Derek walks to his best friends house at a rate of 1 block per minute, then turns around and walks home. The graph shows the distance Derek walks in the given amount of time. Write an equation for the graph.

Derek Walks To His Best Friends House At A Rate Of 1 Block Per Minute, Then Turns Around And Walks Home.

Answers

Answer 1

In this question, we have to find an equation for two lines, depending on the input x, which creates the following piecewise function for this graph:

[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]

Equation of a line:

The equation of a line is given by:

[tex]y = mt + b[/tex]

In which m is the slope and b is the y-intercept(value of y when x = 0).

This situation:

One line for x between 0 and 10;Another for x between 10 and 20;

x between 0 and 10:

From here, we can take two points (t,y). I will take (0,0) and (10,10).

From point (0,0), we get that when [tex]x = 0, y = 0[/tex], which means that the y-intercept is [tex]b = 0[/tex], thus:

[tex]y_1 = mt[/tex]

To find the slope, when we have two points, it is given by change in y divided by change in t, so:

Change in t: 10 - 0 = 10

Change in y: 10 - 0 = 10

Slope: [tex]m = \frac{10}{10} = 1[/tex]

Thus, the first definition is:

[tex]y_1 = t, 0 \leq t < 10[/tex]

x between 10 and 20:

I will take the points (10,10) and (20,0).

First, we find the slope:

Change in t: 20 - 10 = 10

Change in y: 0 - 10 = -10

Slope: [tex]m = \frac{-10}{10} = -1[/tex]

Thus:

[tex]y_2 = -t + b[/tex]

For the intercept, we have point (20,0), which means that when [tex]t = 20, y = 0[/tex]. So

[tex]0 = -20 + b[/tex]

[tex]b = 20[/tex]

Thus, the second definition is:

[tex]y_2 = -t + 20, 10 \leq t \leq 20[/tex]

Write an equation for the graph.

We use the two definitions, that is:

[tex]y = y_1, 0 \leq t \leq 10, y_2, 10 \leq t \leq 20[/tex]

So

[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]

A similar question can be found at https://brainly.com/question/16024991


Related Questions

whats the answer to this problem/how to figure it out?!

Answers

6x^2+4x+8

6x7^2+4x+8

blah  blah blah

ANSWER

330

pls say if im right

Answer:

330

Step-by-step explanation:

[tex]6x^2 +4x +8\\x =7\\\\6(7)^2 +4(7) +8\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:\left(7\right)^2\::\quad 49\\\\=6\cdot \:49+4\left(7\right)+8\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:6\cdot \:49\::\quad 294\\\\=294+4\left(7\right)+8\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:4\left(7\right)\::\quad 28\\\\=294+28+8\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:294+28+8\:\\:\quad 330[/tex]

Correct answer gets 5 stars

Answers

Answer:

C

Step-by-step explanation:

The slope is (6-8)/(0-(-2))=-1. The y intercept is (0,6)

Anyone who can help me with this?

Answers

Answer:

C

Step-by-step explanation:

We know that the first integer will be "l" so the second will be l + 1, third will be l + 2, fourth will be l + 3, and the fifth will be l + 4. The question says "the greatest is g" so that means that the fifth integer is the greatest meaning that is the value of g. Now that we know the value of g, we can substitute it into the equation they gave us and simplify.

l+(l+4)/2

2l+4/2

l + 2

Best of Luck!

Answer:

C

Step-by-step explanation:

say your 5 consecutive numbers are 6-10

if 6 is l and 10 is g then

6+10 over 2 equals 8

this proves that l+2 is correct since 6+2=8

Combine like terms in the given polynomial. Then, evaluate for x = 4, y = – 2.
xy – 2xy + 3x2 y — 4x y2 + 2xy2
3x2 y + 2xy2 – xy; – 56
C - xy – 2xy2 + 3x2y; – 56
Cx? y2 – 2; 62
C
– 2x y2 + 3x2y – xy; – 120

Need explanation please

Answers

Answer:

- 2 x y^2+3 x^2 y -xy

-120

Step-by-step explanation:

xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2

Combine like terms

xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2

- x y+3 x^2 y - 2 x y^2

Let x = 4 y = -2

-(4)(-2) +3(4)^2 (-2) -2(4)(-2)^2

Exponents first

-(4)(-2) +3(16) (-2) -2(4)(4)

Multiply

+8 -96-32

Add and subtract

-120

PLEASE help me solve this question! No nonsense answers please!

Answers

Answer:

[tex]\boxed{\sf Option \ 1}[/tex]

Step-by-step explanation:

The profit is revenue (R ) - costs (C ).

Subtract the expression of costs (C ) from revenue (R ).

[tex]10x-0.01x^2-(2x+100)[/tex]

Distribute negative sign.

[tex]10x-0.01x^2-2x-100[/tex]

Combine like terms.

[tex]8x-0.01x^2-100[/tex]

The first option has a positive 100, which is wrong.

The rest options are right, when we expand brackets the result is same.

Om had a balance of 546 in his checking account. He made a deposit of $56, and wrote checks for $17 and $30. His bank charged him a $3 service fee. How much
honey does Om have in the account?

Answers

Answer:

540

Step-by-step explanation:

546-56=490

490+17+30=537

537+3=540

In 2002, the population of a district was 22,800. With a continuous annual growth rate of approximately 5% what will the population be in 2012 according to the exponential growth function?

Answers

Answer:

37,139

Step-by-step explanation:

Given the following :

Population in 2002 = Initial population (P0) = 22,800

Growth rate (r) = 5% = 0.05

Growth in 2012 using the exponential growth function?

Time or period (t) = 2012 - 2002 = 10years

Exponential growth function:

P(t) = P0 * (1 + r) ^t

Where P(t) = population in t years

P(10) = 22800 * (1 + 0.05)^10

P(10) = 22800 * (1.05)^10

P(10) = 22800 * 1.62889

P(10) = 37138.797

P(10) = 37,139 ( to the nearest whole number)

Is this right answer??????………

Answers

Yes ?!???!?!?!?!?!??!?

Answer:

6 is correct....

actually this problem is quite si,p;e to see that it is correct

notice that the length of the triangle is 4 and the height is 3

thus a rectangle 4*3 area is twelve ...

if you make a copy of the triangle and flip it you will see it makes

a 4x3 rectangle ... the original and copy = 12 thus 1/2 of the 12 is the area of the original triangle

Step-by-step explanation:

A trader bought a bag for 125gh cedis. he later sold it at a profit of 30%. What is his selling price

Answers

Answer:

162.5 Cedis

Step-by-step explanation:

Cost Price= 125

Profit % = 30%

Selling price=?

Selling price= Cost price+ profit

Profit = ?

[tex]profit \% = \frac{profit}{cost \: price} \times 100[/tex]

[tex]30 \% = \frac{x}{125} \times 100[/tex]

[tex]30 \% = \frac{100x}{125} \\ 30 \times 125 = 100x[/tex]

[tex]3750 = 100x \\ \frac{3750}{100} = \frac{100x}{100} \\ x = 37.5[/tex]

Profit = 37.5 gh Cedis

Selling price= 125+37.5

Selling price= 162.5 gh Cedis

The selling price of a bag is 162.5Cedis.

It is required to find the selling price.

What is profit?

The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product.

Given that :

Let the profit be x.

Cost Price= 125

Profit % = 30%

profit%=profit/cp*100

30=profit/125*100

3750=100x

x=37.5

profit=37.5

Selling price= Cost price+ profit

Selling price=125+37.5

Selling price=162.5ghcedis

So, the selling price of a bag is 162.5Cedis.

Learn more about profit here:

https://brainly.com/question/17189085

#SPJ2

I'LL GIVE BRAINLIEST !!! FASTERR !

Answers

Answer:

opt. B

Step-by-step explanation:

g=60 because equilateral triangle ang=60

<KMN=120 because of linear pair

<h= 180-(120+29)= 31

g+h= 60+31= 91

asap!!
~~~~~~
A line passes through point (–6, –1) and is parallel to the equation y = –2x – 5. What's the equation of the line?

Question 25 options:

y = –2x – 13

y = 12{"version":"1.1","math":"\(\frac{1}{2}\)"}x + 3

y = –12{"version":"1.1","math":"\(\frac{1}{2}\)"}x – 1

y = 2x + 5

click on picture for a, b, c ,or d

Answers

Answer:

y=−2x−13.

Step-by-step explanation:

The equation of the line in the slope-intercept form is y=−2x−5.

The slope of the parallel line is the same: m=−2.

So, the equation of the parallel line is y=−2x+a.

To find a, we use the fact that the line should pass through the given point: −1=(−2)⋅(−6)+a.

Thus, a=−13.

Therefore, the equation of the line is y=−2x−13.

Write the Roman numeral CLXXIX in standard form.​

Answers

179 is the answer

hope it helps

Answer:

179 = CLXXIX = 100 + 50 + 10 + 10 + 10 − 1

Step-by-step explanation:

Numbers close to CLXXIX

Below are the numbers CLXXVI through CLXXXII, which are close to CLXXIX. The right column shows how each roman numeral adds up to the total.

176 = CLXXVI = 100 + 50 + 10 + 10 + 5 + 1

177 = CLXXVII = 100 + 50 + 10 + 10 + 5 + 1 + 1

178 = CLXXVIII = 100 + 50 + 10 + 10 + 5 + 1 + 1 + 1

179 = CLXXIX = 100 + 50 + 10 + 10 + 10 − 1

180 = CLXXX = 100 + 50 + 10 + 10 + 10

181 = CLXXXI = 100 + 50 + 10 + 10 + 10 + 1

182 = CLXXXII = 100 + 50 + 10 + 10 + 10 + 1 + 1

Symbol Value

I 1

V 5

X 10

L 50

C 100

D 500

M 1000

I hope this helps.

Evaluate the expression

Answers

Answer:

3

Step-by-step explanation:

(5x -2y) / y

Let x = -4 and y = -4

(5*-4  - 2*-4) / -4

(-20 +8) / -4

-12/ -4

3

Hey there!

5x - 2y / y

= 5(-4) - 2(-4) / -4

5(-4)

= -20

(2)(-4)

= -8

= -20 - (-8) / -4

= -20 + 8 / -4

-20 + 8

= -12

= -12 / -4

= 3

Therefore, your answer is: 3

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Will Give Brainliest, Answer ASAP m∠O =
m∠N =

Answers

Answer:

∠ O = 61°, ∠ N = 119°

Step-by-step explanation:

In a parallelogram

Consecutive angles are supplementary

Opposite angles are congruent, thus

x + 2x - 3 = 180

3x - 3 = 180 ( add 3 to both sides )

3x = 183 ( divide both sides by 3 )

x = 61°

Thus

∠ O = ∠ M = x = 61°

∠ N = ∠ P = 2x - 3 = 2(61) - 3 = 122 - 3 = 119°

a sequence starts a 200 and 30 is subtracted each time 200,170,140 what are the first two numbers in the sequence that are less
then zero

Answers

Answer:

- 10, - 40

Step-by-step explanation:

200, 170, 140, .... - 10, - 40 ....

30 × 5 = 150

140 - 150 = - 10

- 10 - 30 = - 40

0.21212121 as a fraction

Answers

Answer:

21212121/100000000

Step-by-step explanation:

21212121/100000000 cannot be simplified

Hope this helps!

Answer:

0.21212121 Cannot be converted into a fraction

What are the coordinates of the point on the directed line segment from (−5,−9) to (-1, 7) that partitions the segment into a ratio of 5 to 3?

Answers

Answer:

(-2.5,1)

Step-by-step explanation:

Let the point be (m, n). Using section formula we have

m=(5*(-1)+3*(-5))/(5+3)=-20/8=-2.5

n=(5*(7)+3*(-9))/(5+3)=1

How many bicycles and how many skateboards are in the shop? Show your work.

Answers

Answer:75

Step-by-step explanation:54+21

Answer:

15 bicycles, 6 skateboards

Step-by-step explanation:

We are looking for the number of skateboards and the number of bicycles. Those two numbers are our unknowns.

We define variables for those two numbers.

Let s = number of skateboards.

Let b = number of bicycles.

A skateboard has 4 wheels. s number of skateboards have 4s wheels.

A bicycle has 2 wheels. b bicycles have 2b wheels.

The total number of wheels is 4s + 2b.

The total number of wheels is 54, so our first equation is

4s + 2b = 54

The total number of skateboards and bicycles combined is s + b.

We are told the total number of skateboards and bicycles combined is 21.

The second equation is

s + b = 21

We have a system of two equations in two unknowns.

4s + 2b = 54

s + b = 21

We can solve it by the elimination method.

Rewrite the first equation below.

Multiply both sides of the second equation by 2 and write it below that. Then add the equations.

          4s + 2b = 54

(+)      -2s - 2b = -42

-----------------------------

          2s         = 12

s = 6

There are 6 skateboards.

Now we substitute 6 for s in the second original equation and solve for b.

s + b = 21

6 + b = 21

b = 15

There are 15 bicycles.

Answer: 15 bicycles, 6 skateboards

29. SCUBA DIVING The sign shows the equipment rented or sold by a scuba
diving store.
a. Write two expressions to represent the total sales to rent 2 wet suits,
3 air tanks, 2 dive flags, and selling 5 underwater cameras.
b. What are the total sales?

Answers

The total sales to rent the diving items are :

2(17.25) + 3(15.50) + 2(5.00) + 5(18.99)

2(17.25 + 5.00) + 3(15.50) + 5(18.99)

The total sales to rent the diving items is : $185.95

Given the following rental cost:

Underwater Camera = $18.99

Air tank = $15.50

Wet Suit = $17.25

Dive Flag = $5.00

Expressions to represent the cost of :

2 wet suits, 3 air tanks, 2 dive flags and 5 underwater cameras

Price = price per item × quantity purchased

Expression 1 :

2(17.25) + 3(15.50) + 2(5.00) + 5(18.99)

Similarly, we could group items with the same quantity together :

2(17.25 + 5.00) + 3(15.50) + 5(18.99)

Using either of the two expressions above, the total sales can be calculated thus :

2(17.25 + 5.00) + 3(15.50) + 5(18.99)

2(22.25) + 3(15.50) + 5(18.99)

44.50 + 46.50 + 94.95

= $185.95

The expressions for the total sales to rent the diving items are given above with a total sales value of $185.95

Learn more : https://brainly.com/question/24395568

Two trains station at the same time one travels east at 8 miles per hour .The other train traveles east at 8 millas per hour the other train travels west at 11 miles per hour in how many hours will the two trains apart

Answers

What is your question ? This isn’t clear

cho tam giác ABC cân tại A trung tuyến AM.Biết BC=6cm,AM=4cm .Tính độ dài các cạnh AB và AC

Answers

Vì tam giác ABC cân tại A (gt) mà AM là đg trung tuyến nên AM đồng thời là đg cao của t/giác đó:

AM là trung tuyến của t/giác ABC nên M là trung điểm BC:

=> BM =BC/2 =6:2=3(cm)

Xét tam giác AMB vuông tại M

AB^2 =AM^2+BM^2 ( theo định lý Py-ta -go)

A tent is in the form of a right circular cylinder and cone. The radius of the cone and cylinder is 4 meters. The height of the cylinder and cone are 4.5 meters and 3 meters respectively. Find the outer surface area of the tent. (Assume π = 22 /7)

Answers

Answer:

176m²

Step-by-step explanation:

When we are asked to find the outer surface area of a geometric shape, it means to find the Lateral or Curved Surface Area of the shape. We are given two shapes above.

Step 1

Find the Outer surface area of the cone

Outer / Lateral surface area of a cone =

πrl

Where l = √r² + h²

r = 4 m

h = 3m

Outer surface area = 22/7 ×√4² + 3²

= 22/7 × √16 + 9

= 22/7 × √25

= 22/7 × 5

= 62.83185m²

Step 2

Find the outer surface area of a cylinder

= 2πrh

π = 22/7

r = 4m

h = 4.5

π = 22/7

Outer surface area of a cylinder = 2 × 22/7 × 4 × 4.5

= 113.09734m²

Step 3

The Outer Surface Area of the Tent = Outer Surface Area of the cone + Outer Surface Area of the cylinder

= 62.83185m² + 113.09734m²

= 175.92919m²

Approximately ≈ 176m²

Therefore, the outer surface area of the tent = 176m²

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
A ___________________ summarizes all values in a data set and lists how many times they occur.
A. tally chart
B. data value
C. data summary
D. frequency table

Answers

Answer:

Step-by-step explanation:

B) data summary its in the words it sums up the answers to all the data you've collected over timew

Clifton drove for 3 hours at 52 mph. How fast must he drive during the next hour in order to have an average speed of 55 mph?

Answers

Answer:

64 mph

Step-by-step explanation:

Given that:

Speed for the first 3 hours = 52 mph

Average speed for 4 hours = 55 mph

To find:

Speed for the next hour = ?

Solution:

Formula for average speed is given as:

[tex]Average\ Speed = \dfrac{Total\ Distance}{Total \ Time \ Taken}[/tex]

Formula for Distance:

[tex]Distance =Speed \times Time[/tex]

Distance traveled in first 3 hours:

[tex]Distance =52\times 3 = 156\ miles[/tex]

Let the speed for the next hour = u mph

Distance traveled in 1 hour = [tex]u \times 1 = u\ miles[/tex]

Total distance traveled = (156 + u) miles

Total time = 4 hours

Average Speed = 55 mph

Putting the values in formula:

[tex]55 = \dfrac{156+u}{4}\\\Rightarrow 220 = 156+u\\\Rightarrow \bold{u = 64\ mph }[/tex]

So, the answer is: 64 mph

Find the equation of the line that
is parallel to y = 4x + 1 and
contains the point (1, 1).
y = [? ]X + [ ]

Answers

Answer:

y = 4x - 3

Step-by-step explanation:

A parallel line will have the same slope so the slope will remain 4. To fine the new y-intercept, we can substitite the point we are given.

1 = 4(1) + b

1 = 4 + b

-3 = b

Now, we can create the new equation with the information we found.

y = 4x - 3

Best of Luck!

Answer: y = 4x - 3

Step-by-step explanation:

y-y=m(x-x)

y-1=4(x-1)

y-1=4x-4

y=4x-3

Write the gradient and the y intercept of the line y=-2x +4

Answers

Answer:

[tex]{ \bf{gradient = { \boxed{ - 2}}}} \\ \\ { \bf{y - intercept = { \boxed{4}}}}[/tex]

The slope of a line parallel to y=-1/2x+1 is:

A. 2.
B. -1/2.
C. 1.

Answers

Answer:

-1/2. The slope of a line parallel to another line will be the same. Using the slope-intercept form formula, y=mx + b where m is the slope, we know that the slope is -1/2.

Simplify each of the following, giving your answers with positive indices. f⁴÷f³×f​

Answers

Answer:

The answer

f^2

Step-by-step explanation:

So first we write down the expression

f^4/f^3 x f

now we follow the BODMAS

B - Brackets

O - Power

D - Division

M - Multiplication

A - Addition

S - Subraction

________________________________________

So this in equation (f^4/f^3 x f) we have to first divide. So in algebra when dividing, we have subtract the number.

Here

f^4-3 = f

so now we are left

f x f

when you times sometimes by itself we call it squared so you write it as

= f^2

On a horizontal number line, numbers to the...... are less than numbers to the..... Numbers to the right are........ numbers to the left.

Answers

on a horizontal number line . numbers to the left are less than numbers to the right .. numbers to the right are less than numbers to the left

Which of the following is true about these similar triangles?
A. AB/BC = DE/DF
B. AB/BC = DE/EF
C. AB/BC = BC/DF
D/ AB/BC = BC/AB

Answers

Answer:

B

Step-by-step explanation:

You have to match up the corresponding sides in the 2 triangles

The sides you have to find are AB/BC

The side that corresponds to AB in triangle DEF is DE

The side that corresponds to BC is EF

Other Questions
What is the calculation to determine your maximal heart rate? 8.11 LAB: Earthquakes here and there The US Geological Survey is a US Government Agency whose mission is stated as: "We provide science about the natural hazards that threaten lives and livelihoods; the water, energy, minerals, and other natural resources we rely on; Write the correct active or passive forms of the verbs in brackets and list in the spaces provided below. my colleagues A,B and I--------(design) an experiment to test the impact on worker perceptions of well-being when domesticated cats-----(allow)to freely roam various work environment in which the subject were normally employed.three test environment-----(select)for our experiments :a law office,to laboratory in which experiments-----(perform)using laboratory rats.we secretly inserted observers directly in to work environment. The observers---------(draw from the students who had into experimental psychology courses from which this study---------(develop) as an example of such studies generally. Why the city of Jerusalem might become a centre of conflict after 2 years the population of a town will be 33620 at the population growth rate of 2.5% pa find the present population of the town. State the correct polar coordinate for the graph shown.It is not the option selected. Och, Inc., is considering a project that will result in initial aftertax cash savings of $1.75 million at the end of the first year, and these savings will grow at a rate of 2 percent per year indefinitely. The firm has a target debt-equity ratio of .8, a cost of equity of 11.5 percent, and an aftertax cost of debt of 4.3 percent. The cost-saving proposal is somewhat riskier than the usual projects the firm undertakes; management uses the subjective approach and applies an adjustment factor of +3 percent to the cost of capital for such risky projects. What is the maximum initial cost the company would be willing to pay for the project? Peter's Pans makes cast-iron cookware. It decides to acquire another similar-sized cast-iron cookware company in the hope that its larger size will enable it to snag some market share away from Iron Maiden, the industry leader. What is Peter's Pans strategy? Based on the context, a blunderbuss is most likely which of the following? (4 points) describe about your family Please help simple alebgra! Write an equation representing the translation of f(x) = 7x + 3 down 4 units.Will mark brainliest! A test-preparation company advertises that its training program raises SAT scores by an average of at least 30 points. A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points. (a) Write the hypotheses for a left-tailed test of the mean.(b) Explain the consequences of a Type I error in this context. A Circuit has a 5000 V power supply(AC), A load resistance of 4 ohms and open switch how much Current will flow in a circuit as it is ? Sketch the graph of the following equations:y-3x+5y=-3x-5 Solve for x: the quantity of x plus 4 over 3 = 2. Hola, Silvia, cmo ests? Barron, Inc. sold goods for on account. The company operates in a state that imposes a % sales tax. What is the amount of the sales tax payable to the state What does "The product of n and 6 is subtracted from five-sixths of b" mean Solve for f.-f + 2 + 4f = 8 - 3f= What is a macromolecule? Question 6 options: a) a molecule that contains carbon b) a very large molecule c) a molecule that has two hydrogen atoms and one oxygen atom d) a molecule you can see with the naked eye