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3 years ago

What Is The Length Of Each Leg Of The Triangle Below

Mathematics

2 answers:

sesenic [268]3 years ago

8 0

About 18; remember the rules for a 45-45-90 triangle

kicyunya [14]3 years ago

4 0

Use a ruler. I can't see the picture.

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The measure of an angle is 28 degrees less than its supplement. find each angle

DIA [1.3K]

Supplementary angles measure 180°. Make an equation:

Subtract 28 to leave the variable in the parentheses alone:

Add the 2 x's together:

Your new equation is:

Divide both sides by 2 to leave the variable alone

The supplement measures 76°

4 0

2 years ago

Can someone help me my grade are bad

Likurg_2 [28]

Answer:

8.31

Step-by-step explanation:

Using the Pythagorean Theorem:

$a^2+b^2=c^2$

$10^2+b^2=13^2$

$100+b^2=169$

$b^2=69$

$b = \sqrt{69}$

$b = 8.306623863$

The side length for $x$ , rounded to the nearest hundredths, would be 8.31.

8 0

3 years ago

Read 2 more answers

Half a number increased by 10 is 12. Find the number.

Lady_Fox [76]

Answer:

Step-by-step explanation:

Equation:

1/2x + 10 = 12

Subtract 10 from both sides:

1/2x = 2

Divide by 1/2 from both sides:

x = 4

-Chetan K

3 0

3 years ago

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circu

Sunny_sXe [5.5K]

Answer:

0.0221 feet per minute.

Step-by-step explanation:

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

Rate of Change of the Volume, $\dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Since gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. Therefore, the Volume of the cone is increasing at a rate of 10 cubic feet per minute.

$\dfrac{dV}{dt}=10$ ft^3/min$

We want to determine how fast is the height of the pile is increasing when the pile is 24 feet high.

We have:

$\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10\\\\$When h=24$ feet$\\\dfrac{3\pi *24^2}{12}\dfrac{dh}{dt}=10\\144\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{144\pi}\\ \dfrac{dh}{dt}=0.0221$ feet per minute$

When the pile is 24 feet high, the height of the pile is increasing at a rate of 0.0221 feet per minute.

4 0

3 years ago

(HURRY! I'M BEING TIMED)Write the partial fraction decomposition of the rational expression.

Aleonysh [2.5K]

Answer:

The partial fraction decomposition is $\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}=\frac{50}{x + 1}+\frac{-29}{\left(x + 1\right)^{2}}+\frac{-54}{x + 2}$ .

Step-by-step explanation:

Partial-fraction decomposition is the process of starting with the simplified answer and taking it back apart, of "decomposing" the final expression into its initial polynomial fractions.

To find the partial fraction decomposition of $\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}$ :

First, the form of the partial fraction decomposition is

$\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}=\frac{A}{x + 1}+\frac{B}{\left(x + 1\right)^{2}}+\frac{C}{x + 2}$

Write the right-hand side as a single fraction:

$\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}=\frac{\left(x + 1\right)^{2} C + \left(x + 1\right) \left(x + 2\right) A + \left(x + 2\right) B}{\left(x + 1\right)^{2} \left(x + 2\right)}$