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alexandr402 [8]
2 years ago
12

The length of a rectangle is 2 inches more than a number. The width is 1 inch less than twice the same number. If the area of th

e rectangle is 42 in2 find the dimensions of the rectangle
Mathematics
1 answer:
Tanya [424]2 years ago
6 0

Answer:

length: 6 inches

width: 7 inches

Step-by-step explanation:

Let n represent the number. Then the length is (n+2) and the width is (2n-1). The product of these dimensions is the area:

42 = (n+2)(2n -1) = 2n^2 +3n -2

2n^2 +3n -44 = 0 . . . . subtract 42

(n -4)(2n +11) = 0 . . . . . factor

n = 4 . . . . . . . . we aren't interested in the negative solution

Length = 4+2 = 6 . . . inches

Width = 2·4 -1 = 7 . . . inches

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Mrs. Neary bought a leaf-blower that was 19% off the original price. If Mrs. Neary saved $40, what is the best estimate of the o
Nastasia [14]

Answer:

47.6

Step-by-step explanation:

40+19%=47.6

6 0
2 years ago
What is the approximate area of the shaded portion of the diagram? (Use 3.14 as an estimate for pi.)
Nadusha1986 [10]

Answer:

218

Step-by-step explanation:

first find the area of the circle-

A=\pi r^{2} \\A=\pi 10^{2} \\A=100\pi \\A=314

to find the area of the triangle, we need the base and the height. The base we know is 16, since we don't know the height yet, use the Pythagorean theorem to find the height. One leg is 16 the hypotenuse is 20 (2* the radius).

a^{2} +b^{2} =c^{2} \\a^{2} +16^{2} =20^{2} \\a^{2} +256=400\\a^{2} =144\\a=12

Now I know the height is 12. Find the area of the triangle

A=\frac{1}{2} bh\\A=\frac{1}{2} (16)(20)\\A=96

subtract the area of the triangle from the area of the circle

314-96=218

6 0
3 years ago
The width of a slot of a duralumin forging is (in inches) normally distributed with μ= 0.9000 and σ = 0.0030. The specification
Lubov Fominskaja [6]

Answer:

a) 9.56%

b) 0.0019

Step-by-step explanation:

a) Find the z-scores.

z = (x − μ) / σ

z₁ = (-0.0050) / 0.0030

z₁ = -1.67

z₂ = (0.0050) / 0.0030

z₂ = 1.67

Find the probability using a chart or calculator.

P(Z < -1.67 or Z > 1.67) = 2 P(Z < -1.67)

P(Z < -1.67 or Z > 1.67) = 2 (0.0478)

P(Z < -1.67 or Z > 1.67) = 0.0956

b) Use a chart or calculator to find the z-score.

P(Z < -z or Z > z) = 0.01

P(Z < -z) = 0.005

z = 2.576

Find the standard deviation.

z = (x − μ) / σ

2.576 = (0.0050) / σ

σ = 0.0019

4 0
3 years ago
Ryan Katie and Mike are roommates. They need to pay an electric bill. The bill is $155.52 The billing cycle is from nov23-dec23.
rusak2 [61]

Answer: Step-by-step explanation:

if I am correct.. Katie is gonna be paying $77.76. Meanwhile, Mike and Ryan are paying $38.88

half of 155.52 = 77.76

half of 77.76 = 38.88

$77.76 + $33.88 + $38.88 = $155.52

7 0
2 years ago
Jeannie got a new pair of eye glasses. She was able to pay $15 at the time
Lisa [10]

Answer:

6 months, i used the equation from part a so i know it’s right

Step-by-step explanation:

a) 15 + 12x = 87

b) 12x = 87-15=72

72/12 = 6

3 0
3 years ago
Read 2 more answers
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