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Fynjy0 [20]
1 year ago
5

The length of a rectangle is 23 cm less than 6 times it's width. it's area is 35 square centimeters. find the dimensions of the

rectangle use the formula,area equal length times width.
Mathematics
1 answer:
Diano4ka-milaya [45]1 year ago
7 0

We are given that the area of a rectangle is 42 square meters. The formula for the area of a rectangle is:

A=wl

Where "w" is the width and "l" is the length. We are also told that the width is 5 meters longer than one-third of the length, this can be written mathematically as:

w=\frac{1}{3}l+5

Replacing in the formula for the area:

A=(\frac{1}{3}l+5)l

Now we use the distributive property:

A=\frac{1}{3}l^2+5l

Now we replace the value of the area:

42=\frac{1}{3}l^2+5l

Now we subtract 42 to both sides:

\frac{1}{3}l^2+5l-42=0

Now we can multiply both sides by 3:

l^2+15l-126=0

Now we factor this equation, we need two numbers which sum is 15 and their product is 126, we get:

(l+21)(l-6)=0

Now we set each factor to zero:

\begin{gathered} l+21=0 \\ l=-21 \end{gathered}\begin{gathered} l-6=0 \\ l=6 \end{gathered}

We take the positive value and therefore, the length of the rectangle is 6 meters.

To determine the width we use the relationship given by the problem:

w=\frac{1}{3}l+5

Replacing l = 6:

\begin{gathered} w=\frac{1}{3}(6)+5 \\ w=2+5 \\ w=7 \end{gathered}

The width is 7 meters.

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4 0
3 years ago
f five times a number is subtracted from twelve times a number, the result is seven less than twice the number. Find the number
gayaneshka [121]
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7 0
3 years ago
Almost all companies utilize some type of year-end performance review for their employees. Human Resource (HR) at a university's
balu736 [363]

Answer:

The Answer is 76.

Step-by-step explanation:

Given the normal distribution " 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable'',  we can see that exemplary employees are top 10% rated employees.

We have the formula for normal distribution:

z=(X-M)÷σ

where z is the <em>minimum z-score </em>for top 10% employee, X is the <em>minimum </em>score for top 10% employee, M is the <em>mean</em> of the score distribution, σ is the <em>standard deviation</em> of the score distribution.

The z-score we are looking for is the value "a" that separates the highest 10% from the lowest 90% i.e. P(z≤a)=0.90

If we look at z-table, corresponding value for a is 1.28155

We can now put the values in the formula:

1.28155=\frac{X-50}{20}

So X=(1.28155×20)+50=75.631

Therefore minimum score for exemplary employee is 76.

3 0
3 years ago
Help please been stuck on this for a week.
Anettt [7]
They give the formula as:
Surface Area =<span> (2 • <span>π <span>• r²) + (2 • <span>π • r • height)</span></span></span></span>
However the 2*PI*r^2 part of the formula is used to calculate the 2 "ends" of a cylinder.  Since the problem states that you are NOT to count any of surface area of the "ends" then you only need the <span>(2 • <span>π • r • height) part of the formula.
So, r = 3 inches and height = 8 * 3 inches, the side area equals
2 * PI * r * height
2 * 3.14159 * 3 * 24 =
</span></span>
<span> <span> <span> 452.39 cubic inches which is the lateral area.</span></span></span>



6 0
3 years ago
Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.) 13x^2 +1 = -10
12345 [234]

Step-by-step explanation:

The given quadratic equation is :

13x^2 +1 = -10x\\\\or\\\\13x^2+10x+1=0

The formula to solve a quadratic equation is :

x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}

Put a = 13, b = 10 and c = 1

So,

x=\dfrac{-10\pm \sqrt{10^2-4(13)(1)} }{2(13)}\\\\x=-0.118, -0.651

Hence, this is the required solution.

3 0
3 years ago
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