The longer leg of a right triangle is 17 cm longer than the length of the shorter leg x. The hypotenuse is 25 cm.

Solving systems of Equations Word Problems - CLASSWORK

dem82 [27]

Answer:

Part A) For the number of hours less than 5 hours it make more sense to rent a scooter from Rosie's

Part B) For the number of hours greater than 5 hours it make more sense to rent a scooter from Sam's

Part C) Yes, for the number of hours equal to 5 the cost of Sam'scooters is equal to the cost of Rosie's scooters

Part D) The cost is $90

Step-by-step explanation:

Let

x-------> the number of hours (independent variable)

y-----> the total cost of rent scooters (dependent variable)

we know that

Sam's scooters

$y=8x+30$

Rosie's scooters

$y=10x+20$

using a graphing tool

see the attached figure

A. when does it make more sense to rent a scooter from Rosie's? How do you know?

For the number of hours less than 5 hours it make more sense to rent a scooter from Rosie's (see the attached figure) because the cost in less than Sam' scooters

B. when does it make more sense to rent a scooter from Sam's? How do you know?

For the number of hours greater than 5 hours it make more sense to rent a scooter from Sam's (see the attached figure) because the cost in less than Rosie' scooters

C. Is there ever a time where it wouldn't matter which store to choose?

Yes, for the number of hours equal to 5 the cost of Sam'scooters is equal to the cost of Rosie's scooters. The cost is $70 (see the graph)

D. If you were renting a scooter from Rosie's, how much would you pay if you were planning on renting for 7 hours?

Rosie's scooters

$y=10x+20$

For x=7 hours

substitute

$y=10(7)+20=90$

The cost is $90

4 0

3 years ago

The sum of two numbers is equal to 63, and their difference is equal to 12. Find the numbers

Ainat [17]

Answer:

25.5 and 37.5

Step-by-step explanation:

x+y=63

x-y = 12 then x = 12 + y sub this into the first equation

(12+y) + y = 63

12 + 2y = 63

2y = 51

y = 25.5 then x = 37.5

6 0

2 years ago

Find the extreme values of f(x y)=xy subject to the constraint x^2 + y^2 -4 = 0

KATRIN_1 [288]

Via Lagrange multipliers:

$L(x,y,\lambda)=xy+\lambda(x^2+y^2-4)$

$L_x=y+2\lambda x=0$
$L_y=x+2\lambda y=0$
$L_\lambda=x^2+y^2-4=0$

$yL_x=y^2+2\lambda xy=0$
$xL_y=x^2+2\lambda xy=0$
$\implies yL_x-xL_y=y^2-x^2=0\implies y^2=x^2$
$\implies x^2+y^2=4=2x^2\implies x^2=2\implies x=\pm\sqrt2\implies y=\pm\sqrt2$

So we have four critical points to consider, $(\sqrt2,\sqrt2),(-\sqrt2,\sqrt2),(\sqrt2,-\sqrt2),(-\sqrt2,-\sqrt2)$ . If both coordinates are positive or both are negative, we get a maximum value of $(\pm\sqrt2)^2=2$ ; otherwise, we get a minimum of $(-\sqrt2)(\sqrt2)=-2$ .

4 0

3 years ago

Evaluate (6.1 x 10-3) (8 x 109). Write your answer in scientific notation and standard form.

DerKrebs [107]

Answer:

Scientific Notation: 4.88 ×10^7

Standard Form: 4.88 ×10^7

Step-by-step explanation:

6.1×10^(-3) = 0.0061

8×10^9 = 8000000000

0.0061×8000000000 = 48800000

$= 4.88 \times {10}^{7}$

3 0

3 years ago

Can anyone help me with this question please ? <br> I’ll mark you as a brainliest

DanielleElmas [232]

B is the answer i beleive

4 0

3 years ago