MATHEMATICS MIDDLE SCHOOL

A rectangle has the length of 22 inches less than 7 times the width. If the area of the rectangle is 3197 square inches, find the length of the rectangle

Answers

Answer 1
Answer:

The length of rectangle is 139 inches

Solution:

Given that, area of the rectangle is 3197 square inches

Let "L" be the length of rectangle and "W" be the width of rectangle

Also given that rectangle has the length of 22 inches less than 7 times the width

Length = 7 times width - 22

L = 7W - 22

The area of rectangle is given as:

\text {Area of rectangle }=\text { length } * \text { width }

Substituting the values we get,

\begin{array}{l}{3197=(7 W-22)(W)} \n\n {3197=7 W^(2)-22 W} \n\n {7 W^(2)-22 W-3197=0}\end{array}

On solving the above quadratic equation using quadratic formula,

\text {For the quadratic equation } a x^(2)+b x+c=0 \text { where } a \neq 0

x=\frac{-b \pm \sqrt{\left(b^(2)-4 a c\right)}}{2 a}

\begin{array}{l}{\text {Here in } 7 \mathrm{W}^(2)-22 \mathrm{W}-3197=0} \n\n {a=7 ; b=-22 ; c=-3197}\end{array}

Substituting in above quadratic formula,

\begin{array}{l}{W=\frac{-(-22) \pm \sqrt{\left((-22)^(2)-4(7)(-3197)\right)}}{2 * 7}} \n\n {W=(22 \pm √(90000))/(14)=(22 \pm 300)/(14)} \n\n {W=(22+300)/(14) \text { or } W=(22-300)/(14)} \n\n {W=23 \text { or } W=-19.85}\end{array}

Since width of rectangle cannot be negative, ignore negative value of "W"

So width W = 23 inches

Length L = 7W - 22 = 7(23) - 22 = 139 inches

Thus length of rectangle is 139 inches

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Answers

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answer: 39

Translate each verbal description into an algebraic expression. Then simplify Five-ninths of (3p+1) subtracted from one-thirf of q+p

Answers

Answer:

(1/3)q  - (4/3) p - 5/9

Step-by-step explanation:

Step one

Write the fractional form of the givens

(1/3)(q + p)

(5/9)(3p + 1)

Step Two

Write out the expression

(1/3)(q + p) - (5/9)(3p + 1)          Remove the brackets

(1/3)q  + (1/3)p - (5/9)*3p - 5/9 Combine the 2 p terms

(1/3)q  + (1/3 - 15/9 )p - 5/9       Reduce 15/9 down to 5/3

(1/3)q  + (1/3 - 5/3)p - 5/9         Combine what is inside the brackets

(1/3)q  + ( - 4/3)p - 5/9              Bring out the minus sign

(1/3)q  - (4/3) p - 5/9                 This should be your answer.

What is the sum of 3 1/10 and 1 3/4 . please help me with this .

Answers

the sum is 4 and 17/20.
first, you have to create a common denominator. the least common multiple of 4 and 10 is 20, so I used that.
since 10 is multiplied by 2 to achieve, twenty, we also multiply 1 by 2, which makes 3 and 2/10
4 on the other hand, is multiplied by 5 to achieve 20, so we multiply 3 by 5 also, which is 15.
from there, we have 3 2/20 + 1 15/20, which equals 4 17/20.
The sum or 3 1/10 and 1 3/4 is 5.
Hope this helped you!

What the value of 9 in 69,143

Answers

Hi there!

The 9 in 69,143 represents 9,000.

WHY?

Because the 9 is in the thousands place. So, therefore, our answer is correct.

Hope this helps! :D
Actually ,it's 9000, because the breakdown is-
60000+9000+100+40+3. Try that in the calculator and you'll know I'm correct

Anyone know this question

Answers

answer is 70degree because if angle 1 is 70 then angle 2 also will be the same then it means even angle 3 will be 70.
HOPE IT HELPS :)

Which of the following is equivalent to log9w

Answers

log 9 + log w is equivalent to log9w

Hope my answer helped :)
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