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 the rectangle is 42 in2 find the dimensions of the rectangle

Answers

Answer 1

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

Answer 2

Answer:

Final answer:

The dimensions of the rectangle given that its area is 42 square inches, the length is 2 inches more than a number, and the width is 1 inch less than twice the same number, are 6 inches by 7 inches.

Explanation:

To solve this problem, let's define the unknown number as

x. According to the problem, the length of the rectangle is 2 inches more than x (so it's x + 2), and the width is 1 inch less than twice the number x (which makes it 2x - 1).

Now, we'll use the formula for the area of a rectangle, which is length times width: (x + 2) * (2x - 1) = 42.

Solve this equation by expanding the parentheses (2x^2 + 4x - x - 2 = 42), simplifying (2x^2 + 3x - 2 - 42 = 0), and rearranging (2x^2 + 3x - 44 = 0).

Using the quadratic formula, we find that the possible values of x are 4 and -5.5. However, a negative size doesn't make sense in this context, so x = 4 inches. That makes the length = 4 + 2 = 6 inches, and the width = 2*4 - 1 = 7 inches. Therefore, "the dimensions of the rectangle are 6 inches by 7 inches".

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If 5x+4y=23 and 4x+5y=22, then what is the value of (x + y)

Answers

Answer:

x=3 and y=2

Step-by-step explanation:

I plugged in a lot of numbers until it worked out.

5(3) + 4(2) = 15+8 which equals 23

then 4(3) + 5(2) = 12+10 which equals 22.

hope that helps!

x=3 and y=2

3+2=5

yay

solve for y.try factoring first,if factoring is not possible or difficult use quadratic formula,(y2 2isabovey -10y+23=0)

Answers

$y^2-10y+23=0\n y^2-10y+25-2=0\n (y-5)^2=2\n |y-5|=\sqrt2\n y-5=\sqrt 2 \vee y-5=-\sqrt2\n y=5+\sqrt2 \vee y=5-\sqrt2$

Find the balance in the account. $2,500 principal earning 4%, compounded quarterly, after 4 years

Answers

Answer:

$2941.45 will be the balance.

Step-by-step explanation:

Formula to find the final amount after 4 years with compound interest is

$A=A_(0)[1+(r)/(n)]^(nt)=2500[1+.04/4]^(4.4)=2500(1.01)^(16)$

= 2500×1.173 = $2931.45

Therefore $2931.45 is the final amount.

Formula:
A(t)=P(1+(r/n))^)nt)

A(4)=2500(1+(0.04/4))^(4*4)
A(4) = 2500(1.01)^16
A(4) = 2500*1.1726
A(4) = $2931.45

Elliott's bed is 75 inches long. During his growth spurt, Elliott grew 6 inches. Before his growth spurt, he was 5 feet 11 inches tall. How much shorter is Elliott's bed than Elliott?inches

Answers

Elliott's bed -> 75 in
Elliott before -> 5 ft 11 in = 71 in
Elliott after -> 71 + 6 = 77 in

77 - 75 = 2 in

Elliott's bed is shorter than him by 2 inches.

How much will you save per lb, by buying the least expensive? Round to the nearest cent. 2.5 lbs for $8.75 or 3 pounds for $9.75.