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2 years ago

13

One side of a rectangle is 10 feet shorter than twice another side. Find the length of the shorter side if we also know the peri

meter of the rectangle is 28 feet.

1 answer:

seropon [69]2 years ago

8 0

Answer:

6 feet

Step-by-step explanation:

Let x represent the length of "another side." Then "one side" is ...

2x -10 . . . . . . 10 feet shorter than twice another side

The sum of these two side lengths is half the perimeter, so is ...

x + (2x -10) = 14 . . . . . two sides are half the perimeter

3x = 24 . . . . . . . . . . . . add 10, collect terms

x = 8 . . . . . . . . . . . . . . .divide by the coefficient of x

(2x -10) = 2·8 -10 = 6 . . . . find "one side"

We have found "one side" to be 6 feet long, and "another side" to be 8 feet long. The shorter side is 6 feet.

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SVETLANKA909090 [29]

Answer:

B-$100=$372

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$372 - $100= b

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MARNIE OUT!

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3 years ago

Smallville High School scored more than 30 points in their last football game entirely from safeties and field goals. (In

Reika [66]

Inequalities help us to compare two unequal expressions. The inequality for this scenario in standard form is 2x + 3y > 30.

<h3>What are inequalities?</h3>

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Let the safety counts be represented by x, while the field goal count is represented by y.

Part A: The inequality for this scenario in standard form.

2x + 3y > 30

Part B: The inequality in slope-intercept form.

2x + 3y > 30

3y > 30 - 2x

y > 10 - (2/3)x

y < (2/3)x - 10

PartC: The inequality is represented below.

Learn more about Inequality:

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7 0

1 year ago

Tanya took a cab from her home to the airport. Her total fare including a tip of $5.00, was $28.50. EZ Cab Company has a pick-up

ValentinkaMS [17]

16.2 miles.

Since she paid a $5 tip, the cost for her fare was $23.50. Let x be the number of 0.2-mile increments in the trip:
23.50 = 2.50 + 1 + 0.25(x-1)

This equation comes from the 2.50 home pick-up fee; $1 for the first 0.2-mile increment; and 0.25 for each other 0.2-mile increment.

Using the distributive property, we have:
23.50 = 2.50 + 1 + 0.25*x - 0.25*1
23.50 = 2.50 + 1 + 0.25x - 0.25

Combining like terms,
23.50 = 0.25x + 2.75

Subtracting 2.75 from both sides, we have:
23.50 - 2.75 = 0.25x + 2.75 - 2.75
20.25 = 0.25x

Dividing both sides by 0.25, we have:
20.25/0.25 = 0.25x/0.25
81 = x

This means there are 81 0.2-mile increments in her trip. 81(0.2) = 16.2 miles

6 0

3 years ago

Lee filled up his gas tank before starting a road trip. If he has used 5.8 gallons two hours into the trip, and has 12.4 gallons

KATRIN_1 [288]

He started out with 19.1 gallons because if you add 5.8 and 12.4 you get 19.1

3 0

3 years ago

LOTS OF POINTS <br> Simplify the expression by factoring, showing the steps in your work

julia-pushkina [17]

Answer:

$\frac{3x+7}{4x+1}$

Step-by-step explanation:

$\frac{12x^2+31x+7}{16x^2+8x+1}$

First you factor $12x^2+31x+7$ :

$=\left(12x^2+3x\right)+\left(28x+7\right)$

Then you factor out $3x$ from $12x^2+3x$ :

$12x^2+3x$

$=12xx+3x$

$=3\cdot \:4xx+3x$

$=3x\left(4x+1\right)$

Then you factor out 7 from $28x+7$ :

$28x+7$

$=7\cdot \:4x+7$

$=7\left(4x+1\right)$

$=3x\left(4x+1\right)+7\left(4x+1\right)$

Factor out common term $4x+1$ :

$=\left(4x+1\right)\left(3x+7\right)$

$\frac{\left(4x+1\right)\left(3x+7\right)}{16x^2+8x+1}$

Factor $16x^2+8x+1$ :

$=4^2x^2+8x+1$

$=4^2x^2+8x+1^2$

$=\left(4x\right)^2+8x+1^2$

$=\left(4x\right)^2+2\cdot \:4x\cdot \:1+1^2$

Use the perfect square formula:

$=\left(4x+1\right)^2$

$\frac{\left(4x+1\right)\left(3x+7\right)}{\left(4x+1\right)^2}$

Cancel out common factor $4x+1$ :

$=\frac{3x+7}{4x+1}$

8 0

2 years ago