James is participating in a 5-mile walk to raise money for a charity. he has received $200 in fixed pledges and raises $20 extra for every mile he walks. use a point-slope equation to find the amount he will raise ifhe completes the walk.

Answers

Answer 1

Answer:

The amount James will collect if he completes the walk is $ 300

Step-by-step explanation:

The line can be understood as an infinite set of points aligned in a single direction. A line can be expressed by an equation that follows the model y = m * x + b, where "x" e "y" are the variables in a plane. In this expression m is called the slope of the line and is related to the inclination of the line, and b is the independent term and is the value of the point at which the line cuts to the vertical axis (y axis) in the plane.

In general, the slope represents the variation of y with respect to the variation of x. That is, if the value of "x" varies, the value of "y" will also vary. On the other hand, the value of "b", being the interserction with the y-axis, means that the value of "x" must be zero. Then it represents the initial condition of the problem. Then, in this case, James has initially received $ 200 in fixed commitments, 200 being the value of "b". James raises an additional $ 20 for every mile he walks, so the value of the "m" slope is 20 and "x" represents every mile James walks.

Finally, the equation of the line represented is:

y=20*x+200

One type of linear equation is the point-slope form, which provides the slope of a line and the coordinates of a point on it. The point-slope form of a linear equation is written as

y-y1 = m (x-x1)

where m is the slope and (x1, y1) are the coordinates of the point.

In this particular case, it was mentioned that the value of the slope is 20. The values of (x1, y1) must be known. In this case, James initially received $ 200 in fixed commitments, meaning that the value of x1 = 0 and the value of y1 = 200. Replacing these values in the desired equation you get:

y-200=20*(x-0)

y-200=20*x

To find the amount that will be collected if you complete the walk, you must replace the value of x (which represents each mile walked) by 5, the distance to travel on the walk:

y-200=20*5

y-200=100

y=100+200

y=300

The amount James will collect if he completes the walk is $ 300

Related Questions

explain, in complete sentences, three steps one could take to pay off their debts?

Answers

.1. Create a debt payoff strategy. If one of your financial goals for the year is to get a better handle on debt, put together a debt payoff strategy that complements your budget and won't overextend you financially. It's also a good idea to create a master list of all your recent holiday-related expenditures that were paid for with a credit card or a personal loan. Knowing what your total debt load is will make it much easier to create a realistic payoff strategy. And reward yourself when you hit certain milestones to keep the momentum going!

2. Pay off the most expensive debt first. Look at the interest rates of all of the credit cards you use to make purchases and sort them from highest to lowest. By paying off the balance with the highest interest first, you increase your payment on the credit card with the highest annual percentage rate while continuing to make the minimum payment on the rest of your credit cards.

3. Lower your interest rate. You can often lower your credit card interest rates by doing a balance transfer. This means moving your credit card to another bank that might lower the interest rate to get your business. Shop around and try to get the lowest interest rate for the longest duration (preferably until the debt is paid off completely). Just make sure you fight the temptation to use that new card, and commit to paying off the balance you moved over in a timely manner.

What is the x-intercept of the equation 2x-6y=12?

Answers

x-intercept y = 0 then
2x = 12
x = 6

x=3y+6 that is the anwer

The perimeter of triangle ABC is 54 inches. Find the length of each side. A right triangle. The vertices of the triangle are labeled A, B, and C. Leg AB is labeled 3x. Leg BC is labeled 4x. Side AC is the hypotenuse and is labeled 5x.

Answers

54=3x+4x+5x
54=12x
x=4.5
AB-3(4.5)=13.5
BC-4(4.5)=18
AC-5(4.5)=22.5

Hello! Keith's dog weighs 90 pounds. A healthy weight for his dog would be less than 75 pounds. If Keith's dog can lose an average of 1.25 pounds per week on a certain diet, after how long will the dog reach healthy weight?

Answers

It would take Keith's dog 12 weeks to be to the healthy weight of 75 pounds. 90-(1.25x)=75

Final answer:

In this mathematical problem involving weight reduction over time, Keith's dog has to lose 15 pounds to reach a healthy weight. If the dog can lose an average of 1.25 pounds per week, it would take the dog 12 weeks to achieve the desired weight.

Explanation:

The subject of the question is Mathematics, specifically a problem concerning weight loss over time, which is a real-world application of arithmetic and rate problems. In the given scenario, Keith's dog weighs 90 pounds, and the desired healthy weight is less than 75 pounds. Therefore, the dog needs to lose a total of 15 pounds. Given the dog can lose an average of 1.25 pounds per week, we can calculate the number of weeks it would take for the dog to reach a healthy weight.

Step 1: Identify the total amount of weight to be lost, which is the difference between the current weight and desired weight. This is calculated as 90 pounds - 75 pounds = 15 pounds.

Step 2: Divide the total weight to be lost by the average weight loss per week. This is calculated as 15 pounds ÷ 1.25 pounds per week = 12 weeks.

Therefore, it would take the dog 12 weeks to reach a healthy weight if he loses an average of 1.25 pounds per week.

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Help please!!

Solve for r.

p = 4r + 3t
A) r =
p - 3t
4
B) r =
p - 4t
3
C) r =
p + 3t
4
Eliminate
D) r =
p + 4t
3

Answers

I hope this helps you

4r=p-3t

r=p-3t/4

If p^ is equal to 0.86, then q^ is equal to ______.

Answers

that's answer is q^86

What is the volume of a cube with a side of length 11 units?

Answers

there is not enough information we need to know the other 2 sides

@bobross plz help I have another question
A particle moves on a line away from its initial position so that after t hours it is s = 6t^2 + 2t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.

Answers

Answer:

Average velocity is 32 miles/hr.

Step-by-step explanation:

Given that a particle moves on a line away from its initial position so that after t hours it is [tex]s=6t^2+2t[/tex] miles from its initial position.

We have to find the average velocity of the particle over the interval [1, 4].

As, average velocity is the change is position over the change in time.

[tex]s(4)=6(4)^2+2(4)=104[/tex]

[tex]s(1)=6(1)^2+2(1)=8[/tex]

∴ [tex]\text{Average Velocity=}\frac{s(4)-s(1)}{4-1}[/tex]

=[tex]\frac{104-8}{3}=\frac{96}{3}=32miles/hr[/tex]

Hence, average velocity is 32 miles/hr.

The average velocity of the particle is [tex]\boxed{{\mathbf{21 units}}}[/tex] .

Further explanation:

Velocity is the speed of an object in a given direction. Velocity is the vector quantity.

The average velocity can be calculated as,

[tex]{\text{average velocity}}=\frac{{{\text{distance travelled}}}}{{{\text{time taken}}}}[/tex]

Given:

The position of the particle after [tex]t[/tex] hours is [tex]s\left(t\right)=4{t^2}+t[/tex] . The given interval is [tex]\left[{1,4}\right][/tex] .

Step by step explanation:

Step 1:

The position of the particle after [tex]t[/tex] hours is [tex]s\left(t\right)=4{t^2}+t[/tex]

First we need to find the distance travelled in the interval of [tex]\left[{1,4}\right][/tex] .

The distance travelled by the particle at [tex]t=1[/tex] is as follows,

[tex]\begin{gathered}s\left(t\right)=4{\left(t\right)^2}+t\hfill\\s\left(1\right)=4{\left(1\right)^2}+1\hfill\\s\left( 1 \right)=5\hfill\\\end{gathered}[/tex]

The distance travelled by the particle at [tex]t=4[/tex] is as follows,

[tex]\begin{gathered}s\left(t\right)=4{\left(t\right)^2}+t\hfill\\s\left(4\right)=4{\left(4\right)^2}+1\hfill\\s\left( 1 \right)=68\hfill\\\end{gathered}[/tex]

Now find the distance travelled by the particle in the interval of [tex]\left[{1,4}\right][/tex] .

[tex]\begin{aligned}{\text{distance travelled}}&=s\left(4\right)-s\left(1\right)\\&=68-5\\&=63\\\end{aligned}[/tex]

Step 2:

The given interval is [tex]\left[{1,4}\right][/tex] .

Now we need to find the time as,

[tex]\begin{aligned}{\text{time elapsed}}&=4-1\\&=3\\\end{aligned}[/tex]

Step 3:

Now we find the average velocity of the particle.

The average velocity can be calculated as,

[tex]\begin{aligned}{\text{average velocity}}&=\frac{{{\text{distance travelled}}}}{{{\text{time taken}}}}\\&=\frac{{63}}{3}\\&=21{\text{units}}\\\end{aligned}[/tex]

Therefore, the average velocity of the particle is [tex]21{\text{ units}}[/tex] .

Learn more:

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Speed, distance and time

Keywords: velocity, initial position, particle, moves, interval, distance travelled, time elapsed, position, average velocity, units, vector quantity, speed, direction, hours.

Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?
a. y – 1 = 6x
b. y – 1 = 3x
c. y – 7 = 2x – 6
d. y – 7 = x – 2

Answers

For this we will use equation that gives us equation of line that goes through 2 given points.

that equation is:
[tex]y - y1= \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]

now we implement our given coordinates.
let Q be point 1 and R be point 2
y - 1 = 6/2(x - 0)
y - 1 = 3x

Answer is b.

The Answer is B.

I took the unit review, as well as did the math myself,

What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)2 + 4?
A: x=3/2
B: x=-1/6
C: x=-1/2
D: x=-3/2

Answers

Axis of symmetry = -b/2a
y + 3x - 6 = -3(x-2)² + 4
y + 3x - 6 = -3 ( x²-4x+4) + 4
y + 3x - 6 = -3x² + 12x -12 + 4
y + 3x - 6 = -3x² + 12x -8
y = -3x² + 12x - 3x -8 + 6
y = -3x² + 9x -2
(a=-3, b=9, c=-2)
Axis of symmetry = -b/2a = -9/2(-3) = -9 / -6 = -3 / -2 = 3/2
Hence, option A) x=3/2 is the correct answer.

Two triangles that have the same side lengths will always be congruent.
A. True
B. False

Answers

True, this is in accordance to the side-side-side postulate.

What are the x– and y–intercepts of the graph of y = 2x^2 – 8x – 10?

Answers

x-intercepts are found by setting y=0
[tex]y=2x^2-8x-10\rightarrow0=2x^2-8x-10[/tex]
factor out a 2 [tex]0=2(x^2-4x-5)\rightarrow0=x^2-4x-5[/tex]
[tex]0=(x-5)(x+1)[/tex] roots should be x=-1,5
therefore, x-intercepts are (-1,0) and (5,0)

y-intercepts are found by setting x=0
[tex]y=2x^2-8x-10\rightarrow y=2(0)^2-8(0)-10[/tex]
[tex]\rightarrow y=0-0-10=-10[/tex]
therefore, y-intercept is (0,-10)

You are climbing a mountain by the steepest route at a slope of 10∘ when you come upon a trail branching off at a 45∘ angle from yours. What is the angle of ascent of the branch trail?

Answers

When a trail branches off from a path with a 10° slope at a 45° angle, the angle of ascent of the branch trail is still 10° if the steepness remains constant.

If you are climbing a mountain by the steepest route at a slope of 10° and then encounter a trail that branches off at a 45° angle from your current path, we can calculate the angle of ascent of the branch trail using geometric relationships. To do this, we must comprehend that slopes can also be represented in percentages and are related to angles. For instance, a 100% slope corresponds to a 45° angle.

The steepest route you are initially taking has a 10° slope. When the branch trail diverts at a 45° angle from your path, this is not the angle of ascent but rather the angle between the two paths. If we consider a straight climb as a slope of 90°, your ascent angle would not change as it is still 10°. The branch trail effectively shifts direction but not necessarily the steepness of the path. Hence, the angle of ascent for the branch trail would also be 10°, assuming it maintains the same steepness as your original path.

A third grade class was given a multiplication quiz. The quiz had 10 problems. Any correctly answered 6 problems, Bobby answered 7 problems correctly, Tom answered 9 problems correctly, and Sue only answered 2 problems correctly.
A. What fraction of the problems did each student get correct on the quiz?
B. ORDER the fraction of problems each student got correct from greatest to least.

Answers

A.
Anne: 6 / 10; Simplified: 3 / 5
Bobby: 7 / 10
Tom: 9 / 10
Sue: 2 / 10; Simplified: 1 / 5

B.
9 / 10 (Tom), 7 / 10 (Bobby), 6 / 10 (Or 3 / 5, Anne), 2 / 10 (Or 1 / 5, Sue)

what is 9(x+86x)-800+900x

Answers

Let's simplify step-by-step.
9(x−866x)(800)+900x
=−6228000x+900x
Combine Like Terms:
=−6228000x+900x
=(−6228000x+900x)
=−6227100x
Answer:
=−6227100x

Hope This Helps!
Do what you love, Love what you do!
~GlitterWolfy~

Simultaneous equation:
Solve:

2x-3y=11
5x+2y=18

Answers

x—2 equations combined: 2(2x - 3y) + 3(5x + 2y) = 2(11) + 3(18) 4x - 6y + 15x + 6y = 22 + 54 19x = 76 x = 4 y—1st equation, substitute x: 2(4) - 3y = 11 8 - 3y = 11 3y = - 3 y = - 1 Answer: x = 4, y = - 1 Proof—2nd equation: 5(4) + 2(- 1) = 18 20 - 2 = 18 18 = 18

2*2x-2*3y=2*11-------------------------(1)
3*5x+3*2y=3*18------------------------(2)
add equation(1)&equation(2)
_____________________________
4x+15x=22+54
19x=76
x=4
put the value of x in equation(1)
2*2*4-2*3y=2*11
16-6y=22
16-22=6y
6y=-6
y=-1
x=4

The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle?

A. length = 5 cm; width = 5 cm
B. length = 7 cm; width = 6 cm
C. length = 6 cm; width = 7 cm
D. length = 4 cm; width = 9 cm ...?

Answers

l = 2w - 5 . . . (1)
2l + 2w = 26
l + w = 13 . . . (2)

Putting (1) into (2), gives
2w - 5 + w = 13
3w = 13 + 5 = 18
w = 18/3 = 6
l = 2(6) - 5 = 12 - 5 = 7

Therefore, length = 7 cm and width = 6 cm. (option B)

Here is the solution to the given problem above.
Given:
Let x be the width and L for length.
L= 2x -5
P = 2w + 2L
26 = 2x + 2(2x -5)
26 = 2x +4x - 10
26 = 6x -10
26 +10 =6x
36 =6x <<< divide both sides by 6
and we get x =6
Therefore the width is 6 centimeters.
Now to find the length.
L = 2x - 5 <<< substitute x with 6.
L = 2(6) - 5
L = 7
Length is 7 centimeters.
Therefore, the final answer would be option B. Length = 7 cm and width is 6cm.
Hope this answer helps.

8.) A linear equation has more than one y-intercept. What can you conclude about the graph of the equation??

Help Idk this question!!
Please help me it is one of my math homework questions!!

Answers

Answer:

Step-by-step explanation:

A straight line can either have 1 y-intercept or infinitely many y intercepts. The only case in which there are infinitely many y-intercepts is when the line represents the y-axis itself. On y-axis, x is always 0. So the line that represents the y-axis is the line x=0. However, it is not a linear equation. In short, only the line representing y-axis has more than 1 y-intercepts. There cannot be such a linear equation(function).

Final answer:

A linear equation cannot have more than one y-intercept. Having multiple y-intercepts would violate the definition of a function as each input (x-value) should only be associated with one output (y-value). Therefore, a linear equation with multiple y-intercepts suggests an error.

Explanation:

In the field of mathematics, specifically in algebra and graphing, a linear equation cannot have more than one y-intercept. The y-intercept of a linear equation is the point at which the line crosses the y-axis on a coordinate plane. Linear equations are represented by the formula y = mx + b, where 'm' is the slope of the line and 'b' is the y-intercept. If an equation were to have more than one y-intercept, it would violate the definition of a function, which states that each input (or x-value) is only associated with one output (or y-value). Hence, if a linear equation was portrayed as having more than one y-intercept, it would imply an error in the equation or in the graph itself.

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Two numbers are of the ratio 3:5. If their difference is 18, find the numbers.

Answers

est Answer: say the numbers are x and y......and y being the bigger number ... If the ratio is 5:3, then difference between ratio = 5-3 = 2 ... Substituting this x = 5y/3 in equation x-y=18 we get ... therefore x = 5 * 27/3 = 5*9 = 45 .... One number is 5 more than another. their sum is 53 what are the two numbers?

How to divide this 4.48÷1.4

Answers

4.48 / 1.4 is = 3.2

:)

A cell phone carrier offers two plans for text messaging. Plan A costs $20 per month plus $0.05 per text. Plan B costs $10 per month plus $0.10 per text. For how many text messages per month are the plans the same cost?

Answers

Answer:

200 texts = same costs

Step-by-step explanation:

Plan A: 20 + (.05 x 200)

20 + 10 =30

Plan B 10 + (.10 x 200)

10 + 20 = 30

What is 15.6 over 100 in simplest form?

Answers

[tex] \frac{15.6}{100} [/tex] ← multiply both the numerator and the denominator by 10
[tex] \frac{156}{1000} [/tex] ← simplify
[tex]\frac{39}{250}[/tex]

The answer's [tex]\frac{39}{250}[/tex].

1 is what percent of 52.6?

Answers

the answer to the equation is 45%

The price of a stock is $3.17 per share. what is the greatest number of whole shares mr. smith can buy with $200?
a. 15
b. 63
c. 66
d. 117

Answers

I think the answer is B

Answer:

the answer is b.63

Step-by-step explanation:

Hello, I can help you with this

Step 1

to solve this you must divide the money Mr Smith has by the price of a stock per share, it is

Money Mr smith has = $200

The price of a stock is $3.17

[tex]\frac{200 usd}{3.17\frac{usd}{share} }\\ =63.09\ shares\\\\[/tex]

he cand by whole shares, so he can buy exactly 63 shares

so, the answer is b.63

I really hope it helps, Have a great day.

If a Canadian dollar is worth $0.82 in American money, how much is an American dollar in Canadian money?

Answers

the currect exchange rate in canada is .96 euro per 1 american dollar

i would have to say 2$because of the price to buy a canadian dolar

The graph of F(x), shown below, has the same shape as the graph of G(x) = x2, but it is shifted to the left 3 units. What is its equation?

Answers

Answer:

f(x) = (x - 3)²

Step-by-step explanation:

If the function given below is g(x) = x²

Then we have to find the function f(x) which is same as g(x) but shifted 3 units left.

As we know in the given equation f(x) = (a + x)²+ k, x defines the shift of the function and and k defines the shift of a graph on y-axis upwards or downwards.

Here the graph is shifted left so the value of x will be (-3) which defines the shifting of 3 left on x-axis.

Therefore the new function will be f(x) = (x - 3)²

Answer:

F(x)=(x+3)^2

Step-by-step explanation:

Cristiano Ronaldo has a messy house. He hires a maid to clean his house for $125 per visit.
Part A:Write a function to represent the total cost Cristiano spends having his house cleaned.
Part B: Define the input and output in the given scenario.

Answers

y = 125x x (input) represents each visit and y (output) represents the total cost per visit.

Answer: y (x)= 125 x

input : number of visits "x"

output :total cost "y"

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

Cost per visit: $125

So, to obtain the total cost (y) we have to multiply the cost per visit by the number of visits (x)

y (x)= 125 x

Where the input is the number of visits "x" and the output is the total cost "y"

Feel free to ask for more if needed or if you did not understand something.

125% of what number is 264

Answers

Let, the number = x
x * 125 / 100 = 264
x = 264*100 / 125
x = 26400/125
x = 211.2

So, that number & your final answer is 211.2

Hope this helps!

Final answer:

To find out what number 125% is equal to 264, one should set up the equation 1.25x = 264 and solve for x, which gives x = 211.2.

Explanation:

The question asks to find a number such that 125% of it equals 264. To solve for the original number, we set up the equation 1.25x = 264, where 1.25 represents 125% in decimal form, and x is the unknown number we are solving for. We divide both sides of the equation by 1.25 to isolate x, giving us x = 264 / 1.25.

By performing this division, we get:

x = 211.2

Therefore, 125% of 211.2 is 264.

What is the equation of the line that has a y-intercept of -7 and is perpendicular to the line represented by the equation below? 8x 7y=19

Answers

8x + 7y = 19
- 8x
7y = 19 - 8x
÷ 7
y = 2 5/7 - 8/7x
So if that line is perpendicular to the line you're looking for, then the gradient (x value/slope) is the negative reciprocal to the gradient you're looking for, which would then be 7/8. You are told it has a y intercept of -7, so your final answer is:
y = -7/8x - 7
Hope this helps!

Answer: red sus tbh

Step-by-step explanation:

What is the sale price of $59 with a 10% discount??

Answers

10% of 59 = 5.9

59 - 5.9 = 53.1

answer: sale price is $53.1

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