The following equation can be used to model the distance remaining on route to a destination while traveling at a constant rate of speed

d = 125 - 35t

How many miles will be left to drive after 3 hours?

The two solutions are (0, 1) and (-4, 0)

From the question, we have the following parameters that can be used in our computation:

Graph of a linear relationship

From the graph of the linear relationship, we have the following points on the line

(0, 1) and (-4, 0)

Hence, the solutions are (0, 1) and (-4, 0)

On the graph, we can see that as x increases, the y value increases

This means that the graph is an increasing graph

In (a), we have

(0, 1) and (-4, 0)

These points represent the intercepts

So, we have

x-intercept= -4

y-intercept = 1

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 1) and (-4, 0)

Substitute the known values in the above equation

So, we have the following equation

Slope = (0 - 1)/(-4 - 0)

Evaluate

Slope = 0.25

Hence, the slope of the line is 0.25

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a) Rachel's monthly payment for the $10,000 three-year loan with an APR of 7.25% is $309.92.

b) The total amount of the monthly payments is $11,157.12.

c) Rachel's finance charge for the loan is $1,157.12.

The finance charge is the interest and other fees paid for a loan or credit.

The finance charge is based on the annual percentage rate (APR).

The monthly payments, total monthly payments, and the finance charge can be determined using an online finance calculator as follows:

N (# of periods) = 36 months (3 years x 12)

I/Y (Interest per year) = 7.25%

PV (Present Value) = $10,000

FV (Future Value) = $0

Results:

Monthly Payment (PMT) = $309.92

Sum of all periodic payments = $11,157.12 ($309.92 x 36)

Total Interest (finance charge) = $1,157.12

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Answer:

Sorry just trying to get points

The Equation for the given line in the graph is x+ y = 3.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

From the Graph take two points (0, 3) and ( 3, 0)

So, slope for the line

= ( 0-3 ) ( 3-0)

= -3/3

= -1

So, the Equation of line is

y[tex]- y_1[/tex]  = m(x[tex]-x_1[/tex])

y- 3 = (-1)(x- 0)

y- 3 = -x

y+ x = 3

x+ y = 3

Hence, the Equation line is x+ y= 3.

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The composition of the two functions g of x and f of x is:

(g o f)(x) = 3x² - 15x + 1

Here we have three known functions, these are:

And we want to find the composition of functions:

(g o f)(x)

That means that we need to evaluate the function g(x) on f(x), so we will get:

(g o f)(x) = g( f(x))

Then we will get:

g( f(x)) = 3*f(x) + 1

Now we can replace the actual function f(x) there, so we will get:

g( f(x)) = 3*f(x) + 1

g( f(x)) = 3*(x² - 5x) + 1

Now we can simplify that:

g( f(x)) = 3*(x² - 5x) + 1

g( f(x)) = 3*x² - 3*5x + 1

g( f(x)) = 3x² - 15x + 1

Then the composition of functions is:

(g o f)(x) = 3x² - 15x + 1

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Answer:

Yes

Step-by-step explanation:

A simple way to know is by simplifying them.

70/100 divided by 10 is 7/10

First divide 70 by 10: you get 7

Then divide 100 by ten: you get 10

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Answer:

18x−6

Step-by-step explanation:

Distribute

The approximate value of -12 + [tex]\sqrt{32}[/tex] is option (A) -6.3

The given expression is

-12 + [tex]\sqrt{32}[/tex]

First find the value of  [tex]\sqrt{32}[/tex]

Prime factorization of 32

Prime factorization is defined as the method of expressing a number as a product of its prime factors

32 = 2 × 2 × 2 × 2 × 2

Therefore,

[tex]\sqrt{32}[/tex] = 2 × 2[tex]\sqrt{2}[/tex]

Multiply the numbers

[tex]\sqrt{32}[/tex] = 4[tex]\sqrt{2}[/tex]

The value of [tex]\sqrt{2}[/tex] = 1.414

The the value of 4[tex]\sqrt{2}[/tex] = 4 × 1.414

Multiply the numbers
= 5.656

The value of the expression

-12 + [tex]\sqrt{32}[/tex] = -12 + 5.656

Add the numbers

= -6.344

Approximate value will be

≈ -6.3

Therefore, the result of the expression -12 + [tex]\sqrt{32}[/tex] is -6.3

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The minimum sample size needed for the desired margin of error of the confidence interval is given as follows:

44.

The sample size needed is obtained using the z-distribution, as the standard deviation for the population is known.

The equation that gives the margin of error for a z-distribution confidence interval is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which the parameters are given as follows:

The known measures in this problem are given as follows:

[tex]M = 20, \sigma = 80, z = 1.645[/tex]

Then the desired sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]20 = 1.645\frac{80}{\sqrt{n}}[/tex]

[tex]20\sqrt{n} = 1.645 \times 80[/tex]

Simplifying by 4, we have that:

[tex]\sqrt{n} = 1.645 \times 4[/tex]

[tex](\sqrt{n})^2 = (1.645 \times 4)^2[/tex]

n = 43.3.

Rounding up, as a sample size of 43 would have a margin of error slightly  above 20, the sample size needed is of 44.

The problem is given by the image shown at the end of the answer.

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The equation of the line in slope intercept form is y = 1 / 5 x + 7.

The equation of a line can be represented in slope intercept form as follows:

y = mx +  b

where

Therefore, let's find the slope of the line as follows:

using (0, 7) and (5, 8)

m = 8 - 7 / 5 - 0

m = 1 / 5

m = 1 / 5

Therefore, let's find the y-intercept using (0, 7).

Hence,

y = 1 / 5 x + b

7 = 1 / 5 (0) + b

b = 7

Therefore, the equation of the line is y = 1 / 5 x + 7

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Using basic geometry and applying the fence only on 3 sides, The required dimensions of the plot to have maximum area is 200 x 200.

A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.

fence length available = 600m

We only need to fence 3 sides. So length in each side = 600/3

=200m

So, Final dimension = 200 x 200

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⇒Sum of interior angles of a triangle is 180°

⇒ The above statement means that

[tex]70+35+x=180[/tex]

⇒Solving for x :

[tex]105+x=180\\x=180-105\\x=75[/tex]

∴ x=75°

Option D is the answer.

The value of the expression is 5.2.

The equivalent expression with a whole number divisor is 145.6/28.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

14.56 ÷ 2.8

= 14.56 / 2.8

= 14.56 x 10 / 28

= 145.6 / 28
= 5.2

Thus,

The value of the 14.56÷ 2.8 is 5.2.

The equivalent expression is 145.6/28.

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Answer:

The expression answer is 5.2.

145.6/28 is the equivalent expression using a whole number divisor.

Explanation:

For the time being, we have: 

14.56 2.8 

= 14.56 / 2.8

= 14.56 x 10 / 28 

For the time being, we have: 

As a result, the value of 14.56 2.8 is 5.2.

145.6/28 is an equivalent expression.

The end behaviour of the function [tex]y = -x^{2} + 4[/tex] is

f(x) → −∞, as x → −∞

f(x) → −∞, as x → +∞

The degree of the function is even, and the leading coefficient is negative.

End behaviour of a function:

A polynomial function's final behaviour is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behaviour is determined by a polynomial function's degree and leading coefficient.

For very big or very small values, the leading coefficient is more important than the other function coefficients. Therefore, it is sufficient to forecast the function's final behaviour based on the sign of the leading coefficient.

To predict the end-behaviour of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative.

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Answer:

[tex]\frac{3ab^2 + 2a^2 b}{5b^2 - 2a^2}[/tex]

Step-by-step explanation:

[tex]\frac{\frac{3}{a}+\frac{2}{b}}{\frac{5}{a^2}-\frac{2}{b^2}} \\ \\ =\frac{a^2 b^2 \left(\frac{3}{a}+\frac{2}{b} \right)}{a^2 b^2 \left(\frac{5}{a^2}-\frac{2}{b^2} \right)} \\ \\ =\frac{3ab^2 + 2a^2 b}{5b^2 - 2a^2}[/tex]

the required standard error is 6.9 for the sampling distribution.

The standard error of the sampling distribution is given by the formula SE = sqrt( (SD1² / n1) + (SD2² / n2) )

As per the question, we are given that samples of size 51 are drawn from population A with a standard deviation of 5.49, and samples of size 76 are drawn from population B with a standard deviation of 5.06.

Substituting these values into the formula, we get:

SE = √( (5.49² / 51) + (5.06² / 76) )

SE = √( (30.11) + (17.93) )

SE = √(48.04)

SE = 6.9

Therefore, the required standard error is 6.9 for the sampling distribution.

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I don't know .............

An equilateral ABC with a side length of 2 cm is placed on top of a square to form a pentagon. BCDE Draw a circle around points A, D, and E. The circle's diameter is: A 1+ 2 3

An equilateral pentagon is a polygon in the Euclidean plane in geometry that has five equal-length sides. It may create a family of pentagons because the five of its vertex angles can take on a variety of sets of values.

An equilateral pentagon is a polygon with five equal sides in geometry. In turn, its five internal angles may accept a variety of sets of values, allowing it to create a family of pentagons. It is necessary for all angles to sum up to 540 degrees and fall within the range of 0 to 360 degrees.

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13 cars needed both repairs and 10 cars needed new brakes, but not a new exhaust system.

In the given question, at Automotive Shop, 50 cars were inspected. 23 of the cars needed new brakes, 34 needed new exhaust systems, and 6 cars needed neither repair.

(a) We have to find the how many cars needed both repairs.

Total inspected cars = 50

The cars needed new brakes = 23

The cars needed new exhaust systems = 34

The cars needed neither repair = 6

So the cars that needed repair = 50-6 = 44

Total cars that needed new brakes and new exhaust systems = 23+34 = 57

So, the cars that needed both repairs = 57-44

The cars that needed both repairs = 13

Hence, 13 cars needed both repairs.

(b) Now we have to find how many cars needed new brakes, but not a new exhaust system.

The cars needed new exhaust systems = 34

The cars that needed repair = 44

So, the cars needed new brakes, but not a new exhaust system = 44-34

The cars needed new brakes, but not a new exhaust system = 10

Hence, 10 cars needed new brakes, but not a new exhaust system.

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Answer: It would take her 38 minutes to plant 57 bulbs.

Step-by-step explanation:

Answer:

36.8%

Step-by-step explanation:

PLEASE MARK BRAINLIEST

42.5-31=11.4

11.4/31 is approx  0.367741935 , or 36.7741935 %.

Rounding it to the nearest tenth gives you 36.8%.

1. The position (distance covered) of each elevator relative to the surface after additional 17 seconds is as follows:

2. After 17 seconds, the miners' elevator is deeper by 79 feet than the equipment elevator.

Distance is a function of speed and time.

This implies that distance is the product of speed and time.

The descent speed of the equipment elevator = 4 feet per second

The total time in seconds the equipment elevator descended = 44 seconds (27 + 17)

The descent distance covered in 44 seconds = 176 feet (44 x 4)

The descent speed of the miners' elevator = 15 feet per second

The total time in seconds the miners' elevator descended = 17 seconds

The descent distance covered in 17 seconds = 255 feet (17 x 15)

Thus, the difference in the descent distance between the equipment elevator and the miners' is 79 feet (255 - 176).

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The key points of option (B) are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.

Write the equation in the form y = MX + b to determine the slope m and the y-intercept.

This will allow you to graph the equation using the slope and y-intercept (0, b). The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, we have the equation:

y=2x^2+4x-6

Now, plot this equation in the graph as follows:

(Refer to the image attached below)

x-axis: (1, 0)

y-axis: (-3, 0)

Vertex: (-1, -8)

Therefore, the key points of option (B) which are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.

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Answer: So Cute!

Step-by-step explanation:

Answer:

Yes. I also think he is adorable.

Answer:

a.

Car A: $26.50

Car B: $53.00

b.

Car A: 13 1/3

Car B: 10

c.

Car A: $353

Car B: $530

Step-by-step explanation:

Car A: 10 gal, 30 mpg

Car B: 20 gal, 20 mpg

a.

Car A: 10 gal × $2.65/gal = $26.50

Car B: 20 gal × $2.65/gal = $53.00

b.

Car A: 1 full tank will drive 10 gal × 30 mpg = 300 miles

4000 miles / 300 miles = 13 1/3

Car B: 1 full tank will drive 20 gal × 20 mpg = 400 miles

4000 miles / 400 miles = 10

c.

Car A: 13 1/3 × 10 gal × $2.65/gal = $353

Car B: 10 × 20 gal × $2.65/gal = $530

Answer:

39 inches of wire would cost 156 cents

Step-by-step explanation:

1) Make an Equation

18x = 72

2) Solve for x to determine cost per inch of wire

x = 72/18

x = 4

3. Multiply x value by 39 to get the cost for 32 inches of wire (c)

39x = c

39 (4) = c

156 = c

An equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1 is y = -1/3x-17/3.

When the line to be examined slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula. In order to make it simple to identify the slope and y-intercept of a line, its equation can be written in the slope-intercept form. The y-intercept, or point where the line crosses the y-axis, is referred to as the slope.

Perpendicular line slopes are reciprocals with a negative sign. In the slope-intercept form, y = mx + b, where m is the slope, the supplied line, y = 3x+1, is already in the slope-intercept form.

The line in the example has a slope of 3.

The negative reciprocal of three, or -1/3, is the slope of the perpendicular.

Y = -1/3x + b is the equation for the line that we are looking for.

We must track down b. We solve for b by using the x and y coordinates of the provided location as x and y in the equation above.

y = -1/3x + b

5 = (1/3)(2) + b

5 = (2/3) + b

b = -5-(2/3)

b= -17/3

B is now substituted for in the equation

y = -1/3x-17/3 as we know that b =-17/3.

Therefore, an equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1 is y = -1/3x-17/3.

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To reach his goal, Marcus will have to save $(600/m) each month.

Given is that Marcus has $400 in his savings account. He decides that he will put a fixed amount of money into his account every month. His goal is to save $1,000.

The formula describing the Marcus saving's scheme is -

1000 = 400 + xm.

where -

[x] - amount saved per  month

[m] - number of months

Solving the equation further to find the amount saved per month is -

1000 = 400 + xm

1000 - 400 = xm

600 = xm

x = (600/m)

Therefore, Marcus will have to save $(600/m) each month to reach his goal.

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