answer choices:
a. 111
b. 69
c. 86
d. 71

Answer:

Exact Length = 2*sqrt(30)

Approximate Length = 10.95445

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Work Shown:

(tangent)^2 = (external secant)*(whole secant)

(CD)^2 = (CB)*(CA)

(CD)^2 = (CB)*(CB+BA)

x^2 = 5*(5+19)

x^2 = 120

x = sqrt(120)

x = sqrt(4*30)

x = sqrt(4)*sqrt(30)

x = 2*sqrt(30)  .......... exact length

x = 10.95445 ............. approximate length

The length of the tangent segment is; x = 10.95

From secant theorem, we know that;

Tangent ² = length of external secant × total length of secant.

From the image, we see that;

Length of tangent is x.

External secant = 5

Total length of secant = 19 + 5 = 24

Thus;

x² = 5 × 24

x² = 120

x = √120

x ≈ 10.95

Read more about length of tangent at;https://brainly.com/question/9132922

Answer:

a. 26 cm²

b. 55 cm²

c. 78 cm²

d. 89.27 cm²

Step-by-step explanation:

a. The shape can be decomposed into two rectangles

Area of the larger rectangle = L*W

L = 7 cm

W = 2 cm

Area of the larger rectangle = 7*2 = 14 cm²

Area of the smaller rectangle = L*W

L = 4 cm

W = 5 - 2 = 3 cm

Area of the larger rectangle = 4*3 = 12 cm²

Area of the compound shape = 14 + 12 = 26 cm²

b. The shape can be decomposed into a rectangle and a triangle.

Area of the compound shape = area of rectangle + area of triangle

= L*W + ½*b*h

L = 8 cm

W = 5 cm

b = 5 cm

h = 14 - 8 = 6 cm

Plug in the values

Area = 8*5 + ½*5*6

Area = 40 + 15

= 55 cm²

c. The shape can be decomposed into a rectangle and a trapezoid

Area of the compound shape = area of the rectangle + area of the trapezoid

= L*W + ½(a + b)h

L = 12 cm

W = 3 cm

a = 12 cm

b = 9 cm

h = 4 cm

Plug in the values

Area = 12*3 + ½(12 + 9)4

Area = 36 + 42

Area = 78 cm²

d. The shape can be decomposed into a rectangle and a semicircle

Area of the compound shape = area of the rectangle + area of the semicircle

= L*W + ½(πr²)

L = 10 cm

W = 5 cm

r = ½(10) = 5 cm

Plug in the values

Area = 10*5 + ½(π*5²)

Area = 50 + 39.27

Area = 89.27 cm²

Answer:

79.5 + 5.5x = Y

Step-by-step explanation:

Sumo wrestler gained 5.5 kg per month

After 11 month, he weighed 140 kg.

Let x be his current weight.

Then x + 11(5.5) = 140

  x = 140 - 60.5

  x = 79.5

If Y is the weight of the wrestler after t months, then the linear equation would be:

 79.5 + 5.5t = Y

Answer:

Height = 6000 m

Step-by-step explanation:

[tex]Volume = length \times breadth \times height \\\\480000 = 10 \times 8 \times height\\\\480000 = 80 \times height\\\\height = \frac{480000}{80} = 6000 \ m[/tex]

Answer:

A. 4:5

B. 600 girls

Step-by-step explanation:

A. g : b = 12 : 15 = 4 : 5

B. the numbers of girls = 4/(4+5) × 1350

= 4/9 × 1350 = 600

Answer:

minimum value of 6

Step-by-step explanation:

Given

y = x² - 10x + 31

with a = 1, b = - 10

Since a > 0 then the function has a minimum value

The minimum value is the y- coordinate of the vertex.

The x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{-10}{2}[/tex] = 5

Substitute x = 5 into the function for y- coordinate of vertex

y = 5² - 10(5) + 31 = 25 - 50 + 31 = 6

The function has a minimum value of 6

Answer: [tex]P=795(1.84)^n[/tex]

Step-by-step explanation:

Given

Initial population was [tex]795[/tex] people

By 2020, it becomes [tex]1262[/tex] people

Suppose the population follows the trend [tex]P=P_oa^{n}[/tex]

where, [tex]n[/tex] is the number of years after 2014

For year 2020 it is 6. Insert the values

[tex]\Rightarrow 1262=795a^{6}\\\\\Rightarrow 1.587=a^{6}\\\\\text{Taking log both sides}\\\\\Rightarrow \log (1.587)=6\log (a)\\\Rightarrow \log (a)=0.2645\\\\\Rightarrow a=10^{0.2645}\\\Rightarrow a=1.84[/tex]

Thus, the exponential population trend is [tex]P=795(1.84)^n[/tex]

Answer:

3(x)^3 + 2(x)^2 + 22x - 15

Step-by-step explanation:

(3(x)^2 + 2x - 3) (x + 5)

=>(3(x)^2 + 2x - 3) (x) + (3(x)^2 + 2x - 3) (5)

=>3(x)^3 + 2(x)^2 - 3x + 15x + 10x - 15

=>3(x)^3 + 2(x)^2 + 22x - 15

Answer:

-2 = -6

Step-by-step explanation:

first, you type -2 in the left box and -6 in the middle box

Answer:

C) 2

Step-by-step explanation:

Answer:

none

Step-by-step explanation:

any value on y cancel 4y and then we will have -12=12 which is not true.

Answer:

160°

Step-by-step explanation:

since it is a parallelogram it's opposite angles must be equal . So,

angle GHE = angle EFG

160 degree = angle EFG

Answer:

The answer is below

Step-by-step explanation:

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate is:

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\[/tex]

An equilateral triangle is a triangle with three equal sides (all sides are equal).

a) Given vertices at A(-2,2), B(1,5), and C(-3,6):

[tex]AC=\sqrt{(-3-(-2))^2+(6-2)^2}=\sqrt{1+16}=\sqrt{17}=4.12\ unit\\\\AB=BC=AC=4.12\ unit[/tex]

b) Perimeter = AB + BC + AC = 3 * AC = 3 * 4.12 = 12.36 unit

c) If the scale factor is increased by 4, all the sides would also increase by 4. Hence the new length would be:

A'B' = B'C' = A'C' = 4 * AC = 4 * 4.12 = 16.48 unit

d) Perimeter = A'B' + B'C' + A'C' = 3 * A'C' = 3 * 16.48 = 49.44 unit

e) Area = [tex]\frac{\sqrt{3} }{4}*AC^2=\frac{\sqrt{3} }{4} *4.12^2=7.35\ unit^2[/tex]

Answer:

81

Step-by-step explanation:

the answer is 81, just out this in the solution

Answer:

81

Step-by-step explanation:

29-2=27

27*3=81

if we divide 81 by 3 we get 27 and 27 plus 2 is 29 so it is 81

Q. Determine if the rates are equilvalent. Explain your reasoning. 25 hours in 5 days; 8 hours in 2 days. . .

[tex] \dashrightarrow [/tex] No!, as, we have 25 hours in 5 dyas is the equals to 5. While, 8 hours in 2 days is equals to 4.

Here, is a difference of 1 in 5 and 4.

9514 1404 393

Answer:

  p = 3/4n +3

Step-by-step explanation:

Expressing the given equation in terms of powers of 3, we have ...

  (27^(n+3))/(81^(p-1)) = 3

  (3^3)^(n+3)/(3^4)^(p-1) = 3^1 . . . . as powers of 3

  3(n +3) -4(p -1) = 1 . . . . . . . . . . . . log base 3 (or, equate exponents)

  3n +9 -4p +4 = 1 . . . . . . . . . . . . . eliminate parentheses

  3n +12 = 4p . . . . . . . . . . . . . . . . add 4p -1

  p = 3/4n +3 . . . . . . . . . . divide by 4

Answer:

12 nutted chocolates

Step-by-step explanation:

0.6 is equal to 60% and 60% 0f 20 is 12.

Answer:

30°

Hope this answer is right!

Step-by-step explanation:

to go around the shape, you make a complete circle: 360°. So, divide 360° by the dodecagon's twelve exterior angles. Each exterior angle is 30°.

Answer:

this is from a angle I think you want to write perimeter and area of this ×+1= and you want see that

Answer:

find X in X with x if you find X with x in with x you got a formula

Answer:

Answer is y = 6

Step-by-step explanation:

Solve for y.

Answer:

Y=6 I think but I’m not positive.

sorry if I’m wrong.

haha

get it? POSITIVE?

Answer:

N-8

Step-by-step explanation:

Answer:

[tex]b(a) = \frac{a}{7} -5[/tex]

Step-by-step explanation:

Given

[tex]a(b) = 14 * \frac{b + 5}{2}[/tex]

Required

The inverse function

We have:

[tex]a(b) = 14 * \frac{b + 5}{2}[/tex]

[tex]a(b) = 7(b + 5)[/tex]

Rewrite as:

[tex]a = 7(b + 5)[/tex]

Divide by 7

[tex]\frac{a}{7} =b + 5[/tex]

Subtract 5

[tex]b = \frac{a}{7} -5[/tex]

Express as:

[tex]b(a) = \frac{a}{7} -5[/tex] --- the inverse function

Answer:

Options (2) and (3)

Step-by-step explanation:

Rigid transformation like translation, rotation or reflection form the image with no change in the area or shape.

By applying dilation, area of the image shape gets dilated by the scale factor 'k'.

If k > 1, area of the image will be greater than the original shape.

If 0 < k < 1, are of the image will be smaller than the original.

Option (1),

There is a dilation by a scale factor of [tex]\frac{2}{3}[/tex] and [tex]0<\frac{2}{3}<1[/tex],

Therefore, image will be smaller than the original.

Option (2)

There are two dilations.

First dilation is by a scale factor of 2 and the second is by a scale factor of [tex]\frac{2}{3}[/tex].

By first dilation area of the image will get doubled.

Followed by the dilation by a scale factor of [tex]\frac{2}{3}[/tex], area of the image will be dilated by the scale factor = [tex]2\times \frac{2}{3}[/tex]

                                         = [tex]\frac{4}{3}[/tex]

Since, [tex]\frac{4}{3}>1[/tex], image will be greater than the original.

Option (3)

In this option polygon is dilated by a scale factor [tex]\frac{3}{2}[/tex].

Since, [tex]\frac{3}{2}>1[/tex]

Image will have the greater area than the original.

Option (4)

In this option polygon is dilated by a scale factor [tex]\frac{1}{2}[/tex].

Therefore, area of the image will be less than the area of the original.

Options (2) and (3) will be the correct options.

Step-by-step explanation:

1. length ×breadth ×height

12× 6 ×3= 216

2. A is the area of the base, h is the height

18×16=288

3.10×14×5=700

Answer:

21. 216m^3

22. 4071.5m^3

23. 700m^3

Step-by-step explanation:

21. V =  L*W*H

V = 3*6*12

V = 216

22. V = [tex]\pi r^{2} h[/tex]

The diameter is 18 so the radius is 9

V = [tex]\pi[/tex](9^2)(16)

V= 4071.50408

23.  V =  L*W*H

V= 10*5*14

V=700

Answer:

1,2, and 5

Step-by-step explanation:

y=2*(3+x)  

y=3x-2

3x-y=2

Answer:

future value = $8700(1.091)^x

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r) n

FV = Future value  

P = Present value = 8700

R = interest rate = 9.1%

N = number of years  = x

future value = $8700(1.091)^x

From the graph it seems to be around the area of 10%.

So,

18,000 * 0.10 = $1,800