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3 years ago

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A slide is 21 feet long. To get to the top of the slide, you use a vertical 9-foot high rung ladder. What is the distance, b, fr

om the bottom of the slide to the bottom of the stairs? Round your answer to the nearest tenth.

1 answer:

mojhsa [17]3 years ago

3 0

Its a right angled triangle. You have C and have B all you need to find is A. usually for a question like this you would use the Pythagorean theorem which is A2+B2=C2 but since we already have c we will use C2-B2=A2
Now we fill in the values. (21)2-(9)2=A2
441-81=360^2 so now with the 360^2 we have to squareroot it so the square root of 360 is 18.973f

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A car salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $16.

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10%

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3 years ago

U − u + 2u + 3u − 2u = 15

iVinArrow [24]

Step-by-step explanation:

$\tt{u-u+2u+3u-2u=15 }$ ⠀

$\tt{6u-3u=15 }$ ⠀

$\tt{3u=15 }$ ⠀

$\tt{ u=\dfrac{15}{3} }$ ⠀

$\tt{ u=\dfrac{\cancel{15}}{\cancel{3}} }$ ⠀

$\tt{u=5 }$ ⠀

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3 years ago

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In an observational study, which of the following refers to a description of how the data are collected and the decisions are ma

ikadub [295]

Answer:

B. Methodology

Step-by-step explanation:

The methodology of anything is how it's done. In an observational study, methodology would describe how the study is done: how the data is collected and how decisions are made.

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3 years ago

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Simplify the following equation (70 points :D)

olga_2 [115]

It is D. I looked it up on a calculator.

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Solve for x<br><br> THANK YOU

Anestetic [448]

Answer:

$x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}$

Step-by-step explanation:

$\textsf{Given equation}:$

$\dfrac{2}{3}x+\dfrac{3x}{x}=\dfrac{4x}{2}(3x+6)$

$\textsf{Cancel the common factor } x \textsf{ in }\dfrac{3x}{x}:$

$\implies \dfrac{2}{3}x+3=\dfrac{4x}{2}(3x+6)$

$\textsf{Simplify }\dfrac{4x}{2}\textsf{ by dividing the numbers}:$

$\implies \dfrac{2}{3}x+3=2x(3x+6)$

$\textsf{Apply the distributive law}\quad \:a\left(b+c\right)=ab+ac:$

$\implies \dfrac{2}{3}x+3=6x^2+12x$

$\textsf{Multiply both sides by 3 to cancel the denominator of }\dfrac{2}{3}:$

$\implies \dfrac{2}{3}x\cdot 3+3\cdot 3=6x^2\cdot 3+12x \cdot 3$

$\implies 2x+9=18x^2+36x$

$\textsf{Switch sides}:$

$\implies 18x^2+36x=2x+9$

$\textsf{Subtract }2x \textsf{ from both sides}:$

$\implies 18x^2+36x-2x=2x+9-2x$

$\implies 18x^2+34x=9$

$\textsf{Subtract 9 from both sides}:$

$\implies 18x^2+34x-9=9-9$

$\implies 18x^2+34x-9=0$

Solve using the <u>Quadratic Formula:</u>

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Define the variables:

$\implies a=18, \quad b=34, \quad c=-9$

Substitute the defined variables into the quadratic formula and solve for x:

$\implies x=\dfrac{-34 \pm \sqrt{34^2-4(18)(-9)} }{2(18)}$

$\implies x=\dfrac{-34 \pm \sqrt{1156+648} }{36}$

$\implies x=\dfrac{-34 \pm \sqrt{1804} }{36}$

$\implies x=\dfrac{-34 \pm \sqrt{4 \cdot 451} }{36}$

$\implies x=\dfrac{-34 \pm \sqrt{4}\sqrt{451} }{36}$

$\implies x=\dfrac{-34 \pm 2\sqrt{451} }{36}$

$\implies x=\dfrac{-17 \pm \sqrt{451} }{18}$

Therefore, the solutions to the given equation are:

$x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}$

Learn more about the Quadratic Formula here:

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2 years ago

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