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3 years ago

Solve for r and t: 6r - 3t = 6 6r + 8t = -16

2 answers:

4 0

6r - 3t = 6 /*8
6r + 8t = - 16 /*3

48r - 24t = 48
48r + 24t = - 48
---------------------- +
96r = 0
r = 0

t = ( -16 + 6r)/8 = - 16/8 = - 2

Slav-nsk [51]3 years ago

3 0

6r - 3t = 6 /*8
6r + 8t = - 16 /*3

48r - 24t = 48
48r + 24t = - 48
---------------------- +
96r = 0
r = 0

t = ( -16 + 6r)/8 = - 16/8 = - 2

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Isaac shoveled 9 of his neighbors' driveways after a snow storm. He charged $25 for a short driveway and $45 for a long driveway

e-lub [12.9K]

Answer:

y($) = 405- 20x

Step-by-step explanation:

Number of short driveways = x

Number of long driveways = 9-x

Fee per long driveway = $45

Fee per short driveway= $25

Total amount = y

y ($) = 25x + 45 (9-x)

= 25x + 405 -45x

= 405- 20x

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3 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

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$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

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3 years ago

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3 years ago

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Anna11 [10]

Answer:

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Step-by-step explanation:

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3 years ago

(4x2 - 10x -24) (2x + 3)

jeyben [28]

Answer:

Apply BODMAS

Step-by-step explanation:

PLEASE FIND THE PICTURE BELLOW

SOLUTION STEPS

(4⋅2−10x−24)(2x+3)

Multiply 4 and 2 to get 8.

(8−10x−24)(2x+3)

Subtract 24 from 8 to get −16.

(−16−10x)(2x+3)

Apply the distributive property by multiplying each term of −16−10x by each term of 2x+3.

−32x−48−20x

−30x

Combine −32x and −30x to get −62x.

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2 years ago