Annie lives 12 miles directly south of her school. The grocery store is 5 miles east of Annie's house. Annie needs to stop by the grocery store before driving down the road that connects the store to her school. How far does Annie drive to get to school?

18 miles.

Step-by-step explanation:

We can think on this as a triangle rectangle, where one cathetus is 12miles, and the other cathetus is 5 miles. (so the vertex of the triangle rectangle are Annie's house, the school, and the store)

The path that Annie would do is:

From her house to the store (so she drives 5 miles)

And from the store to the school, so here she drives through the hypotenuse of the triangle rectangle.

Then we need to find the length of this triangle rectangle.

We know that the square of the hypotenuse is equal to the sum of the squares of the cathetus, then:

H^2 = (12mi)^2 + (5mi)^2

H = √( (12mi)^2 + (5mi)^2) = 13mi

Then she first drives 5 miles from her house to the store, and then drives 13 miles from the store to the school, then the total distance that she drives is:

5 miles + 13 miles = 18 miles.

company a

step-by-step explanation:

using the linear regression models , it is found that company a   pays about $14 more. but using the same regression (linear) company b pays about $10 more.

so company a pays more than b

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb