The population of a species of rabbit triples every year. This
can be modeled by f(x) = 4(3) and f(5) = 972. What does the 4
represent? (1 point)

Answer:

[tex]\boxed{\text{160 ft}}[/tex]

Step-by-step explanation:

The angle of depression from the ranger at point A and the angle of elevation from the fire on the ground at Point C are congruent (interior opposite angles).

The distance from the ranger up in the tower to the fire on the ground is the hypotenuse AC  of the right triangle ABC.

sin 30 = 80/AC

AC  = 80/sin30 = 80/0.5 = 160 ft

The distance is [tex]\boxed{\textbf{160 ft}}[/tex]

For the equation to work, you have to have the same number on both sides of the equal sign

so to find ?, you can do:

13 - 2 = 12 - ?       Simplify

11 = 12 - ?       Subtract 12 on both sides

-1 = - ?     Multiply -1 on both sides

1 = ?

To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.

To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.

In the equation 13-2=12-x, we need to find the missing number x.

We can solve this equation by subtracting the known numbers on both sides.

Using the concept of simple mathematics, we found the subtraction of the given number.

So the missing number in the equation 13-2=12-x is 11.

https://brainly.com/question/33596593

#SPJ2

Answer:

A)13.3

Step-by-step explanation:

20² + y² = 24²

400 + y² = 576

y²  = 176

y=13.3

By Pythagoras theorem, in the given right triangle, the missing length to the nearest tenth is Option(A) 13.3 ft.

According to Pythagoras theorem, the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

Mathematically,

(Hypotenuse)² = (Base)² + (Height)² .

For the given triangle, length of hypotenuse is 24ft., height is 20ft and base is y ft.

Using Pythagoras theorem,

⇒ (24)² = y² + (20)²

⇒ y² = 24² - 20²

⇒ y² = 176

∴ y = √176 = 13.2665 ≈ 13.3 ft.

Thus, by Pythagoras theorem, in the given right triangle, the missing length to the nearest tenth is Option(A) 13.3 ft.

To learn more about Pythagoras theorem, refer -

https://brainly.com/question/231802

#SPJ2

Add by positive 3 for each of the numbers

-6+3=-3

-3+3=0

0+3= 3

3+3= 6

Answer is 6

ANSWER

The next term is 6.

EXPLANATION

The given arithmetic sequence is -6,-3,0,3,

There is a constant difference of 3.

That is,

-3--6=-3+6=3

This means that, we need to add 3 to the previous terms to get the subsequent terms.

To get the next term after 3, we add 3 to obtain 3+3=6

Therefore the next term of the sequence is 6.

The answer is:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to isolate one in function of the other.

So, let be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

[tex]x_{FirstCar}=x_o+v*t[/tex]

For the second car:

We know that the speed of the second car is the speed of the first car plus 14 mph, so:

[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]

Now, we already know that both cars met after 2 hours and 45 minutes, meaning that positions will be the same at that moment, and the distance between A and B is 264 miles,  so, we can calculate the relative speed between them:

If the cars are moving towards each other the relative speed will be:

[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]

Then, since we know that they covered a combined distance which is equal to 264 miles of distance in 2 hours + 45 minutes, we  have:

[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]

Writing the equation, we have:

[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]

We have that the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]

Hence, we have that:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

Have a nice day!

Answer:

55 miles per hour and 41 miles per hour.

Step-by-step explanation:

Enjoy...It is correct because RSM told me so.

The volume of the cylinder is:

3.14 x 0.3^2 x 0.75 = 0.21 cubic meters.

Multiply the density of the kerosene by the volume of the cylinder:

0.21 x 815 = 17.85 kg.

Answer:

173

Step-by-step explanation:

Answer:

y= (.37)x + 3

Step-by-step explanation:

1. Best thing to use would be y=mx + b.

2. Flat fee is $3 so that is your b.

3. Every additional message is $0.37, that is your slope(m)

4. That is your answer, x represents the number of text messages

Answer:

The monthly cost for x messages is (3 + 0.37x)$.

Step-by-step explanation:

We are given the following information in the question:

Monthly cost for text message = $3 per month

Cost of each text message = $0.37

Let x be the number of total text messages.

Monthly cost for x messages =

Formula:

[tex]\text{Monthly charges} + (\text{Text messages}\times \text{Cost of each message})\\\text{Putting the values, we get}\\= 3 + (0.37\times x)\\=3 + 0.37x[/tex]

Hence, the monthly cost for x messages is (3 + 0.37x)$.

Answer: Option A

[tex]P = 5.3 + 0.09125t[/tex]

Step-by-step explanation:

Note that for the initial year, 1990, the population was 5.3 billion.

The exchange rate is 0.09125 billion per year. In other words, each year there are 0.09125 billion more people.

In year 2 there will be 0.09125 * 2 billion people

In year 3 there will be 0.09125 * 3 billion people

In year 4 there will be 0.09125 * 4 billion people

In year t there will be 0.09125 * t billion of people

So the equation that models the number of people that there will be as a function of time is:

[tex]P = P_0 + rt[/tex]

Where [tex]P_0[/tex] is the initial population

[tex]P_0 = 5.3[/tex] billion

r is the rate of increase

[tex]r = 0.09125[/tex] billion per year

finally the equation is:

[tex]P = 5.3 + 0.09125t[/tex]

The correct answer is option A.

Answer:

122

Step-by-step explanation:

The average of her two scores is calculated by the sum of her two scores divided by 2.

[tex]\boxed{\text{Average}=\frac{\text{sum of data}}{\text{number of data sets}} }[/tex]

Total score= 116(2)

Total score= 232

Total score= score of 1st game +score of 2nd game

Substituting value of first score and total score:

110 +score of 2nd game= 232

Subtract 110 from both sides:

score of 2nd game

= 232 -110

= 122

Additional:

To learn more about average, do check out the following!

Answer:-250

Step-by-step explanation:

#17: Domain: [−4,∞),{x|x≥−4}

Range: [−2,∞),{y|y≥−2}

#18 g(2)=4(2)+2

g(2)=10

f(10)=3(10)^2-2

f(10)=298

For this case we have:

Question 1:

We have the following functions:

[tex]f (x) = 2x-1\\g (x) = x ^ 2-2[/tex]

We must find (g_ {0} f) (x).

By definition of composition of fusions we have to:

[tex](g_ {0} f) (x) = g [f (x)]\\(g_ {0} f) (x) = g [2x-1]\\(g_ {0} f) (x) = (2x-1) ^ 2-2\\(g_ {0} f) (x) = 4x ^ 2-2 (2x) + 1-2\\(g_ {0} f) (x) = 4x ^ 2-4x-1[/tex]

Answer:

[tex](g_ {0} f) (x) = 4x ^ 2-4x-1[/tex]

Question 2:

For this case we have a function of the form[tex]y = f (x)[/tex], where: [tex]f (x) = \sqrt {x + 4} -2[/tex]

We must graph the given function.

By definition, the domain of the function will be given by the values for which the function is defined. The function is not defined when the root is negative, that is to say for values of "x" less than -4. Then, the domain is:

[-4, ∞)

For its part, the range is the set of values that correspond to the domain. When replacing the values from -4 to infinity we have the following range:

[-2, ∞)

Answer:

See attached image

Domain: [-4, ∞)

Range: [-2, ∞)

Question 3:

For this case we have the following functions:

[tex]f (x) = 3x ^ 2-2\\g (x) = 4x + 2[/tex]

We must find, (f + g) (x):

By definition, we have to:

[tex](f + g) (x) = f (x) + g (x)\\(f + g) (x) = 3x ^ 2-2 + (4x + 2)\\(f + g) (x) = 3x ^ 2-2 + 4x + 2\\(f + g) (x) = 3x ^ 2 + 4x[/tex]

Now, we must find [tex](f + g) (2):[/tex]

[tex](f + g) (2) = 3 (2) ^ 2 + 4 (2)\\(f + g) (2) = 3 (4) +4 (2)\\(f + g) (2) = 12 + 8\\(f + g) (2) = 20[/tex]

Answer:

[tex](f + g) (2) = 20[/tex]

Answer:

[tex]h(17)=\sqrt{17\times17}=\boxed{17}[/tex]

Answer:

k = 25

Step-by-step explanation:

Step 1: Isolate k by adding 2 on both sides.

1/5k = 5

Step 2: Simplify by multiplying 5 on both sides.

k = 25

Answer: d

Step-by-step explanation:

Answer:

This is frankly impossible.

Step-by-step explanation:

What you have given me are three x-intercepts. And it is impossible for a quadratic function to have more than two roots. However, if this was an cubic function, we could multiply (x+5)(x-1)(x-4) which results in the equation which simplifies into x^3 -21x + 20. However, this is a cubic function, not a quadratic function, so something must be wrong with this problem all together.

Answer:

All positive integers and zero

A is correct

Step-by-step explanation:

A box of pencils costs $10

The total cost (c) as a function of the number of boxes (b) is expressed as

c = f(b) = 10b

The function, f(b) = 10b

b is independent variable and c is dependent variable.

For any function find domain using independent variable.

b represents number of boxes.

Number of boxes neither be negative nor decimal.

Possible value of b: {0,1,2,3,4,5,.......}

All positive integers and zero.

Domain: All positive integers and zero

Answer is..

ab= 18

Explanation..

a + b = 11...---> a= 11-b

a -b = 7

11 - b - b = 7

11 - 2b = 7

2b = 18

b = 9

and a = 11 - 7

a = 2

So

ab = 2 * 9 =18

90 degrees is a right angle

The answer is:

The function is greater or equal to 0 at the points (-3,6), (-2,0), (0,6) and (4,0).

To find where the function is greater or equal to 0, we need to look (using the graph) where the function is above the x-axis

So, we can see that the function is above the x-axis from the point (-3,6)  to the point (4,0), for these points, the function is greater or equal to 0.

Hence, the function is greater or equal to 0 at the points (-3,6), (-2,0), (0,6) and (4,0), or the function is greater or equal to 0,  from -3 to 4 (x-axis values or input).

We have that:

[tex]f(-3)=6\\6\geq 0\\\\f(-2)=0\\0=0\\\\f(0)=6\\6\geq 0\\\\f(4)=0\\0=0[/tex]

Have a nice day!

Answer:

You can find the perpendicular bisector of MA and then plug in the point.

Step-by-step explanation:

To find the perpendicular bisector of MA, you have to go through a 4 step process.

1. Find the midpoint of MA

2. Find the slope of MA

3. Find the perpendicular slope to the slope of MA.

4. Substitute in your midpoint into the equation and solve for the y-intercept.

Plug in your point into the equation and see if it works out.

You'll have to do the actual work yourself though!

The point which satisfy the equation of line having the slope -2/3 and point (-4,1), lies on the perpendicular bisector of MA.

The perpendicular bisector on a line segment is the line which divides the line in two equal parts and intersect the line at 90 degrees.

The line segment MA has the end points as M(−2, 4) and A(−6, −2). The midpoint of this line segment is,

[tex]p=(\dfrac{-2+(-6)}{2},\dfrac{4+(-2)}{2})\\p=(\dfrac{-8}{2},\dfrac{2}{2})\\\\p=(-4,1)[/tex]

The slope of this line segment MA is,

[tex]m=\dfrac{-2-4}{-6-(-2)}\\m=\dfrac{-6}{-4}\\m=\dfrac{3}{2}[/tex]

The slope of MA is 3/2. Thus, the slope of a line segment which is perpendicular to this is -2/3.

Thus, the point which satisfy the equation of line having the slope -2/3 and point (-4,1), lies on the perpendicular bisector of MA.

Learn more about the perpendicular bisector on a line here:

https://brainly.com/question/11006922

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}\dfrac{1}{3}x+y=\dfrac{0}{3}&\text{multiply both sides by 3}\\\\\dfrac{1}{6}x+\dfrac{1}{5}y=\dfrac{9}{10}&\text{multiply both sides by 30}\end{array}\right\\[tex]\left\{\begin{array}{ccc}x+3y=0&\text{multiply both sides by (-2)}\\5x+6y=27\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-2x-6y=0\\5x+6y=27\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=27\qquad\text{divide both sides by 3}\\.\qquad\boxed{x=9}\\\\\text{Put the value of x to the first equation:}\\\\9+3y=0\qquad\text{subtract 9 from both sides}\\3y=-9\qquad\text{divide both sides by 3}\\\boxed{y=-3}[/tex][/tex]

Answer: 432 units²

Step-by-step explanation:

The figure is composed by two trapezoids.

The formula for calculate the area of a trapezoid is:

[tex]A=\frac{h}{2}(B+b)[/tex]

Where "B" is the larger base, "b" is the smaller base and "h" is the height.

Let be [tex]A_f[/tex] the area of the figure, [tex]A_1[/tex] the area of the trapezoid on the left and [tex]A_2[/tex] the area of the trapezoid of the right. Then the area of the figure will be:

 [tex]A_f=A_1+A_2[/tex]

[tex]A_f=\frac{h_1}{2}(B_1+b_1)+\frac{h_2}{2}(B_2+b_2)[/tex]

Substituting values, you get:

[tex]A_f=\frac{16units}{2}(25units+4units)+\frac{10units}{2}(25units+15units)=432units^2[/tex]

Answer:

Area of given figure = 432 unit ²

Step-by-step explanation:

Points to remember

Area of trapezoid = h(a + b)/2

Where h - height  and a and b  are two parallel sides

To find the area of given figure

It is given two trapezoid

Area of 1st trapezoid

h = 16, a = 25 and b = 4

Area = h(a+ b)/2

 = 16(25 + 4)/2

 = 232 units ²

Area of 2nd trapezoid

h = 10, a = 25 and b = 15

Area = h(a+ b)/2

 = 10(25 + 15)/2

 = 200 units ²

Total area = 232 + 200 = 432 units²

Answer:

$432.00

Step-by-step explanation:

$12.00x36= $432.00

The sum of first 10 terms is 620.

Arithmetic Progression (AP) is a numerical series in which the difference between any two subsequent numbers is always the same.

Here a1= 8,a2 = 20,a3  = 32 and a4= 44

Find the difference between two terms

a2 - a1 = 20 - 8 = 12

a3 - a2 = 32 - 20 = 12

a4 - a3 = 44 - 32 = 12 sum of n terms is = n/2[2a1 + (n-1)d]

For the given sequence we have n = 10, a1= 8 and d = 12

substituting values of a1 and n in S = 10/2[2x8 + (10-1)x12]

S = 5[16+9x12]

S = 5[16+108]

S = 5[124]

S = 5x124

S = 620

Learn more about arithmetic progression here: https://brainly.com/question/236376

#SPJ2

Answer:

Jasmine ran last week 37.2 miles

Step-by-step explanation:

Let

x ----> number of miles Rob ran last week

y ----> number of miles Jasmine ran last week

we know that

x=y-27.2 ----> equation A

x=10 ----> equation B

Substitute equation B in equation A and solve for y

10=y-27.2

y=10+27.2

y=37.2 miles

Check the picture below.

Answer:

3x² - 9x + 5

Step-by-step explanation:

Given

(5x² - 3x + 4) - (2x² + 6x - 1)

Distribute the first parenthesis by 1 and the second by - 1

= 5x² - 3x + 4 - 2x² - 6x + 1 ← collect like terms

= (5x² - 2x²) + (- 3x - 6x) + (4 + 1)

= 3x² - 9x + 5

One is going up and then going down and then going up and all the way up. You’re welcome

Answer: $450,000

Step-by-step explanation:

Answer: $450,000

Step-by-step explanation:

We know that Jerome's earnings were from $150,000

And we know that this was 1/3 of the company's overall earnings.

Then let's call "x" to the company's general earnings

So a third multiplied by x must equal Jerome's earnings

[tex]\frac{1}{3}x=150,000[/tex]

Now we solve the equation for the variable x

[tex]x=150,000*3\\\\x= \$450,000[/tex]

Finally, the general earnings of the company were $450,000

Answer:

The answer is C) 54 pounds

Step-by-step explanation:

because im batman