}{25} }[/tex] so

x = [tex]\frac{1}{5},- \frac{1}{5}[/tex]. When you plug those into the original equation, you get the coordinates

[tex](\frac{1}{5},10)[/tex] and [tex](-\frac{1}{5},-10)[/tex]

Answer:

72

Step-by-step explanation:

all you had to do was divide by 2

Answer:

6 people

Step-by-step explanation:

$230 - $8 = $222

x · 35.75 = 222

x · 35.75 ÷ 35.75 = 222 ÷ 35.75

[tex]x=6\frac{30}{143}[/tex]

Answer:

A

Step-by-step explanation:

x + 9 = 26

x = 17

Answer:

A.17

Step-by-step explanation:

17+9=26

Answer:

x = -28

Step-by-step explanation:

−1/4x=7

Multiply each side by -4 to isolate the variable

-4 *  −1/4x= -4*7

−1/4x=7

Answer:

Step-by-step explanation:

100 sq cm

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:33}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]x = 42 - 9[/tex]

➼[tex]\:x = 33[/tex]

Therefore, the value of [tex]x[/tex] is 33.

[tex]\sf\pink{Thank\:you. \:ヅ}[/tex]

Answer:

x =33

Step-by-step explanation:

x = 42-9

We are solving for x, which is already isolated

42-9 = 33

x = 33

Check 33+9 = 42

Answer:

2ab

Step-by-step explanation:

6ba + 2ab = 2ab(3+1)

= 2ab (4)

so, the common factor = 2ab

Answer:

2ab

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

1/2bh

1/2 (6*4) =12

Considering there are three triangles we will multiply by 3

12*3=36

Answer:

a. 7.2

Step-by-step explanation:

CAH (cos = adj/hyp)

cos53 = b/12; cross multiply

cos53*12 = 7.2

Answer:

£9000

Step-by-step explanation:

= £10 000× 5 ×2

100

= 1000

= £10 000-1000

= £9000

Answer:

So 1) x²-2x-8

= x(x-2-8/x)

2) y²-13y+42

= y(y-13+42/y)

3) m²-6m-7

= m(m-6-7/m)

Hope it helps

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Answer:

b. 113.04 ft³

Step-by-step explanation:

To find the volume of this composite figure, we must find the volumes of the shapes it is composed of. After finding the volumes, add the volumes.

This figure is composed of a circular cone and a cylinder.

To find the volume of a cylinder, multiply the radius by itself twice, then multiply the product pi, lastly multiply the product by its height.

[tex]v=\pi *r^2*h[/tex]

To find the volume of a circular cone, multiply the radius by itself twice, then multiply the product by the height, then multiply the product by pi, lastly multiply the product by 1/3.

[tex]v=1/3*h*\pi* r^2[/tex]

Now that we know the formulas, we can find the volume of this figure.

----------------------------------------------------------------------

The height of the cylinder is 3 feet. The radius is 3 feet as well.

Remember: 3.14 will be used for pi (π).

[tex]v=\pi *3^2*3=84.78[/tex]

The volume of the cylinder is 84.78 feet.

----------------------------------------------------------------------

Further more, we find the volume of the circular cone.

The height of the cone is 3 feet. The radius is 3 feet as well.

[tex]v=1/3*3*\pi *3^2=28.26[/tex]

Lastly, we add the volumes of both shapes.

[tex](84.78+28.26)[/tex]

[tex]=113.04.[/tex]

113.04 does not need to be rounded to the nearest hundredth.

----------------------------------------------------------------------

Therefore, the volume of this composite figure is 113.04 ft.

Answer:

31/20

Step-by-step explanation:

You need to plug in x as y-3.

so instead of 10x+10y=1 it is 10(y-3)+10y=1

Then just simplify the equation to find the value of y

Answer:

Step-by-step explanation:

(x+4)^2.(x+4)^2

= x^4 +16x^3+96x^2+256x+256

Answer:

 [tex]x_{n} =[/tex] -10 - 3(n-1)

Step-by-step explanation:

The answer is

xn =  -10 - 3(n-1)

Answer:

5.348

Step-by-step explanation:

5 + 0.3 + 0.04 + 0.008

If you find this difficult to calculate put zeroes in Hundredths place and thousandths place

=> 5.000 + 0.300 + 0.040 + 0.008

=>5.348

Answer:

f(x)=x+5

Step-by-step explanation:

x=-1 therefore -1+5=4

Answer:

Step-by-step explanation: