find the missing number in the factor tree

for 20 points

i hope you will help

First, we imagine a right triangle. Second, we are given that the building is 62 feet tall. Since the height of building is vertical straight - that means the height is opposite side of triangle. It also casts a shadow 21 meters long. Shadow should be the adjacent side because it casts on the ground and not on the air.

If we imagine the right triangle + the problem in our head, we'd get the triangle that the opposite side is 62 feet tall and the adjacent side is 21 meters long.

Use the tangent ratio to find the angle of sun shining.

[tex] \large \boxed{ \tan \theta = \frac{opposite}{adjacent} }[/tex]

Substitute adjacent = 21 and opposite = 62 in the ratio.

[tex] \large{tan \theta = \frac{62}{21} }[/tex]

For this part, you might need a calculator or trigonometric table because some values cannot be exactly found.

From the equation, we should get 71.288 which we round the answer to nearest hundreth and the answer would be 71.29

Answer

Answer:

71.29°

Step-by-step explanation:

By question its given that , a 62 feet tall tree cast a shadow of 21 m long. We need to find the angle at which the sun is shining on the building .

For this we gonna imagine a right angle triangle . Where , the length of the shadow will be the base of the triangle and the height of the building will be the perpendicular on the triangle .

Here since we have got perpendicular and base , we can use the ratio of tan . We know that tan is defined as perpendicular by base , that is ,

[tex]\implies tan \theta =\dfrac{perpendicular}{base}[/tex]

Plug in the respective values , we have ,

[tex]\implies tan \theta =\dfrac{62}{21} \\\\\implies\theta = tan^{-1}\bigg( \dfrac{62}{21}\bigg) \\\\\implies \underline{\underline{\theta = 71.29^o }}[/tex]

Hence the required answer is 71.29° .

By definition of coterminal angles, the negative angle that is equivalent to an angle of 285° is equal to - 75° degrees. (Correct choice: D)

In this problem we must determine a negative angle coterminal to a given angle, two angles are coterminal when both have the same direction. Given that a complete revolution is done each 360°, we can derive an expression for angles coterminal to a given one:

θ' = θ + i · 360°     (1)

Where i is the index of the coterminal angle.

If we know that θ = 285° and i = - 1, then the negative angle is:

θ' = 285° + (- 1) · 360°

θ' = - 75°

By definition of coterminal angles, the negative angle that is equivalent to an angle of 285° is equal to - 75° degrees. (Correct choice: D)

To learn more on coterminal angles: https://brainly.com/question/23093580

#SPJ1

Answer:

9,000

Step-by-step explanation:

180/400 × 20,000 = 9,000

Answer:

9,000

Step-by-step explanation:

180÷400= 0.45

0.45×20,000= 9,000

Answer:

[tex]17\sqrt{2}[/tex] ft

Step-by-step explanation:

take angle b as reference angle

using sin rule

sin 45 = opposite / hypotenuse

[tex]\frac{1}{\sqrt{2} }[/tex] = 17 / BC

BC =17 / [tex]\frac{1}{\sqrt{2} }[/tex]

BC = 17 * [tex]\sqrt{2}[/tex]

BC =  [tex]17\sqrt{2}[/tex] ft

Answer:

BC = 17[tex]\sqrt{2}[/tex] ft

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{17}{BC}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

BC = 17[tex]\sqrt{2}[/tex] ft

Answer:

Step-by-step explanation:

use formula

A(x,y)=A'(-x,-y)

D(-4,-2)=D'(4,2)

Answer:

No, the volume will be incresed by 8 times (2x2x2=8)

Step-by-step explanation:

[tex]Volume=3*5*9=135 in^{3} \\increased -Volume=6*10*18=1080 in^{3}\\\frac{1080}{135} =8[/tex]

Answer:

A, B, & D

Step-by-step explanation:

A. isosceles - 2 sides equal (actually) all sides are equal

B. equilateral - all sides equal and all angles are equal too

D acute - all angles are less than 90 degrees

Answer:

is there  a picture or something i cant understand

Step-by-step explanation:

Answer:

C. log(1/3)

Step-by-step explanation:

log a - log b = log(a/b)

Answer:

11

Step-by-step explanation:

To add fractions, find the LCD and then combine or Pemdas

Answer:

Your answer should be 1.5

Step-by-step explanation:

Can I get brainliest

Answer:

[tex]1 = {5}^{0} [/tex]

[tex]5 = {5}^{1} [/tex]

[tex]25 = {5}^{2} [/tex]

[tex]125 = {5}^{3} [/tex]

[tex]625 = {5}^{4} [/tex]

option A is correct, it starts with the power of zero (equals always one, see it as

[tex] \frac{5}{5} [/tex]

and it goes up to the power of 4

Letter D thanks for asking for help

Answer:

just sum up the 3 sides.

quick side note: I lost my previews writing bc I waited too long too post it :(

but long story short: you get the length of, say, AB by using pythagoras theorem.

[tex] \sqrt{ {2}^{2} + {6}^{2} } [/tex]

do this with BC and CA too

the 2 is just the distance in x-direction and the 6 is just the distance in y-direction

and since a²+b²=c², we need to take the root to get the distance between 2 points

see screenshot for summing up the three distances. the part out of screen is written out above

the sum is 21.011 length units

hope it helps. have a nice day.

feel free to ask questions.

and maybe, if I'm feeling really nice and a lil bored, i leave greeting answers under yours to enable posters to give gives brainliests. if theres no 2and answer at least

Answer:

a² + 16a - 612 = 0

Step-by-step explanation:

Here is the complete question :

The width of an extra large rectangle poster is 8 inches more than half its length. The area of this poster is 306 square inches

Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster.

Area of a rectangle = length x width

Let length = a

width = 8 + 1/2a

Area =  (8 + 1/2a) x a

306 =  (8 + 1/2a) x a

multiply both sides of the equation by 2

612 = 16a + a²

a² + 16a - 612 = 0

the dimensions of the poster can be determined using quadratic formula

Answer:

yes..

Step-by-step explanation:

Answer:

9t + 4

Step-by-step explanation:

6t + 3t + 4

= 9t +4

Answer:

Part A

positive=132

negative=220

Part B=88

Step-by-step explanation:

Part A

3:5

positive: negative

3+5=8

352/8=44

3x44=132 positive or 3/8 of 352

5x44=220 negative 5/8 0f 352

Part B

220

-132

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

     88

Step-by-step explanation:

3×‐9×-5y-2y =0-7

-6x-7y =-7

Answer:

[tex]x = \frac{9}{13} \ , \ y = - \frac{5}{13}[/tex]

Step-by-step explanation:

                         3x - 5y = 4 ----------- ( 1 )

                         9x - 2y = 7 -----------( 2 )

                 ______________________

( 1 ) x 9  =>       27x - 45y = 36   ----------------- ( 3 )

( 2) x 3 =>        27x - 6y = 21     -------------------( 4 )

                  _____________________

( 3 )  =>          27x - 45y = 36

- ( 4 ) =>         -27x + 6y = - 21

                   ____________________

( 3 ) - ( 4 ) =>     0x - 39y = 15

                            -39y = 15

                                [tex]y = \frac{15}{-39} = -\frac{5}{13}[/tex]

Substitute y in ( 1 ) :

                     [tex]3x - 5y = 4\\\\3x - ( 5 \times -\frac{5}{13}) = 4\\\\3x + \frac{25}{13} = 4\\\\3x = 4 - \frac{25}{13}\\\\3x = \frac{52 - 25}{13}\\\\3x = \frac{27}{13}\\\\x = \frac{27}{13 \times 3}\\\\x= \frac{9}{13}[/tex]                        

Answer:

25

Step-by-step explanation:

Answer:

x = 25

Step-by-step explanation:

Okay so as you can see there is an x shape and whenever you have that it means they are verticle angles. So we can conclude that 25 is verticle to x and so x is equal to 25.

Answer:

answer:

(x+34)+(2X+2)=180

3X+36=180

X=72

Step-by-step explanation:

Answer:

Your answer for the above equation is D

Answer:

1- c=(-2,1) , R =9

2-c=(2,-1) , R=3

3-c=(-2,-1) , R=4

4-c=(2,1) , R=16

5-c=(0,0) , R=2

Answer and Step-by-step explanation:

To find the volume, simply multiply all the sides together.

0.5 × 0.5 × 1 = 0.25 is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

Length arc AB = 3.14 in

Step-by-step explanation:

Length of arc AB = central angle/360 * 2πr

Central angle = 30°

Radius (r) = 6 in.

Substitute

Length of arc AB = 30/360 * 2*π*6

Length arc AB = 3.14 in. (Nearest tenth)

Answer:

3.14

Step-by-step explanation:

its just right

Answer:

-14

Step-by-step explanation:

2a + 4b

Let a = 5 and b = -6

2*5 +4(-6)

Multiply

10 - 24

Subtract

-14

Answer:

-14

Step-by-step explanation:

2a + 4b

= 2(5) + 4(-6)

= 10 -24

= -14

Answer:

Yes.

Step-by-step explanation:

That sign means greater than and/or equal to (the little line) since 10 is equal to 10, then r can be 10

Answer:

60%

Step-by-step explanation:

Fruit = 10+15 = 25

Percent oranges = oranges / fruit

                             = 15/25 = .6 = 60%

Answer:

3

Step-by-step explanation:

-17 = -2y + 13 - 8y

-17 = -10y + 13

-30 = -10y

3 = y

y = 3

Answer:

y = 3

Step-by-step explanation:

- 17 = - 2y + 13 - 8y

- 10y + 13 = - 17

- 10y + 13 - 13 = - 17 - 13

- 10y = - 30

- 10y ÷ - 10 = - 30 ÷ - 10

y = 3

Answer:

Domain:  (-infinity, infinity)

Range:  [0, infinity)

Step-by-step explanation:

y = 4x^2 is a quadratic function whose parabolic graph goes through (0, 0) and opens upward.  (0, 0) is both the vertex and the minimum of this function and graph.  Here x can take on any value, but y is limited to [0, infinity).