Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two hours, the velocity of the runner is 3 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)

Answers

Answer 1
You only have two observations to work the equation for the velocity.

You only can assume a linear relation.

Part a.

Calling x the independent variable (time in hours) and y the dependent variable (velocity in km/h) =>

x (time in hours)         y (velocity in km/h)

1                                  5
2                                  3

Now you use the linear relation:

slope: (3 - 5) km/h/ (2 - 1)h = - 2 km/1h^2 = - 2 km/h ^2

Equation:

y - 3 = slope * (x - 2)

=> y - 3 = - 2 ( x - 2)

=> y - 3 = - 2x + 4

=> y = 3 - 2x + 4

=> y = - 2x + 7

that is the slope-intercept form.

the standard form is y + 2x - 7 = 0

part B.

to draw the graph you can make a table with the points for the first four hours:

x (time in hours)            y (velocity in km/h)
                                        -2x + 7

1                                      -2(1) + 7 = 5

2                                      -2(2) + 7 = 3

3                                      -2(3) + 7 = 1

4                                     -2(4) + 7 = - 1

The graph, of course, is a straight line, because we started from that assumption.

Related Questions

Which of the following is a solution of x2 + 4x + 10?

2 + i times the square root of 6
−2 + i times the square root of 24
−2 + i times the square root of 6
2 + i times the square root of 24

Answers

x^2+4x+10=0

x^2+4x=-10

x^2+4x+4=-6

(x+2)^2=-6

x+2=±i√6

x=-2±i√6

So the correct answer is the third one down from the top.

Answer:

[tex]x=2+-i \sqrt{6}[/tex]

Step-by-step explanation:

[tex]x^2 + 4x + 10[/tex]

To find out the solution we set the expression =0 and solve for x

[tex]x^2 + 4x + 10=0[/tex]

Apply quadratic formula to solve for x

[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

a=1, b=4, c=10 plug in the values in the formula

[tex]x=\frac{-4+-\sqrt{4^2-4(1)(10)}}{2a}[/tex]

[tex]x=\frac{-4+-\sqrt{-24}}{2(1)}[/tex]

The value of square root (-1) is 'i'

[tex]x=\frac{-4+-2i\sqrt{6}}{2}[/tex]

Divide each term by 2

[tex]x=2+-i\sqrt{6}[/tex]

[tex] \frac{x}{5}+\frac{3x}{15}=\frac{2x}{3} } [/tex]+2 Answer plz math help

Answers

Multiply all terms by 15
3x+3x= 10x+30

Combine like terms
6x=10x+30

Subtract 10x from both sides
-4x=30

Divide both sides by -4
x= -7.5

Final answer: -7.5

75% of our 1000 products are shipped on time each month the remainder have defects that take two weeks to fix and ship our clients complain about 10% of the anti-products are defective and 5% of the product shipped late or defective what is the overall percentage of defective products

Answers

The number of products shipped on time is 75% of 1000 = 750
The number of products shipped late is 25% of 1000 = 250

The number of defective product from the products that shipped on-time is 10% of 750 = 75

The number of defective product from the products that shipped late is 5% of 250 = 12.5

The total number of defective products is 75+12.5 = 87.5.

This is 87.5 out of 1000 products and as percentage it's [tex] \frac{87.5}{1000}=0.0875 [/tex]×100 = 8.75%

Final answer:

Calculating the overall percentage of defective products from the given data, we find that 150 out of 1000 products are defective, leading to an overall defect rate of 15%.

Explanation:

The question asks us to calculate the overall percentage of defective products based on the given scenarios. Firstly, it's mentioned that 75% of 1000 products are shipped on time, which means 750 are shipped on time and 250 are initially defective.

Since clients complain that 10% of the products are defective and 5% of the products are shipped late or are defective, we need to consider these percentages in our calculations.

To find the number of defective products, we can assume the 10% complaint rate on the entire batch of products which would lead to 100 out of 1000 products being defective. This is the initial estimated number of defective products.

To address the 5% of the products that are both shipped late and are defective, we consider this as an additional defect rate on top of the existing one, which would be another 50 products.

Total defects would then be the sum of defects from the complaints about defects and the defects because of shipping delay, which amounts to 100 + 50 = 150 defective products. To find the overall percentage, we divide 150 by 1000 and multiply by 100, giving us an overall defect rate of 15%.

Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans. Plan A: Raise the price by $0.05 each week until the price reaches $8.00. Plan B: Raise the price by 10 percent each week until the price reaches $8.00. Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00. Plan D: Raise the price by $0.25 each week until the price reaches $8.00. Which plan will result in the price of the bagels reaching $8.00 fastest? plan A plan B plan C

Answers

Plan C. He already has $5, so to get to $8 it needs to be raised $3. In Plan C, he wants to raise it the same amount for 6 weeks. $3.00 / 6 = .50... 6 weeks would give him the fastest Plan out of all the Plans.... Making your answer Plan C

Hope This Helps
Correct If I'm Wrong

Answer:

Plan B is correct answer.

Step-by-step explanation:

Raise the price by 10 percent each week until the price reaches $8.00.

Week 1. Starting price $5

[tex]0.1\times5=0.5[/tex]

price becomes = [tex]5+0.5=5.5[/tex]

Week 2.

[tex]0.1\times5.5=0.55[/tex]

Price becomes = [tex]5.5+0.55=6.05[/tex]

Week 3.

[tex]0.1\times6.05=0.605[/tex]

Price become = [tex]6.05+0.605=6.655[/tex]

Week 4.

[tex]0.1\times6.655=0.6655[/tex]

Price becomes = [tex]6.655+0.6655=7.320[/tex]

Week 5.

[tex]0.1\times7.320=0.732[/tex]

Price becomes = [tex]7.320+0.732=8.052[/tex]

So, we can see that in 5 weeks the price becomes $8 from $5. Therefore, plan B is the best plan.

Find PS if ABC=PQR, AD is an altitude of ABC, PS is an altitude of PQR, AD=12, AC=16 and PR=10

a. 7.5
b. 19.2
c. 4.62
d. 19.5

Answers

If ABC = PQR, then PS will also be similar to AD.

First you need to find how they're similar.

16/10 = 1.6

Then, multiply 12 (AD) by 1.6 to find PS.

12 * 1.6 = 19.2

The answer is B. 19.2

A drawer contains five pairs of socks that are brown, black, white, red, and blue. Claude takes the red socks out of the drawer. What is the probability of Claude choosing the red socks on his first pick?

Answers

A drawer contains five pairs of socks that are brown, black, white, red, and blue. Claude takes the red socks out of the drawer. What is the probability of Claude choosing the red socks on his first pick?

Answer: 1/25

Answer:

The answer would be 1/25 Hopefully this any T4L students!

can you help me????????

Answers

check the picture below.

now, if AC is that much, recall, BD is the midsegment, thus AB = BC, so AB is just one of the equal halves of AC, so, AB is AC/2.

What is the answer? (Tip- to undo multiply both sides by 4/7)

x|4/7 = 28

Answers

x / |4/7| = 28

Multiply by |4/7|

x = |4/7| x 28

Ignore the absolute for a second and note 4/7 x 28 is 16 because...
28 / 7 = 4
4 x 4 = 16

x = |16|

[tex]\frac{x}{\frac{4}{7}}=28\\\\(\frac{x}{\frac{4}{7}})*\frac{4}{7}=28*\frac{4}{7}\\\\x=\frac{28*4}{7}=\frac{4*7*4}{7}=\frac{16}{1}\\\\\\x=16[/tex]

Which function below is the inverse of f(x) = The quantity of four x minus three, over two.?

Answers

[tex]\bf f(x)=y=\cfrac{4x-3}{2}\qquad inverse\implies x=\cfrac{4y-3}{2}\impliedby \begin{array}{llll} first\ switch\\ the\ variables\\ then\ solve\\ for\ "y" \end{array} \\\\\\ 2x=4y-3\implies 2x+3=4y\implies \cfrac{2x+3}{4}=y=f^{-1}(x)[/tex]

Given f(x) = x2 + 4x − 1 and g(x) = 5x − 7, identify (fg)(x).

Answers

 f(x) = x^2 + 4x − 1 and g(x) = 5x − 7
(fg)(x) =  (x^2 + 4x − 1)(5x − 7)
(fg)(x) = 5x^3 + 20x^2 - 5x - 7x^2 - 28x + 7
(fg)(x) =  5x^3 + 13x^2 - 33x + 7

answer is C. third choice

(fg)(x) =  5x^3 + 13x^2 - 33x + 7

The product of the functions[tex]\( f(x) = x^2 + 4x - 1 \) and \( g(x) = 5x - 7 \) is \( 5x^3 + 13x^2 - 33x + 7 \).[/tex]

The correct answer is indeed [tex]{C} \),[/tex] which matches [tex]\( 5x^3 + 13x^2 - 33x + 7 \).[/tex]

To find the product[tex]\( (f \cdot g)(x) \)[/tex], where [tex]\( f(x) = x^2 + 4x - 1 \)[/tex] and [tex]\( g(x) = 5x - 7 \),[/tex]we need to perform the multiplication of these two functions.

Start by expanding [tex]\( f(x) \cdot g(x) \):[/tex]

1. Write down ( f(x) ):

[tex]\[ f(x) = x^2 + 4x - 1 \][/tex]

2. Write down ( g(x) ):

[tex]\[ g(x) = 5x - 7 \][/tex]

3. Perform the multiplication [tex]\( f(x) \cdot g(x) \)[/tex]:

 [tex]\[ f(x) \cdot g(x) = (x^2 + 4x - 1)(5x - 7) \][/tex]

4. Distribute [tex]\( x^2 + 4x - 1 \)[/tex] across ( 5x - 7 ):

 [tex]\[ f(x) \cdot g(x) = x^2 \cdot (5x - 7) + 4x \cdot (5x - 7) - 1 \cdot (5x - 7) \][/tex]

5. Perform the multiplications:

[tex]\[ x^2 \cdot (5x - 7) = 5x^3 - 7x^2 \][/tex]

  [tex]\[ 4x \cdot (5x - 7) = 20x^2 - 28x \][/tex]

 [tex]\[ -1 \cdot (5x - 7) = -5x + 7 \][/tex]

6. Combine all the terms:

[tex]\[ f(x) \cdot g(x) = 5x^3 - 7x^2 + 20x^2 - 28x - 5x + 7 \][/tex]

7. Simplify by combining like terms:

[tex]\[ f(x) \cdot g(x) = 5x^3 + (20x^2 - 7x^2) + (-28x - 5x) + 7 \][/tex]

 [tex]\[ f(x) \cdot g(x) = 5x^3 + 13x^2 - 33x + 7 \][/tex]

Therefore, the product [tex]\( (f \cdot g)(x) \) is \( 5x^3 + 13x^2 - 33x + 7 \).[/tex]

The correct answer is indeed [tex]{C} \),[/tex] which matches [tex]\( 5x^3 + 13x^2 - 33x + 7 \).[/tex]

Three cities lie along a perfectly linear route: Springfield, Clarksville, and Allentown. Molly lives in Springfield and works in Allentown. She makes it to work using two gallons of gas in her car. Her friend Edgar lives in Allentown and works in Clarksville. It takes Edgar one gallon of gas to get to work. If Molly's car averages 26 miles per gallon, and Edgar's car averages 17 miles per gallon, about how far apart are Springfield and Clarksville?

Answers

When it says that the cities are routed linearly, it means that these cities are located right next to each other. From the left, the order is Springfield, Clarksville, then Allentown. You have details on the number of gallons and the mileage. To get the distance travelled, just multiply the mileage with the gallons, to cancel out gallons leaving you with the distance in miles.

Now, since Molly travelled from Springfield to Allentown, the total distance she covered is the distance Edward travelled and the unknown distance between Springfield and Clarksville, denoted as x in the picture. So, the equation is then

Molly's distance = x + Edgar's distance
26 miles/gal(2 gal) = x + 17 miles/gal(1 gal)
x = 35 miles

Assume that y varies inversely with x. If y=7 when x=2/3, find y when x=7/3

Answers

Inverse variation is of the form:

y=k/x, which we can express as:

yx=k  we are given the point (2/3, 7) so we can solve for k

7(2/3)=k

14/3=k

y=14/(3x), so when x=7/3

y=(14/3)/(7/3)

y=(14/3)(3/7)

y=2

what is the inverse of the function f(x)=1/9x+2

Answers

Inverse works in this way:

y = 1/9x + 2,

you should swap the places of x and y and find y again, in this case it will be

x = 1/9y + 2    =>     x-2 = 1/9y    =>   (x-2) * 9y = 1   =>    9y = 1/(x-2)

and finally we got y = [tex] \frac{1}{(x-2)*9} [/tex]

The diffrence between a term and
coefficient

Answers

The difference between a term, and a coefficient is...

- A coefficient tells you how many times to multiply a variable.
       · Ex: 4xy = Coefficient: 4

- A term is each of the numbers in an equation, ratio, etc.
       · Ex: 5x + 7y + (4x - 4y) + 2 = Terms: 5x, 7y,  (4x - 4y), and 2



I am 99.9% sure this is the correct answer, but if it isn't I am truly sorry, and please forgive me.

How to find the x intersept

Answers

The x intercept (spelled with a "c", not an "s") is any point where the function curve either touches or crosses the x axis. The x axis is the bold flat horizontal line. This axis is often labeled with an "x" in many diagrams. 

For problem 22, the x intercept is the point (-4,0) as this is where the S shaped curve crosses through the horizontal x axis. See the attached diagram for a visual of what I'm talking about. Note the highlighted point in red.

99 POINTS!!! Find the equation for an ellipse with vertices at (-6, 0) and (6, 0) and foci at (-4, 0) and (4, 0).

Answers

(x^2)/a^2+(y^2)/b^2=1
a>b
a=6, a^2=36
foci=(a^2-b^2)^(1/2)
4=(36-b^2)^(1/2)
16=36-b^2
b^2=36-16
b^2=20
b=2(5)^(1/2) or (20)^(1/2)
1=(x^2/36)+(y^2/20)

(x^2)/a^2+(y^2)/b^2=1

a>b

a=6, a^2=36

foci=(a^2-b^2)^(1/2)

4=(36-b^2)^(1/2)

16=36-b^2

b^2=36-16

b^2=20

b=2(5)^(1/2) or (20)^(1/2)

1=(x^2/36)+(y^2/20)

Convert this percent into decimal form.

Answers

12 1/4 can be rewritten as 12.25

Then move the decimal place two places to the left to divide by 100 (percent means per 100),

Final answer: 0.1225

Determine whether the equation represents y as a function of x 16x-y^4=0

Answers

Given
[tex]16x-y^4=0 \\ \\ \Rightarrow y^4=16x \\ \\ \Rightarrow y= \sqrt[4]{16x} =2 \sqrt[4]{x} [/tex]

For any value of x, there are two possible values of y, thus the equation does not represent y as a function of x.

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Tell which equation you would use to isolate a variable in order to solve the system using substitution. Explain your reasoning.

2x + y=-10
3x-y=0

Answers

2x+y=-10
Multiply both side by 3
2x*3+y*3=-10*3
6x+3y=-30

3x-y=0
Multiply both side by 2
3x*2-y*2=0*2
6x-2y=0
Next, use substitute property
6x+3y=-30
    -
6x-2y=0
    =
y=-30
3x-y=0
Substitute y with -30
3x-30=0
Add 30 to each side
3x-30+30=0+30
3x=30
Divided both side by 3
3x/3=30/3
x=10, so the solution pair is (10,-30). In this case, there is the first way to solve these two equation.
Then, I would use equation 3x+1.5y=-15 in this question by multiply 2x+y=-10 by multiplying both side by 3/2 to eliminate x and to solve variables for y. Hope it help!

last question
help me pls c:

Answers

The answer is 200 cm squared. You can find this out by know the diameter of the circle which is 20 cm and by the photo the square's corners touch the circle so if a line when through the square diagonally you would get 20cm. Now you know the hypotenuse you can find the side lengths. You can use the 45 45 90 triangle where both side lengths equal x and the hypotenuse equals x* the square root of 2, but instead you would divide 20 by the square root of 2 and you would get your side lengths and then just multiply them

Which of the following points lie in the solution set to the following system of inequalities?

y ≤ x − 5
y ≥ −x − 4

(−5, 2)
(5, −2)
(−5, −2)
(5, 2)

Answers

The answer is (5,-2) because when you plug it into the first problem you would get 0 which is greater than or equal to -2 and for the second you would get -9 which is less than or equal to -2

Answer: Second option : (5, −2)


Step-by-step explanation: Given system of inequalities

y ≤ x − 5

y ≥ −x − 4

Plugging x=5 and y=-2 in first inequality

-2  ≤ 5 − 5

-2 ≤  0 : True.

Plugging x=5 and y=-2 in second inequality

-2 ≥ −5 − 4

-2 ≥ -9 : Also true.

Point  (5, −2) satisfied both of the given inequalities in the system.

Therefore, (5,-2) is correct option.

The best approximation for the square root of 10 is.. A).5 B).100 C).3.1 D).25

Answers

The square root of 10 is 3.16 so the closet is c)3.1

Answer:

It is approximately 3.1

Step-by-step explanation:

Conditional probabilities are based on some event occurring given that something else has already occurred?

Answers

The answer is true. A conditional probability is a measure of the probability of an event given that (by assumption, presumption, assertion or evidence) another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A in the condition B", is usually written as P (A|B). The conditional probability of A given B is well-defined as the quotient of the probability of the joint of events A and B, and the probability of B.

Consider the relation y = 4|x + 2| + 7. What are the coordinates of the vertex?

(7, −2)
 (2, 7)
 (4, −2)
 (−2, 7)

Answers

To answer, we set the expression inside the absolute value symbol (II) equal to 0. That is,
                           x + 2 = 0
Then, we solve for the value of x.
                           x + 2 - 2 = 0 - 2
Hence, the value of x from the equation above is equal to -2.

Then, substitute the value of x to the equation and drop the absolute value symbol.
                       y = 4(x + 2) + 7
Substituting,
                       y = 4(-2 + 2) + 7
                             y  = 4(0) + 7
                                 y = 7

Thus, the vertex of the absolute value equation is equal to (-2,7). The answer is the last choice. 

What is the solution of sqrt 2x + 4 = 16 ? x = 6 x = 72 x = 126 no solution

Answers

Answer:  Third option is correct.

Step-by-step explanation:

Since we have given that

[tex]\sqrt{2x+4}=16[/tex]

We need to find the value of 'x'.

First we squaring the both sides:

[tex](\sqrt{2x+4})^2=16^2\\\\2x+4=256\\\\2x=256-4\\\\2x=252\\\\x=\dfrac{252}{2}\\\\x=126[/tex]

Hence, the value of x is 126.

Therefore, Third option is correct.

Answer:

C on Edge

Step-by-step explanation:

Received a 100% on the quiz.

The expression 9n is also considered a _____.
constant
variable
term

Answers

Answer:

Term

Step-by-step explanation:

hope this helps

Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 4 - (x - 6)^2 ??

Answers

Taking the derivative will give you the velocity at any time.

g(x)=4-(x-6)^2

g(x)=4-(x^2-12x+36)

g(x)=4-x^2+12x-36

g(x)=-x^2+12x-32

dg/dx=-2x+12

So g(x) will be increasing when dg/dx>0

-2x+12>0

-2x>-12

x<6

So g(x) is increasing on the interval (-oo, 6)

g(x) will be decreasing when dg/dx<0

-2x+12<0

-2x<-12

x>6

So g(x) will be decreasing on the interval (6, +oo)

The local theater has three types of seats for broadway plays: main floor, balcony, and mezzanine. main floor tickets are $⁢59, balcony tickets are $⁢50, and mezzanine tickets are $⁢40. one particular night, sales totaled $73,785. there were 435 more main floor tickets sold than balcony and mezzanine tickets combined. the number of balcony tickets sold is 78 more than 33 times the number of mezzanine tickets sold. how many of each type of ticket were sold?

Answers

Final answer:

10 mezzanine tickets, 408 balcony tickets, and 853 main floor tickets were sold.

Explanation:

Let's solve this problem step-by-step to find out how many of each type of ticket were sold:

Let's assume that the number of mezzanine tickets sold is x. Therefore, the number of balcony tickets sold is 33x + 78 (since it is 78 more than 33 times the number of mezzanine tickets sold).

The number of main floor tickets sold is 435 + (33x + 78) + x = 435 + 34x + 78 = 34x + 513 (since there were 435 more main floor tickets sold than balcony and mezzanine tickets combined).

The total sales amount is $73,785.

Now, we can set up an equation to solve for x:

$40x + $50(33x + 78) + $59(34x + 513) = $73,785

Simplifying the equation:

40x + 1650x + 3900 + 59(34x + 513) = 73785

40x + 1650x + 3900 + 2006x + 30567 = 73785

3696x + 34467 = 73785

3696x = 39318

x = 39318/3696

x = 10.65

Since we can't have a fraction of a ticket, we can round down to the nearest whole number. So, x = 10.

Therefore, 10 mezzanine tickets were sold, 33x + 78 = 408 balcony tickets were sold, and 34x + 513 = 853 main floor tickets were sold.

The length of a rectangle is 2 yd longer than its width. if the perimeter of the rectangle is 40 yd , find its area.

Answers

perimeter = 2L+2W

L=2+w

40 = 2L+2W

40= 2(2+w)+2W

40=4+2w+2w

36=4w

w=9

L=9+2=11

2(9) = 18, 2(11) = 22, 22+18 = 40

L=11

W=9

 Area = L x w

area = 11x9= 99 square yards

John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours). Which is an appropriate range for this situation?

Answers

The appropriate range for John's distance in miles (d) during the marathon is A. [tex]$0 \leq d \leq 26.2$[/tex].

In a marathon, the distance (d) John covers depends on the time (t) he spends running. The distance is fixed at 26.2 miles, so we need to find the appropriate range for the time (t) he spends running.

Let's calculate John's average speed (v) during the marathon. We know that speed is given by:

[tex]\[ v = \frac{d}{t} \][/tex]

Where:

- v = average speed (miles per hour)

- d = distance covered (miles)

- t = time spent running (hours)

Given that John's distance is 26.2 miles, and the marathon covers this distance, we have:

[tex]\[ 26.2 = \frac{26.2}{t} \][/tex]

Solving for t:

[tex]\[ t = \frac{26.2}{26.2} = 1 \][/tex]

So, John takes 1 hour to cover the 26.2 miles.

Now, let's consider the maximum and minimum possible times for John to complete the marathon:

- Minimum time: John completes the marathon in the fastest time possible. Let's say this is 0. This implies he runs the marathon in 0 hours.

- Maximum time: John takes his time and completes the marathon at the slowest pace possible. Let's use the average time for a marathon, which is around 4.5 hours.

Thus, the appropriate range for the time (t) is:

[tex]\[ 0 \leq t \leq 4.5 \][/tex]

This corresponds to option C: [tex]$0 \leq t \leq 4.5$[/tex].

Complete Question:
John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours) Which is an appropriate range for this situation?

A. [tex]$0 \leq d \leq 26.2$[/tex]

B. [tex]$0 \leq d \leq 4.5$[/tex]

c. [tex]$0 \leq t \leq 4.5$[/tex]

D. [tex]$0 \leq t \leq 26.2$[/tex]

Other Questions
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