The table shows expressions to represent the number of students involved in different activities. The number of students involved in sports and student council is equal to the number of students involved in band and drama club. Model the situation with an equation. Select the correct expression for each box. Then solve the equation.​

a) The deepest that the diver went is of: 432 yards deep.

b) It took 12 minutes for the diver to return to the surface.

c) After one minute, the diver was 132 yards deep.

The quadratic function modeling the diver's height after x seconds is given as follows:

d(x) = 12x² - 144x.

The coefficients are given as follows:

a = 12, b = -144, c = 0.

The x-coordinate of the vertex is given as follows:

x = -b/2a

x = 144/24

x = 6.

Item a:

As a > 0, in item a, the minimum height is given as follows:

d(6) = 12(6)² - 144(6)

d(6) = -432 feet.

Item b:

The roots of the function, in item b, are obtained as follows:

12x² - 144x = 0

12x(x - 12) = 0

Hence:

12 - 0 = 12, hence it took 12 minutes for the diver to return to the surface.

Item c:

After one minute, the depth of the diver, in item c, is given as follows:

d(1) = 12(1)² - 144

d(1) = -132 yards.

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Answer:

Five times the quotient of two numbers

5*( r/t)

Step-by-step explanation:

5 times the qoutient of 2 numbers is 5+rt

For the given function the value of limits are

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\) is 5

\(\lim _{x\to 0^+}\left(f\left(x\right)\right)\) is 0

\(\lim _{x\to 0}\left x^2+5\)is 5

The given function is f(x)= x²+5, when x≤0

f(x)=2x when x>0

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0^-}\left x^2+5\)

The given limit is a left hand limit as there is minus in the limits

When we apply x as 0 we get the value 5

Now \(\lim _{x\to 0^+}\left(f\left(x\right)\right)\)

So \(\lim _{x\to 0^+}\left 2x\)

The given limit is a right hand limit as there is positive in the limits

When we apply x as 0 we get 0

Now \(\lim _{x\to 0}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0}\left x^2+5\)

We get 5

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Step-by-step explanation:

6 2/7is rational

-19is rational but next I dont know

Answer:

21x

Step-by-step explanation:

Answer:

yea

Step-by-step explanation:

Answer:

A.

Explaintion:

n=13. 13+2 = 15

I hope this helps ( :

Answer: B

Step-by-step explanation:

because 4 is the number of (n) plus the 2

Answer:

P represents the population in year 0

Step-by-step explanation:

The exponential growth function is f(x) = a (1 + r)^t, where a is the initial

amount (at t = 0), (1 + r) is the factor of growth , r is the rate of growth

in decimal ant is the time of growth

the function C(t) = P(1 + r)^t represents the population of

centerville at year t, where P is the initial population and r is the

rate of increase

If your investment is increased 10% annually, then that means

each year, your total has multiplied itself by 110% (the growth factor

is 1 + 10/100 = 1.1)

(1 + r) is the factor grows each year

C(t) = P(1 + r)^t

C depends on P(starting population) , r(the increasing rate and

t(the time in year)

r is the rate of increase means the percentage of increasing , then

0 < r < 1

r is not less than 0

P is the initial amount when t = 0

P represents the population in year 0

Answer:

P represents the population in year 0

Step-by-step explanation:

Answer:

The scale factor is 3

Step-by-step explanation:

7 times 3= 21

5 times 3= 15

9 times 3= 27

Therefore the scale factor is three

Answer: \(\Large\boxed{x=-\frac{4}{5} }\)

Step-by-step explanation:

Given equation

\(-9+log_{4}(-5x)=-8\)

Add 9 on both sides

\(-9+log_{4}(-5x)+9=-8+9\)

\(log_{4}(-5x)=1\)

Simplify the logarithm

\(-5x=4^1\)

\(-5x=4\)

Divide -5 on both sides

\(-5x\div-5=4\div-5\)

\(\Large\boxed{x=-\frac{4}{5} }\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

k/4+3=14

First you need to isolate the variable.

multiply both sides by 4

Answer:

y= 7 and -1

Step-by-step explanation:

The growth rate function indicates that the number of years The Iron Man's net worth will reach the net worth of T'Challa is about 87 years

The growth rate is the rate of growth of a function with regards to the input variable.

T'Challa's net worth in the Marvel comics = 80 trillion (8 × 10¹³) Dollars

The Iron Man's net worth = 20 billion (2 × 10¹⁰) Dollars

The growth rate per annum of The Iron Man's net worth = 10% per annum

The number of years it will take to reach T'Challa can therefore, be found as follows;;

(2 × 10¹⁰) × (1 + 0.1)ˣ = (8 × 10¹³)

(1 + 0.1)ˣ = (8 × 10¹³)/(2 × 10¹⁰)

x·ln(1 + 0.1) = ln((8 × 10¹³)/(2 × 10¹⁰))

x = (ln((8 × 10¹³)/(2 × 10¹⁰)))/(ln(1 + 0.1)) ≈ 87 years

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The unknown number if "four more than x is twelve." is 8

Equations are expressions separated by an equal to sign. From the given information, we can say:

If the result of the expression is 12, hence 4 + x  = 12

Get the value of x

4 + x = 12

x  = 12 - 4

x = 8

Hence the unknown number is 8

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The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

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Answer:

11 miles

Step-by-step explanation:

find how many miles per minute

66 / 60 = 1.1

find how many miles in 10 minutes

1.1 • 10 = 11

11 miles

Answer:

11 miles

Step-by-step explanation:

66 miles per hour

Convert minutes to hours

10 minutes * 1 hour/ 60 minutes = 1/6 hour

distance = rate * time

              = 66 miles per hour * 1/6 hour

               = 11 miles

Answer:

discrete probability distribution

Step-by-step explanation:

A discrete probability distribution is a term that describes a form of a probability distribution that is used in a situation where the set of possible outcomes is discrete.

While it also has a tendency to take on a countable number of values, it is a probability distribution where a sample is drawn from a larger population, this sample points possess an empirical distribution that is considered to be discrete, which resulted in information about the population distribution.

Hence, given that Bob is dealing with discrete data and the samples are drawn without replacement, the likely probability distribution is DISCRETE PROBABILITY DISTRIBUTION

Answer:

width = 4in

length = 8in

Step-by-step explanation:

A = LxW = 32

L = W + 4

W(W+4) = 32

W² + 4W - 32 = 0

(W + 8)(W - 4) = 0

W ≠ -8 (dimensions cannot be negative)

W = 4in

L = W+4 = 4+4 = 8in

Answer:

\( \sqrt[4]{ {x}^{3} } \)

Step-by-step explanation:

\( \sqrt{x} \times \sqrt[4]{x} \\ = {x}^{ \frac{1}{2} } \times {x}^{ \frac{1}{4} } \\ = {x}^{ \frac{1}{2} + \frac{1}{4} } \\ = {x}^{ \frac{3}{4} } \\ = \sqrt[4]{ {x}^{3} } \)

The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.

The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.

As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:

When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).

As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.

For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.

The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.

Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.

The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.

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Answer:14

Step-by-step explanation:

14

Answer:

It is not a factor

Step-by-step explanation:

It is because p(x)=-12 at x=3

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

\( \fbox \colorbox{black}{ \colorbox{white}{n} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{3.6}}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

Let's solve for n ~

I hope it helps ~

The table is completed as follows:

x              0     1     2     3      

g(x)          -2    0    6     24

Given data

x              0     1     2     3      

f(x)            0    2     8     26

vertical shift downwards represents subtraction of the value of the units as required, this is done as follows:

first

0 - 2 = -2

second

2 - 2 = 0

third

8 - 2 = 6

fourth

26 - 2 = 24

This is represented in a tabular form as follows

x              0     1     2     3      

g(x)          -2    0    6     24

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The Angle Bisector Theorem states that:

From the diagram, we see that:

• |AB| = 11,

• |AC| = 9,

• |BD| = x,

• |CD| = 7.

Replacing these data in the equation above, we have:

Solving for x, we get:

Answer

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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15+2.5x <55

1.15

Answer: -5b cubed

Step-by-step explanation: