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1 year ago

8

Samantha and Matt are each saving for new bikes. So far, Samantha has saved $15 and can earn $2 per hour for babysitting. Matt h

as saved $3 and can earn $4 per hour working at his family's restaurant. After how many hours of work will Samantha and Matt have earned the same amount?

1 answer:

Sophie [7]1 year ago

7 0

Answer:

6 hours

Step-by-step explanation:

<u>We know that:</u>

Samantha = 15 + 2x
Matt = 3 + 4x
Samantha = Matt
[x = Number of hours]

<u>Solution:</u>

15 + 2x = 3 + 4x
=> 15 - 3 = -2x + 4x
=> 12 = 2x
=> x = 6

Hence, after 6 hours of work, Samantha and Matt will have the same amount.

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Answer:

<h3> -2a³ + 9a² + 6ab² + 45a + 18b² </h3>

Step-by-step explanation:

(a + 3)×(−2a² + 15a + 6b²) =

= a×(−2a² + 15a + 6b²) + 3×(−2a² + 15a + 6b²) =

= -2a³ + <u>15a²</u> + 6ab² - <u>6a²</u> + 45a + 18b² =

= -2a³ + 9a² + 6ab² + 45a + 18b²

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I'm not entirely sure what the question was to begin with, but I hope this answers it!

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2 years ago

Help!! Solving absolute value inequalities

goblinko [34]

Answer:

48. $x \geq -7$ or $x \leq 31$

51. $x \leq 13$ or $x \geq 3$

54. $x < \frac{5}{2}$ or $x > \frac{-15}{2}$

57. $x < \frac{18}{7}$ or $x > -4$

Step-by-step explanation:

48. $| 12 - x | \leq 19$

-There are two equations:

Equation 1:

$12 - x \leq 19$

or

Equation 2:

$12 - x \geq -19$

Solving equation 1:

$12 - x \leq 19$

$12- 12 - x \leq 19 - 12$

$-x \leq 7$

$\frac{-x}{-1} \leq \frac{7}{-1}$

$x \geq -7$ (Inequality sign changed, because of dividing by a negative number)

-Solving equation 2:

$12 - x \geq -19$

$12 - 12 - x \geq -19 - 12$

$-x \geq -31$

$\frac{-x}{-1} \geq \frac{-31}{-1}$

$x \leq 31$ (Inequality sign changed, because of dividing by a negative number)

-Answers:

$x \geq -7$ or $x \leq 31$

51. $| x - 8 | \leq 5$

-There are two equations:

Equation 1:

$x - 8 \leq 5$

or

Equation 2:

$x - 8 \geq - 5$

-Solving equation 1:

$x - 8 \leq 5$

$x - 8 + 8 \leq 5 + 8$

$x \leq 13$

-Solving equation 2:

$x - 8 \geq - 5$

$x - 8 + 8 \geq - 5 + 8$

$x \geq 3$

Answers:

$x \leq 13$ or $x \geq 3$

54. $| 4x + 10 | < 20$

-There are two equations:

Equation 1:

$4x + 10 < 20$

or

Equation 2:

$4x + 10 > -20$

-Solving equation 1:

$4x + 10 < 20$

$4x + 10 - 10 < 20 - 10$

$4x < 10$

$\frac{4x}{4} < \frac{10}{4}$

$x < \frac{5}{2}$

-Solving equation 2:

$4x + 10 > -20$

$4x + 10 - 10 > -20 - 10$

$4x > -30$

$\frac{4x}{4} > \frac{-30}{4}$

$x > \frac{-15}{2}$

-Answers:

$x < \frac{5}{2}$ or $x > \frac{-15}{2}$

57. $| 7x + 5 | < 23$

-There are two equations:

Equation 1:

$7x + 5 < 23$

or

Equation 2:

$7x + 5 > -23$

-Solving equation 1:

$7x + 5 < 23$

$7x + 5 - 5 < 23 - 5$

$7x < 18$

$\frac{7x}{7} < \frac{18}{7}$

$x < \frac{18}{7}$

Solving equation 2:

$7x + 5 > -23$

$7x + 5 - 5 > -23 - 5$

$7x > -28$

$\frac{7x}{7} > \frac{-28}{7}$

$x > -4$

Answers:

$x < \frac{18}{7}$ or $x > -4$

And we are finished.

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