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andre [41]
3 years ago
8

Reggie currently has a square rug in his living room. He is moving soon and has determined that for his new living room, he will

need a rug that has a width that is two feet shorter than his current rug and a length that is five feet longer than his current rug. Let x represents the side measure of Reggie's current rug, in feet. Determine the equation that represents the area, y, in square feet, of the rug needed for his new living room.
Mathematics
1 answer:
lara [203]3 years ago
7 0
Reggie currently has a square shaped rug in his living room. The side lengths of square are all equal. The length of a side of a square is given to be x feet.
So length and width of current rug are x feet and x feet respectively.

For his new room, he needs a rug that is 2 feet shorter in width than his current rug. So the width of new rug will be (x - 2) feet. The length of his new rug will be 5 feet more than the length of his current rug. So the length of new rug will be (x + 5) feet.

The new rug will have unequal length and width, hence it will be rectangular in shape. The area of new rug will be:

Area = Length x Width

y = (x + 5)(x - 2) square feet

This equation represents the Area of the rug Reggie needs for his new room.
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The figure shows two intersecting lines and the measures of the resulting angles. Write an equation to help you solve for x. The
Svetlanka [38]

<u>Given</u>:

The given figure shows the intersection of the two lines.

The angles formed by the intersection of the two lines are (3x - 8)° and (2x + 12)°

We need to determine the equation to solve for x and to find the value of x.

<u>Equation to solve for x:</u>

Since, the two angles (3x - 8)° and (2x + 12)° are vertically opposite angles and the vertical angles are always equal.

Hence, we have;

3x-8=2x+12

Thus, the equation to solve for x is 3x-8=2x+12

<u>Value of x:</u>

The value of x can be determined by solving the equation 3x-8=2x+12

Thus, we have;

x-8=12

     x=20

Thus, the value of x is 20.

3 0
3 years ago
Given: ΔWXY is isosceles with legs WX and WY; ΔWVZ is isosceles with legs WV and WZ. Prove: ΔWXY ~ ΔWVZ
Alex777 [14]

Answer:

By AA

ΔWXY ~ΔWVZ

Step-by-step explanation:

Here WXY is an isosceles triangle with legs WX & WY

So WX = WY

Hence ∠X = ∠Y

So ∠2= ∠3.

Now by angle sum property

∠1 + ∠2+∠3 = 180°

∠1+∠2+∠2=180°

2∠2 = 180° - ∠1     .......(1)

In triangle WVZ

WV = WZ

So ∠V = ∠Z

∠4 = ∠5

Once again by angle sum property

∠1 + ∠4 + ∠5=180°

∠1 + ∠4 + ∠4 = 180°

2∠4 = 180° - ∠1       ...(2)

From (1) & (2)

2∠2 = 2∠4

∠2=∠4

Now ∠W is common to both triangles

Hence by AA

ΔWXY ~ΔWVZ

8 0
3 years ago
Read 2 more answers
Find the perimeter of the triangle defined by the coordinates (7, 1), (-6, 1), and (10, 6). (Round to nearest tenth)
matrenka [14]

Answer:

35.6\ units

Step-by-step explanation:

we know that

The perimeter of triangle is equal to the sum of the length of the three sides

Let

A(7, 1), B(-6, 1), C(10, 6)

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Find the distance AB

A(7, 1), B(-6, 1)

substitute in the formula

d=\sqrt{(1-1)^{2}+(-6-7)^{2}}

d=\sqrt{(0)^{2}+(-13)^{2}}

dAB=13\ units

Find the distance BC

B(-6, 1), C(10, 6)

substitute in the formula

d=\sqrt{(6-1)^{2}+(10+6)^{2}}

d=\sqrt{(5)^{2}+(16)^{2}}

dBC=16.8\ units

Find the distance AC

A(7, 1), C(10, 6)

substitute in the formula

d=\sqrt{(6-1)^{2}+(10-7)^{2}}

d=\sqrt{(5)^{2}+(3)^{2}}

dAC=5.8\ units

Find the perimeter

P=dAB+dBC+dAC

P=13+16.8+5.8=35.6\ units


4 0
3 years ago
There is a 5% per year decline in water in the following reservoir. if the reservoir had 2000 gallons of water in year 2001, how
egoroff_w [7]
Answer is 85% count by 5 17 times 5=5%
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3 years ago
In the right triangle shown, ∠ B = 6 0 ∘ ∠B=60 ∘ angle, B, equals, 60, degree and A C = 6 3 AC=6 3 ​ A, C, equals, 6, square roo
liberstina [14]

Answer:

the answer is 18

Step-by-step explanation:

9root3/sin60

8 0
3 years ago
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