14540(squared by2) x 35=?

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 th

Nikolay [14]

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:

$\text {Area of rectangle }=\text { length } \times \text { width }$

Substituting the values we get,

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

On solving the above quadratic equation using quadratic formula,

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

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

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

Substituting in above quadratic formula,

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

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

8 0

4 years ago

PLS PLS HELP FIND THE VOLUME!!! PLS PLS I GIVE U ALL MY POINTS

ICE Princess25 [194]

Answer:

1232

Step-by-step explanation:

Step 1: 8x14 to find the base

Step 2: Base times Height

Good Luck! And have a great day!

5 0

3 years ago

Read 2 more answers

A pizza has a diameter of 10 inches. If the

s344n2d4d5 [400]

Answer:

78.5

Step-by-step explanation:

The formula for area of a circle is pir^2

So we have 5 for r, so r^2 would be 25.

Using 3.14 for pi, we get the answer is 78.5

4 0

3 years ago

Read 2 more answers

Natalie's group brought in pizza but is buying drinks at the concession stand medium sodas are a dollar and $.25 how many medium

Phantasy [73]

Keywords:

Medium sodas, buy, dollars, divide

For this case we must find the amount of medium sodas that Natalie's group can buy, taking into account that they have 20 dollars and that each medium soda costs 1.25 dollars. To solve, we must divide:

Let "x" be the number of medium sodas you can buy, then:

$x = \frac {20} {1.25}\\x = 16$

So, Natalie's group can buy 16 medium sodas with 20 dollars

Answer:

16 medium sodas

8 0

3 years ago

2 Probability and Stats questions!!

mart [117]

1) To find the confidence interval
the sample mean x = 38 σ = 9; n = 85;
The confidence level is 95% (CL = 0.95) CL = 0.95
so α = 1 – CL = 0.05
α/2 = 0.025 Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer, or using a probability table for the standard normal distribution.
EBM = (1.645)*(9)/(85^0.5)=1.6058 x - EBM = 38 – 1.6058 = 36.3941 x + EBM = 38 + 1.6058 = 39.6058
The 95% confidence interval is (36.3941, 39.6058).
The answer is the letter D
The value of 40.2 is within the 95% confidence interval for the mean of the sample

2) To find the confidence interval 
the sample mean x = 76 σ = 20; n = 102; 
The confidence level is 95% (CL = 0.95) CL = 0.95
so α = 1 – CL = 0.05
α/2 = 0.025 Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer, or using a probability table for the standard normal distribution.
EBM = (1.645)*(20)/(102^0.5)=3.2575 x - EBM = 76 – 3.2575 = 72.7424 x + EBM = 76 + 3.2575 = 79.2575 
The 95% confidence interval is (72.7424 ,79.2575).
The answer is the letter A and the letter D
The value of 71.8 and 79.8 are outside the 95% confidence interval for the mean of the sample

5 0

3 years ago