Jose drove to the mountains last weekend. There was heavy traffic on the way there, the trip took eight hours. When jose drove home, there was no traffic and the trip only took five hours. If his average rate was 21 mph faster on the trip home, how far away does jose live from the mountains

Answers

Answer 1

Answer:

The distance is 280 miles

Step-by-step explanation:

Given

When going to the mountain:

Let the speed be x.

[tex]Speed = x[/tex]

[tex]Time = 8[/tex]

When going home:

[tex]Speed = 21 + x[/tex]

[tex]Time = 5[/tex]

Required

Determine the distance of the mountains

Distance is calculated as:

[tex]Distance = Speed * Time[/tex]

When going to the mountains, the distance is:

[tex]Distance = x * 8[/tex]

When going home, the distance is:

[tex]Distance = (21 + x) * 5[/tex]

It should be noted that, the distance is the same.

So, we have:

[tex]x * 8 = (21 + x) * 5[/tex]

Open bracket

[tex]x * 8 = 21* 5 + x * 5[/tex]

[tex]8x = 105 + 5x[/tex]

Collect Like Terms

[tex]8x - 5x= 105[/tex]

[tex]3x= 105[/tex]

Divide both sides by 3

[tex]x= \frac{105}{3}[/tex]

[tex]x= 35[/tex]

Substitute 35 for x in

[tex]Distance = x * 8[/tex]

[tex]Distance = 35 * 8[/tex]

[tex]Distance = 280[/tex]

The distance is 280 miles


Related Questions

Bro I am so bad at math and I need help ;-;

Answers

Answer:

1. M > -7

2. y < -1

3. m < -12

4. k > -2

5. c > -9

Please let me know if you need me to explain these answers! :)

The absolute value of 7

−12

is ​

Answers

Answer:

7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Do you mean 7-12, or 7/(-12)?

7-12 = -5, so the absolute value of 7-12 is 5.

The absolute value of 7/(-12) is 7/12.

Josie bought a soda and 2 candy bars. The soda costs $1.10. Her total bill was $2.40. How much was each candy bar

Answers

Answer:

$0.65

Step-by-step explanation:

2.40-1.10=1.3

1.3/2=.65


The volume of a cube is 413cm3.
Work out the length of its side rounded to 1 DP.

Answers

Answer:

Write the full question please

The length of the side of the cube, rounded to 1 decimal place, is approximately 7.6 cm .

To find the length of the side of a cube given its volume, we need to find the cube root of the volume .

Given that the volume of the cube is 413 cm³, we can calculate the length of its side as follows:

side length = ∛( volume )

side length = ∛( 413 cm³)

side length ≈ 7.6 cm (rounded to 1 decimal place)

Therefore, the length of the side of the cube, rounded to 1 decimal place, is approximately 7.6 cm .

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If a triangle ABC is classified as a right triangle, which statement is true?

Answers

Answer:

Two slopes of triangle ABC are opposite reciprocals

Step-by-step explanation:

Hope This Helps!!!

Brainliest PLZ???

Answer:

Two slopes of triangle ABC are opposite reciprocals

Step-by-step explanation:

took the test

Please help this is the last problem I need

Answers

Answer:

[tex]sin 54 = \frac{x}{14}[/tex]

Step-by-step explanation:

[tex]sine = \frac{opposite}{hypotenuse}[/tex]

Side z is the adjacent, since it is next to the angle you are solving for.

Side x is the opposite, since it is opposite the angle you are solving for.

The side measuring 14 is the hypotenuse, since it is across from the right angle.

[tex]sin 54 = \frac{x}{14}[/tex]

I will give brainliest. Please help fast! (Solve for number 5)

Answers

Answer:

the area of the parallelogram is 120 units

Help me in number 10 please 6 points!!!!

Answers

Answer:

answer is 8.5

Step-by-step explanation:

What is the solution for xsquared= 64

A. Positive or r 4
B. 4
C. Positive or negative 8
D. 8

Answers

Answer:

64 rooted is D. 8

Graph y + 2 = -1(x + 3).

Answers

you should use desmos

Answer: y= -10x - 10

Step by step explanation: All you need to do is distrubute then solve for y and then graph, and that is all you need to do, you can do this on Desmos

Find the equation of the line specified.
The slope is -4, and it passes through (5,8).
a. y = 4x + 8
b. y = -4x + 28
c. y = -4x - 12
d. y = -8x + 28

Answers

Answer:

B) y=-4x+28

Step-by-step explanation:

y-y1=m(x-x1)

y-8=-4(x-5)

y=-4x+20+8

y=-4x+28

In this question use
1 cubic foot = 6.23 gallons
1 cubic foot = 0.028 cubic metres
Convert 3738 gallons into cubic metres.

Answers

Answer:

16.8 cubic metres

Step-by-step explanation:

Given: 1 cubic foot = 6.23 gallons

           1 cubic foot = 0.028 cubic metres

Let the conversion into cubic metres be represented by x.

Thus we can say that;

6.23 gallons = 0.028 cubic metres

and

3738 gallons = x cubic metres

So that,

x = [tex]\frac{3738*0.028}{6.23}[/tex]

   = 16.8

x = 16.8 cubic metres

The conversion of 3738 gallons into cubic metres is 16.8 cubic metres.

4+3 (x+2) simplify the expression

Answers

Answer:

4+3x+6

10+3x

this is the answer

Answer: 3x+10

Step-by-step explanation:

Distribute:

=4+(3)(x)+(3)(2)

=4+3x+6

Combine Like Terms:

=4+3x+6

=(3x)+(4+6)

=3x+10

4 times 12 divided by 16

Answers

Answer:

3

Step-by-step explanation:

4x12=48

48/16=3

=3

Answer:

the awnser is 60

Step-by-step explanation:

Two airplanes leave an airport at the same time on different runways. One flies on a bearing of N 66°W at 325 miles per hour. The other airplane flies on a bearing of S 26°W at 300 miles per hour. How far apart will the airplanes be after two hours

Answers

I think 861.2 miles

If correct, can you mark as brainliest?

After solving the equations, the distance between two airplanes after two hours will be equal to 861.21 miles.

What is Speed?

The speed of an entity, which is a scalar quantity in regular usage and kinematics, can be defined as the size of the change in direction per unit of time or the size of the change in position over time for an object. The initial speed is the upper limit of maximum pace as the duration of a time interval gets closer to zero.

Assume that both the planes are on similar point A at the start.

Assume that x is the 325 mph flying object.

Consequently, it would have traveled a distance of after two hours of 325 × 2 = 650 miles.

Let B represent the location of the plane two hours later.

That means AB = 650 miles

Assume that y is the 300 mph flying object.

It would have traveled a distance of two hours = 300×2=600 miles.

After two hours, let C represent the location of the second plane.

This means AC=600 miles

After two hours, BC separates the two aircraft.

So, the angle between their paths is 87°.

Cos A = (AC² + AB² - AC²)/(2(AC)(AB))

cos 87 = (600² - 650² - AC²)/(2 × 600 × 500)

40822.04 = 782500 - AC²

AC² = 782500 - 4082204

AC = 861.21 miles.

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y^2-y-42
pls helpppppp i dunno how to do this one??

Answers

(y-7)(y+6)
Hopefully this is right :)
(y-7) (y+6) is the correct answer for this question

Which number line shows the solution of -3x+6>12?

Answers

Answer:

when I solve the equation of -3×+6>12

-3×>12-6...........subtract 6 from both side

-3×>6................simplify

-3×/-3 <6/-3......when we divide or multiple by negative number the sign will be in opposite direction

×<-2 ...........× is solved

s.s( solution set ) ={x<-2 like -3,-4,-5 infinity }

Step-by-step explanation:

i hope it is help full

What is the scale factor?
please help!

Answers

Answers:

Scale factor = 5/3  (which is approximately equal to 1.67)x = 10

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

Work Shown:

To find the scale factor, we divide a side of triangle MNO over a corresponding side of triangle FGH. We can only pick the horizontal bottom sides since we don't know what x is yet.

scale factor = ON/HG = 15/9 = (5*3)/(3*3) = 5/3

In decimal form, this is approximately 5/3 = 1.67; however, I find it's better to stick with the fraction since it's exact.

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

Let's solve for x

One way to do so is to follow these steps

(FG)/(MN) = (HG)/(ON)

6/x = 9/15

6*15 = x*9 ..... cross multiply

90 = 9x

9x = 90

x = 90/9

x = 10

Or we could solve like this

(FG)/(HG) = (MN)/(ON)

6/9 = x/15

6*15 = 9x

90 = 9x

9x = 90

x = 90/9

x = 10

We end up with the same result because we got to 90 = 9x after cross multiplying, which was found in the previous set of steps as well. There are other ways to solve using a proportion. But they should all lead to x = 10.

Note how,

MN/FG = 10/6 = (5*2)/(3*2) = 5/3

which was the scale factor we found earlier

5/3 is going to be your answer.

what is the slope between point B and point C

Answers

4/3 because you count down then to the left

Answer: 4/3

Step-by-step explanation:

Slope is ratio of change in y with the change in x. From points C-->B, the change in y is 4. The change in x is 3. Therefore, the slope is 4/3

$12 per pizza how many pizzas can i get for $400

Answers

Answer:

$388

Step-by-step explanation:

subtract 400 and 12

(sorry if its wrong)

Need help
Value of n2(m+r)if m=3,n=2,r=4

Answers

Answer 28 because you plug it in for your answer.

please help asap((((:

Answers

Answer:

Angle 3 is 95, angle 1 is 30.

Step-by-step explanation:

I already answered a lot of your other angle questions so I will make this one QUICK...

Angle 4 is 85, so to find angle 3, simply subtract: 180 - 85 = 95

So angle 3 is 95

We know two out of the three angles in a triangle and they are: 95 and 55, so 95 + 55 = 150. The sum of the angles in a triangle is 180 so we have: 180-150 = 30, which is the answer for angle 1.

So angle 1 is 30

First to completly answer will be marked brainliest if you give a random answer just to get points you will be reported

Answers

Answer:

Pi: Irrational

2/9: Rational

225: Rational

0.167: Irrational  <--- fourth one

Step-by-step explanation:

Not sure about the 4th one, but the others are good :)

Solve for the roots in simplest form using the quadratic formula:
x2 – 14x = -33

Answers

Answer:

i think its x = 11 , 3

Step-by-step explanation:

which fraction is equivalent to -3/2?

3/-2
-(3/-2)
-3/-2
-(-3/2)​

Answers

The answer is 3/-2 hope that helps!

Answer the eqation
6h=-24

Answers

Answer:

h=-4

Step-by-step explanation:

6 times -4 is -24

helloo

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

Answer:

-4

Step-by-step explanation:

6h= -24

h = -24/6

h = -4

hope this helps

please mark it as a brainiest

In the figure, BC is a support for the roof
of a garage. What is the length of BC?

Answers

Answer:

Bc = √63 ft

Step-by-step explanation:

Here, we want to get the length of BC

As we can see, there is a right angled triangle ABC, with 12ft being the hypotenuse and 9 ft the other side

So we want to get the third leg which is BC

we can use the Pythagoras’ theorem here

And that states that the square of the hypotenuse equals the sum of the squares of the two other sides

let the missing length be x

12^2 = x^2 + 9^2

144 = x^2 + 81

x^2 = 144-81

x^2 = 63

x = √63 ft

What does -2 - 10 equal to?​

Answers

8. Because when you add or subtract a negative it’s always the other way around.

If you wanted to figure
out how much air is in
a basketball, would
you use plane
geometry or solid
geometry?

Answers

Answer:

solid gemontery

Step-by-step explanation: Plane geomentry is flat and soild is balls sqaures and other types of shapes.  

I need help with math trigonometry and law of sines

Answers

Answer:

Step-by-step explanation:

sinx/6=sin90/19

sinx=6sin90/19

x=arcsin(6sin90/19

x=18 degrees

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