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GalinKa [24]
3 years ago
10

Starting at home, Luis traveled uphill to the gift store for 50 minutes at just 6 mph. He then traveled back home along the same

path downhill at a speed of 12 mph.
What is his average speed for the entire trip from home to the gift store and back?
Mathematics
1 answer:
Orlov [11]3 years ago
8 0

Let S = his average speed.

Let D = distance traveled one way

Time = distance / speed

Set up an equation:

d/6 + d/12 = 2d/S

Multiply the equation by 12s:

12s(d/6) + 12s(d/12) = 12s(2d/s)

Simplify to get:

2sd + sd = 24d

Combine like terms:

3sd = 24d

Divide both sides by d:

3s = 24

Divide both sides by 3:

s = 24/3

s = 8

His average speed was 8 mph.

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Mr. Jackson filled up his 15-gallon gas tank for $37.50. What was the price 10
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Step-by-step explanation:

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Janeel has a 10-inch by 12-inch photograph. She wants to scan the photograph, then reduce the result
Vaselesa [24]

<u>Complete Question:</u>

Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the area of the image to be one eight of the original photograph. Write an equation to represent the area of the reduced image. Find the dimensions of the reduced image.

<u>Correct Answer:</u>

A) (10-x)(12-x)=15

B) Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

<u>Step-by-step explanation:</u>

a. Write an equation to represent the area of the reduced image.

Let the reduced dimensions is by x , So the new dimensions are

length=10-x\\breadth=12-x

According to question , Area of new image is :

⇒ Area = \frac{1}{8}Length(breadth)

⇒ Area = \frac{1}{8}(10)(12)

⇒ Area = 15

So the equation will be :

⇒ (10-x)(12-x)=15

b. Find the dimensions of the reduced image

Let's solve :  (10-x)(12-x)=15

⇒ 120-10x-12x+x^2=15

⇒ 120-22x+x^2=15

⇒ x^2-22x+105=0

By Quadratic formula :

⇒ x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}

⇒ x = \frac{22 \pm8 }{2}

⇒ x = \frac{22 +8 }{2} , x = \frac{22 -8 }{2}

⇒ x = 15 , x =7

x = 15 is rejected ! as 15 > 10 ! Side can't be negative

⇒ x =7

Therefore, Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

5 0
3 years ago
A store is having a 20% off sale on all merchandise. If Mai buys one item and saves 13$, what was the original sale price of her
Montano1993 [528]

Answer:

$65 is the original price

Step-by-step explanation:

65 x .8 = 52 which is 13 off

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3 years ago
Find the 58"" term of the following arithmetic sequence,<br> 18, 23, 28, 33,
Anna11 [10]

Answer:

303

Step-by-step explanation:

So the equation to find a term is An=a1+(n-1)d

An represents the value of the number (n)

and n is the selective that you want

d is the difference between the first and second term which is 23-18=5, and you can see that adding 5 to the previous term gives the following term.

a1 is the first term in the sequence

so knowing all that now you can go back and inset all variables into the equation

An=18+(58-1)5

An=303

Hope that helps :)

Please give brainliest

6 0
3 years ago
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