Brayden and his friends are driving across the US from New York to Los Angeles at a constant speed without stopping. When they have driven for 10 hours, they are 1700 miles away from Los Angeles. When they have driven for 15 hours, they are 1500 miles away from Los Angeles.a) Find a linear function that models the remaining distance, DD, to Los Angeles as a function of the amount of time, t, that Brayden and his friends have been driving.

Answers

Answer 1

Answer:

d=-40t+2100

Step-by-step explanation:

Let d be the distance between New York to Los Angeles and speed of driving is v miles/hour.

As when they have driven for 10 hours, they are 1700 miles away from Los Angeles, so the distance covered in 10 hours is d-1700 miles.

Similarly, the distance covered in 15 hours is d-1500 miles.

So, the distance covered in 5 hours = (d-1500)-(d-1700) =d-1500-d+1700=200 miles.

As speed = distance/time,

So the speed of driving, v=200/5=40 miles/hour

Let d (in miles) be the remaining distance at any time instant t (in hour) and the linear relation between d and t is

d=at+b ...(i)

where a and b are constants.

When they have driven for 10 hours, they are 1700 miles away from Los Angeles, so putting t=10 and d=1700 in the equation (i), we have

1700=10a+b

b=1700-10a...(ii)

Similarly, when they have driven for 15 hours, they are 1500 miles away from Los Angeles, so

1500=15a+b

1500=15a+1700-10a

1500-1700=5a

-200=5a

a= -200/5

a= -40

From equation (ii), we have

b=1700-10(-40)=1700+400=2100

From equation (i), the required equation is

d=-40t+2100

Hence the required linear function is d=-40t+2100.


Related Questions

HELPPPPPP!!!!!!!!!!!!!

Answers

Answer:

Statement F is true

Step-by-step explanation:

Let x represent number of yoga classes

Let y represent total cost

Let m represent the additional fee per yoga class

Let b represent the membership fee

y=mx+b

Notice that after every 2 classes, the price goes up by 7.5 so m=7.5/2

m=3.75

Thus the first statement is true

Note you can also find the membership fee if you plug this in with some points

y=mx+b

67.5=3.75(6)+b

b=45 so membership fee is $45

How many meters are in 100 millimeters? 1
10
0.1
100​

Answers

Answer:

0.1

Step-by-step explanation:

divide the length value by 1000

To make lemonade, Brandon mixes 9 cups of water with 2 cans of frozen lemonade concentrate.

Answers

Answer:

Step-by-step explanation:

Y la pregunta?

Blake drives 448 miles on 16 gallons. How many miles does Blake drive on one gallon?

Answers

28 miles! Just devide em hope it helped! Pls brainest

Answer:

28

Step-by-step explanation:

i just divided 448 and 16 and got that, om on that same question

here is how to divide that so you know on  your own

Step 1:

Start by setting it up with the divisor 16 on the left side and the dividend 448 on the right side like this:

           

 1 6 ⟌ 4 4 8

Step 2:

The divisor (16) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:

       0    

 1 6 ⟌ 4 4 8

Step 3:

Multiply the divisor by the result in the previous step (16 x 0 = 0) and write that answer below the dividend.

       0    

 1 6 ⟌ 4 4 8

      0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.

       0    

 1 6 ⟌ 4 4 8

     - 0    

       4    

Step 5:

Move down the 2nd digit of the dividend (4) like this:

       0    

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

Step 6:

The divisor (16) goes into the bottom number (44), 2 time(s). Therefore, put 2 on top:

       0 2  

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

Step 7:

Multiply the divisor by the result in the previous step (16 x 2 = 32) and write that answer at the bottom:

       0 2  

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

       3 2  

Step 8:

Subtract the result in the previous step from the number written above it. (44 - 32 = 12) and write the answer at the bottom.

       0 2  

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2  

Step 9:

Move down the last digit of the dividend (8) like this:

       0 2  

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2 8

Step 10:

The divisor (16) goes into the bottom number (128), 8 time(s). Therefore put 8 on top:

       0 2 8

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2 8

Step 11:

Multiply the divisor by the result in the previous step (16 x 8 = 128) and write the answer at the bottom:

       0 2 8

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2 8

       1 2 8

Step 12:

Subtract the result in the previous step from the number written above it. (128 - 128 = 0) and write the answer at the bottom.

       0 2 8

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2 8

     - 1 2 8

           0

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 448 divided by 16 calculated using Long Division is:

28

0 Remaind

3. Last year 858 people attended the Middleton County Fair. This year 1,635 people attended. What was the percent increase from last year to this year? (Round to the nearest percent)

A.90%

B.91%

C.47%

D.48%

Answers

Answer: 47?

Step-by-step explanation:

Heather drives 130 miles in 2 hours. If she travels the same distance each hour, how many miles does she drive per hour?​

Answers

Answer:

she drive 65 miles Per hour

Answer:

if she drive for two more hours that means she drove 4 hours and plus 130 plus 130 and that will equal 260. so the answeris 260.

Step-by-step explanation:

8. Iris wants to buy two necklaces, one for her sister and one for herself. The necklace for her sister costs $42.00, and the necklace for herself costs $28.00. The sales tax on the purchases is 8%. Find the total cost of Iris's purchases, including sales tax. If necessary, round your answer to the nearest cent. C $75.60 A $64.40 B $5.60 B D $70.00​

Answers

the answer is C!
Hope this helps

Solve for x 1000 = 500e^2x
Can someone help me please

Answers

Answer: A

Step-by-step explanation:

1000 = 500e^(2x)

2 = e^(2x)

ln2 = 2x

Step-by-step explanation:

1000 = 500e^(2x)

2 = e^(2x)

ln2 = 2x

x = ln2 / 2. (A)

2/3y + 1/6y =

Please help me, I am unsure about this one. I just need a grasp on where to start.

Answers

The answer is 5/6y when you add both together
You can double 2/3 since the common denominator for 2/3 and 1/6 is 6 and you have 4/6y+1/6y which equals 5/6y

A June 2009 Harris Interactive poll asked people their opinions about the influence of advertising on the products they buy. Among the people aged 18 to 34 years, 45% view advertisements as being influential, whereas among the people aged 35 to 44 years, 37% view advertisements as being influential. Suppose that this survey included 655 people in the 18- to 34-year age group and 420 in the 35- to 44- year age group. At the 1% significance level, can you conclude that the proportion of all people aged 18 to 34 years who view advertisements as being influential in their purchases is greater than the proportion of all people aged 35 to 44 years who hold the same opinion

Answers

Answer:

We accept with 99 % of confidence that p₁ ( the proportion in the group aged 18 - 34 ) is bigger than p₂ (the proportion in the group aged 35-44)

Step-by-step explanation:

Group aged  18 - 34

Sample size n₁  =  655  sample size enough to apply a normal distribution aproximation for the test

p₁ = 0,45      and   q₁ =  1 - p₁      q₁ = 0,55

p₁*n₁  =  0,45*655 = 294     q₁*n₁  = 0,55*655 = 360

both bigger than 5

p₁  = 45 %     or     p₁  = 0,45          then  q₁  = 1 - 0,45    q₁ = 0,55

Group aged 35 - 44

Sample size  n₂  =  420 sample size enough to apply a normal distribution aproximation for the test

p₂  =  37%   p₂ = 0,37     and    q₂  = 0,63

p₂*n₂  =  0, 37*420 =  155     q₁*n₁  = 0,63*420 = 264

Test Hypothesis

Null Hypothesis        H₀                                             p₁  =  p₂

Alternative Hypothesis Hₐ                                        p₁  >  p₂

Significance level    α  =  1%   α  = 0,01

Confidence Interval     CI = 99 %

Then   from z table  we find   critical z   z (c )  = 3,1

Calculating   z(s)

z(s)  =  (  p₁ - p₂ )/ √[ ( p₁*q₁)/n₁ ] + [ (p₂*q₂)/n₂ ]

z(s ) = (0,45 - 0,37 ) /  √ 0,45*0,55)/655  +  0,37*0,63 /420

z(s)  = 0,08  /0,03

z(s) = 2,66

Comparing  z(s)  and z(c)

z(s) < z(c)

Then z (s) is inside the acceptance region for H₀


I need help with this question can anyone help ?

Answers

Answer:

m < 1 = 72

Step-by-step explanation:

Since we know that line l and line m are parallel and that p is one of their transversals, it sets up a situation where we can identify which angles are congruent (equal) to one another according to their positions.

In this case, we can see that < 3 and < 1 are in the same matching corners created by the transversal. When angles are in the same matching corners they are called corresponding angles - and according to the Corresponding Angles Postulate, corresponding angles are congruent.

Therefore, m < 3 = m < 1, and since it's given that  m < 3 = 72, we know that m < 1 = 72 too.

30 points On a certain hole, a golfer knows that he has a 70% chance of reaching the green (putting surface) in one stroke, 20% in two strokes, 8% in three, and 2% in four or more. If he reaches the green on his first stroke, he has an 80% chance of putting the golf ball in the cup on his second stroke. If he does not reach the green on his first stroke, then he has a 30% chance of putting the golf ball in the cup on his second stroke. What is the probability that the golfer will reach the green in one stroke and put the ball in the cup on his second stroke?

0.09
0.21
0.56
0.80

Answers

0.56 i might be wrong tho

Answer:

.56

Step-by-step explanation:

find the inverse with respect to addition of -6​

Answers

Given:

The number is -6.

To find:

The inverse with respect to addition of the given number.

Solution:

We need to find the additive inverse of -6, to get the inverse with respect to addition of -6.

We know that, the sum of a number and its additive inverse is 0.

Let the additive inverse of -6 be x. Then,

[tex]-6+x=0[/tex]

Adding 6 on both sides, we get

[tex]-6+x+6=0+6[/tex]

[tex]x=6[/tex]

Therefore, the inverse with respect to addition of -6 is 6.

Ashley has sold 20% of candy bars she is supposed to sell for her softball team. How many candy bars does she have left to sell???

Answers

Answer:

Step-by-step explanation:

She has 80% of the total amount she had before she sold any. Can't solve any further for you, unless you provide me the number sold or the amount she had before she sold them.

Answer:

no

Step-by-step explanation:

(8m-2)(3m+7)
Multiply

Answers

Answer:

24m^2+50m-14

Step-by-step explanation:

how to find x of the (x+95) and (4x-10)

Answers

Answer:

x=35

Step-by-step explanation:

x+95=4x-10

Subtract x on both sides

95=3x-10

Add x on both sides

105 = 3x

x=35

Hope this helps plz hit the crown :D

Answer:

x = 35

Step-by-step explanation:

(x + 95) = (4x - 10)             get rid of the parentheses

x + 95 = 4x - 10                 put the x's together and put your constants together

105 = 3x                            divide 3 from both sides

35 = x

Hope this helps

Evaluate.
0^2=
I do not get this way toooooooo hard

Answers

Answer:

zero

Step-by-step explanation:

Answer:The answer is 0

Step-by-step explanation: Sorry i didn't explain it.

Aleena expands 2xx+3-5(x-2) as 2x2+3-5x-10. Has she expanded it correctly? Please identify the mistakes and write the correct way in which 2xx+3-5(x-2) should be expanded.

Answers

The given expression is :

2xx+3-5(x-2)

We know that, [tex]x{\cdot}x=x^2[/tex]

[tex]=2x^2+3-5(x-2)\\\\=2x^2+3+(-5)(x)+(-5)(-2)\\\\=2x^2+3-5x+10[/tex]

Aleena expands 2xx+3-5(x-2) as 2x²+3-5x-10. She is mistaken because the sign before 10 should be +10 instead of -10. Hence, the correct expanded form is 2x²+3-5x+10. Hence, this is the required solution.

The width of a box is two-third of it's length and height is one-third of it's length.If the volume of the box is 384 cubic meter,find the dimensions of the box.​

Answers

Answer:

Length = 12

Width = 8

Height = 4

Step-by-step explanation:

Let length of box = l

Width = 2/3 * l

Height = 1/3 * l

Volume of the box = 384 ft³

Volume = Length * width * height

Volume of box = l * 2/3 l * 1/3 l

384 = 2l³ / 9

384 * 9 = 2l³

3456 = 2l³

l³ = 3456 / 2

l³ = 1728

Take the Cube root of 1728

l = 12

Length = 12

Width = 2/3 * 12 = 8

Height = 1/3 * 12 = 4

Solve for x and y. (5x+2) y 6x

Answers

Answer:

x=8

y=138

Step-by-step explanation:

5x+2+6x=90

11x+2=90

11x=88

x=8

y+5x+2=180

y+40+2=180

y+42=180

y= 138

Is the function f(x) = 3(.96)x an exponential growth or exponential
decay function? Why?

Answers

Answer:

exponential decay

Step-by-step explanation:

anything less than 1 in the parenthesis is decay

In a right triangle, the tangent of angle A is 9/12 and the cosine of angle a is 12/15 based on these values what is the sine of angle a

a. 9/15
b 15/16
c 1, 1/15
d 1. 11/20

Answers

Answer:

option A 9/15

im srry i suck at math

Could someone help me with these problems ?

Answers

Answer:

Step-by-step explanation:

1. is 10

4. is 6

6. is $3.19

7. is $6

Answer asap please it will be much appreciated

Answers

Answer:

9 cm.

Step-by-step explanation:

First, let's form an equation. We'll represent the final depth of snow on Cherry Street with the variable d. We'll represent the hours with the variable h.

10 - 1/3h = d

Now, you already know what h equals so you can replace h with 3 for 3 hours.

10 - 1/3(3) = d

1/3 * 3 = 1.

10 - 1 = d

10 - 1 = 9

Now, we know what d equals.

10 - 1/3(3) = 9.

Do NOT forget the unit of measurement in your final answer, cm. In the photo, it looks as though it has already been provided.

The final answer is 9 cm.

Evaluate -3x^3 - 4x for x=-1.

Answers

Answer:

-x.(3x^2+4)

Step-by-step explanation:

Brain-list?

Answer:

-3(-1)^3-4(-1)= 27+4=31

Step-by-step explanation:-3 and -1 when you multiply both minus will change into plus. same for -4 and -1 when you multiply will change the signs. so you will get 27+4=31

Really need help !!!!!!!!

Answers

With what? You didn’t put a picture lol

A scientist add drops of liquid to a test tube. Each drop contains o.14mL. After 6 drops how much liquid has the scientist added?​

Answers

Answer:

We conclude that after 6 drops how much liquid the scientist has added 0.84 mL.

Step-by-step explanation:

Given that the scientist adds drops of liquid to a test tube.

The amount of liquid in 1 drop = 0.14 mL

In order to determine the amount of liquid after 6 drops, all we need is to multiply 0.14 mL by 6.

i.e.

The amount of liquid in 6 drops = 0.14 × 6

                                                     = 0.84 mL

Therefore, we conclude that after 6 drops how much liquid the scientist has added 0.84 mL.

5x = 1/125
What is X

Answers

Answer:

x= 1/25

Step-by-step explanation:

Can some on check over my work pls

Answers

Not exactly correct.

y=mx+b Slope is m and y intercept is b.

So, here count the units for the slope. it goes barley to the 7th box. Now, count the units for the y intercept. It goes to the fourth box.

Thus, your equation is y=7x+4

[tex]\underline{Hope\;it\;helps\;out!}[/tex]

Twice a number is 42 less then five times a number. What is the number? Define a variable, write an equation, and then solve.

Answers

Answer:

Given - Twice a no. is 42 less than 5 times a no.

To find - The no.

Solution -

Let the no. be X

According to the question the equation made is -

2x = 5x - 42

2x - 5x = (-42)

(-3x) = (-42)

x= (-42)/(-3)

x = 14

The no. is 14

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