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4 years ago

1.

Mathematics

1 answer:

Pepsi [2]4 years ago

7 0

Answer:

The value of x is 8, and m<ST = 48 degrees.

Step-by-step explanation:

With the given information, we know the worth of each angle. To solve it, an equation must be made.

RS (part) + RT (part) = ST (whole)

Should look like this: 5x - 13 + 2x + 5 = 3x + 24.

Then solve the equation.

First, add up all that has in common:

Should look like: 7x - 8 = 3x + 24

Then move 3x from the right to the left by subtraction.

Should look like: 4x - 8 = 24

Next, move the 8 to the other side by addition.

Should look like: 4x = 32

Finally, to find what the value of x is, divide 4 on both sides.

You should get an answer of x = 8.

To find the measurement of ST, replace the x in 3x + 24.

3(8) + 24 = 48.

m<ST = 48 degrees.

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Solving Rational equations. LCD method. Show work. Image attached.

Dmitry [639]

Answer:

$b=1$

Step-by-step explanation:

The given rational equation is

$\frac{2b-5}{b-2} -2=\frac{3}{b+2}$

The Least Common Denominator is $(b+2)(b-2)$ .

Multiply each term in the equation by the LCD.

$(b+2)(b-2)\times \frac{2b-5}{b-2} -(b+2)(b-2)\times2=(b+2)(b-2)\times\frac{3}{b+2}$

Simplify;

$(b+2)\times \frac{2b-5}{1} -2(b+2)(b-2)=(b-2)\times\frac{3}{1}$

$(b+2)(2b-5) -2(b+2)(b-2)=3(b-2)$

Expand and group similar terms

$2b^2-5b+4b-10 -2(b^2-4)=3b-6$

$2b^2-5b+4b-10 -2b^2+8=3b-6$

$-b-2=3b-6$

$3b+b=-2+6$

$4b=4$

$b=1$

3 0

3 years ago

Find the number of positive integers n is less than or equal to 1000 such that 15n is a perfect square.

boyakko [2]

Answer:

8 positive integers.

Step-by-step explanation:

One value of n would be 15 because 225 = 15^2.

Other values are 225 * n where 15n <= 1000 and n is a perfect square.

So n = 4 gives us 225* 4 = 900 which is a perfect square and 15*4 = 60.

n = 9 gives us 225 * 9 which is a perfect square and 15*9 = 135.

n = 16 gives us 225*16 and 15*16 = 240 , so OK.

n = 25 gives a perfect square and and 15*25 = 375 - so OK.

n = 36 gives a perfect square and 15*36 = 540 - so OK.

n = 49 gives a perfect square and 15*49 = 735 - so OK.

n = 64 gives a perfect square and 15*64 = 960 - so ok.

n = 81 gives a perfect square and 15 * 81 = 1215 so NOT ok.

3 0

3 years ago

Paige has 1 ½ feet of rope for a project. She only needs 2/3 of it. How much rope does she need?

Grace [21]

Answer:

1 foot

Step-by-step explanation:

1 1/2 = 3/2

2/3*3/2 = 1

4 0

3 years ago

Read 2 more answers

What adds to give you 1, but multiplies to give you -90?

ella [17]

I would say -9 and 10

4 0

4 years ago

Please asap<br>for 10 points!

kari74 [83]

<h3>Given:</h3><h3>Large cone:</h3>

r= 8 cm
h= 20 cm

<h3>Small cone:</h3>

r= 4 cm
h= 10cm

r: radius
h: height

The volume of the frustum of the given cone.

<h3>Solution:</h3>

Frustum is a part of a cone formed by cutting off the top by a parallel plane.

$\large\boxed{Formula: V= \frac{1}{3}\pi{r}^{2}h}$

Let's solve!

First, let's find the volume of the smaller cone.

Substitute the values according to the

formula.

$V= \frac{1}{3}×\pi×{4}^{2}×10$

$V= 167.5516082 \: {cm}^{3}$

Now, we can round off to the nearest hundredth.

The value in the thousandths place is smaller than 5 so we won't have to round up.

$\boxed{V= 167.55 \: {cm}^{3}}$

Next, let's find the volume of the bigger cone.

Substitute the values according to the formula.

$V= \frac{1}{3}×\pi×{8}^{2}×20$

$V= 1340.412866 \: {cm}^{3}$

Now, we can round off to the nearest hundredth.

The value in thousandths place is smaller than 5 so we won't have to round up.

$\boxed{V=1340.41 \: {cm}^{3}}$

Now, we can find the volume of the frustum.

We'll have to minus the volume of the smaller cone from the bigger cone.

$V= 1340.41-167.55$

$\large\boxed{V= 1172.86 \: {cm}^{3}}$

<u>Hence, the volume of the frustum is 1172.86 cubic centimeters.</u>

8 0

2 years ago