Ask question

Ask question

All categories

geniusboy [140]

4 years ago

9

The Hypotenuse-Leg Theorem states that if the hypotenuse and leg of one right triangle is congruent to the hypotenuse and corres

ponding leg of another right triangle, then the triangles are similar.

1 answer:

Dovator [93]4 years ago

4 0

The <span>hypotenuse leg theorem states that any two </span>right triangles<span> that have a </span>congruent hypotenuse<span> and a </span>corresponding<span>, congruent leg are </span>congruent <span>triangles.</span>

You might be interested in

Find the roots of the equation<br> x ^ 2 + 3x-8 ^ -14 = 0 with three precision digits

scoray [572]

Answer:

Step-by-step explanation:

Given quadratic equation:

$x^{2} + 3x - 8^{- 14} = 0$

The solution of the given quadratic eqn is given by using Sri Dharacharya formula:

$x_{1, 1'} = \frac{- b \pm \sqrt{b^{2} - 4ac}}{2a}$

The above solution is for the quadratic equation of the form:

$ax^{2} + bx + c = 0$

$x_{1, 1'} = \frac{- b \pm \sqrt{b^{2} - 4ac}}{2a}$

From the given eqn

a = 1

b = 3

c = $- 8^{- 14}$

Now, using the above values in the formula mentioned above:

$x_{1, 1'} = \frac{- 3 \pm \sqrt{3^{2} - 4(1)(- 8^{- 14})}}{2(1)}$

$x_{1, 1'} = \frac{1}{2} (\pm \sqrt{9 - 4(1)(- 8^{- 14})})$

$x_{1, 1'} = \frac{1}{2} (\pm \sqrt{9 - 4(1)(- 8^{- 14})} - 3)$

Now, Rationalizing the above eqn:

$x_{1, 1'} = \frac{1}{2} (\pm \sqrt{9 - 4(- 8^{- 14})} - 3)\times (\frac{\sqrt{9 - 4(- 8^{- 14})} + 3}{\sqrt{9 - 4(- 8^{- 14})} + 3}$

$x_{1, 1'} = \frac{1}{2}.\frac{(\pm {9 - 4(- 8^{- 14})^{2}} - 3^{2})}{\sqrt{9 - 4(- 8^{- 14})} + 3}$

Solving the above eqn:

$x_{1, 1'} = \frac{2\times 8^{- 14}}{\sqrt{9 + 4\times 8^{-14}} + 3}$

Solving with the help of caculator:

$x_{1, 1'} = \frac{2\times 2.27\times 10^{- 14}}{\sqrt{9 + 42.27\times 10^{- 14}} + 3}$

The precise value upto three decimal places comes out to be:

$x_{1, 1'} = 0.758\times 10^{- 14}$

5 0

3 years ago

Allison earns $14 an hour plus $20 an hour for every hour of overtime. Overtime hours are any hours more than 35 hours for the w

Ronch [10]

<u>Part a)</u> Create an equation that shows the amount of money earned, E, for working x hours in a week when there is no overtime

Let

E-------> the amount of money earned

x------> number of hours worked

we know that

For $x\leq35$

$E=14x$

therefore

<u>the answer part a) is</u>

$E=14x$

<u>Part b) </u>Create an equation that shows the amount of wages earned, T, for working y hours of overtime

Let

T-------> the amount of money earned

y------> number of hours of overtime

we know that

$T=14*35+20y$

$T=\$490+20y$

therefore

<u>the answer part b) is</u>

$T=\$490+20y$

<u>Part c)</u> Allison earned $610 in 1 week. How many hours (regular plus overtime) did she work?

we know that

$35\ hours=\$490$

$\$610-\$490=\$120$

Divide $\$120$ by $\$20$ ----> to obtain the hours of overtime

$\frac{120}{20}=6\ hours\ of\ overtime$

So

Allison works

$35+6=41\ hours$

$Regular=35\ hours\\ Overtime=6\ hours$

therefore

<u>the answer part c) is</u>

$Regular=35\ hours\\ Overtime=6\ hours$

4 0

3 years ago

At Hogwarts School of Witchcraft and Wizardry, Professor Snape was concerned about grade inflation, and suggested that the schoo

ExtremeBDS [4]

Answers:

The z scores are approximately:

Care of Magical Creatures: z = 0.333
Defense Against the Dark Arts: z = 0.583
Transfiguration: z = -0.263
Potions: z = -0.533

From those scores, we can say:

Best grade = Defense Against the Dark Arts
Worst grade = Potions

=====================================================

Further Explanation:

We'll need to convert each given score to a corresponding standardized z score.

The formula to use is

z = (x - mu)/sigma

where,

x = given grade for each class
mu = mean
sigma = standard deviation

Let's find the z score for the Care of Magical Creatures class

z = (x - mu)/sigma

z = (3.80 - 3.75)/(0.15)

z = 0.333 approximately

Repeat this process for the Defense Against the Dark Arts score.

z = (x - mu)/sigma

z = (3.60 - 3.25)/(0.60)

z = 0.583 approximately

And for the Transfiguration class as well

z = (x - mu)/sigma

z = (3.10 - 3.20)/(0.38)

z = -0.263 approximately

The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.

Now do the final class (Potions) to get this z score

z = (x - mu)/sigma

z = (2.50 - 2.90)/(0.75)

z = -0.533 approximately

This grade is below average as well.

----------------------------

To summarize, we have these z scores

Care of Magical Creatures: z = 0.333
Defense Against the Dark Arts: z = 0.583
Transfiguration: z = -0.263
Potions: z = -0.533

Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.

3 0

2 years ago

Explain how to write and evaluate an algebraic expression.

BabaBlast [244]

So you would start with 40/n because quotient means division and then it would be (40/n) - 13 (40 divided by n then minus 13) because the answer is thirteen less than the quotient of those numbers. since it wants you to evaluate for n=2 you would do 40/2 which is 20 then subtract 13 which is 7.

So write the expression as (40/n) -13 and when you evaluate just stick the 2 where the n is for (40/2) - 13
20 - 13
= 7

8 0

4 years ago

Read 2 more answers

How much larger or smaller is the 3 in the number labeled A than the 3 in the number labeled B? A 4.632. B 67.493

Studentka2010 [4]

It Is 2.861 Because YOU SUBTRACT THE To numbers . Ghggdydhdhdydyydu ghffydt ed Cheney fuchsia hjdjdj

5 0

3 years ago