The following box plot represents the average heights of the students in Mr. Taylor's fourth grade math class.

Using Two point formula in getting the equation of the line.

x1 = -6

y1 = -3

x2 = 2

y2 = -5

Substitute to the formula :

The answer is :

y = -1/4 x - 9/2

The perimeter of the Garden is 76 meters. and the length is 32m.

Area= L × B

(L×6) = 16 × 12

L = [tex]\frac{288}{6}[/tex] = 32m

Therefore L works out to 32 meters.

Perimeter of Garden = 2 × (32+6) = 76 meter.

The area is the quantity that expresses the extent of a place on the plane or on a curved floor. The area of an aircraft area or aircraft location refers to the region of a shape or planar lamina, at the same time as floor vicinity refers back to the region of an open surface or the boundary of a three-dimensional object. the vicinity may be understood as the quantity of cloth with a given thickness that would be essential to fashion a version of the form, or the amount of paint necessary to cover the floor with an unmarried coat. it's miles the two-dimensional analog of the period of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).

vicinity of a form may be measured by evaluating the form to squares of a fixed size. inside the international system of devices (SI), the usual unit of the region is the rectangular meter (written as m²), which is the region of a square whose facets are one meter lengthy. A shape with a place of three square meters would have the same place as 3 such squares. In arithmetic, the unit rectangular is defined to have region one, and the place of any other shape or floor is a dimensionless actual wide variety.

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Solution

where:

F=future value = 45000

P=present value

r=rate (as a decimal) = 7%=0.07

n=number of compounding periods per year = 1

t=number of years = 6

Therefore the present value deposited today = $29,985.40

Answer: ∠WZY=150°

Step-by-step explanation:

Analysis :

ΔWXY is an isosceles triangle

perpendicular to WX intersecting:

XY at A

∠XWA = 21°

∠WXA = 90°-21° = 69°

Now, ΔXYZ is equilateral,

∠XYZ = ∠YXZ = 60°

Then,

∠WXZ = ∠WXA - ∠YXZ

= 69°-60°

= 9°

Since the angles of a triangle = 180°

∠WZY = ∠WZX = 180° - ∠XWA - ∠WXZ

= 180° - 21° - 9°

= 150°

The dimension of the rectangle that has the maximum area is 7.5 by 7.5 feet.

Let the length of the rectangular field be x and the width be y

Now the perimeter is 30

Therefore 2(x + y)=30

or, x + y = 15

or, y = 15 - x

Area of the rectangle = xy

Now we substitute the value of y

area = x ( 15 - x ) = 15x - x²

Now for the maximum area we have to differentiate the area function.

f(x) = 15x - x²

f'(x) = 15-2x

Now the differentiated function is equated to 0 to get the value of x for which the area is  maximum.

15-2x = 0

or, x =7.5

therefore y -= 15 - x = 1 5 - 7.5 = 7.5 feet.

Hence for the area to be maximum the dimension of the field should be 7.5feet by 7.5 feet .

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Mode

2 x 5 = 10

6 x 5 = 30

5 x 5 = 25

3 x 5 = 15

7 x 5 = 35

8 x 5 = 40

9 x 5 = 45

2 x 5 = 10

4 x 5 = 20

7 x 5 = 35

4 x 5 = 20

7 x 5 = 35

The mode is 35 because it is repeated 3 times.

The function given is,

The graph of the function will be shown below

a) The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).

Hence, from the graph above the zeros of the function is at

b) The function's domain is

c) The function's long-run behaviour is that:

Hence, the answer is

Solution:

Given:

An exponential function is of the form:

To get the exponential function for the relation;

Part A:

Relating this to the parameters given:

The exponential function that models the problem is;

Part B:

On the twenty-third day,

Therefore, he would have saved 4,194,304 pennies on the twenty-third day.

The value of x and y of system of equations are 3 and -1. A group of equations involving one or more variables is known as a system of equations.

A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

Solution for x-y=4, 2x+y=5

x - y = 4

2x + y = 5

Substitute 4 = x+ y

2(4+y) + y =5

Simplify

8 + 3y = 5

Isolate y for 8 + 3y = 5 ; y = -1

For x = 4 + y

Substitute y= -1

x= 4-1

x=3

The solutions to the system of equation are :

x =3 , y = -1

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╭┄┈┄────────❥

Answer:

↣ A.) Third person limited

Explanation:

A story told from a third person limited point-of-view, or POV, is defined as a narration that describes the thoughts, feelings, and actions of one character.

. . • ☆ . ° . • °: . * ₊ ° . ☆

I hope this helps!

peachtea ^-^

╰┄┈┄──❥

functionWe have:

The functions f and g have the same y-intercept, this is (0,4).

And the behavior as x approaches infinity is:

In the function f, value of the function approaches - 1.

In the function g, value of the function approaches - 1, too.

Therefore, they have the same behavior.

Answer: they have the same y-intercept and the same behavior as x approaches infinity.

Answer: 9/20 or 0.45 as a decimal :)

a. The images coincide because rotations preserve rays.

b. Transformations preserve distances, so the image of point A and point E are the same distance along the same ray from C and they have to coincide.

c. The rotation would also make the image of B equal with D. So there is a rigid motion that takes CBA onto CDE.

Transformations are classified into rigid and non-rigid, according to the definitions presented as follows:

In this problem, the transformation was a rotation of triangle BAC over vertex C, generating triangle EDC.

A rotation is a rigid transformation, hence the distances are preserved.

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A false statement could be that

"the maximum height attained by the diver was 20 feet

The inequality represented by the graph attached is y > -3x + 6

An equation is an expression showing the relationship between two or more numbers and variables.

An inequality is used to show that two numbers or variables are non equal to each other.

The graph attached shows a straight line inequality. It passes through the point (0, 6) and (2, 0). Hence, the straight line has the equation:

y - 6 = [(0 - 6)/(2 - 0)](x - 0)

y - 6 = -3(x)

y = -3x + 6

Based on the dotted line and the shaded region, the inequality is y > -3x + 6

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The number of gallons of paints that will be made if 28 drops is used is 20 gallons

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

The total number of drops used to make 5 gallons is 7drops, i.e 4+3=7

this means to make 1 gallon 5/7 drops of color will be used

Therefore for 28 drops , 5/7×20 gallons will be made

= 20gallons

Therefore the gallons made with 28drops is 20gallons.

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x=-6

Explanation

to solve this, let´s complete the tables and then compare

Step 1

complete the table:

to do that we need to input the x value and evaluate to obtain f(x)

so

a) for

i)when x=-12

ii) when x= -9

iii) when x=-6

iv) when x= -3

hence

Step 2

Now , for equation(2) g(x)

a) when x=-12

b) when x=-9

c) when x=-6

d)when x=-3

so

Step 3

finally, compare and check wich input value produces the same out put

therefore, the answer is

x=-6

I hope this helps you

Answer:

x=-6

Step-by-step explanation:

exam

Answer:

$104.14

Step-by-step explanation:

5.2% of $98.99

= $5.15

Price of the shoes + tax

= $98.99 + $5.15

= $104.14

Answer:

134.375

Step-by-step explanation:

43 is 32% of what number

32% = 0.32

43/0.32 = 134.375

Let  p be the function that gives the cost , in dollars, of producing 1 watt of solar energy years after 1977. Here is a table showing the values of  from 1977 to 1987.

t         p(t)                       p(10)-p(0)

0 80                          p(10)

1 60                          p(10)- p(0)/10-0

2 45                            p(10-0)

3 33.75

4 25.31

5 18.98

6 14.24

7 10.68

8 8.01

9 6.01

10 4.51

Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?

Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?

Which equation best captures the yearly average increase rate of solar prices between 1977 and 1987?

This discussion aims to help students remember what average rate of change for a function means and how it is computed. Select students to explain what each expression's value in this context means. For instance, the cost difference for a solar cell between 1977 and 1987 is represented by the formula p(10)- p(0), whereas the percent change between 1977 and 1987 may be calculated as p(10)/p(0). The fact that the real phrase for the average rate of change, p(10)-p(0)/10-0=-7.55, reveals that the price declined by -$7.55 on average per year since the expression considers the whole difference in price between the 1977 and 1987 divided by the total number of years that passed.

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a) Tyler ran 0.07 miles farther than Elena in 10 minutes.

b) The paces of each runner are given as follows:

c) Due to the lower measure of minutes per mile, Tyler ran faster during the run.

For this situation, the input and the output are given as follows:

This situation is represented by a proportional relationship, in this following format:

t = dv.

In which v is the pace in minutes per mile.

From the graph, Tyler runs 1 mile in 8 minutes, hence:

Elena's equation is:

y = 8.5x.

Hence her pace is of 8.5 minutes per mile, meaning that she is slower than Tyler, as she takes more time to run a mile.

The distances in 10 minutes are given as follows:

Hence Tyler ran 0.07 miles farther.

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Answer:

[tex]a_n=n^2 + 3[/tex]

Step-by-step explanation:

To find the nth term of a quadratic sequence, we need to determine the quadratic function that generates the sequence.

Given quadratic sequence:

4, 7, 12, 19, 28, ...

Begin by calculating the first differences between consecutive terms:

[tex]4 \underset{+3}{\longrightarrow}7 \underset{+5}{\longrightarrow} 12\underset{+7}{\longrightarrow} 19\underset{+9}{\longrightarrow} 28[/tex]

As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):

[tex]3\underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7\underset{+2}{\longrightarrow}9[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

As the second difference is 2, the coefficient of the n² term is 1.

Now we need to compare n² with the given sequence (where n is the position of the term in the sequence).

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}n&1&2&3&4&5\\\cline{1-6}n^2&1&4&9&16&25\\\cline{1-6}\sf operation&+3&+3&+3&+3&+3\\\cline{1-6}\sf sequence&4&7&12&19&28\\\cline{1-6}\end{array}[/tex]

We can clearly see that the algebraic operation that takes n² to the terms of the sequence is add 3.

Therefore, the expression to find the the nth term of the given quadratic sequence is:

[tex]\boxed{a_n=n^2 +3}[/tex]

The amount invested at 8% is $26,333.33.

The amount invested at 2% is $8,666.66.

What is simple interest?

Simple compound interest is a method of calculating the amount of interest charged for a fixed rate and total over a fixed period of time. With simple interest, the principal is always the same, unlike compound interest, which adds interest to the previous year's principal to calculate the next year's interest.

                        interest = principal * rate * time

Given data:

             Principal  = $35000

             Interest = $2280

             time = one year.

Let 'x' represent the amount invested at 8%, then '35000-x' represents the amount invested at 2%.

                         interest = principal * rate * time

                         2280 = 0.08x + 0.02(35000 - x)

                         2280 = 0.08x + 700 - 0.02x

                         2280 - 700 = 0.06x

                         x = 1580/0.06

                         x = 26333.33

and

          35000 - x = 35000 - 26333.33

                         x = 8666.66

Hence, The amount invested at 8% is $26,333.33.

             The amount invested at 2% is $8,666.66.

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The equation which represents total pay P and the number of copies sold N is P = 2300 + 90N and the total pay for 22 copies sells will be $4280.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Total pay = base salary + additional

Total pay = base salary + number of copies × per copy price

P = 2300 + N × 90

P = 2300 + 90N

Now for 22 copies

P = 2300 + 90(22) = $4280

Hence, the equation which represents total pay P and the number of copies sold N is P = 2300 + 90N and the total pay for 22 copies sells will be $4280.

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Answer:

exponents / the little x next to the 5

Answer: You move "x"s to one side, numbers to another and so the first operation is moving +4 to another side and making it -4

Answer:  360,000

Reason:

Think of 360 as 360.0

We move the decimal point 3 spots to the right to get to 360,000.0 or simply 360,000; this movement of 3 to the right is directly because of the exponent over the 10.

The 10^3 represents "thousand", so "360 x 10^3" is "360 thousand" = 360,000.

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

Answer:

4 shots were scored

Answer:

y=1/3x-3

Step-by-step explanation: