What is the area of triangle ABC?
3 square units
O 7 Sguare units
11 square units
15 square units

Answer:

x-9.3 = 86.7

Step-by-step explanation:

Answer:

The height of the tree is 6.12 meters and the height of the building is 33.12 meters.

Step-by-step explanation:

Since the person is 1.8 meters tall, HC = 1.8

And since their shadow is 10 meters long, HD = 10.

We are also given that GH is 24 meters and that FG is 150 meters.

Height of the Tree:

The height of the tree is given by GB.

Again, since m∠BGD = m∠CHD = 90°, ∠BGD ≅ ∠CHD.

Likewise, ∠D ≅ ∠D. So, by AA-Similarity:

[tex]\displaystyle \Delta BGD\sim \Delta CHD[/tex]

Corresponding parts of similar triangles are in proportion. Therefore:

[tex]\displaystyle \frac{GB}{GD}=\frac{HC}{HD}[/tex]

Note that:

[tex]GD=GH+HD[/tex]

Find GD:

[tex]GD=(24)+(10)=34[/tex]

Substitute the known values into the proportion:

[tex]\displaystyle \frac{GB}{34}=\frac{1.8}{10}[/tex]

Cross-multiply:

[tex]10GB=61.2[/tex]

Therefore:

[tex]GB=6.12\text{ meters}[/tex]

The height of the tree is 6.12 meters.

Height of the Building:

The height of the building is given by FA.

Since m∠AFD = m∠CHD = 90°, ∠AFD ≅ ∠CHD.

∠D ≅ ∠D. So, by AA-Similarity:

[tex]\Delta AFD\sim \Delta CHD[/tex]

Corresponding parts of similar triangles are in proportion. Therefore:

[tex]\displaystyle \frac{FA}{FD}=\frac{HC}{HD}[/tex]

Note that:

[tex]FD=FG+GH+HD[/tex]

Find FD:

[tex]FD=(150)+(24)+(10)=184[/tex]

Substitute the known values into the proportion:

[tex]\displaystyle \frac{FA}{184}=\frac{1.8}{10}[/tex]

Cross-multiply:

[tex]10FA=331.2[/tex]

Therefore:

[tex]FA=33.12\text{ meters}[/tex]

The height of the building is 33.12 meters.

Step-by-step explanation:

everything can be found in the picture

Answer:

w = - (7/2) z

Step-by-step explanation:

5w + 9z = 2z + 3w

Subtract 3w from both sides

2w + 9z = 2z

Subtract 9z from both sides

2w = -7z

Divide both sides by 2

w = - (7/2) z

Answer:

8%

Step-by-step explanation:

To find the percent change, we first have to find the amount changed, which is (46000-42500) = 3500. Then, we find what percentage that is of the original amount. Remember that when calculating percentage change, it's important to calculate change with respect to the initial value.

To find the percentage, we can divide 3500 by 42500, and multiply that by 100, resulting in 8 being our nearest whole percent

Answer:

5x^2+10x+6

Step-by-step explanation:

Step-by-step explanation:

it's called answer is minus 7

Answer:

[tex]{ \tt{f(x) = 5x + 3}} \\ { \tt{f( - 2) = 5( - 2) + 3 }}\\ { \bf{f( - 2) = - 7}}[/tex]

Answer:

Alice - £124.62

Bernice - £290.77

Carol - £184.62

Step-by-step explanation:

Let the amount of money Alice has be a. This way, the sentence "The ratio of Alice’s money to Bernice’s money is 3:7." can be translated into a proportion:

Alice's money / Bernice's money = 3 / 7

We can substitute Alice's money with a, and cross multiply and solve for Bernice's money:

a / Bernice's money = 3 / 7

7a = 3(Bernice's money)

Bernice's money = 7/3 a

Now, we can represent Carol's money in terms of Alice's money, she has 60 more, or a + 60. We can create can equation to represent the total:

Alice's money + Bernice's money + Carol's money = total

We can plug in what we have and solve for a:

a + 7/3 a + a + 60 = 600

13/3 a = 540

a = 124.62

This means Alice has £124.62

Bernice has 7/3 a amount of money, so we can substitute the value of a to get Bernice has 7/3 (124.62), or £290.77

We can do the same for Carol who has 60 more, 124.62 + 60 is £184.62

Answer:

1000 cubic metre

Step-by-step explanation:

hopes it help

Answer:

solution,

length=10 cm

volume=?

now,

volume of cube=l×l×l

=10×10×10

therefore,the answer is 1000 cubic centimeter

Answer:

8 : 27

Step-by-step explanation:

The ratio of the volumes is the ratio of the scale factor cubed

2^3 : 3^3

8 : 27

Answer:

8 : 27

Step-by-step explanation:

Given 2 similar cylinders with height ratio = a : b , then

ratio of volumes = a³ : b³

Here height ratio = 2 : 3

ratio of volumes = 2³ : 3³ = 8 : 27

Answer:

The area of the circular garden is approximately 7.1 square yards

Step-by-step explanation:

The given parameters are;

The area surrounding the circular garden = A rectangular grassy area

The area of the circular garden ≈ (1/2) × The base of the grassy rectangular area

The dimensions of the base of the rectangular grassy area = 6 yards by 3 yards

The diameter of the circle, D = 3 yards

The area of the rectangular grassy area = 6 yards × 3 yards = 18 yards²

∴ The approximate area of the circular garden = (1/2) × 18 yards² = 9 yards²

The area of the circular garden, A = π·D²/4

∴ A = 3.14 × (3 yards)²/4 = 7.065

The area of the circular garden, A ≈ 7.1 yd².

Answer:

1152\pi\

Step-by-step explanation:

Answer:

∅ = 44.9º

Step-by-step explanation:

sin = opp/hyp

Assuming ∅ is the top angle

∅ = arcsin(353/500)

use calculator

∅ = 44.910389254710144

∅ = 44.9º

Answer:

y = ( x-4)(x+7)

Step-by-step explanation:

When we know the zeros of the equation, we can write the equation in the form

y= a(x-z1) (x-z2)   where a is a constant and z1 and z2 are the zeros (solutions)

y = a( x-4)(x--7)

y =a( x-4)(x+7)

Since its says write an equation, we can pick a and I will let a=1

y = ( x-4)(x+7)

Step-by-step explanation:

sketch the mother function of |x| then go 3 steps to the right horizontally and that's it

Answer:

cos A =1.0

sin B=0.02

tan C=9.1

Answer:

multiply the bottom equation by 6

Answer:

g = 7

Step-by-step explanation:

3g - 4 = 17

+ 4 + 4

3g = 21

÷3 ÷3

g = 7

Answer:

g=7

Step-by-step explanation:

First add 17+4=21 to find out how much 3g needs to equal. 3g needs to get to 21. Next, do 21/3=7. g=7

Hope this helps!

Answer:

21600

Step-by-step explanation:

20000*1.2*.9=21600

Answer:

Option(B) & Option(C)

Step-by-step explanation:

Right angled triangle (One angle is 90 degree)

Isosceles(Two sides of triangle are equal)

Answer:

[25+(-13)+(-17)

25-13-17

-5

Answer:

-1/3

(the second choice)

Answer:

John's share = £72

Kate's share = £108

Step-by-step explanation:

Given:-

Share amount of John and Kate = £180

Share amount given in ratio = 2:3

Find:-

Work out how much money each person

receives.

Solution:-

Ratio:

John        Kate

 2        :      3

Add the ratio:

2 + 3 = 5

Divide the total amount from the added ratio:

180 / 5 = 36

Each part of the ratio is 36.

John's amount:

{multiply 36 with 2}

36 × 2 = £72

Kate's amount:

{multiply 36 with 3}

36 × 3 =  £108

(CHECK:- £108 + £72 = £180 )

Answer:

56851200

Step-by-step explanation:

The expanded form of the number is 5000 + 600+ 80 + 5 + 0.1 + 0.02 and the number is 5685.12

A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56 etc. are the numbers.

It is given that:

The word expression:

"five thousand six hundred eighty-five and twelve hundredths"

The number would be:

= 5685.12

In the expanded form the number can be written as:

The expanding form can be used to indicate the value of each digit in a number in arithmetic.

Numbers that are expressed as the sum of each digit multiplied by its place value are known as expanded numbers.

Expanded Form:

5685.12 = 5000 + 600+ 80 + 5 + 0.1 + 0.02

Thus, the expanded form of the number is 5000 + 600+ 80 + 5 + 0.1 + 0.02 and the number is 5685.12

Learn more about the number here:

brainly.com/question/17429689

#SPJ2

Answer:

18x

Step-by-step explanation:

If f(x) is 5x which can also be expressed 5(x)

Then r(x) is a number then x

f is the fifth digit in the alphabet

So fx is 5x

r is the 18 th letter so

18x

Answer:

(12 + 6) / (3 + 3) =  18 / 6 = 3

your answer is : (12 + 6) / (3 + 3)

Answer:

A

Step-by-step explanation:

A) 18/6 = 3

B) 12+5 = 17

C) (18 / 3) + 3 = 9

D) 12 +(6/6) = 13

Answer:

[tex]16x^{2}+44x+61[/tex]

Step-by-step explanation:

g(f(x)) means that you substitute f(x) as x in g(x)

[tex]2(2x+7)^{2}-(6)(2x+7)+5[/tex]

expand

(2x+7)(2x+7)=

4x^2+28x+49

(2)(2x+7)(2x+7)=16x^2+56x+98

16x^2+56x+98-12x-42+5

16x^2+44x+61

Answer:

y = -50x +775

Step-by-step explanation:

Answer:

3.3333 (repeating)

Step-by-step explanation:

He has 50 missing assignments and 15 days to do them.

So you do 50 missing assignments divided by 15 days, to see how many assignments a day he would have to do.

50 / 15 = 3.33 (repeating)

Answer:

3.333333333333333

Step-by-step explanation:

You will have to divide 15 by 50 to get the answer. That will give you 3.333333333333333 which is your answer.

Answer:

6

Step-by-step explanation:

Arc length ACB = 6 pi

The arc length = fraction of a circle times the circumference

6 pi = 180/360 * 2 * pi *r

6 pi = 1/2 * 2 * pi*r

6 pi =  pi r

The radius is 6