$7x +8y = 25 ~~~....(i)\\\\9x +10y = 35~~~ ....(ii)\\\\\text{Multiply equation (ii) by}~ \dfrac 79 ~ \text{and do (ii) - (i):}\\\\\dfrac 79 (9x +10y) - (7x +8y) = \dfrac 79 (35) - 25\\\\\\\implies 7x +\dfrac{70y}9 - 7x -8y = \dfrac{245}9 -25\\\\\\\implies - \dfrac{2y}9 = \dfrac{20}9\\\\\\\implies -2y =20\\\\\implies y =-10\\\\\text{Substitute}~ y = -10~ \text{in equation (i):}\\\\\\7x +8(-10) = 25\\\\\implies 7x = 25 +80\\\\\implies 7x = 105 \\\\\implies x =15\\\\$

$\\\text{Hence}~ (x,y) = (15,-10)$

3 0

2 years ago

Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

nydimaria [60]

Answer: For 10 sessions, the cost of the two plans the same.

Step-by-step explanation:

Let x= Number of sessions.

Given: Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

Total charge for x sessions = 50+30x

Nicole's fitness center charges a yearly fee of $250 plus $10 for each session with a trainer.

Total charge for x sessions = 250+10x

When both plan charges the same, then

$50+30x=250+10x\\\\\Rightarrow\ 30x-10x=250-50\\\\\Rightarrow\ 20x=200\\\\\Rightarrow\ x=10$

i.e. For 10 sessions, the cost of the two plans the same.

3 0

3 years ago

Determine the x-intercept for 3x + 2y = 14.

spin [16.1K]

First isolate y

3x + 2y = 14

-3x -3x

2y = -3x + 14

y = -3/2x + 14/2

y = -3/2x + 7

X-intercept is found when y = 0

0 = -3/2x + 7

-7 = -3/2x

x = 14/3

x-in. = (14/3,0)

3 0

3 years ago

Pls answer this question with complete answers thank u❤️❤️❤️

MAVERICK [17]

Yes Clare should switch because $96 + 12% is $107.52 but if she get the other one, it would be $105 in one year because $8.75 x 12 is $105

5 0

2 years ago

Read 2 more answers

What is the area of the pentagon shown? 16 cm 15 cm 18 cm 20 cm 360 cm2 354 cm2 300 cm2 297 cm2​

What is the area of the pentagon shown? 16 cm 15 cm 18 cm 20 cm 360 cm2 354 cm2 300 cm2 297 cm2