1. A population of 20 rabbits is released into a wildlife region. The population is growing at a rate of 60% per year. What is the population of rabbits after 8 years and what equation did you use? 2. The population of white rhinos in 2001 was 11,670. The population is declining by 9% each year. What is the population expected to be in the year 2021 and what equation did you use?

Answer:

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

The surface area of a sphere with radius r is given by

S = 4 pi r^2

for a radius of 11 units,

S =  4 pi 11^2 = 484 pi = 1520.5 sq. units

This does not correspond to any of the answers.

Please check question.

Answer:

484[tex]\pi[/tex]

Step-by-step explanation:

Surface Area of Sphere Formula: 4[tex]\pi[/tex]r[tex]r^{2}[/tex]

When you plug it in it is 4[tex]\pi[/tex][tex]11^2[/tex]

Then you would get 484[tex]\pi[/tex]

Answer: B C D

Step-by-step explanation:

just answered it for AP3X

Reasons used in the proof that the angle-bisector construction can be used to bisect any angle are as follows:

B. All of the radii of a circle are congruent

C .CPCTC

D. SSS triangle congruence postulate

" Angle bisector is defined as the ray which divides the angle into two equal parts."

According to the question,

A. Any Line segment can be extended indefinitely is not required to bisect any angle .

Therefore , it is not a correct option.

B. All of the radii of a circle are congruent : To bisect an angle draw an arc with same radii is used in constructing an angle bisector .

Therefore , Option B is a correct option.

C. CPCTC : Corresponding parts of a congruent triangle are congruent is required to proof angle bisector. As it proofs two triangles are congruent.

Therefore, Option C is the correct option.

D. SSS triangle congruence postulate : It is required an important step to prove that two triangles are congruent which imply proof of angle - bisector construction.

Therefore, Option D is the correct option.

Hence, Option B, Option C , Option D are the correct answer.

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Answer:

-17.5℃

Step-by-step explanation:

Current temperature = 0 ℃

Rate of falling per hour = -3.5 ℃

Temperature in 5 hours = -3.5 * 5 = -17.5 ℃  

Answer:

Bob's home will worth $296,779.25 after 12 years.

Equation used is [tex]FV = $175,000( 1 + 4.5/100)^(12)\\[/tex]

Step-by-step explanation:

Current value of Bob's house =[tex]FV = $175,000( 1 + 4.5/100)^12\\FV = $175,000( (100+ 4.5)/100)^12\\FV = $175,000( (104.5)/100)^12\\FV = $296,779.25[/tex]

market is improving at 4.5% annually.

This, means that the value of house gets appreciated by 4.5% each year from its previous year value.

This is a problem of compound interest formula

[tex]FV = PV(1+r/100)^n[/tex]

where PV is the present value of any thing

FV is the future value

r is the annual rate of interest

t is the time in number of year for which rate is applicable.

_____________________________________

Given

PV = $175,000.

r = 4.5%

t = 12 years

Value after 12 year will be given by

[tex]FV = $175,000( 1 + 4.5/100)^(12)\\FV = $175,000( (100+ 4.5)/100)^(12)\\FV = $175,000( (104.5)/100)^(12)\\FV = $296,779.25[/tex]

Thus, Bob's home will worth $296,779.25 after 12 years.

Equation used is [tex]FV = $175,000( 1 + 4.5/100)^(12)\\[/tex]

Answer:

f(x) = |x|

g(x) = |x| - 2

h(x) = |x| + 3

Step-by-step explanation:

All the functions graphed represent the absolute value functions.

Since function g(x) passes through (0, 0) and (1, 1),

Let the equation of a line passing through these points is,

y = mx + b

Slope of the line passing through these points 'm' = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{1-0}{1-0}[/tex]

m = 1

y-intercept of the line 'b' = 0

Therefore, equation of the line will be,

y = x

And the function representing the two lines (both are the mirror images) joining at the origin will be,

f(x) = |x|

When the parent function is shifted 3 units up, the new function will be

h(x) = |x| + 3

When the parent function is shifted 2 units down,

g(x) = |x| - 2

Answer:

m(-6,2)

Step-by-step explanation:

m=(-8+-4/2,-6+10/2)

=(-12/2,4/2)

=(-6,2)

The coordinates of the midpoint M of CD of the line segment CD with endpoints, C(−8,−6) and D(−4, 10), are (-6,2).

For a line segment, mid-point is the middle point of it which divides the line segment into the two equal parts.

The formula to find the midpoint using the coordinates of the line is,

[tex]m=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

Here, (x1,y1) and (x2,y2) are the coordinates of the endpoints of the line.

The endpoints of CD are C(−8,−6) and D(−4, 10). To find the coordinates of the midpoint M, put the values in the above formula as,

[tex]m=\left(\dfrac{-8+(-4)}{2},\dfrac{-6+10}{2}\right)\\m=\left(\dfrac{-12}{2},\dfrac{4}{2}\right)\\m=\left(-6,2)[/tex]

Thus, the coordinates of the midpoint M of CD of the line segment CD with endpoints, C(−8,−6) and D(−4, 10), are (-6,2).

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Answer: 10.

Step-by-step explanation:

You are given the equation

(ax+b)(ax+c)=4x^2-25

Expand the Left hand side by opening the bracket.

a^2x^2 + axc + abx + bc

a^2x^2 + (axc + abx) + bc = 4x^2 + 0x - 25

From the equation above, we can see that;

a^2x^2 = 4x^2

a^2 = 4

a =  √4

a = 2

Also, axc + abx = 0x

axc = abx

ax will cancel out from both sides

c = b

From the equation, bc = 25

But c = b. Substitute c for b

b^2 = 25

b =  √25

b = 5 = c

b + c is therefore 5 + 5 = 10

Answer:

-(4x + 7)/2 - (3x - 2)/2 = (-4x - 7 - 3x + 2)/2 = (-7x - 5)/2

The number of buttons in C is 17 buttons

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the three tins be A , B and C respectively

The number of buttons in tin A = x

The number of buttons in tin B = 4 times the number of buttons in tin A

                                                   = 4x

The number of buttons in tin C = 7 fewer buttons than tin A

                                                    = x - 7

The total number of buttons in tin A , tin B and tin C together = 137 buttons

So , the total number of buttons =
number of buttons in tin A + number of buttons in tin B + number of buttons in tin C

So , the equation will be

Total number of buttons = x + 4x + ( x - 7 )

x + 4x + ( x - 7 ) = 137

6x - 7 = 137

Adding 7 on both sides , we get

6x = 144

Divide by 6 on both sides , we get

x = 24 buttons

So , the number of buttons in tin A is 24 buttons

So , number of buttons in tin B = 4 x 24

                                                   = 96 buttons

Therefore , the number of buttons in tin C = 17 buttons

Hence , the number of buttons in tin C is 17 buttons

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To find the common difference, subtract all the numbers in order.

56 - 49 = 7

49 - 42 = 7

42 - 35 = 7

Therefore, common difference is 7.

Best of Luck!

Answer:

The answer is -7

(got this answer right on the lesson)

Step-by-step explanation:

Problem 9, part a)

Compass bearings always have north as the starting point. This is where 0 degrees is situated, and 360 degrees as well. As the bearing angle increases, you'll turn to the right toward the eastward direction. Effectively you're sweeping out a clockwise rotation. The bearing 322 degrees is in a northwest position as the diagram shows (place the ship at the bottom right corner of the triangle). The bottom right acute angle of the triangle is 322 - 270 = 52 degrees. This is the reference angle we'll use for finding the distance d.

With respect to the reference angle of 52 degrees, the side 18.5 is the opposite side and d is the adjacent side. Use the tangent ratio to get...

tan(angle) = opposite/adjacent

tan(52) = 18.5/d

d*tan(52) = 18.5

d = 18.5/tan(52)

d = 14.4537840903742

The approximate value of d is 14.4537840903742 km

This rounds to 14.5 when rounding to one decimal place.

=======================================================

Problem 9, part b)

Recall that

distance = rate*time

where "rate" is another term for "speed" or "velocity"

We can solve this for the time to get

time = distance/rate

------

We found the distance back in part a) above. We are given the rate of 48 km/h

So,

time = distance/rate

time = 14.4537840903742/48

time = 0.3011205018828

This is the time it takes in hours. Multiply by 60 to convert to minutes

0.3011205018828 hours = 60*0.3011205018828 = 18.067230112968 minutes

This rounds to the whole number 18

Answer:

A

Step-by-step explanation:

62 +65=127

C+127=180

C=180-127=53°

so x=53°

53-y=11

y=53-11=42

Answer: A

Step-by-step explanation:

Since ΔCDE and ΔGHI are congruent triangles, they are equal to each other. This means x-y=11. We want to find y, but we first need to find x. We can do that by finding x° on ΔGHI.

We know that the sum of the angles is 180° in a triangle. We are given 2 angles from ΔCDE. We can use those to find x°.

62+65+x=180             [combine like terms]

127+x=180                   [subtract 127 on both sides]

x=53

Now that we have x, we can find y by plugging in.

53-y=11                         [subtract both sides by 53]

-y=-42                           [divide both sides by -1]

y=42

Answer:

12 different outfits

Step-by-step explanation:

2 x 2 x 3 = 12 outfits.

Answer:

12

Step-by-step explanation:

He has 2 possibilities for a shirt, 2 possibilities for a pant, and 3 possibilities for a cap. You just multiply them together:

2 * 2 * 3 = 12 outfits

Answer:

I'm confused what's the question ?

Answer:

25 units.

Step-by-step explanation:

The first thing we need to do is find the hypotenuse of the triangle with side lengths 12 and 16. 12^2 + 16^2 = 144 + 256 = 400. sqrt(400) = 20. So, the hypotenuse of that triangle is 20 units.

Because the smaller length of the smaller triangle bisects the largest triangle's right angle, the two triangles are similar, with the side length 12 corresponding to the smaller side length of the larger triangle, the side length 16 corresponding to the 20 unit side, and the 20 unit hypotenuse corresponding to x.

Now that we know the triangles are similar, we can construct a proportion...

[tex]\frac{16}{20} =\frac{20}{x}[/tex]

That means that 4/5 = 20/x

1/5 = 5/x

x = 25

Hope this helps!

Step-by-step explanation:

total ratio = 3+4+7 = 14

3/14×180= 38.57°

4/14×180= 51.43°

7/14×180 = 90°

Answer:

total ratio = 3+4+7 = 14

3/14×180= 38.57°

4/14×180= 51.43°

7/14×180 = 90°

Step-by-step explanation:

Answer:

13.896 kg

Step-by-step explanation:

You can find the mass of the bar by first finding the volume.

V = BH

where B = area of the base (the trapezium), and

H = height (distance trapezium between bases)

The area of a trapezium is

A = (b1 + b2)h/2

where b1 and b2 are the lengths of the bases of the trapezium (the parallel sides), and

h = the altitude of the trapezium (distance between the bases of the trapezium)

V = (b1 + b2)h/2 * H

V = (12 cm + 6 cm)(5 cm)/2 * 16 cm

V = 720 cm^3

The volume of the bar is 720 cm^3.

Now we use the density and the volume to find the mass.

density = mass/volume

mass = density * volume

mass = 19.3 g/cm^3 * 720 cm^3

mass = 13,896 g

Now we convert grams into kilograms.

1 kg = 1000 g

mass = 13,896 g * (1 kg)/(1000 g)

mass = 13.896 kg

Answer: 1.3896 kg

Answer: 2(y + 6)(-y + 6)

Step-by-step explanation: Factor 72 - 2y^2

                                             -2y^2 + 72

                                             = 2(y + 6)(-y + 6)

Answer:

[tex]-2\left(y+6\right)\left(y-6\right)[/tex]

Step-by-step explanation:

[tex]72-2y^2[/tex]

[tex]-2y^2+72[/tex]

Factor out GCF.

[tex]2(-y^2+36)[/tex]

Apply difference of two squares formula.

[tex]-2\left(y+6\right)\left(y-6\right)[/tex]

Answer: 0.20

Step-by-step explanation:

As per given :

P(student enrolled in a math class ) = 65% = 0.65

P( student enrolled in a science class) = 43%= 0.43

P( student enrolled in both ) = 13% = 0.13

Formula of conditional probability :

[tex]P(A|B)=\dfrac{P(A\text{ and }B)}{P(B)}[/tex]

Using the above formula,

The probability that the student is enrolled in a science class given that he is enrolled in maths class :

[tex]P(\text{science}|\text{math})=\dfrac{P(\text{science and maths})}{P(\text{math})}\\\\=\dfrac{0.13}{0.65}\\\\=\dfrac{13}{65}\\\\=\dfrac{1}{5}=0.20[/tex]

Hence, the probability that the student is also enrolled in a science class =  0.20 .

Answer:

The answer is 3 mark as brainliest

Step-by-step explanation:

3 *3-4*4+2*5

9-16+10

9-6=

3

Answer:

Hey there!

3a-4b+2c

3(3)-4(4)+2(5)

9-16+10

3

Your answer would be 3.

Hope this helps :)

Answer:

can you please make the question more clear!

Step-by-step explanation:

i am guessing you are asking if 1/ (2·2) (3+(3.4·5))=

1/ 4+17+3

1/24?

Answer:

C; x = 900

Step-by-step explanation:

1. Write out the problem: x/15 = 60

2. Multiply each side by 15 to solve for x. This is because of inverse operations, so if you divide x by 15 you have to multiply 15 to both sides. THis way the 15 cancels out in 15(x/15).

3. Equation then becomes this: x = 15*60

4. Answer: 900

5. Substitute to see if you were right. Ask yourself: Does 900 divided by 15 equal 60. If it does, then you are correct.

Answer: 62

Step-by-step explanation:

The surface area of a rectangular prism is 2(wl+hl+hw).

Simply plug in the values to get 62

Answer:

62cm ^2

Step-by-step explanation:

every cube has 6 sides,

2(3*5) + 2(2*3)+ 2(2*5)=

2(15)+2(6)+2(10)=

30+12+20=

62

Answer:

£48

Step-by-step explanation:

56 ÷ 7 = £8

56 - 8 = £48

Please let me know if my answer is correct.

Answer:

48

Step-by-step explanation:

Answer: [tex](x+10)^2+119=0[/tex]

Step-by-step explanation:

For a quadratic equation, the vertex form is given by : [tex]y=a(x-h)^2+k[/tex], where (h, k) is the vertex.

The given quadratic equation: [tex]x^2 + 20x + 28 = 9[/tex]

Subtract 9 from both sides

[tex]=x^2+20x+19=0[/tex]

compare this to [tex]x^2+bx=c[/tex], and add [tex](\frac{b}{2})^2[/tex] both sides

b= 20

[tex]x^2+20+100+19=-100[/tex]   [(b/2)²=20/2=10]

[tex]\Rightarrow\ x^2+2(x)(10)+10^2+119=0[/tex]

[tex]\Rightarrow\ (x+10)^2+119=0\ \ \ [\because\ (a+b)^2=a^2+b^2+2ab][/tex]

So, the vertex form : [tex](x+10)^2+119=0[/tex]

Answer:   [tex]6\dfrac{3}{8}\text{ inches}[/tex]

Step-by-step explanation:

Given: Original length = [tex]15\dfrac{1}{8}[/tex] inches

[tex]=\dfrac{8\times15+1}{8}=\dfrac{121}{8}[/tex] inches                      ( In improper fraction )

Length of piece cut from original = [tex]8\dfrac{3}{4}[/tex] inches

[tex]=\dfrac{4\times8+3}{4}[/tex][tex]= \dfrac{35}{4}[/tex] inches                 ( In improper fraction )

Length of piece leftover piece =  (Original length ) - (Length of piece cut )

[tex]=\dfrac{121}{8}-\dfrac{35}{4}\\\\=\dfrac{121-2\times35}{8}\\\\=\dfrac{121-70}{8}\\\\=\dfrac{51}{8}\\\\=6\dfrac{3}{8}\text{ inches}[/tex]

Hence, the leftover piece will be [tex]6\dfrac{3}{8}\text{ inches}[/tex]  long.

Hey there! :)

Answer:

x = 5, x = -i√7, x = i√7

Step-by-step explanation:

We can factor the equation x³ - 5x² + 7x - 35 = 0 by grouping:

x²(x - 5) + 7(x -5) = 0

We get:

(x² + 7)(x - 5) = 0

or

(x + i√7)(x - i√7)(x - 5) = 0

Use the Zero Product Property to solve for the solutions:

x - 5 = 0

x = 5.

-----------

x² + 7 = 0

x² = -7 (We will have imaginary solutions in this instance)

x = ±i√7

Therefore, the zeros of this equation are:

x = 5, x = -i√7, x = i√7