The graph shows the function f(x) = |x – h| + k. What is the value of k? k = –2.5 k = –1 k = 1 k = 2.5

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

(x₁, y₁) - point on a line

We have the slope m = -5, and the point (-1, -3). Substitute:

[tex]y-(-3)=-5(x-(-1))\\\\y+3=-5(x+1)[/tex]

Convert to the slope-intercept form (y = mx + b):

[tex]y+3=-5(x+1)[/tex]          use the distributive property

[tex]y+3=-5x-5[/tex]            subtract 3 from both sides

[tex]y=-5x-8[/tex]

Answer:

Alonzo baseball

Your question is incomplete and lacks a graph. Please check below for the full content.

Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?

A. Both baseballs reach the same height.

B. Chase's baseball

C. Alonzo's baseball

The misssing graph is shown below.

The correct option is option C: Alonzo's baseball

The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.

Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7

To compare the height of both paths followed by the ball

we have to first calculate the height of the path of Chase's ball.

the path of Chase's ball is f(x)=-4x²+ 5x+ 7

The function will have the highest value when f'(x) will be 0.

f'(x)=-8x+5

f'(x)=0

⇒-8x+5=0

⇒-8x=-5

⇒x=5/8

at x=5/8, function value is

f(x)=-4x²+ 5x+ 7

=-4(5/8)²+ 5(5/8)+ 7

=-4(25/64)+(25/8)+7

=(-25/16)+25/8+7

=8.5625

There maximum value of f(x) is 8.5625.

The maximum height reached by Chase's ball will be 8.5625m.

From the graph of the path of Alonzo's ball, it is clear that

The maximum height reached by Alonzo's ball will be 9m.

As 8.5625m < 9m

Alonzo's baseball will reach greater height.

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This answer does not make sense because you can't buy half a movie ticket

Answer: If h(x) represents the amount of money spent and x the amount of friends, then we can write it as in a pair as (x, h(x))

Then the pair given is (6.5, $92.25)

Here you see a problem, x is 6.5, knowing that x represents the amount of friends, this is a problem because you need to have a whole number ( you can't have a 0.5 of a friend)

So the domain of h(x) is only the natural numbers, then the possible solution of (6.5, $92.25) doesn't make sense because 6.5 is not a natural number.

Answer:

triangle; area = 90 ft2

Step-by-step explanation:

THe type of two dimensional solid created by a vertical cross section of the cone that passes through the apex is a triangle, as you can see in the picture, if you draw a line that cuts the cone in half passing through the apex it would just be a triangle, and the area of the cross section is given by the formula:

[tex]a=\frac{b*h}{2}[/tex]

Since you have the radius of the base of the cone, you need the diameter to calculate the area, the diameter is given by the next formula:

[tex]D=2r[/tex]

[tex]D=2(6)[/tex]

[tex]D=12[/tex]

Now you just put your values into the formula of the triangle:

[tex]a=\frac{(12)(15)}{2}[/tex]

[tex]a=\frac{(180}{2}[/tex]

[tex]a=90[/tex]

So the area of the triangle formed is:

[tex]90ft^{2}[/tex]

Answer:

B

Step-by-step explanation:

correct on ed2020

Answer:

A

Step-by-step explanation:

all we need to do is to plug the point (6,4) in the inequality and see if it satisfies it :

pay attention that here we have x=6  y=4

4<[tex]\frac{3}{4} (6) - 3[/tex]

we simplify we get :

4<4.5-3  

4<1.5  which is incorrect  so (6,4) is not a solution. moreover

notice that 4 is > than 1.5  so the point lies above the line

thus the answer is : A

you can also solve this problem by graphing the line [tex]y= [/tex][tex]\frac{3}{4} x-3[/tex]  and plotting the point (6,4)  and hence you will notice that the point is above the line

Answer:

Step-by-step explanation:

[tex]y<\dfrac{3}{4}x-3\\\\\text{Put the coordinates of the point and check the inequality:}\\\\(6,\ 4)\to x=6,\ y=4\\\\4<\dfrac{3}{4}\cdot6-3\\\\4<\dfrac{18}{4}-3\\\\4<4.5-3\\\\4<1.5\qquad\bold{FALSE}\\\\\text{Therefore your answer is NO, because (6, 4) is above the line.}[/tex]

[tex]\text{Other mathod:}\\\\\text{Show this inequality in the coordinate system.}\\\\\text{Draw the dotted line}\ y=\dfrac{3}{4}x-3.\\\\for\ x=0\to y=\dfrac{3}{4}(0)-3=0-3=-3\to(0,\ -3)\\\\for\ x=4\to y=\dfrac{3}{4}(4)-3=3-3=0\to(4,\ 0)\\\\\text{shaded region below the line}\\\\\text{Mark point (6, 4) and check if it lies in the shaded region.}[/tex]

To find the cost of buying 15 baseball caps, we set up a proportion using the information about the cost per cap from last year. The cost of buying 15 caps is $75.

To write a proportion that gives the cost of buying 15 baseball caps, we can use the fact that the cost per cap is the same as last year. Let c represent the cost of buying 15 caps. We can set up the proportion as follows:

11 caps / $55 = 15 caps / c

To solve for c, we can cross-multiply and solve for the unknown variable:

11c = 15 * $55

c = (15 * $55) / 11 = $75

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To find the cost of buying 15 baseball caps, set up a proportion of 11 caps for $55 and 15 caps for (c). Solve for (c) by cross multiplying and dividing by 11. The cost of buying 15 baseball caps would be $75.

To write a proportion that gives the cost (c) of buying 15 baseball caps, we can set up the ratio of the number of caps to the cost of the caps in two scenarios: 11 caps for $55 and 15 caps for (c). Since the cost per cap is the same in both scenarios, the proportion would be:

11/55 = 15/(c)

To solve for (c), we can cross multiply:

11 * c = 15 * 55

Dividing both sides of the equation by 11, we find:

c = 15 * 55 / 11 = 75

Therefore, the cost of buying 15 baseball caps would be $75.

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Answer:

The distance from the pole is 11.8 ft

Step-by-step explanation:

Let

x------> the distance from the pole

we know that

The tangent of angle of 28 degrees is equal to divide the opposite side to angle of 28 degrees ( the height of the pole) by the adjacent side to angle of 28 degrees ( the horizontal distance from the pole)

so

tan(28°)=6.3/x

Solve for x

x=6.3/tan(28°)=11.8 ft

Final answer:

The distance from the pole is found by using the tangent function with the given angle of elevation (28 degrees) and the pole's height (6.3 feet), resulting in a distance of approximately 12.04 feet.

Explanation:

To calculate the distance from the pole given the angle of elevation and the height of the pole, you can use trigonometric functions. The angle of elevation is 28 degrees and the height of the pole is 6.3 feet. You can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.

Let d represent the distance from the pole. The tangent of the angle of elevation (28 degrees) equals the opposite side (6.3 feet) over the adjacent side (distance d).

tan(28°) = 6.3 / d

To find d, rearrange the equation: d = 6.3 / tan(28°). Using a calculator for tan(28°), you obtain d ≈ 12.04 feet.

Therefore, the distance from the pole is approximately 12.04 feet.

Answer:

B.44 mph and 46 mph

Step-by-step explanation:

This question is on relative speed

when cars move towards each other, you add their individual speeds to get their relative speed

Lets have two cars , A and B

Let  car A to have an average speed of x m/h towards the right hand side

Let car B to have an average speed of x+2 m/h towards the opposite direction

The distance between the cars is 270 miles

Time of meeting is 3 hours

The relative speed will be x+x+2=2x+2 miles per hour

Apply the formula for time=Distance/speed =D/S

[tex]t=\frac{D}{S} \\\\\\3=\frac{270}{2x+2} \\\\\\3(2x+2)=270\\\\\\6x+6=270\\\\\\6x=270-6\\\\\\6x=264\\\\\\x=\frac{264}{6} =44[/tex]

x=44 miles per hour

x+2=44+2=46 miles per hour

solution

44 mph and 46 mph

Final answer:

Two cars are traveling towards each other at speeds where one car is 2 mph faster than the other. They meet after 3 hours covering 270 miles. By setting an equation with the distance formula, we find that the slower car's speed is 44mph and the faster car's speed is 46mph. (Option B)

Explanation:

The question involves calculating the average speed of two cars traveling towards each other on the same road and meeting after a certain time. To solve this, we can set up an equation using the formula for speed, which is distance divided by time.

Let's denote the speed of the slower car as ‘s’ mph (miles per hour). Consequently, the faster car travels at ‘s+2’ mph. When they meet after 3 hours, both cars together will have covered a distance of 270 miles. Thus, the total distance covered by both cars can be written as:

Total distance = (speed of car A)×(time) + (speed of car B)×(time)

270 miles = s×3 hours + (s+2)×3 hours

This simplifies to:

270 = 3s + 3s+ 6

Combining like terms and simplifying, we get:

270 = 6s + 6

Subtract 6 from both sides to find:

264 = 6s

Dividing both sides by 6 yields:

s = 44 mph

Therefore, the slower car travels at 44 mph and the faster car at 44+2 = 46 mph.

The correct answer is B. 44 mph and 46 mph.

Add the bases together, divide that by 2 then multiply by the height.

15.8 + 21.8 = 37.6

37.6/2 = 18.8

18.8 x 11.7 = 219.96 yd^2

Answer:

B) 219.96 yd2

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

(a + b) /2*h

Now you would plug in the numbers

(15.8 + 21.8) /2*11.7

Now solve this in order of operations

(15.8 + 21.8) /2*11.7

37.6/2*11.7

18.8*11.7

219.96

Answer:

0

Step-by-step explanation:

Anything multiplied by 0 gives you an answer of 0, therefore 2*2*2*2*0=0

Answer:

0

Step-by-step explanation:

In most cases, zero times anything is zero.

Here we have 2*2*2*2 = 2^4 = 16.  Thus,

2*2*2*2*0 = 16(0) = 0

Answer:

1) 8x5

2) 8x10

3)8x20

[tex]\( f(x) + g(x) \) equals \( 2x^2 - 5x - 8 \).[/tex] (option b)

To find [tex]\( f(x) + g(x) \)[/tex], we need to add the functions f(x) and g(x):

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

[tex]\[ = 2x^2 + 3x - 4 - 8x - 4 \][/tex]

[tex]\[ = 2x^2 + (3x - 8x) + (-4 - 4) \][/tex]

[tex]\[ = 2x^2 - 5x - 8 \][/tex]

Therefore, the correct answer is:

[tex]\[ f(x) = 2x^2 - 5x - 8 \][/tex]

Complete question: If f(x)=2x²+3x−4, and g(x)=−8x−4, what does f(x)+g(x) equal?

a-f(x)=2x²+5x+8

b-f(x)=2x²−5x−8

c-f(x)=2x²+11x−8

d-f(x)=2x²+5x

Answer:

Step-by-step explanation:

the answer is 4/5

Because there are 5 section and the blueberry takes up 4 of the sections it is 4/5

Answer:

4/5

Step-by-step explanation:

So he divided something into 5 sections.

He fills one section with graph jelly and 4 sections with blueberry jelly.

Since there are 5 sections and 4 are filled with blueberry, then 4/5 is the fraction of the table he filled will blueberry.

To find out which equation has no real solutions, we need to calculate the discriminant for each of these given equations.

For calculating the discriminant, we need to first compare these equations with the general formula which is ax²+bx+c.

So, let's get started.

1) x² + 4x + 16 = 0

a=1, b=4, c=16

D = b²-4ac

= (4)² - 4(1)(16)

= 16-64

= -48

√D = √-48

2) 4x² + 4x - 24 = 0

a=4, b=4, c=-24

D = b²-4ac

= (4)² - 4(4)(-24)

= 16 - 16(-24)

= 16 + 384

= 400

√D = √400 = +20 or -20

3) 5x² + 3x - 1 = 0

a=5, b=3, c=-1

D = b²-4ac

= (3)² - 4(5)(-1)

= 9 + 20

= 29

√D = √29

4) 2x² - 4x + 4 = 0

a=2, b=-4, c=4

D = b²-4ac

= (-4)² - 4(2)(4)

= 16 - 32

= -16

√D = √-16

Now from all these above calculations, we can see that discriminant was negative in first equation and in last equation.

If D<0 then roots does not exist, as the square root can not contain a negative value or the equation does not have any real solutions.

Roots in such case can be calculated but those roots are known as imaginary roots, which is a higher concept.

So Final answer is,

Equation 1 => x² + 4x + 16 = 0

and

Equation 4 => 2x² - 4x + 4 = 0

has no real solutions.

e = Euler's constant

e ≈ 2.718281828459045, rounded up e = 2.7183.

= 4.17356

the number after the line is lower than 5, round the number down (keep it the same). If the number is 5 and more than it round the number upwards. therefore in example 1 you need to round 4.17356 to 4 decimal places. This means you have 2 choices, either 4.17356 or 4.17357.

When we say round to 4 it means to fewer the digits to 4 to the right of the decimal point. The basic rule of remember is, if the number in the 5th place ( to round it any decimal place, consider this next digit) is > 5 then add 1 on the 4th digit and else remains the same.

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Answer:

it should be 1/2

Step-by-step explanation:

because the sequence is going down by 0.05 each time;

7/10= 0.70

13/20= 0.65

3/5= 0.6

11/20= 0.55

so to continue the pattern,

1/2= 0.5

Answer:

-1/4

Step-by-step explanation:

You can find the slope from a graph several ways.

Here are two ways of doing it.

Method 1. Slope formula

Find two points, then apply the slope formula, m = (y2 - y1)/(x2 - x1)

We read two easy  to read points of the graph: (0, -2) and (4, -3)

m = (y2 - y1)(/(x2 - x1) = [-3 - (-2)]/(4 - 0) = (-3 + 2)/4 = -1/4

Method 2. Rise/Run

Slope = m = rise/run

Pick two points. Start at one point and go to the other point by going vertically (rise) and horizontally). The vertical distance is the rise, and the horizontal distance is the run. Up is positive, and down is negative. Right is positive, and left is negative.

Pick points (0, -2) and (4, -3).

Start at (0, -2). To go to (4, -3), move 1 unit down. That is a rise of -1. Now go horizontally 4 inits to the right. That is a run of 4.

slope = rise/run = -1/4

Answer:

4:3

Step-by-step explanation:

You divide 8 and 6 by 2 to simplify it

Answer:

Table for y = 2|x-4| + 3 on domain {2,3,4,5,6} is given as:

x                           y

2         2|x-4| + 3 = 2|2-4| + 3 = 7

3         2|x-4| + 3 = 2|3-4| + 3 = 5

4         2|x-4| + 3 = 2|4-4| + 3 = 3

5         2|x-4| + 3 = 2|5-4| + 3 = 5

6         2|x-4| + 3 = 2|6-4| + 3 = 7

The graph of the absolute value function y = 2|x-4| + 3 for the given domain is attached.

Step-by-step explanation:

The absolute value parent function, written as function(x) = | x |, is defined as:

|x| = x          and           |-x| = x

In our case;

For x = 2        

y = 2|x-4| + 3

= 2|2-4| + 3

= 2|-2| + 3

= 2*2 + 3

= 4 + 3

= 7

Similarly, for all other values of x in the given domain, value of y can be calculated.

Answer:

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&for\ a\geq0\\-a&for\ a<0\end{array}\right[/tex]

Put each value of x from the set {2, 3, 4, 5, 6}

to the equation y = 2|x - 4| + 3:

x = 2 → y = 2|2 - 4| + 3 = 2|-2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (2, 7)

x = 3 → y = 2|3 - 4| + 3 = 2|-1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (3, 5)

x = 4 → y = 2|4 - 4| + 3 = 2|0| + 3 = 2(0) + 3 = 0 + 3 = 3 → (4, 3)

x = 5 → y = 2|5 - 4| + 3 = 2|1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (5, 5)

x = 6 → y = 2|6 - 4| + 3 = 2|2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (6, 7)

Mark the points in the coordinates system.

The domain is only five numbers, therefore the graph of this function is only five points.

Answer:

[tex]\huge \boxed{z=176}\checkmark[/tex]

Step-by-step explanation:

Add by 135 from both sides of equation.

[tex]\displaystyle z-135+135=41+135[/tex]

Simplify, to find the answer.

[tex]\displaystyle41+135=176[/tex]

[tex]\huge \boxed{z=176}[/tex], which is our answer.

Hope this helps!

Answer: Z=176

Step-by-step explanation: All you need to do is isolate z. Add 135 to each side.

135+41=176=Z

Answer:

The vertex of the parabola is (105 , 7)

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation of the parabola is y = a(x - h)² + k, where (h , k) are

  the coordinates of the vertex point of the parabola

- The points (0 , 27) , (52.5 , 12) , (105 , 7) ,  (157.6 , 12) , (210 , 27) are

 the points lie on the parabola

- We have three unknown a , h , k to find them we will substitute the x

 and y in the equation by the coordinates of some point on the

 parabola

- Lets start with point (0 , 27)

∵ x = 0 and y = 27

∴ 27 = a(0 - h)² + k

∴ 27 = ah² + k ⇒ (1)

- Lets use point (210 , 27)

∵ x = 210 and y = 27

∴ 27 = a(210 - h)² + k ⇒ (2)

- Equations (1) and (2) have the same L.H.S, so we can equate them

∴ ah² + k = a(210 - h)² + k ⇒ subtract k from both sides

∴ ah² = a(210 - h)² ⇒ divide both sides by a

∴ h² = (210 - h)² ⇒ take √ for both sides

∴ h = ± (210 - h)

∵ h = 210 - h ⇒ add h to both sides

∴ 2h = 210 ⇒ divide both sides by 2

∴ h = 105

∵ h = - (210 - h)

∴ h = -210 + h ⇒ no value of h from this equation so we will ignore it

∴ The value of h is 105

- Lets substitute this value of h in the equation

∴ y = a(x - 105)² + k

- Lets use the point (105 , 7)

∵ x = 105 and y = 7

∴ 7 = a(105 - 105)² + k

∴ 7 = a(0) + k

∴ k = 7

- The coordinates of the vertex point are (h , k)

∵ h = 105 and k = 7

∴ The vertex of the parabola is (105 , 7)

Answer:

105, 7 and then for the next one y= 0.0018(x – 105)2 + 7

Step-by-step explanation:

Answer:

[tex]\large\boxed{3m+(m+5)=4m+5}[/tex]

Step-by-step explanation:

[tex]3m+(m+5)=3m+m+5\qquad\text{combine like terms}\\\\=(3m+m)+5=4m+5[/tex]

[1, 4, 3]

Solve for the first variable in one of the equations, then substitute the result into the other equation.

**For more information on how to solve a system of equations in three variables, paste and copy this link:

https://youtu.be/zcC7wsn3b2g

Subscribe to my channel [USERNAME: MATHEMATICS WIZARD].

I am joyous to assist you anytime.

***By the way, in the final line, that "+" next to the 6 should be replaced with an "=".

Answer:

Her average speed = 7.5 miles/hour

Explanation:

First, since the required speed unit is miles/hour, we need to make sure that all units given are in miles (for distance) and hour (for time)

We are given that:

Distance covered = 2400 miles

Times taken = 13 days and 8 hours

We know that 1 day has 24 hours

Therefore:

13 days = 13 x 24 = 312 hours

Time taken = 13 days and 8 hours = 312 + 8 = 320 hours

Now, average speed is calculated as the total distance divided by the total time

This means that:

[tex]Average Speed=\frac{Total Distance}{Total Time} = \frac{2400}{320}=7.5[/tex] miles/hour

Hope this helps :)

To find the average speed, convert the total migration time of 13 days and 8 hours to hours, which is 320 hours. Then divide the total distance, 2400 miles, by the total time to get an average speed of 7.5 miles per hour.

To calculate the average speed of the Canada goose on its $2400$-mile migration completed in $13$ days and $8$ hours, we must first convert the total time into hours. There are $24$ hours in a day, so $13$ days is equal to $13 \times 24 = 312$ hours. Adding the additional $8$ hours, we have a total travel time of $320$ hours. The average speed is then calculated by dividing the total distance by the total time.

The average speed of the goose is:

The average speed is $\frac{2400}{320} = 7.5$ miles per hour.

Answer:

Ratio: 20:36

Rate: 20 squids per 36 eels

Simplified ratio:

[tex] = \frac{20}{36 } = \frac{10}{18} = \frac{5}{9} [/tex]

Unit ratio:

20/36 squids per eel (dividing by 36)

Please mark Brainliest if this helps!

Answer:

Step-by-step explanation:

Number of squid in the tank = [tex]20[/tex]

Number of eels in the tank = [tex]36[/tex]

Rate of squids to eels will be obtained by creating a fraction of number of squids over number of eels

Rate of squid to eels = [tex]\frac{20}{36}[/tex]

also ratio of squid to eels will be written as [tex]20:36[/tex]

Simplified ratio = [tex]\frac{20}{36} = \frac{5}{9} = 5:9[/tex]

Unit rate will be defined as number of squid per eels

Unit rate = [tex]\frac{20}{36} = 0.55[/tex]

Answer:

Option C. 1:11

Step-by-step explanation:

Let

x-----> dollars  spent on office space

y ----> dollars spent  on other costs

we know that

x+y=$360,000 -----> equation A

x=$30,000 ----> equation B

substitute equation B in equation A and solve for y

30,000+y=360,000

y=360,000-30,000=$330,000

Find the ratio of dollars  spent on office space to dollars spent  on other costs

Divide the dollars  spent on office space by the dollars spent  on other costs

so

x/y

substitute

30,000/330,000=1/11

You meant pi, pi is a irrational number, but they use 3.14 for approximation, so that is your answer.

Hope this helped!

Nate

[tex]\pi-\bold{pi}\\\\\pi\ \text{it's the ratio of a circle's circumference to its diameter}\\\\\pi=\dfrac{\text{circumference of a circle}}{\text{circle diameter}}\\\\\pi\ \text{it's irrarional number}\\\\\pi=3.14159265358979323846264338327...\\\\\text{Approximation of}\ \pi:\\\\\pi\approx3.14\\\\\pi\approx\dfrac{22}{7}\\\\\pi\approx\dfrac{355}{113}[/tex]

The number pi occurs when calculating the surface area or volume of the rotational solids.

Cylinder:

[tex]S.A.=2\pi r^2+2\pi rH\\\\V=\pi r^2H[/tex]

Cone:

[tex]S.A.=\pi r^2+\pi rl\\\\V=\dfrac{1}{3}\pi r^2H[/tex]

Sphere:

[tex]S.A.=4\pi R^2\\\\V=\dfrac{4}{3}\pi R^3[/tex]

The number pi occurs when calculating the area and the circumference of a circle.

[tex]C=\pi d=2\pi r\\\\A=\pi r^2[/tex]

It is also used to convert angle measure in degrees to radians.

[tex]x^o=\dfrac{x\pi}{180}\ rad[/tex]

Answer:

220 miles

Step-by-step explanation:

Joe got $301 for an overnight trip.

As the employees get $125 for lodging. The lodging expense will be subtracted from the total amount to get the amount for the miles he drove.

So,

Expense by company for miles driver = 301 - 125 = $176

So, Joe received $176 for miles driven

Now,

amount for one mile = $0.80

Miles driven in $176 = 176/0.80 = 220 miles

Joe drove 220 miles ..

Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip, after considering the fixed lodging cost and the per mile reimbursement rate.

The student wishes to know how many miles Joe drove if his company reimbursed him $301 for an overnight trip wherein he receives $125 for lodging plus $0.80 per mile driven. To solve this problem, we start by subtracting the fixed lodging cost from the total reimbursement to find the total amount reimbursed for mileage. Let's denote the number of miles driven by Joe as m.

Total reimbursement for mileage = Total reimbursement - Lodging cost
$301 - $125 = $176

Now, since Joe gets reimbursed $0.80 per mile, we can calculate the number of miles driven as follows:

$176 / $0.80 per mile = 220 miles

Therefore, Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip.

Answer:

y=3x+1  (slope-intercept form)

-3x+y=1 (standard form)

3x-y=-1 (another version of standard form)

y-7=3(x-2) (point-slope form)

Step-by-step explanation:

y=mx+b is slope intercept form where m is slope and b is y-intercept.

The slope of perpendicular lines are opposite reciprocals.

The opposite reciprocal of -1/3 is 3.

So we are looking for a line of the form y=3x+b going through (2,7)

y=3x+b with (x,y)=(2,7)

7=3(2)+b

7=6+b

7-6=b

1=b

b=1

So the equation is y=3x+1.

Now you can also put it in standard form:

Subtract 3x on both sides:

-3x+y=1

You can also multiply both sides by -1:

3x-y=-1

ax+by=c is standard form.

We can also use point slope form.

y-y1=m(x-x1) where (x1,y1) is a point contained by our line and m is the slope.

We have m=3 and (x1,y1)=(2,7)

y-7=3(x-2)

Answer:

5 < √32 < 6.

Step-by-step explanation:

√25 = 5 and √36 = 6 so

5 < √32 <  6.