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zzz [600]
3 years ago
6

The area of a square is 144cm2.what is the measurement of each side​

Mathematics
1 answer:
Dmitry [639]3 years ago
8 0

The area of a square is 144 cm^2. The measurement of each side​ is 12 cm

<u>Solution:</u>

Given, The area of a square is 144 cm^2

We have to find that what is the measurement of each side.

Now, we know that, area of a square = product of side value with another side value.

Let the side value of given square be "s"

Then, <em>Area of square is given as:</em>

\begin{array}{l}{\text {area of square}=s \times s} \\\\ {\text {Area of square}=s^{2}} \\\\ {144=s^{2}} \\\\ {s=\sqrt{144}} \\\\ {s=\sqrt{12^{2}}}\end{array}

On cancelling square root and square on right side,we get

s = 12

Hence, the side value of the square is 12 cm.

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What is the length of AC¯¯¯¯¯ ?
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Answer:

AC = 12.38 cm

Step-by-step explanation:

When there are 2 pairs given, we can use the sine rule to solve the problem.

By pairs we mean "an angle and side opposite to it"

<em>1 pair is 85.2 degree angle and 13 cm, and another pair is 71.6 degree angle and the side AC (which we want to figure out).</em>

<em />

Sine Rule is given by \frac{SinA}{a}=\frac{SinB}{b}

where,

A and B are the two respective angles and a and b are the two respective sides (of the pairs). Plugging all the info and using algebra, we have:

\frac{Sin85.2}{13}=\frac{Sin71.6}{AC}\\AC*Sin85.2=13*Sin71.6\\AC=\frac{13*Sin71.6}{Sin85.2}\\AC=12.38

Thus, AC = 12.38 cm

5 0
3 years ago
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Use the factors of the function and the y-intercept to find the standard form of the equation representing Jared’s function. Typ
Georgia [21]

The y-intercept of a function is the point where the graph crosses the \mathbf{y = x^3 + 2x^2 - 193x - 270 }

  • The factors of the Jared's graph are: (x - 10), (x + 3) and (x + 9)
  • The y-intercept is -13.5
  • The standard equation of the function is: \mathbf{y = x^3 + 2x^2 - 193x - 270 }

<u>(a) The factors</u>

First, we write out the points where the function cross the x-axis.

The points are:

\mathbf{x = 10}

\mathbf{x = -3}

\mathbf{x = -9}

Equate the above points to 0

\mathbf{x -10 = 0}

\mathbf{x +3 = 0}

\mathbf{x +9 = 0}

Hence, the factors are: (x - 10), (x + 3) and (x + 9)

<u>(b) The y-intercept</u>

This is the point where the graph crosses the y-axis.

From the attached graph, the graph crosses the y-axis at -13.5.

Hence, the y-intercept is -13.5

<u>(c) The standard form</u>

In (a), we have:

\mathbf{x -10 = 0}

\mathbf{x +3 = 0}

\mathbf{x +9 = 0}

Multiply the above equations

\mathbf{(x - 10) \times (x + 3) \times (x + 9) = 0 \times 0 \times 0}

\mathbf{(x - 10) \times (x + 3) \times (x + 9) = 0 }

Expand

\mathbf{(x - 10) \times (x^2 + 3x + 9x + 27) = 0 }

\mathbf{(x - 10) \times (x^2 + 12x + 27) = 0 }

Expand

\mathbf{x^3 + 12x^2 + 27x - 10x^2 - 220x - 270 = 0 }

Collect like terms

\mathbf{x^3 + 12x^2 - 10x^2+ 27x  - 220x - 270 = 0 }

\mathbf{x^3 + 2x^2 - 193x - 270 = 0 }

Replace 0 with y

\mathbf{y = x^3 + 2x^2 - 193x - 270 }

Hence, the standard form is: \mathbf{y = x^3 + 2x^2 - 193x - 270 }

Read more about graphs and functions at:

brainly.com/question/18806107

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Daniella is interviewing for a job. She wants her take-home pay to be at least $51,000$51,000. What is the least salary she can
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If Daniella is paying 15% of her salary as income tax, the other 85% should be her take-home pay. In this case, Daniella wants to have at least $51,000 as take-home pay.

0.85 (Salary) = $51,000

Salary = $51,000 / 0.85

Salary = $60,000

 

Therefore Daniella should have at least a salary of $60,000.

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The central angle of a regular polygon is 18 degrees. Th e perimeter of the polygon is 144 ft. What is the area of the polygon t
Diano4ka-milaya [45]
Given that the central angle of a polygon is 18, then the number of sides of the polygon will be:
360/18
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thus the side length will be:
144/20
=7.2 ft
hence the area will b given by:
p=s×n
a=s/[2tan(180)/n]
where:
Area=(a×p)/2
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p=7.2×20=144
a=7.2/[2tan (180/20)]=22.73
thus
A=(144×22.73)/2
A=1632.524 ft²
7 0
3 years ago
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