Wayne rents a car from a company that charges $35 per day plus $0.10 per mile he drives. What is a linear equation for the monthly charge, C, dollars, in terms of the number of miles driven, n?

The conclusions for the given points  (1.-2) and (4.-2) are

(A) The slope is 0.

(B) The y-intercept is -2.

(D) The line is horizontal.

(E) The equation of the line is y = -2

The formula used to calculate the equation of the line passing through the points (x₁, y₁) with slope m is given by

Where the formula for Slope is given by

Here we have

Given points  (1, -2) and (4, -2)  

Let us check each point one by one

(A) The slope is 0.

To find the slope of the line with given points using the formula

=> m = (y₂ - y₁) /(x₂ - x₁)

=> m = (-2 - (2)) /(4 - (-2)) = 0/6 = 0

∴ The slope of the line = 0

(B) The y-intercept is -2

To find the y-intercept calculate the equation line using the formula

=> (y -y₁) = m(x - x₁)  

=> [y - (-2) ] = 0 (x - 1)

=> y + 2 = 0

=> y = -2

On comparing with the slope-intercept form y = mx+c, we get

y-intercept = -2

∴ The y-intercept is -2.

(D) Here the line is in the form of y = a then the given line will be a Horizontal line.

(E) The equation of the line is y = -2

Therefore,

The conclusions for the given points  (1.-2) and (4.-2) is

(A) The slope is 0.

(B) The y-intercept is -2.

(D) The line is horizontal.

(E) The equation of the line is y = -2

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The complete question:

What can be concluded about a line that passes through the points (1, -2) and (4, -2) Check all that apply.

The slope is 0.

The y-intercept is -2.

The line is vertical.

The line is horizontal.

The line has no y-intercept.

The equation of the line is y = -2

Answer:

28

Step-by-step explanation:

[tex] {2}^{3} = 8[/tex]

The units digit (8) is the tens digit (2) raised to the third power.

Answer:

160.1 divided by 22.3 = 7.179 miles per litre.

This is 7.179 x 4.544 = 32.62 miles per gallon.

hope that will help

keeping in mind that there are about 1.609 Km in 1 mile and that there are about 3.78L in 1 gallon(US)

[tex]\cfrac{24~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{mile}{1.609~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{3.78~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{gallon(US)} \\\\\\ \cfrac{24(3.78)}{1.609}\cfrac{mile}{gallon(US)} ~~ \approx ~~ 56.38\frac{mile}{gallon}[/tex]

Answer:

z = 30x + 110y

x = y + 2

z = royalties

x = no of commercial

y = no of movies

Answer:

Step-by-step explanation:

7 1/4 is what i think

Answer:-8

Step-by-step explanation:

You are basically adding -4+(-4)

Answer:

Step-by-step explanation:

2(-4)

2 x -4

answer: -8

Answer: 25.12 in

Step-by-step explanation:

The circumference of a circle with a diameter of [tex]d[/tex] is [tex]\pi d[/tex].

So, the circumference is [tex]8\pi \approx 25.12[/tex] in.

Considering the quadratic equation, it is found that:

a) The initial height of the object is of 58.8 meters.

b) The object first hits the ground after 39.2 seconds.

c) The maximum height reached by the object is of: 1912 meters.

The quadratic equation that models the projectile's height is defined as follows:

s(t) = -4.9t² + 190.6t + 58.8.

Which has the coefficients given as follows:

a = 4.9, b = 190.6, c = 58.8.

The initial height is obtained as follows:

s(0) = -4.9(0)² + 190.6(0) + 58.8 = 58.8 meters.

It hits the ground at the positive root for which s(t) = 0, hence, using a quadratic equation calculator, this root is of:

t = 39.2 seconds.

The maximum height obtained by the object is the y-coordinate of the vertex, hence:

hMAX = -(b² - 4ac)/4a = -(190.6² - 4(-4.9)(58.8))/(4(-4.9)) = 1912 meters.

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Answer:

below

Step-by-step explanation:

(7p^9)^-4     a negative exponent means move the number up or down in the fraction

=   1 / [ (7 p^9) ^4  ]

           = 1 / ( 7^4 p^36) =   1/(2401 p^36)   <===don't omit the parentheses!

Answer:

There are two pairs of numbers:

-8      -18

and

18        8

Step-by-step explanation:

a * b = 144      EQ. 1

a - b = 10         EQ. 2

From EQ. 2:

a = 10 + b          EQ. 3

Replacing EQ. 3 in EQ. 1:

(10+b)b = 144

10*b + b*b = 144

b² + 10b - 144 = 0

b = {-10±√((10²)-(4*1*-144))} / (2*1)

b = {-10±√(100+576)} / 2

b = {-10±√676} / 2

b = {-10±26} / 2

b₁ = {-10-26} / 2 = -36/2 = -18

b₂ = {-10+26} / 2 = 16/2 = 8

a₁ - b₁ = 10

a₁ - (-18) = 10

a₁ + 18 = 10

a₁ = 10 - 18

a₁ = -8

a₂ - b₂ = 10

a₂ - 8 = 10

a₂ = 10 + 8

a₂ = 18

Check:

a₁ * b₁ = -8 * -18 = 144

a₂ * b₂ = 8 * 18 = 144

to get the equation of any straight line, we simply need two points off of it, let's use those two in red in the picture below

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 2 } \implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 3}(x-\stackrel{x_1}{1}) \\\\\\ y-6=3x-3\implies {\Large \begin{array}{llll} y=3x+3 \end{array}}[/tex]

We are looking for the functions which are symmetric with respect to the y-axis.

This should be an even function with the vertex on the y-axis.

All functions of odd degree or restricted domain or range are excluded:

Possible symmetric functions:

See the attached. Those with red cross are excluded, with green mark are correct choices.

Answer:

[tex]y=-7x^2[/tex]

[tex]y=8x^2-3[/tex]

Step-by-step explanation:

Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:

To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.

Therefore, any function that includes the term x² will be symmetric with respect to the x-axis since (-x)² = x².

[tex]\begin{aligned}&\textsf{Given}: \quad& y&=-7x^2\\&\textsf{Replace $x$ for $(-x)$}: \quad& y&=-7(-x)^2\\&\textsf{Simplify}: \quad &y&=-7x^2\\\end{aligned}[/tex]

Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the y-axis.

[tex]\begin{aligned}&\textsf{Given}: \quad& y&=8x^2-3\\&\textsf{Replace $x$ for $(-x)$}: \quad& y&=8(-x)^2-3\\&\textsf{Simplify}: \quad &y&=8x^2-3\\\end{aligned}[/tex]

Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the y-axis.

Answer: 10

Step-by-step explanation:

    To find the slope, we will take two points and find the change in y over change in x.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} } = \frac{35-15}{3-1}=\frac{20}{2} =10[/tex]

    The slope of the table is 10.

Answer:

the answer is 4

Step-by-step explanation:

the answer is 4

Answer:

[tex]m=38[/tex]

Step-by-step explanation:

An interior angle and its corresponding exterior angle are supplementary, so:

[tex]3m-12+2m+2=180 \\ \\ 5m-10=180 \\ \\ 5m=190 \\ \\ m=38[/tex]

Answer: 247.97

Step-by-step explanation:

The nearest cent is two decimal places.

Answer:

2.0 x 10^3

Step-by-step explanation:

 7.2x10^8/3.6x10^5= 2000= 2.0 x 10^3

Your net income and Net profit margin percentage, given the cost of the pack of lenses, and your operating expenses are:

To find the net income, first find the revenue:

= Number of packs x selling price

= 8, 000 x 59.95

= $479,600

The cost of goods sold is:

= Cost of lenses x number of lenses

= 29.95 x 8,000

= $239, 600

The net income is:
= Revenue - cost of goods sold - operating expenses

= 479, 600 - 239,600 - 144,080

= $95, 920

The net profit margin percentage is:

= Net income / total revenue

= 95, 920 / 497, 600

= 19.3%

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Answer:

17.8

Step-by-step explanation:

You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3

The probability of the person favoring rock music is 0.257, favoring country music is 0.285, and favoring something other than rock, country, or classical music is 0.342.

Given that:

Total people = 70

Chose rock = 18

Chose country = 20

Chose classical = 8

Chose something other than rock, country, or classical = 24

a) The empirical probability that the next person entering the store favors rock music is = Total people choosing rock music/ Total people

                                = 18/70 = 9/35 = 0.257

b) The empirical probability that the next person entering the store favors country music is = Total people choosing country music/ Total people = 20/70 = 2/7 = 0.285

c) The empirical probability that the next person entering the store favors something other than rock, country, or classical music is = Total people choosing something other than rock, country, or classical music/ Total people = 24/70 = 12/35 = 0.342.

Hence, the empirical probability that the next person favors rock music is 0.257, favors country music is 0.285, and favors something other than rock, country, or classical music is 0.342.

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The function is y = 3(x+3)^2-9

The equation of a parabola is

y=a(x-h)^2+k

where (h,k) are the coordinates of the vertex and a, is a constant.

From the question, we have

(h,k)=(-3,-9)

⇒y=a(x+3)^2-9

To find a, substitute x=-2,y=-6

-6=a(-2+3)^2-9

⇒a=3

The equation, y=3(x+3)^2-9

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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According to the concept of translation, the function of g(x) = x² + 2.

Translation:

The concept of translation is defined by using the function f(x) then f(x + a) is a horizontal translation of f(x)

If the value of a > 0 then a shift to the left of a units

If the value of  a < 0 then a shift to the right of a units

Given,

Here we have the function f(x) = x².

Now, we have to find  the equation of the graph of g(x) and how it change in corresponds to f(x).

While we looking the graph, the function f(x) has curved on the origin (0, 0).

Where the function g(x)  has curved the point (2,0).

Which tells the the graph is move left side by 2 units.

So, according to the rule of translation, the value of a is 2.

Then the function g(x) is written as,

=> g(x) = x² + 2.

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Answer:

volume is approximately 73.6 to the nearest tenth

Step-by-step explanation:

The volume of a pipe is volume = π * radius² * length

diameter = 2.5

radius = 2.5/2 = 1.25 inches

volume = π * 1.25² * 15

volume = π * 1.5625 * 15

volume =  π * 23.4

which is approximately 73.6 to the nearest tenth

The maximum cost that a patient would pay if he is in the lowest 4% of all paying patients is C) $14,725.

Given that

mean = $19800

standard deviation = $2900

Using standard normal table ,

P(Z < z) = 4%

P(Z < z) = 0.04

P(Z < -1.75) = 0.04

z = -1.75

Using z-score formula,

x = z * standard deviation + mean

x = -1.75 * 2900 + 19800 = 14725

The maximum cost is $14725

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Answer:

AB = 75cm

Step-by-step explanation:

Let BC equal x. Then AB is 5x because it is 5 times as long.

The whole length is 90, that was given.

Add the pieces, 5x and x, and set them equal to 90.

Solve the equation. See image. Last, calculate AB.

see image.

Answer:

C) The y-intercept of Function A is 1 unit greater than the y-intercept of Function B

Step-by-step explanation:

The y-int of Function A is (0,1), while the y-int of Function B is (0,0).

Answer:

C

Step-by-step explanation:

For Function A, the y-intercept occurs at 1. For B, it occurs at 0. Therefore, the y-intercept of Function A is 1 unit greater than the y-intercept of Function B.

Answer:

375=5^3 * 3

Step-by-step explanation:

375/5 = 75

75/5 = 15

15/5 = 3

3/3 = 1

Answer:

Y= -1.67x + 0.67

Step-by-step explanation:

Hope this was ok

Answer:

the 2 x 0.5 triangle fabric piece cost $2.25

Step-by-step explanation: