1). A population of 20 rabbits is released into a wildlife region. The population is growing at a rate of 60% per year.
A) the General Equation from the Video was: P(x) = (blank)


What is the population of rabbits after 5 years?

B) the Evaluated equation I used to get the following answer is (blank)
and After five years there will be(blank)
rabbits.

And What is the population of rabbits after 8 years?

c) the Evaluated equation I used to get the following answer is(blank)
and After eight years there will be(blank)
rabbits.

Answer:

x = 3

y = 8

Step-by-step explanation:

In the given triangle FGH,

m∠F + m∠G + m∠H = 180° [Triangle sum theorem]

60° + 90° + m∠H = 180°

m∠H = 30°

If the given triangles FGH and TUV are congruent, their corresponding sides will be equal in measure.

m∠F = m∠T

7y + 4 = 60°

7y = 56

y = 8

GH ≅ UV

8x - 12 = 12

8x = 24

x = 3

Using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.

According to the angle-angle-side congruence theorem (AAS), two triangles are congruent if they have two corresponding congruent angles and one pair of corresponding non-included sides that are congruent.

Thus, by the AAS theorem, we have:

8x - 12 = 12

8x = 12 + 12

8x = 24

x = 3

Also,

7y + 4 = 60

7y = 60 - 4

7y = 56

y = 8

Therefore, using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.

Learn more about AAS congruence theorem on:

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Answer:

Step-by-step explanation:

The mean the the average of 5 numbers. If the next score is x, then the mean is:

Solve it for x:

It is given that,

The mean is the average of 5 numbers.

Then if the,

Next score is x the mean will be.

We can solve now,

→ (85 +78 +77 + 69 + x)/5 = 80

→ (309 + x)/5 = 80

→ 309 + x = 80 × 5

→ 309 + x = 400

→ x = 400 - 309

→ x = 91

Hence, the next score is 91.

Answer:

Step-by-step explanation:

A)

The opposite sides of a rectangle are equal. The width make this obvious because both of them are x.

B)

The lengths are not so obvious, but it is never the less true. The two sides are obvious and they are therefore true.

4x + 1 = 2x + 12                   Subtract 1 from both sides.

   - 1              -1

4x = 2x + 11                         Subtract 2x from both sides

-2x   -2x

2x  =  11                               Divide by 2

x = 11/2

x = 5.5

C)

P = L + L + w + w

P = 4(5.5) + 1  + 2(5.5) + 12 + 5.5 + 5.5

P = 22 + 1 + 11 + 12 + 11

P = 23 + 23 + 11

P = 57

Explanation:

The coefficients -24 and 8 divide to -24/8 = -3. Based on this alone, the answer is between choices B and C.

The m terms divide to [tex]\frac{m^5}{m^{-7}} = m^{5-(-7)} = m^{5+7} = m^{12}[/tex]

Notice how I subtracted the exponents. The general rule is [tex]\frac{a^b}{a^{c}} = a^{b-c}[/tex]

Since we get m^12, this points us to choice C as the final answer

For the sake of completeness, here's what the n terms divide to

[tex]\frac{n^4}{n^{-2}} = n^{4-(-2)} = n^{4+2} = n^{6}[/tex]

Answer:

///////

Step-by-step explanation:

Hello!

1) -3x - 4 = 23

-3x = 23 + 4

-3x = 27

x = 27 : (-3)

x = -9

2) x/2 - 12 = -4

x - 24 = -8

x = -8 + 24

x = 16

3) 6a + (-1) = 10

6a - 1 = 10

6a = 10 + 1

6a = 11

a = 11 : 6

a = 11/6

4) -(x + 2) = 12

x + 2 = -12

x = -12 - 2

x = -14

5) 7a + 12 = 10

7a = 10 - 12

7a = -2

a = -2 : 7

a = -2/7

6) -4(a + 2) = 12

a + 2 = -3

a = -3 - 2

a = -5

Good luck! :)

Answer:

39.7

Step-by-step explanation:

Answer:

[tex] {3}^{2} \div 48 - 6 \\ 9 \div 48 - 6 \\ = - 5.8125[/tex]

Answer:

Step-by-step explanation:

If the tank holds 2500 liters and there are already 750 liters in there, he only needs to buy 1750 liters.

If he is saving 6%, he is still spending 94%, so

.94(58.4) = 54.896 (what he'll be paying per liter after the 6% comes off, then

54.896(1750) = $96,068

Answer:

D = [4, 10]

Step-by-step explanation:

Since the line starts when x = 4, the domain begins there. And since the line ends when x=10, the domain ends there.

Answer:

Given that m∠abc=70° and m∠bcd=110°. Is it possible (consider all cases): Line AB intersects line CD?

Step-by-step explanation:

#CarryOnLearning

Answer:

24 mph

Step-by-step explanation:

1 hour of 36 mph

3 hours of 20 mph

(36 + 20 + 20 + 20)/4

96/4

24

Answer:

24 mph

Step-by-step explanation:

36 miles = 1 hour

60 miles = 3 hours

36+60= 96

1+3+4

96/4= 24

Answer:

The first equation; x-2y=8

Step-by-step explanation:

Hi there!

We're told that Ty wants to isolate x in one of the equations. To do so in either, he will need to use inverse operations to cancel out values and leave just x remaining on one side of the equation.

In the second equation, he would need to subtract both sides by 6y and then divide both sides by 4 to isolate x. It's a two-step process.

However, in the first equation, he only needs to add 2y to both sides to isolate x.

I hope this helps!

Answer:

using the first equation

cause Being that the first equation has the simplest coefficients (1, -2, for x, and y respectively), it seems logical to use it to develop a definition of one variable in terms of the other

Answer:23

Step-by-step explanation:

Answer:

-3a+3bx+2ab

Step-by-step explanation:

Answer:

Answers are below!

Step-by-step explanation:

(2 + g) (8)

= (2 + g) (8)

Add a 8 after the 2, and flip.

= (2)(8) + (g)(8)

= 16 + 8g

= 8g + 16

= (4) (8 + -5g)

Add another 4, then flip.

= (4) (8) + (4) (-5g)

= 32 − 20g

= - 20g + 32

−7 (5-n)

= (−7) (5 + -n)

Add another 7, then flip.

= (−7) (5) + (-7) (-n)

= −35 + 7n

= 7n - 35

Use the distributive property.

a (b + c) = ab + ac

a = 8

b = 2m

c = 1

= 8 × 2m + 8 × 1

Simplify, you get 16m + 8.

Use the distributive property.

a (b + c) = ab + ac

a = 6x

b = y

c = z

= 6xy - 6xz is the answer.

[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \\\:a\left(b+c\right)=ab+ac[/tex]

[tex]a=-3,\:b=2b,\:c=2a[/tex]

[tex]=-3\cdot \:2b+\left(-3\right)\cdot \:2a[/tex]

Apply minus plus rules.

[tex]=-3\cdot \:2b+\left(-3\right)\cdot \:2a[/tex]

Multiply the numbers.

3 x 2 = 6

Answer:

9. -35+7n

10. 16m+8

11. 6xy-6xz

Step-by-step explanation:

You multiplying the terms inside the ( ) by the outside factor.

This is call distributive property, a(b+c)=ab+ac.

Also, a(b+c)=(b+c)a by commutative property.

It also works over the operation subtraction since subtraction is just a disguised addition (addition of the opposite). That is, a(b-c)=ab-ac.

Anyhow, let's look at 9.,10., and 11..

9.

-7(5-n)

(-7)(5-n)

(-7)(5)-(-7)(n)

-35+7n

10.

8(2m+1)

(8)(2m)+(8)(1)

16m+8

11.

6x(y-z)

(6x)(y-z)

(6x)(y)-(6x)(z)

6xy-6xz

Hint on 7. It's like all the other problems. That is, it is equivalent to doing 8(2+g).

If you want comment below, if you want me to check any of yours or if you have any questions.

Step-by-step explanation:

a) Use sine law:

[tex]\dfrac{g}{\sin 60} = \dfrac{17\:m}{\sin 49}[/tex]

Solving for g,

[tex]g = \left(\dfrac{\sin 60}{\sin 49}\right)(17\:m)=19.5\:m[/tex]

b) Use the cosine law here:

[tex]q^2 = (11\:\text{cm})^2 + (16\:\text{cm})^2 \\ - 2(11\:\text{cm})(16\:\text{cm})\cos 29[/tex]

Solving for q,

[tex]q = 8.3\:\text{cm}[/tex]

Answer:

Atleast 4 women

Step-by-step explanation:

Ratio of

Women to men = 2 : 7

Number of women needed to maintain the ratio if there are 14 men on the roster :

The minimum number of women required :

(2 : 7) * number of men in roster

(2 / 7) * 14

2 * 2 = 4 women

Atleast 4 women are required to main the ratio

Answer:

The level of significance is the

b. maximum allowable probability of Type I error.

Step-by-step explanation:

The significance level provides the maximum probability of rejecting the null hypothesis when it is true.  It is the same as a type I error (also known as false-positive).  This error occurs when a researcher or investigator rejects a true null hypothesis that is supposed to be accepted.  It is the opposite of a type II error (false-negative), which occurs when the researcher fails to reject a false null hypothesis.

Answer:

0,-3

Step-by-step explanation:

it will help u

Answer:

A

Step-by-step explanation:

Given:

Consider the below figure attached with this question.

The table represents a proportional relationship.

To find:

The missing value from the table.

Solution:

If y is proportional to x, then

[tex]y\propto x[/tex]

[tex]y=kx[/tex]                 ...(i)

Where, k is a constant of proportionality.

The relationship passes through the point (-3,-1). Substituting [tex]x=-3,y=-1[/tex] in (i), we get

[tex]-1=k(-3)[/tex]

[tex]\dfrac{-1}{-3}=k[/tex]

[tex]\dfrac{1}{3}=k[/tex]

Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get

[tex]y=\dfrac{1}{3}x[/tex]           ...(ii)

We need to find the y-value for [tex]x=-12[/tex].

Substituting [tex]x=-12[/tex] in (ii), we get

[tex]y=\dfrac{1}{3}(-12)[/tex]

[tex]y=-4[/tex]

Therefore, the missing value in the table is -4. Hence, option D is correct.

Answer:

Cost to pave the road = $4257

Step-by-step explanation:

Area of the pavement = Area of the outer circle - Area of the internal circle

Area of the outer circle = πr²

                                       = π(55)²

                                       = 3025π square feet

Area of the inner circle = π(33)²

                                       = 1089π square feet

Area of the pavement = 3025π - 1089π

                                     = 1936π

                                     = 6082.12 square feet

Cost of pavement = $0.70 per square feet

Therefore, cost of 6082.12 square feet = 6082.12 × 0.70

                                                                 = 4257.49

                                                                 ≈ $4257

Cost to pave the road = $4257                                    

Step-by-step explanation:

she gives each of her children $25 each,if Raul spends $15 then he would have $10 left.

Division then subtraction can be used to solve the problem.

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

Given

she gives each of her children $25 each,if Raul spends $15 then he would have $10 left.

to learn more about mathematical expressions refer to:

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FINAL ANSWER:

1

Step-by-step explanation:

[tex]\frac{2}{3} +\frac{1}{3}[/tex]

the denominators are the same so all we need to do is add.

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

[tex]\frac{3}{3} =[/tex] 1 whole

final answer: 1

hope this answer helps you :)

have a great day and may God Bless You!

Using translation concepts, the vertex of k(x) is 6 units below the vertex of f(x) = x² for:

D. f(x) = x² and k(x) = x² - 6.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

We want to shift the vertex 6 units down, hence the transformation is y -> y - 6, so the correct pair is:

D. f(x) = x² and k(x) = x² - 6.

More can be learned about translation concepts at https://brainly.com/question/4521517

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9514 1404 393

Answer:

  3.  y = 3·4^x

  4.  y = 24·0.5^x

  5.  y = 45·0.9^x

Step-by-step explanation:

Each table appears to represent an exponential function. Such a function can be written in the form ...

  y = a·b^x

where 'a' is the value of y when x=0, and 'b' is the ratio of the values of y when x=1 and x=0.

__

3. a = 3. b = 12/3 = 4

  y = 3·4^x

__

4. a = 24. b = 12/24 = 0.5

  y = 24·0.5^x

__

5. a = 45. b = 40.5/45 = 0.9

  y = 45·0.9^x

Answer:

The slope is -3/4 because it rises goes down 3 and runs 4. the Y-intercept or where the line meets the y line is 3.

Answer:

f(6) = 3

f'(6) = 1/6

Step-by-step explanation:

Remember that for a function f(x), we define f'(x) as the slope of the tangent line to the point (x, f(x))

We know that:

y = f(x) passes through the point (6, 3)

Then we already know that:

f(6) = 3.

Now we also know that the tangent at this point, also passes through (0, 2)

Remember that a line can be written as:

y = a*x + b

Where in this case, a = f'(6)

so we just want to find the slope of this line.

Remember that for a line that passes through (x₁, y₁) and (x₂, y₂) the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

And we know that the tangent line passes through the points (0, 2) and (6, 3)

Then the slope is:

a = (3 - 2)/(6 - 0)  = 1/6

Then we have:

a =  f'(6)  =1/6

Answer:

[tex]g(2) = 6[/tex]

Step-by-step explanation:

Given

[tex]g(x) = 3x[/tex] --- [tex]x > 1[/tex]

[tex]g(x) = -2x[/tex] -- [tex]x < 1[/tex]

Required

[tex]g(2)[/tex]

[tex]2 > 1[/tex]

So, we use:

[tex]g(x) = 3x[/tex]

Substitute [tex]2[/tex] for x

[tex]g(2) = 3 * 2[/tex]

[tex]g(2) = 6[/tex]

Answer:g(-2)=4

Step-by-step explanation:

Since x = -2, use the piece of the function when x ≤ 1. Therefore, use g(x) = -2x and substitute -2 in for x to get g(-2) = -2(-2), which simplifies to g(-2) = 4.