The table below shows a runner's time t, in mintues, and distance traveled d, in miles.

Write an equation that shows a relationships between t and d.

Answers

Answer 1

The equation that shows a relationship between t (time in minutes) and d (distance in miles) is d = 0.075t

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The standard form for linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

Let d represent the runners distance after t minutes.

From the table, using the points (12, 0.9) and (16, 1.20):

d - 0.9 = [(1.2 - 0.9)/(16 - 12)](t - 12)

d - 0.9 = 0.075(t - 12)

d = 0.075t

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Related Questions

find all real and complex zeros for f(x)=x^3-x^2+3x-3

Answers

The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively

How to determine the zeros of the function?

The equation of the function is given as

f(x) = x³ - x² + 3x - 3

Group the terms of the function in two's

So, we have the equation

f(x) = (x³ - x²) + (3x - 3)

Factor each group in the function

f(x) = x²(x - 1) + 3(x - 1)

Factor out x - 1

f(x) = (x² + 3)(x - 1)

Set to 0

(x² + 3)(x - 1) = 0

This gives

x² = - 3 and x = 1

Evaluate the roots

x = ±i√3 and x = 1

Hence, the zeros of the equation are x = ±i√3 and x = 1

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Through how many radians does the minute hand of a clock rotate from12:40 PM to 1:10 PM?o10- 10The minute hand rotates through radians.(Simplify your answer. Type an exact answer in terms of Use integers orfractions for any numbers in the expression)-10

Answers

As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.

A straight angle in radians is π radians.

Then, the minute hand rotates π radians

1. Write the regression2.r =3. what does the r mean?I predict there will be a [blank] relationship between [blank] and [blank] I think it’s because [blank] and I’m gonna send a photo about my graphing points

Answers

First of all, we have to find the mean of x values.

According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.

So, the mean is

[tex]\bar{x}=\frac{0+1+2+2+3+3+4+5+6+7}{10}=\frac{33}{10}=3.3[/tex]

The mean of x values is 3.3.

The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.

The mean would be

[tex]\bar{y}=\frac{2+2+3+4+4+4+5+6+8+9}{10}=\frac{44}{10}=4.4[/tex]

The mean of y values is 4.4.

Now, we find the standard deviation for x values and y values.

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If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is
given by y = 88t - 16t².
When does the ball reach its maximum height? (Round to two decimal places)

Answers

If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.

Maximum height

Given equation:

y = 88t - 16t²

Maximum height dy/dt = 0

88-32t = 0

32t = 88

t = 88/32sec

t = 2.75sec

Hence,

Maximum height attained by the ball :

Maximum height attained by the ball = 88(2.75)-16(2.75)²

Maximum height attained by the ball = 242 - 121

Maximum height attained by the ball = 121 feet

Therefore the maximum height is 121 feet.

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Rewrite the equation in Ax+By=C form. Use integers for A, B, and C. y=-1/6x+3

Answers

The equation y = - 1 / 6 x + 3 in standard form is x + 6y = 18.

How to rewrite equation in standard form?

The standard form for linear equations in two variables is Ax + By = C.

where

A , B and C are constantx and y are the independent and dependent variables respectively

Therefore, let's represent the equation y = - 1 / 6 x + 3 in standard form .

y = - 1 / 6 x + 3

multiply the equation by 6 to eliminate the fraction

6y = 6(- 1 / 6 x) + 6(3)

Therefore,

6y = - x + 18

x + 6y = 18

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Scott is a software salesman. His base salary is $2500, and he makes an additional $80 for every copy of English is Fun he sells.Let P represent his total pay (in dollars), and let N represent the number of copies of English is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 28 copies of English is Fun.

Answers

SOLUTION

Given the question in the question tab, the following are the solution steps to get the equation

Step 1: Represent the statement using mathematical notation

Base salary is $2500 (Base salary is constant since it does not change)

P represent his total pay (in dollars)

N represent the number of copies of English is Fun he sells

price made per copy of the product is $80

The equation relating P to N will be written as:

[tex]P=2500+80N[/tex]

Part B: Using this equation in step 1 above to find his total pay if he sells 28 copies of English is Fun

[tex]\begin{gathered} P=2500+80N \\ N=28 \\ P=2500+80(28) \\ P=2500+2240 \\ P=\text{\$}4740 \end{gathered}[/tex]

Hence, his total pay if he sells 28 copies of English is Fun is $4740

Fill in the blanks below with the correct units.(a) The school bus had a mass of about 9000 ?(b) Last week, Ravi drove about 13?to visit his uncle.(c) Goran added 5 ?e of cream to his coffee.

Answers

The first unit is kilograms because the bus is really heavy.

The second is kilometers because meters are too small.

The third one is milliliters because liters are too much for ice cream.

The graph of a linear function is given below.What is the zero of the function ?A. -3B. -3/2C. -2/3D. -2

Answers

Using the graph, we can deduce the following:

• x-intercept: x = -2

• y-intercept: y = -3

Let's determine the zero of the function.

The zero of a function can be said to be the root of the function. It is also called the x-intercept of the function.

The zero of a function is the point the line crosses the x-axis.

From the graph the x-intercept is at x = -2.

Therefore, the zero of the function is:

x = -2

ANSWER:

D. -2

Please help me I was sick today and missed out on class and I don’t understand this question

Answers

Answer: 72 i think

Step-by-step explanation:

Find the equation for the circle with a diameter whose endpoints are (5,5) and (3,−5).

Answers

The equation of the circle in standard form whose center is at (h, k) = (4, 0) is (x - 4)² + y² = 26.

How to derive the standard equation of the circle based on the coordinates of diameter endpoints

In this question we find the coordinates of the endpoints of the diameter of the circle, then, the center of the circle is the midpoint of the line segment. The center of the circle is found by midpoint formula:

(h, k) = 0.5 · (5, 5) + 0.5 · (3, - 5)

(h, k) = (4, 0)

And the radius of the circle is determined by Pythagorean theorem:

r = √[(4 - 5)² + (0 - 5)²]

r = √[(- 1)² + (- 5)²]

r = √26

Then, the equation of the circle in standard form is describe below:

(x - h)² + (y - k)² = r²

If we know that (h, k) = (4, 0) and r = √26, then the equation of the circle is:

(x - 4)² + y² = 26

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The equation for the line that has a slope of -3/8 and passes through (0, 10) is: y = -3/8x + 10 : y = 3/8 x - 10

Answers

The standard form of expression equation of a straight line is;

[tex]y\text{ = mx+c}[/tex]

where;

m is the slope

c is the intercept

Given

slope m = -3/8

Next is for us to get the y- intercept of the line. This is done by subtituting the slope and the point (0,10) given into the equation y = mx+c and calculating c as shown;

[tex]\begin{gathered} y\text{ = mx+c} \\ 10\text{ = -3/8(0)+c} \\ 10\text{ = 0+c} \\ c\text{ = 10} \end{gathered}[/tex]

Next is to get the equation of the line by substituting m = -3.8 and c= 10 into the standard form of the equation as shown;

[tex]\begin{gathered} y\text{ = mx+c} \\ y\text{ = -}\frac{3}{8}x+10 \end{gathered}[/tex]

Hence the first option is correct

Solve the equation for x.
6(x + 3) - 8 = 4x + 2(4 + x)

Answers

===============================Solve the Equation - Solution and Explanation===============================

Hello! So...

We are given the following to solve:

Solve for x.

[tex]6(x+3)-8=4x+2(4+x)[/tex]

_______________________________________________________

1. Expand both sides of the equation.

[tex]6(x+3)-8=6x+10[/tex]

[tex]4x+2(4+x)=6x+8[/tex]

[tex]6x+10=6x+8[/tex]

______________________________

2. Subtract 10 from both sides.

[tex]6x+10-10=6x+8-10[/tex]

_______________________________

3. Simplify.

[tex]6x=6x - 2[/tex]

_______________________________

4. Subtract 6x from both sides.

[tex]6x-6x=6x-2-6x[/tex]

_______________________________

5. Simplify.

[tex]0=-2[/tex]

^Notice, the sides are not equal in the solution. This being said, there would be no solution.

___________________________________________________

Hope this helps! If you need anything else, feel free to comment below. Thanks and good luck!

How many months does it take $428 to double at a simple interest rate of 12%

Answers

When $428 doubles, it means that the

7. On February 12th, a fire occurred at a local dry cleaning plant and the inpatient service days for the localhospital (120 beds) was reported to be 130. What is the bed occupancy rate for February 12th? Round toone decimal place.

Answers

We can use the following formula:

[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{\#_{\text{ }}of_{\text{ }}inpatient_{\text{ }}days_{\text{ }}for_{\text{ }}a_{\text{ }}given_{\text{ }}period}{_{\text{ }}avalaible_{\text{ }}beds\times\#_{\text{ }}days_{\text{ }}in_{\text{ }}the_{\text{ }}period}_{}\times100[/tex]

So:

[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{130}{120\cdot365}\times100[/tex]

Answer:

0.3%

hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 26∘ and 30∘.
How high (in feet) is the ballon?

Answers

The height of balloon is 1.99 miles above the ground.

What is angle of depression ?

In the event when the line of sight is directed downhill from the horizontal line, an angle is created with it. Angle of depression is the angle produced between the horizontal line and the observer's line of sight when the object being observed is below the level of the observer.

Let's give the balloon's height above the earth and the distance it is from the first milepost horizontally a name.

We can state the following if the angle of this milepost's depression is 24 degrees:

Tan(24)=[tex]\frac{h}{b}[/tex]

b = [tex]\frac{h}{tan(24)}[/tex]

We can state the following for the following milepost as there will be (b+1)miles horizontal distance of and a 20 degree depression at that location.

tan(20)=[tex]\frac{h}{b+1}[/tex]

b +1 = [tex]\frac{h}{tan(20)}[/tex]

Therefore, substituting equation 1

[tex]\frac{h}{tan(24)}[/tex] = [tex]\frac{h}{tan(20)} -1[/tex]

1 = [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex]

1 = h× ( [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex] )

h = 1.99 miles

Consequently, the height of balloon is 1.99 miles above the ground.

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12. The perimeter of a triangle with sides 5x-1, 5x-1, 2.2x +10, and the perimeter of a square with a side length of 6.5x -11.8 are the same. What is the value of x?

Answers

The value of x is 4.

The perimeter of any shape is the sum of lengths of all its sides.

We are provided with the sides of triangle i.e., 5x-1, 5x-1 and 2.2x +10.

So, The perimeter of a triangle = sum of length of all three sides = (5x-1) + (5x-1) + (2.2x +10)

The perimeter of a triangle = 12.2x + 8 equation 1

Also, we are provided with the side of square i.e., 6.5x -11.8.

The perimeter of a square = 4 (side) = 4 (6.5x - 11.8)

The perimeter of a square = 26x - 47.2 equation 2

As per question,

Perimeter of a triangle = Perimeter of a square

12.2x + 8 = 26x - 47.2

13.8x = 55.2

x = 4

So we can write, the value of x is 4.

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Classify the following functions as growth or decay: f(x) = 10 (6/7)^x, g(x)= 1/3e^x, h(x)=5e^-x, k(x)= -10(6/7)^x

Answers

It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.

Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.

Now let's analyze the functions from the problem.

[tex]\text{ Let }f(x)=10\cdot(\frac{6}{7})^x[/tex]

Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.

Use these rules to find whether each function is increasing or decreasing.

Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.

Horatio left a campsite, hiking at a rate of 1 mile per hour. Ivan left 3 hours later, hiking at a rate of 2 miles per hour. How long will it take Ivan to catch up to Horatio?

Answers

Ivan will catch up to Horatio in 3 hours .

In the question ,

it is given that

speed of Horatio is 1 miles per hour

speed of Ivan is 2 miles per hour .

and Ivan leaves 3 hours late than Horatio .

Let "t" be the time ( in hours ) taken for Ivan to meet Horatio ,

So, the distance covered by Ivan will be 2*t .

Since Horatio left 3 hours before so the time taken for Horatio to meet Ivan is (t+3).

So, the distance covered by Horatio will be 1*(t+3) .

The distance covered for Horatio and Ivan will be equal ,

which means

2*t = 1*(t+3)

2t = t + 3

2t - t = 3

t = 3

Therefore , Ivan will catch up to Horatio in 3 hours .

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L is a point of a tangency . Segment PL have a common point at P . Find the length of KN

Answers

[tex]\begin{gathered} PK\cdot PN=100 \\ PN=\frac{100}{8}=12.5 \\ KN=PN-PK=12.5-8=4.5 \end{gathered}[/tex]

a student has 200 Naira if someone gives her 160 Naira how much will she have if someone gives her x Naira how much would she have

Answers

Answer:

360 naira hope it will be helpful

Step-by-step explanation:

find the answer to this problem (15/16) - ( -3/16)

A. 3/4
B. -3/4
C. -1 1/8
D. 1 1/8

Answers

Answer;D.
First you would do change change and it would be (15/16)+3/16,then do 15+3=18,then put it over 16,18/16,then you simplify and it would be 9/8,but you can’t have a bigger numerator over a denominator,so you would divide 9/8 and it would be 1 1/8.

Solve the given equation or inequality graphically. State your answers rounded to two decimals. (a) x3 + 5x2 = −x2 + 5x + 3

Answers

The solutions of the equation x³ + 5x² = - x² + 5x + 3 when solved graphically is x = - 0.41, 1.09.

Draw a graph for each side, or component, of the equation and check to see where the curves intersect or are equal, to solve an equation graphically. The answers to the equation are the x values of these places.

Consider the equation,

x³ + 5x² = - x² + 5x + 3

Solving Equations Graphically:

The solution(s) of the equation f(x) = g(x) are the values of x where the graphs of f and g intersect.

Therefore,

f(x) = x³ + 5x² and g(x) = - x² + 5x + 3

By graphing the function we find the intersection of the two functions.

Hence, the graphs intersect each other at ( - 0.411, 0.776) and ( 1.092, 7.268).

Therefor,e the solution of the equation x³ + 5x² = - x² + 5x + 3 is x = - 0.41 and x = 1.09.

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What is a different common Denominator you could use in problem 2

Answers

Answer:

what is the problem ???

Step-by-step explanation:

Well we need problem 2 to know the answer

Can you check work please?

Answers

When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.

[tex]\begin{gathered} K(-4,-3)\rightarrow K^{\prime}(4,3) \\ L(-3,-1)\rightarrow L^{\prime}(3,1) \\ M(0,-3)\rightarrow M^{\prime}(0,3) \end{gathered}[/tex]

i need help the problem is
solve for y
2x+y=3

Answers

Answer:

y = 3 - 2x

Step-by-step explanation:

Subtract 2x from both sides of the equation.

Answer:

y = x or 1x

Step-by-step explanation:

x as a variable can also be expressed as 1x.

so we can say that 2x + 1x

because x & y are two different type of variables. you think of y as a question mark ( ? ).

Now the new equation is

y = ?

so 1x + ? = 3

because x is the same thing as a 1x you can say that 2x + 1x = 3

Sarah enrolled $10,000 worth of debt with National Debt Relief. We negotiated with the creditors and reduced the debt by 50%. Sarah’s fee for our services was 25% of the enrolled debt ($10,000). How much did Sarah end up saving after reducing her debt and paying us our fee?*

Answers

Answer:

7500$

Step-by-step explanation:

[tex]3-\sqrt{x} 5[/tex]

Answers

The value of the expression given as 3 - √x⁵ is 3 - x^2√x

What are expressions?

Expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the expression?

The expression is given as

3 - √x⁵

Express 5 as the sum of 4 and 1