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

ASAP!!! PLEASE

A pair of equations is shown below: y = 2x − 1 y = 4x − 5 Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points) Part B: What is the solution to the pair of equations? (4 points)

Answers

Step-by-step explanation:

526 133 3821

P: 12345

j _o _I _n g _I _r l

o. n z-oo-o-m

Find the length of the side labeled 2. Round intermediate values to
the nearest tenth. Use the rounded values to calculate the next
value. Round your final answer to the nearest tenth. PLEASE HELP ASAP!

A. 11.6
B. 13
C. 16.6
D. 22.4

Answers

Answer:

B

Step-by-step explanation:

The perpendicular is sin(43)*39=21.82. Next tan(32)=x/21.82. x=21.82*tan(32)=13.6

The value of x in the given question is 16.6

What are trigonometric ratios in a right angle triangle ?

A right angle triangle has 3 sides opposite is the side opposite to the angle formed by two adjacent sides.hypotenuse is the largest side and adjacent is the remaining side.

Assuming height of the triangle = y

Sin∅ = opposite/hypotenuse

sin43° = y/39

y= 39sin43°

y = 26.6
From this we will solve the value of x

tan∅ = opposite/adjacent

here adjacent = 26.6 and opposite = x

tan32° = x/26.6

x = 26.6tan32°

x = 16.6

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One number is three times another number. If the sum of the numbers is 36, determine the two numbers.

Answers

Step-by-step explanation:

A=3B

A+B=36

3B+B=36

4B=36

B=36/4

Step-by-step explanation:

let x represent the smaller number

3x is the second number

x+3x=36

4x=36

4x/4=36/4

x=9

the second number is 3(9)

=27

Ten tiles numbered 1 through 10 are turned face down. One tile is turned up at random, and a die is rolled and the number is square. What is the probability, written as a percent, that the product of the numbers on the tile and the die will be a perfect cube?

Answers

Answer:

18.33333333%. Please mark as brainliest if I’m Correct. :)

Step-by-step explanation:

there are two pots of milk containing 20 liters and 24 liters respectively .find the capacity of the largest container that can measure exactly milk both the cans​

Answers

Answer:

A can with capacity 44 litres

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

at old oak farm, there are chicken and horses. there are 120 legs and 48 heads altogether. how many horses and how many chickens are there?

Answers

Answer:

Step-by-step explanation:

We must use system of equations:

horses = h     chickens = c

horses have 4 legs & chickens have 2 and there are 120 legs total so to set up the first part of the equation...

4h + 2c = 120

They both have only 1 head each and there are 48 heads total so to set up the second part of the equation...

h + c = 48

Now we combine the equations and solve:

4h + 2c = 120

h + c = 48

Now we solve...

4h + 2c = 120

h = 48 - c         (subtract c on both sides to single out h)

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

4(48 - c) + 2c = 120

192 - 4c + 2c = 120

-192                  -192

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

-2c = -72           (divide both sides by -2)

c = 36

Now we go back and find the value of h...

h = 48 - c

h = 48 - 36

h = 12

So there are 36 chickens & 12 horses!

Cho tứ diện ABCD . Trên cạnh AB lấy điểm M , AC lấy N , trong tam giác BCD lấy điểm P tìm giao điểm

a, MP và (ACD)

b, AD và ( MNP)

c , BD và ( MNP)

Answers

Answer:

a.  Trong mp (BCD), nối BP cắt CD tại E

Trong mp (ABP), nối MP cắt AE kéo dài tại F (trong trường hợp MP không song song AE)

⇒F=MP∩(ACD)⇒F=MP∩(ACD)

b. Nếu MN cắt BC, kéo dài MN cắt BC tại G

Nối GP cắt BD tại H

Trong mặt phẳng (ABD), nối MH cắt AD tại K (trong trường howph MH ko song song AD)

⇒K=AD∩(MNP)⇒K=AD∩(MNP)

c. H=BD∩(MNP)

Step-by-step explanation:

which of the following represents…

Answers

The correct answer is the first option

The lengths of the sides of a triangle are 4,5 and 6 if the length of the longest side of a similar triangle is 15,what is the length of the shortest side of the triangle

Answers

Answer:

The length of the shortest side of the triangle is 10.

Step-by-step explanation:

Given that the lengths of the sides of a triangle are 4, 5 and 6, if the length of the longest side of a similar triangle is 15, to determine what is the length of the shortest side of the triangle, the following calculation must be performed :

6 = 15

4 = X

4 x 15/6 = X

10 = X

Therefore, the length of the shortest side of the triangle is 10.

Help anyone can help me do the question,I will mark brainlest.​

Answers

Answer:

Step-by-step explanation:

S=pi*R^2=(area of the sector)*(360/angle of AOB)

so 22/7*9^2=99*360/angle of AOB

-> AOB=140

perimeter of circle: 2*pi*R

permiter of sector : 2*pi*140/360*R+ 2R=22+9*2=40

giá tiền cước của một hãng taxi được tính như sau :giá mở đến 1km đầu là 12000 đồng ; 10500 đồng/km cho 20 km tiếp theo và 99000 đồng/km cho những km còn lại . Hỏi ông sáu đi từ nhà đến khu du lịch sinh thái Bò Cạp Vàng với quãng đường 62km bằng taxi của hãng đó hết bao nhiêu

Answers

Answer:

Ông sáu sẽ mất 4281000 đồng

69°
X/75°
36°
X =
degrees
Enter

Answers

Answer:

x = 105°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles

x is an exterior angle of the triangle , then

x = 69° + 36° = 105°

Find the number of bit strings that satisfies the given conditions. The bit strings of length 11 having at least four 1s

Answers

Answer:

Step-by-step explanation:

log 55 is the power to which ---- must be raised in order to produce a value of 55

Answers

Answer:

10

Step-by-step explanation:

just took the quiz

What is the volume of the solid? Let π=3.14
.

Answers

The volume of the solid as shown in the task content is; 2786.2cm³.

What is the volume of the solid?

It can be obtained from the task content that the solid given is a Cone.

On this note, the volume of the cone can be evaluated by means of the formula;

V = (1/3)π r²h where(r =22/2 = 11 and h=22).

Hence, Volume, V = (1/3) ×3.14× (11)²×22 = 2786.2cm³.

Read more on volume;

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Factor the expression
Thank you so muchh

Answers

Answer:

(x+8)(x-5)

Step-by-step explanation:

x^2 +3x-40

What two numbers multiply to -40 and add to 3

8 * -5 = -40

8+-5 = 3

(x+8)(x-5)

Answer:

(x + 8)(x - 5)

Brainliest, please!

Step-by-step explanation:

(x + )(x - )

Factors of 40: 1 and 40, 2 and 20, 4 and 10, 5 and 8

(x + 8)(x -5)

For there is always light, if only we’re brave enough to see it.

If only we’re brave enough to be it.

Answers

Answer:

sun is the answer to absolutely

Is 9/72 rational or irrational

Answers

i think answer is rational

Answer:

Rational

Step-by-step explanation:

The Numerator and Denominator is a whole number and its a fraction

What is the value of the expression 3.9x10^5/1.3x10^2?

I will mark Brainliest whoever person I actually trust.

Answers

Answer:

3 * 10 ^3

Step-by-step explanation:

Divide the numbers

3.9 / 1.3

3

Subtract the powers of 10

10^5 / 10^2 = 10 ^ (5-2) = 10^3

The result is 3 * 10 ^3

[tex] \frac{3.9 \times {10}^{5} }{1.3 \times {10}^{2} } \\ = \frac{3.9}{1.3} \times {10}^{5 - 2} \\ = 3.0 \times {10}^{3} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNKW THE ANSWER!!

Answers

Answer: will be D

Step-by-step explanation:

please answer and no links please ....​

Answers

Step-by-step explanation:

ℎ = -4, -3×(-4)+2 = 12+2 = 14

ℎ = -2, -3×(-2)+2 = 6+2 = 8

ℎ = 0, -3×0+2 = -3+2 = 2

ℎ = 3, -3×3+2 = -9+2 = -7

ℎ = 5, -3×5+2 = -15+2 = -13

Change 300mm into cm​

Answers

Answer:

30 centimeters

Step-by-step explanation:

true

It’s going to be 30 Cm

If I start a road trip with 10,425 miles on my auto meter and I end it with 23,840 miles showing how many miles was my trip

Answers

Answer:

13,415 miles

Step-by-step explanation:

Final position - initial position = Miles traveled:

23,840 miles - 10,425 miles = 13,415 miles

MUST SHOW WORK.
please do this ASAP!
This is about numerical expressions!

Answers

[tex]{\huge\fcolorbox{blue}{black}{\pink{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: Solution\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}[/tex]

[tex]2(4 - 1) {}^{2} - 3 + 2(5) \\ \\ = 2(3) {}^{2} - 3 + 2(5) \\ \\ = 2 \times 9 - 3 + 2(5) \\ \\ = 18 - 3 +2(5)\\ \\ =>15-10 = 25[/tex]

Hope This Helps You

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{2(4 - 1)^2 - 3 + 2(5)}[/tex]

[tex]\mathsf{4 - 1 = \bf 3}[/tex]

[tex]\mathsf{= 2(3^2) - 3 + 2(5)}[/tex]

[tex]\mathsf{3^2}\\\mathsf{= 3\times3}\\\mathsf{= \bf 9}[/tex]

[tex]\mathsf{= 2(9) - 3 + 2(5)}[/tex]

[tex]\mathsf{2(9)}\\\mathsf{= \bf 18}[/tex]

[tex]\mathsf{= 18 - 3 + 2(5)}[/tex]

[tex]\mathsf{18 - 3}\\\mathsf{= \bf 15}[/tex]

[tex]\mathsf{= 15 + 2(5)}[/tex]

[tex]\mathsf{2(5)}\\\mathsf{= \bf 10}[/tex]

[tex]\mathsf{= 15 + 10}\\\mathsf{= \bf 25}[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{25}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day! }[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

helphelphelphelphelphelp

Answers

Answer:

E - (8,-9)

F - (9,-9)

G - (9,-4)

Step-by-step explanation:

The first number in the bracket relates to the x-axis

The second number relates to the y-axis

which of the following is NOT true about a parallelogram?

Answers

Answer:

Any two consecutive angles are complementary.

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

Opposite sides of a parallelogram are parallel, Opposite sides are congruent. Opposite angles are congruent.

OAmalOHopeO

How can we write an algebraic expression to describe a two-digit number whose unit's digit is 5 less than the ten's digit?

Answers

Answer:

Let x= the ones digit

Then x+5=the tens digit

Hence the equation is: 10(x+5)+x=x+5+x+63

10(x+5)+x=x+5+x+63

10x+50+x=2x+68

11x+50=2x+68

-2x-50  -2x-50

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

       9x=18  Divide both sides of the equation by 9

         x=2

Hence the number is 10(2+5)+2=10(7)+2=70+2=72.


[tex]4 - \frac{2}{3}x = \frac{x - 6}{5} [/tex]
x=? Please tell​

Answers

4-2/3x=x-6/5

Answer: X=6

What is the total area of the figure below?

Answers

Step-by-step explanation:

As we know that,

In area of triangle , breadth =6inch,similarily ,height =8inch

now ,

Area of triangle = 1/2 ×b×h

= 1/2 × 8 ×6

=24inch^2

also,

In another figure,we can say

a=10 inch,b=16 inch and h=9 inch

similarly,

Area of trapizium = 1/2 h(a+b)

= 1/2 ×9(10+16)

=9/2 ×26

=9×13

=117inch^2

now ,

total area of figure =117 +24 =141inch^2

therefore,total area of figure is 141 inch^2

Write the digits used in binary number system

Answers

Answer:

Binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2.

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