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3 years ago

In a 30°-60°-90° triangle, what is the length of the longer leg when the length of the hypotenuse is 18 inches?

Mathematics

1 answer:

max2010maxim [7]3 years ago

8 0

Answer:

9sqrt(3) in.

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is:

short leg : long leg : hypotenuse

1 : sqrt(3) : 2

If the short leg measures 1, then the hypotenuse measures 2.

The length of the hypotenuse is twice the length of the short leg.

The length of the long leg is sqrt(3) times the length of the short leg.

If the hypotenuse measures 18 in., then the short leg measures 9 in.

Then the long leg measures 9sqrt(3) in.

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PLS HELP ME ASAP!!!!!!!!! ill give thanks, and five stars

docker41 [41]

Answer:

Step-by-step explanation:

The additive inverse property states that if we have a number a, then:

$a+(-a)=0$

Here, we have the equation:

$2x=542$

And we divide both sides by 2:

$2x/2=542/2$

To acquire:

$x=271$

So, we did not use the additive inverse property since we didn't add anything.

Instead, we used the division property of equality by dividing both sides by 2.

So, our answer is A.

And we're done!

7 0

2 years ago

Read 2 more answers

4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail

Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

$h^{-1}(x)=\sqrt{\frac{x+1}{3}}$ ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = $f^{-1}(x)$

* Lets use these steps to solve the problems

∵ $f(x)=\sqrt{x-3}$

∵ f(x) = y

∴ $y=\sqrt{x-3}$

- Exchange x and y

∴ $x=\sqrt{y-3}$

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by $f^{-1}(x)$

∴ $f^{-1}(x)=x^{2}+3$

∵ g(x) = x² + 3

∴ $f^{-1}(x)=g(x)$

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ $f(x)=\sqrt{x-3}$

∵ g(x) = x² + 3

∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ $\frac{x + 1}{3}=y^{2}$

- Take √ for both sides

∴ ± $\sqrt{\frac{x+1}{3}}=y$

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

∴ $h^{-1}(x)=\sqrt{\frac{x+1}{3}}$

4 0

3 years ago

Is 14/18 greater then, less then, or equal to 7/9

Musya8 [376]

Answer:

Equal to

Step-by-step explanation:

14/18 is just 7/9 but with the numerator and denominator multiplied by 2

5 0

2 years ago

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A part-time contractor at a manufacturing facility earns $11.00 per hour. He worked 414 hours on Tuesday, 314 hours on Wednesday

Shkiper50 [21]

Answer:

$215.16

Step-by-step explanation:

Assuming he worked:

Tuesday - 4.14 hours

Wednesday - 3.14

Thursday - 7.14

Friday - 5.14

Add all the hours together: 4.14+3.14+7.14+5.14 = 19.56. Now times the hour by his rate of $11.

19.56(11) = $215.16

8 0

3 years ago

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Use two unit multipliers to convert 628 kilometers to centimeters

irina [24]

Using two unit multiplier 628 km is equal to 62800000 cm

Solution:

628 kilometer to centimeter

We will go from kilometers to meters to centimeters.

Start by putting 628 km over 1:

$\frac{628 km}{1}$

We want to get rid of km and bring in m.

We know that 1000 m = 1 km.

Since km is in the numerator, we will make the first unit multiplier by putting 1 km in the denominator and 1000 m in the numerator, so the km will cancel. So we multiply by the unit multiplier,

$\frac{628 km}{1} \times \frac{1000m}{1km}$

Now the km's will cancel:

$\frac{628}{1} \times \frac{1000m}{1}$

Now we want to get rid of m and bring in cm.

We know that 100 cm = 1 m.

Since meter is in the numerator, we will make the first unit multiplier by putting 1 meter in the denominator and 100 cm in the numerator, so the meter's will cancel. So we multiply by the unit multiplier

$\frac{100cm}{1m}$

$\frac{628}{1} \times \frac{1000m}{1} \times \frac{100cm}{1m}$

We cancel the m's and we end up with:

$628 \times 1000 \times 100 cm$

= 62800000 cm

Thus 628 km is equal to 62800000 cm

5 0

3 years ago