The rectangle has a perimeter P of 58 inches.The length l is one more than 3 times the width w.write and solve a system of linear equations to find the length and width of the rectangle?

Answer:

Length(L)=22 inches

Width(W) = 7 inches

Step-by-step explanation:

GIven:-

Perimeter (p)=58 inches,

Length(L)= one more than 3 times the width(W)

Let, W=x ---------------------------------(equation 1

$L=3x+1$ -----------------------(equation 2)

Here x is unknown and to find the Width(W) we have to find the value of x.

Now,

Perimeter of rectangle(p) = 2 times length(L) + 2 times width(W)

$p=2L+2W$

$p=2(3x+1)+2x$ ----------------(from equation 1)

$58=6x+2+2x$ ----------------(given p=58 inches)

$58=8x+2$

$8x=58-2$

$8x=56$

$x=\frac{56}{8}$

$x=7$ ----------------------(equation 3)

Now substituting the value of equation 3 in equation 2.

$L=3x+1$

$L=(3\times 7)+1$

$L=21+1$

$L=22$

$L=22 inches$

as, $W=x$ -----------------------(from equation 1)

$W=7$ inches -------------------(equation 3)

Therefore, Length(L) = 22 inches and Width(W) = 7 inches.

7 0

3 years ago

***PLEASE HELP***

Molodets [167]

Given:
250 sheep in a 40-acre pasture.
Number of sheep grazing in each acre.

250/40 = 6.25 or 6 sheep per acre

n = 6
sample proportion: signified by ρ
Sample 1: 4 → 4/6 = 0.67
Sample 2: 1 → 1/6 = 0.17
Sample 3: 9 → 9/6 = 1.50

multiply the sample proportion by 1-ρ
Sample 1: 0.67(1-0.67) = 0.67(0.33) = 0.2211
Sample 2: 0.17(1-0.17) = 0.17(0.83) = 0.1411
Sample 3: 1.50(1-1.5) = 1.5(-0.5) = -0.75

divide the result by n. n = 6
Sample 1: 0.2211/6 = 0.03685
Sample 2: 0.1411/6 = 0.02352
Sample 3: -0.75/6 = -0.125

square root of the quotient to get the standard error.
Sample 1: √0.03685 = 0.1919
Sample 2: √0.02352 = 0.1534
Sample 3: √-0.125 = invalid

z value 95% confidence 1.96.

Sample 1: 1.96 * 0.1919 = 0.3761 or 37.61% margin of error
Sample 2: 1.96 * 0.1534 = 0.3007 or 30.07% margin of error

8 0

3 years ago