Item 6 Your city is represented in a coordinate plane where each unit represents 1 kilometer. The library is at (−3, −3), the post office is at (2, 2), and your house is at (−5, 2). You ride your bike from your house to the library, then the post office, and then back home. What is the minimum distance that you can ride your bike? Round your answer to the nearest tenth. km

Answers

Answer 1

We know, shortest distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is :

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

So, distance between house and library is :

[tex]d_1=\sqrt{(-5-(-3))^2+(2-(-3))^2}\\\\d_1=5.39\ km[/tex]

Distance between library and post office :

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\D=\sqrt{(-3-2)^2+(-3-2)^2}\\\\D=7.07\ km[/tex]

Distance between post office and house :

[tex]D=\sqrt{(2-(-5)^2)+(2-2)^2}\\\\D=7\ km[/tex]

Therefore, minimum distance that you can ride your bike is (5.39+7.07+7) km = 19.46  km.

Hence, this is the required solution.


Related Questions

Which number line represents all of the values of x for the equation x2 = 36?

Answers

Answer:

x is 18

Step-by-step explanation:

x is 18 because 18 x 2 = 36

Answer:

-6 and 6 are values of x on number line

Step-by-step explanation:

i took the test :)

Jenny ran 5 more miles this week than she ran last week. Let t be the number of miles she ran last week. Write an expression that tells how many miles she ran this week.

Answers

Answer:

t+5+x

Step-by-step explanation:

It says Jenny ran 5 more miles than last week so you find the number from last week then add 5. X is the miles she ran this week

Answer:

t + 5

Step-by-step explanation:

In this problem, you have to recognize what the information is telling you in terms of the vocabulary used. For example, the first sentence tells us that she ran 5 more miles than last week. This is key because it lets us know that our expression will have an addition sign.

Once you recognize that the problem is telling you to add 5 to her previous distance, you get a final expression of t + 5. Hope this helps!

Help meh plsssss ASAP ty

Answers

heres the answer :)))))))))))))))))))))

How many pages do you read in a hour if it takes you 8 hours and 25 minutes to read 500 pages?

PLZZ ANSWER ASAP!!!

Answers

Step-by-step explanation:

165 bc all you had to do was 825 divided by 500.

2,550 gallons in 30 days

Answers

The answer
is 85 gallons
in a day

A chance of X to 21532020(x+5)


I have literally no clue, help please?

Answers

Answer: x+5/21532020

Step-by-step explanation:

This question simply implies that if we need to know the chances of getting the  chance value it would be 21532030 times smaller for the x+5.

Simplify the expression.
9(4+t) - 7(t + 3)
9(4 +t) - 7(t + 3) =

Answers

Answer:

−63t2−439t−741

Step-by-step explanation:

Let's simplify step-by-step.

9(4+t)−7(t+3)(9)(4+t)−7(t+3)

Distribute:

=(9)(4)+(9)(t)+−63t2+−441t+−756+(−7)(t)+(−7)(3)

=36+9t+−63t2+−441t+−756+−7t+−21

Combine Like Terms:

=36+9t+−63t2+−441t+−756+−7t+−21

=(−63t2)+(9t+−441t+−7t)+(36+−756+−21)

=−63t2+−439t+−741

Solve for x in the equation x squared + 10 x + 12 = 36.
x = –12 or x = 2
x = –11 or x = 1
x = –2 or x = 12

Answers

it’s the first one

x = -12 or x=2

Answer:

x= -12 x=2

Step-by-step explanation:

Make a conjecture: What happens to
M AJK, m_BKJ, and m_CLJ as you
change the line of reflection?
The angles change.
The angles do not change.
The angles are always right
angles.

Answers

Answer:

the angles change

Step-by-step explanation:

HELP ME PLS PLS PLS

Answers

A. yes

B. Yes

C. No

Hope this helps :)

Convert 0.04% to a decimal.
1

Answers

it’s 0.0004! i think... if it’s wrong... i’m sorry!

Answer:

0.04%x100/100% = 4.0

Step-by-step explanation:

When converting from a percentage to a whole number, multiply it by 100 to return it to a whole number. since it asks for a decimal, it would become 4.0 instead of 4

A family budgeted 28% of their monthly income to take a family vacation.
What fraction of the family's budget was spent on the vacation?

7/250

1/28

7/25

2/8

Answers

The answer is 1/28 i think

Answer:

7/25

Step-by-step explanation:

The answer is simple. It's a simplified fraction of 28%, or 28/100.

the square root of 39 is between which 2 integers

Answers

9514 1404 393

Answer:

  6 and 7

Step-by-step explanation:

6² = 36

(√39)² = 39

7² = 49

The square root of 39 is between 6 and 7.

ILL GIVE BRAINLIEST IF RIGHT ASAP

Answers

Answer:

Everything with a dilation so B and E

Step-by-step explanation:

The second and last one, because dilations are only transformation that makes figures SIMILAR!

a line passes trough the points(-5,2) and(10,-1). Wich is the equation of the line​

Answers

Answer:

y= -(1/5)x +1

Step-by-step explanation:

Find slope:

(2+1)/(-5-10) = -1/5

Plug a point and slope into equation (I used -5,2):

y-2=-1/5(x+5)

Change it to slope-intercept form:

y-2=-1/5(x+5)

y-2=-1/5x-1

y=-1/5x+1

How many significant figures are in the number 4005?

Answers

Answer:

4

Step-by-step explanation:

Can someone help please?

Answers

Answer:

Can i be brainlest i neeed it

Three months ago, Santos could walk 2 miles in 40 minutes. Today he can walk 2 miles in 25 minutes.
Percentage:
Increase or Decrease?

Thank you ☺️

Answers

It would be an increase in percentage by 60%. Thanks or brainliest? :)

plz help important!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

the cost of gas i think

Step-by-step explanation:

i dont really know

Answer:

I think it is, B( The length of the route

Step-by-step explanation:

which two statements describe the ocean floor

A. there are underwater mountain chains
B. there are many active undersea volcanoes
C. it has only smooth surfaces between continental shelves
D. it is covered with underwater forest of tall trees

Answers

Answer:

I believe the answer is B.

Step-by-step explanation:

If you think about it, none of the other answers really make sense. This is the only one that I can see that actually makes sense. If I am wrong, I am very sorry.

Identify whether the function f(x)= -3.2^1/6 is a monomial function, power function, both, or neither?

A.) Both
B.) Monomial
C.) Power
D.) Neither

Answers

Answer:

both

Step-by-step explanation:

both plus power = neither

What is the equation of the line that passes through the point (4,4) and has a slope
of 3?

Answers

Y=3x-8 I’m pretty sure this is right

Answer:

The right answer is y=-3x-8

Step-by-step explanation:

Find the common difference for the sequence shown


SUPER EASY
1/4, 5/16, 3/8, ...

A. 1/16
B. 1/4
C. 1/2

Answers

Answer:

B.

Step-by-step explanation:

divide the 2nd term to 1st term of sequence

The answer is A. 1/16
If you add 1/16 to 1/4 you get 5/16. If you add 1/16 to 5/16 you get 3/8.

-1/2 + 3/4 - 3/8 what is it?

Answers

Answer:

-1/8

Step-by-step explanation:

-1/2 + 3/4 - 3/8 = -1/8

Can I have Brainliest please?

Answer:

[tex]\frac{-1}{8}[/tex]

Step-by-step explanation:

So first find the greatest common factor of the denominators

GCF of 2 , 4 and 8 is 8

Then :

[tex]\frac{-4 + 6 - 3}{8}[/tex]

So you do this to get the above answer:

8 divided by the denominator times the numerator.

You still need to work it out

-4 + 6 = 2

[tex]\frac{2- 3}{8}[/tex]

2 - 3 is -1

Thus the answer is [tex]\frac{-1}{8}[/tex]

HOPE THIS HELPED

X2-6x-5
completing the square

Answers

(X-3)^2-14 that’s the answer

Can someone please help me on 7

Answers

Answer:

B

Step-by-step explanation:

plug in 5

5^2-5(4)+7=12

Answer: B.  f(x) = x^2-4x+7

===========================================

Work Shown:

A.

f(x) = 3x-8

f(5) = 3*5-8 ... replace every x with 5; simplify with PEMDAS

f(5) = 15-8

f(5) = 7

We can cross choice A off the list since we got 7 as an output, instead of 12.

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

B.

f(x) = x^2-4x+7

f(5) = (5)^2-4(5)+7

f(5) = 25-4(5)+7

f(5) = 25-20+7

f(5) = 5+7

f(5) = 12

We got the output we wanted. So we can stop here.

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

If you're curious about the others, then,

C.

f(x) = -x+14

f(5) = -5+14

f(5) = 9

That doesn't work, so we cross choice C off the list.

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

D.

f(x) = |x-7|

f(5) = |5-7|

f(5) = |-2|

f(5) = 2

Choice D is crossed out as well.

So only choice B works.

Can someone help me confused on how to solve but it might be easy I just think I'm dumb

Answers

Maybe it’s 2? Let me know if I’m wrong

(Segment Proofs)

Given: K is the midpoint of JL, M is the midpoint of LN

JK = MN

Prove: KL LM

Answers

Answer:

It's proved below

Step-by-step explanation:

We are given;

- K is the midpoint of JL

- M is the midpoint of LN

By definition of mid points, we can say that;

JK = KL and LM = MN

Now, we are given that JK = MN.

Thus, by substitution, we can deduce that; KL = LM

Thus is because JK can be replaced with KL and MN can be replaced with LM.

Thus, it is proved that KL = LM

Answer the following questions based on this word problem:
The Beck family is planning on renting a car for their vacation. The two rental car companies have
different pricing plans.
Company A is $0.10 per mile and $25 a day.
Company B is $0.05 per mile and $40 a day.
Let x represent the number of miles and y represents the cost. They are only renting the van for 1 day.

Answers

Answer:

Step-by-step explanation:

A: $0.1(x) + 25(y) = x + 25

B: $0.05(x) + $40(y) = x + 40

Because they didn't give a certain amount of miles traveled, we have to go with we do know.

**this is probably wrong.

Andre is buying snacks for the track and field team. He buys a pound's of apricots for $6 per pound and b pounds of dried bananas for $4 per pound he buys a total of 5 pounds of apricots and dried bananas and spends a total of $24.50 Which system of equations represents the constraints in the situation?

Answers

Answer:

a + b = 5 ...........1

6a + 4b = 24.50 ......... 2

Step-by-step explanation:

Let a be the amount of pounds of apricot bought

Let b be the amount of pounds of banana bought

If he buys a total pounds of 5 pounds then;

a + b = 5 ...........1

Also if a pound's of apricots for $6 per pound, total amount of aprciots bought will be $6a

Also if b pound's of banana is for $4 per pound, total amount of banana bought will be $4b

If he spends a total of $24.50 on both banana and apricots, then:

6a + 4b = 24.50 ......... 2

The system of equations that represents the constraints in the situation is:

a + b = 5 ...........1

6a + 4b = 24.50 ......... 2

Answer: C

Step-by-step explanation:

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