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3 years ago

7w + 6 + 2w = (w + 2)

Mathematics

1 answer:

Sindrei [870]3 years ago

4 0

Hey there!

The correct answer is $w = \frac{-1}{2}$

$7w + 6 + 2w = w + 2$ ~ Write the equation

$9w + 6 = w + 2$ ~ Simplify

$8w + 6 = 2$ ~ Subtract $w$ from both sides

$8w = -4$ ~ Subtract $6$ from both sides

$w = \frac{-1}{2}$ ~ Divide both sides by 8

Hope it helps and have a great day!

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2 years ago

Today joelle walked at a rate of 3 miles per hour and she ran 15 minutes at a rate of 6 miles per hour.How many total miles did

svetoff [14.1K]

I added a screenshot with the complete question

Answer:
Total miles = 2.5 miles

Explanation:
1- While walking:
We are given that Joelle walked 20 minutes at a rate of 3 miles per hour.
This means that she walked $\frac{20}{60} = \frac{1}{3}$ of an hour at a rate of 3 miles per hour
The formula that relates distance, time and velocity is:
Distance = velocity * time
Substitute with the givens to get the distance she covered while walking:
Distance = 3 * $\frac{1}{3}$ = 1 mile

2- While running:
We are given that Joelle ran 15 minutes at a rate of 6 miles per hour
This means that she ran $\frac{15}{60} = \frac{1}{4}$ of an hour at a rate of 6 miles per hour
The formula that relates distance, time and velocity is:
Distance = velocity * time
Substitute with the givens to get the distance she covered while running:
Distance = 6 * $\frac{1}{4}$ = 1.5 miles

3- getting the total mileage:
Total distance she covered = distance while walking + distance while running
Total distance she covered = 1 + 1.5
Total distance she covered = 2.5 miles

Hope this helps :)

4 0

3 years ago

Type the correct answer in each box

Luba_88 [7]

Answer:

We know that the equation of the circle in standard form is equal to (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius of the circle.

We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :

1 - We first group terms with the same variable :

(x²+8x) + (y²+22y) + 37 = 0

2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)

(x²+8x) + (y²+22y) = - 37

3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process "completing the square".

x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²

y²+22y = (y²+22y+11²)-11² = (y+11)²-11²

4 - We plug the new values inside our equation :

(x+4)² - 4² + (y+22)² - 11² = -37

(x+4)² + (y+22)² = -37+4²+11²

(x+4)²+(y+22)² = 100

5 - We re-write in standard form :

(x-(-4)²)² + (y - (-22))² = 10²

And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)

5 0

3 years ago