Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus

Rearranging the equation, making h the subject of the formula, h =  v² / 2g

we rearrange equations and formulas by using inverse operations to make one variable the subject of the formula.

In order to change the subject of, or rearrange, a formula items in the formula need to be arranged so a different variable is the subject.

In our case the the formula needs to be rearrange to make h the subject of the formula.

Therefore,

v = √2gh

square both sides of the equation

v² = (√2gh)²

v² = 2gh

divide both sides by 2g

v² / 2g = 2gh / 2g

h = v² / 2g

Therefore,

h = v² / 2g

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The function f(x) = -3(x + 2)² + 1 has it's vertex as (-2, 1) and an axis of symmetry x = -2

The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.

In the given function;

f(x) = -3(x + 2)² + 1

Kindly find the attached graph of the function below

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Answer:

R = 19 yr old; T = 7 yr old

Step-by-step explanation:

From the information given, we can create a system of equations to find both Richard and Teo's ages, letting R represent Richard's age and T represent Teo's age.

Thus we have:

[tex]R +T=26\\2T+5=R\\\\2T+5+T=26\\3T+5=26\\3T=21\\T=7\\\\R+7=26\\R=19[/tex]

When you plug in the numbers, you find that twice Teo's age is 14 as 7*2 = 14.  5 more than 14 is 19 as 14 + 5 = 19.

1. Her Average would be 80

2. Yes, there are more dots around points 80.

The simple interest that Nike will receive after 2 years is $500.

The principal amount =$5000

Rate = 5% = 0.05

Time = 2 years

Now simple interest = PRT = 5000 × 0.05 × 2 = 500

Hence the simple interest earned by Nike is $500

Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest.

Simple interest does not change the principal amount in the same way as compound interest, which adds the interest of one year's principal to the next year's principal to calculate interest.

A loan is a sum of money that a person obtains from a bank or another type of financial institution in order to pay bills. A few types of loans are personal, student, auto, and mortgage loans.

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Answer:

Evaluating the function [tex]f(x)=2x^2[/tex] for the first five positive integers of [tex]x[/tex]:

[tex]f(1)=2(1)^2=2(1)=2[/tex]

[tex]f(2)=2(2)^2=2(4)=8[/tex]

[tex]f(3)=2(3)^2=2(9)=18[/tex]

[tex]f(4)=2(4)^2=2(16)=32[/tex]

[tex]f(5)=2(5)^2=2(25)=50[/tex]

The measure of each angle of a regular 22-gon is 163.6 degrees.

In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.

Polygon can be named base on the number of sides they possess. For example pentagon has 5 sides, hexagon has 6 sides, heptagon has 7 sides, octagon has 8 sides, nonagon has 9 sides and decagon has 10 sides.

Therefore, a regular polygon is one which sides and angles are congruent.

A regular  22-gon has 22 sides.

The measure of each angle of 22-gon can be found as follows;

angle= 180(n - 2) / n

where

n = number of sides

angle = 180 (22 - 2) / 22

each angle = 180(20) / 22

each angle = 3600 / 22

Therefore,

each angle =  163.636363636

each angle = 163.6 degrees.

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Answer:

arc ABC ≈ 18.2 cm

Step-by-step explanation:

the length of the arc ABC is calculated as

arc = circumference of circle × fraction of circle

the angle around the centre O is 360° , then

angle subtended by arc = 360° - 100° = 260°

then

arc = 2πr × [tex]\frac{260}{360}[/tex] ( t is the radius = 4 )

     = 2π × 4 × [tex]\frac{26}{36}[/tex]

    = 8π × [tex]\frac{13}{18}[/tex]

    = [tex]\frac{8\pi (13)}{18}[/tex]

    ≈ 18.2 cm (to 3 significant figures )

Answer: 2-i

Step-by-step explanation:

multiply the fraction by 3-i/3-i

For the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of sec∅= ( - √106/ 9 ) in simplest radical form.

As given in the question,

For the given angle ∅ (theta) in standard position:

Terminal side of ∅ is passes through the point ( -9, 5 )

( -9 , 5 ) represents ∅ is in the second quadrant.

In second quadrant sine in positive and cosine is negative.

Base is negative and altitude is positive.

Base = -9

Altitude = 5

Using Pythagoras theorem,

Hypotenuse² = (-9)² + (5)²

⇒ Hypotenuse = √106

cos ∅ = -9 / √106

sec ∅ = 1/ cos ∅

         = - √106/9 ( simplest radical form )

Therefore, for the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of

sec∅= ( - √106/ 9 )  in simplest radical form.

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The number that is closest to the mean of the distribution is 4 (option C)/

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is the product of the frequency of the rectangle and the width of the rectangle.  

Mean is the average of a set of numbers. It is determined by multiplying each bar in the histogram by its height, add the multiplication value for all the bars together and dividing it by the total frequency of the bars.

Mean = [(1 x 1) + (2 x 2) + (3 x 3) + (4 x 4) + (5 x 3) + (6 x 2) + (7 x 1)] / (1 + 2 + 3 + 4 + 3 + 2 + 1)

Mean = (1 + 4 + 9 + 16 + 15 + 12 + 7) / 16

Mean = 64 / 16

Mean = 4

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Answer:

Hello there! While I didn't have this assignment, I found the assignment on Coursehero and took the liberty of downloading the pdf.

BE SURE TO USE QUILLBOT FOR PARAPHRASING AND PREPOSTSEO FOR PLAGIARISM CHECKING

Step-by-step explanation:

If traveling with the current certain boat went 9 mph against the same boat it only went 1 mph the speed of the current  is 4km/h  and no current is 5km/h.

Let b represent  the speed of the boat

Let c represent  the speed of the current

Downstream:

b + c = 9

Upstream:

b - c = 1

Subtraction

2c = 9-1

2c = 8

Divide both side by 2c

c = 8/2

c = 4 km/h (current)

No current

b = 9 - 4

b = 5 km/h

Therefore the speed is 4km/h and no current is 5km/h.

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The expected value of the proposition is -$1007.41

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

In which [tex]C_{x},x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{x},x= \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Suppose a basketball player has made 215 out of 322 free throws.

This means that p = 215/322 = 0.6677

2 free throws:

This means that

Probability of making two free throws.

This is P(X = 2).

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

P(X = 2) = [tex]C_{2},2.(0.6677)^2.(0.3323)^0[/tex] = 0.29629

Expected value:

If he makes both free throws, you earn $24. So 0.29629 probability of you earning $24.

Otherwise, you have to pay $32. 1 - 0.29629 = 31.70371 probability of you losing $32.

E = 0.29629*24 - 31.70371*32 = -1007.41

Hence, The expected value of the proposition is -$1007.41

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The descending order to the list is 1, 4/5, 41%, -1.3, -7/4.

What us descending order?

When numbers are arranged from greatest to smallest or highest to lowest it is said to be in descending order.

Main Body:

To solve this question we need to convert all numbers into decimal system.

calculate:

1 can be written as 1.00

4/5 can be written as 0.8

-7/4 = -1.75

41% = 41/100 = 0.41

-1.3 can remain as it is because it itself is in decimal form.

Hence the order from greatest to smallest is as

1 > 0.8 > 0.41 > -1.3 > -1.75

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From the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).

As given in the question,

Given equation is :

y = A(x-h)² +k

Standard basic parabola equation is y = x² where parabola pass through (0, 0) .

In the given quadratic function y = A(x-h)² +k , it represent equation of parabola which is U shaped .

Value of A > 0 then it open in upward direction .

Value of A <0 then it is open in downward direction.

Vertex of the given parabola y = A(x-h)² +k  is (h, k).

Line of symmetry is given by vertical line x =h.

Therefore, from the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).

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By using concept of ratio, it can be calculated that

100 boys attended the camp

What is ratio?

Ratio between two numbers determines how much one number is greater than the other.

The first part of the ratio is called antecedent and the second part of the ratio is called consequent.

Here, concept of ratio will be used

Let the number of boys be 4x and the number of girls be 6x

There were 50 more girls than boys

By the problem,

6x - 4x = 50

2x = 50

[tex]x = \frac{50}{2}[/tex]

x = 25

Number of boys who attended the camp = 4 [tex]\times[/tex] 25 = 100

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Answer:

50 gallons

Step-by-step explanation:

6400 ÷ 128

= 50

Answer:

5x-9=26

Step-by-step explanation:

5x=35

5 5

x = 7

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Answer:

x = 7

Step-by-step explanation:

When five times a number is decreased by 9 ​, the result is 26 . What is the​ number?

5x - 9 = 26

add 9 to both sides:

5x - 9 + 9 = 26 + 9

5x =35

divide both sides by 5:

5x/5 =35/5

x = 7

The slope of the line tangent to f(x) at x = 1 is -8

The instantaneous rate of change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

The tangent line to a curve at a given point is the line which intersects the curve at the point and has the same instantaneous slope as the curve at the point.

so the slope of a line at that point is the slope of the curve at that point.

f(x) = -4[tex]x^{2}[/tex] + 5

To find the slope, we differentiate f(x) with respect to x

dy/dx  = d/dx( -4[tex]x^{2}[/tex]) + d/dx(5)

           = -8x + 0

dy/dx = -8x

The slope = -8x

at x = 1,

the slope becomes, -8(1) = -8

The instantaneous rate of change of f(x) at x = 1 is the same as the slope of the line tangent to f(x) = -8

The slope of the line is -8

to find the equation of the tangent line, we need to find the coordinates of the point the line touches the curve.

one of the coordinates x = 1, to find y, we substitute x into f(x)

f(x) = -4[tex](1)^{2}[/tex] + 5

f(x) = 1

so the point is (1, 1)

so equation of straight line

[tex]\frac{y - y_{1} }{x - x_{1} }[/tex] = m

y - 1/x - 1 = -8

by cross multiplying

y - 1 = -8(x - 1)

y - 1 = -8x +8

y = -8x + 9

In conclusion,

The slope o the line tangent to f(x) at x = 1 is -8

The instantaneous rate off change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

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The first and the second differences are shown in the table, the values of the second differences are constant, therefore, the relation is linear.

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).

The first and the second differences are:

x            y              first differences                second differences

4            18                      ----

5            28                      10                                        ------

6            35                      7                                        -3

7            39                      4                                        -3

8            40                      1                                         -3

9            38                      -2                                        -3

The values of second differences are constant, therefore, the relation is linear.

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The number of ways to fill the tic-tac-toe grid, with at least 4 of each symbol in the grid, using the arrangements formula, is of:

252.

The number of possible arrangements that can be chosen from a set of n elements is given by the factorial of n, as follows:

[tex]A_n = n![/tex]

When the elements arranged can be repeated, the number of arrangements is presented as follows:

[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1! \times n_2! \cdots n_3!}[/tex]

In which [tex]n_1, n_2, \cdots, n_n[/tex] represent the number of repetitions of each element.

For the tic-tac-toe grid, we have that the possible ways to organize the nine positions with at least four instances of each symbol is given as follows:

Hence the number of ways to fill up the grid is given as follows:

[tex]\frac{9!}{5!4!} + \frac{9!}{4!5!} = 2 \times 156 = 252[/tex]

Thus 252 ways to fill up the grid.

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Of the part, the whole, and the percent, an information which is still unknown to Ms. Morgan is the number of non-athletes and it is equal to 84 students.

Of the part, the whole, and the percent, an information which is still unknown to Mr. Gregory is the total number of students and it is equal to 180 students.

Since the Ms. Morgan found that​ 30% of her 120 students are athletes, the known and unknown values include the following:

Known value (whole) = 120 students.

Known value (percent) = 30%

Unknown value (part) = ?

Next, we would determine the unknown value as follows:

Number of athletes = 30/100 × 120

Number of athletes = 30 × 1.2

Number of athletes = 36 students.

Unknown value (non-athletes) = 120 students - 36 students

Unknown value (non-athletes) = 84 students.

Since Mr. Gregory found that​ 27, or​ 15%, of his student are athletes, the known and unknown values include the following:

Known value (part) = 27 students.

Known value (percent) = 15%

Unknown value (whole) = ?

For the unknown value, we have:

Let the variable T represent the total number of students.

15/100 × T = 27

0.15T = 27

Total number of students, T = 27/0.15

Total number of students, T = 180 students.

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Complete Question:

Ms. Morgan is a science teacher. She found that​ 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that​ 27, or​ 15%, of his student are athletes. Complete parts a and b below.

a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value.  

b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.​

The decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.

According to the question,

We have the following information:

The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000.

We will find the 13.6% of 42,000 to find the decrease in the price of the next model:

(13.6*42000)/100

$5712

Now, the price of next model will be:

42000-5712

$36288

Hence, the decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.

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The area of the plot is 193 sq.yd.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, A developer buys an empty lot to build a small house.

To find the area, we need to be divided the figure into triangles and rectangles

Area of the first triangle = (1/2) * base * height

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5=85 sq. unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq. unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

Adding all the areas to get the area of the plot = 85+36+63+9

Hence, Area of the plot = 193 sq.yd.

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Answer:

$12,312

Step-by-step explanation:

$2,052 * 6 = $12,312

84 i think?

im not sure if i did my math properly

Answer:

80

Step-by-step explanation:

40 ÷ 6 = 6.66666667 x 12 = 80