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maria [59]
3 years ago
10

The perimeter of a triangle is 133 inches. If one side of the triangle is five more than the shortest side, and the longest side

is 14 more than the shortest side, find the lengths of the three sides?
Mathematics
1 answer:
barxatty [35]3 years ago
8 0

133=x + (x+5) + (x+14)

133 = 3x+19

3x=114

x= 114/3 =38

5+38 =43

38+14 =52

check: 38 +43 +52 = 133

3 sides are : 38, 43 & 52

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<h2>Solving Equations</h2>

To solve linear equations, we must perform inverse operations on both sides of the equal sign to <em>cancel values out</em>.

  • If something is being added to x, subtract it from both sides.
  • If something is being subtracted from x, add it on both sides.
  • Same with multiplication and division. If x is being divided, multiply. If x is being multiplied, divide.

We perform inverse operations to<em> combine like terms</em>. This means to get x to one side and everything else on the other.

<h2>Solving the Questions</h2><h3>Question 1</h3>

5x+7=15

Because 7 is being added to x, subtract it from both sides:

5x+7-7=15-7\\5x=8

Because x is being multiplied by 5, divide both sides by 5:

\dfrac{5x}{5}=\dfrac{8}{5}\\\\x=\dfrac{8}{5}

Therefore. x=\dfrac{8}{5}.

<h3>Question 2</h3>

7x+4=5x-18

Here, we can group all the x values on the left side of the equation. Subtract 5x from both sides:

7x+4-5x=5x-18-5x\\2x+4=-18

To isolate x, subtract 4 from both sides:

2x+4-4=-18-4\\2x=-22

Divide both sides by 2:

\dfrac{2x}{2}=\dfrac{-22}{2}\\\\x=-11

Therefore, x=-11.

6 0
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The scale of a map is 6 km = 4 mi. What is the length on the map if the actual is 40.1<br> miles.
beks73 [17]

Answer:

60.15 km

Step-by-step explanation:

If 6 km on the map represents 4 mi on land, then we'd get the answer by using the relation

6 km -> 4 mi

x km -> 40.1 mi

Where x km is the length on the map we're looking for. If we cross multiply

6 * 40.1 = 4x

240.6 = 4x

x = 240.6/4

x = 60.15 km.

That is the length we're looking for

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Sue Has 44 Rib bones on display. there are 22 on the right side and 22 on the left on the right of its body on the right side 9/
Murljashka [212]

Answer:

18/44

Step-by-step explanation:

To turn 9/22 into something over 44, we need to figure out what to multiply it by.

44 / 22 = 2.

Multiply 9/22 by 2:

9/22 * 2 = 18/44

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Three friends go grocery shopping together, and each buys the same kind of
dalvyx [7]

Answer:

C

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Because if you plug those numbers into the graph, only C and D fit. Now we have to look at the unit price. If LaMar buys 2 lbs and pays 3.00 dollars, we know that the unit price is 3/2=1.5 dollars per pound. You could also check with the other peoples. $7.5/5lbs=1.5 dollars. $4.5/3lbs=$1.5

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What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)?
Lady_Fox [76]

Answer:

<h2>y = 3x - 5</h2>

Step-by-step explanation:

\text{The slope-intercept form of an equation of a line:}\\y=mx+b\\m-slope\\b-y\ intercept

\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

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\text{From the graph we have two points (-3, 2) and (0, 1).}\\\text{Calculate the slope of the given line:}\\\\m=\dfrac{1-2}{0-(-3)}=\dfrac{-1}{3}=-\dfrac{1}{3}.\\\\\text{Therefore the slope of the perpendicular line is:}\\\\m=-\dfrac{1}{-\frac{1}{3}}=3\\\\\text{Put it and the coordinates of the point (3, 4) to the equation of a line:}\\\\4=3(3)+b\\4=9+b\qquad\text{subtract 9 from both sides}\\-5=b\to b=-5\\\\\text{Finally:}\\\\y=3x-5

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