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3 years ago

If a number a is chosen at random from the set

Mathematics

1 answer:

Paraphin [41]3 years ago

7 0

Answer:

D. 3/19

Step-by-step explanation:

12/1 = 12

12/2 = 6

12/3 = 4

These are the only ones that make the equation true.

There are also only 19 numbers because they need to be less than 20 like the question indicated. Therefore, the answer is D.

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The product of two

inessss [21]

Answer:

11 and 12

Step-by-step explanation:

x(x+1)=132

x^2+x=132

x^2+x-132=0

(x-11)(x+12)=0

x = 11 or x = -12

when x=11 ,

x+1=12

11*12=132

7 0

3 years ago

Simplify -4+5x-17-22x

Elina [12.6K]

<h3>Answer:</h3>

$\large\boxed{-17x-21}$

<h3>Step-by-step explanation:</h3>

In this question, we're simply combining "like-terms" in order to simplify the expression.

Lets solve:

$-4+5x-17-22x\\\\\text{First, lets add 5x and -22x}\\\\-17x-4-17\\\\\text{Now we would add the -4 and -17. Adding 2 negatives still keeps it a negative}\\\\-17x-21$

When you're done solving, you should get -17x-21

This means that -17x-21 would be the simplified version.

<h3>I hope this helped you out.</h3><h3>Good luck on your academics.</h3><h3>Have a fantastic day!</h3>

4 0

3 years ago

Read 2 more answers

Find both possible pairs of numbers if two numbers have a product of 14 and a difference of 5

I am Lyosha [343]

Answer:

Step-by-step explanation:

ttt

5 0

3 years ago

Read 2 more answers

A normal window is constructed by adjoining a semicircle to the top of an ordinary rectangular window, (see figure ) The perimet

Dima020 [189]

Let's find the perimeter of the window.

The bottom side is $x$ . The left and right sides make $2y$ .
The perimeter of a circle is $2\pi r$ , so the perimeter of a semicircle must be $\pi r$ , The radius is $\frac{1}2x$ , so that gives $\frac{1}2\pi x$ for the curve. All of that is equal to 12.

$x+2y+\frac{1}2\pi x=12$

We only want to use one variable to create the area formula, so let's solve for $y$ .

$2y=12-x-\frac{1}2\pi x$

$y=6-\frac{1}2x-\frac{1}4\pi x$

Now that we have a value for $y$ in terms of $x$ , we can find the area in terms of $x$ .

The area of the rectangle is going to be $xy$ , which then becomes

$A_r=x(6-\frac{1}2x-\frac{1}4\pi x$

$A_r=6x-\frac{1}2x^2-\frac{1}4\pi x^2$

The area of the semicircle is going to be $\frac{1}2\pi r^2$ .

Since $r=\frac{1}2x$ , $A_{sc}=\frac{1}2\pi (\frac{1}2x)^2$ .

$A_{sc}=\frac{1}2\pi \frac{1}4x^2$

$A_{sc}=\frac{1}8\pi x^2$

Now let's add the areas of the rectangle and semicircle.

$A=A_r+A_{sc}$

$A=6x-\frac{1}2x^2-\frac{1}4\pi x^2+\frac{1}8\pi x^2$

$A=6x-\frac{1}2x^2-\frac{1}8\pi x^2$

If you wanted to factor out $\frac{1}8$ like you did, this would become

$\boxed{A(x)=\frac{1}8(48x=4x^2-\pi x^2)}$

Now what we want to do is find what $x$ is when $A$ is at its highest point, Once we have the value for $x$ we can also find the value for $y$ , of course.

Let's put our equation in the general form of a quadratic.

$A(x)=(-\frac{1}2-\frac{1}8\pi )x^2+6x$

Now we can use the vertex formula $x=\frac{-b}{2a}$ .
( $a$ and $b$ refer to $ax^2+bx+c$ .)

$x=\frac{-6}{2(-\frac{1}2-\frac{1}8\pi)}$

$x=\frac{-6}{-\frac{1}4\pi -1}$

$x=\frac{-24}{-\pi -4}$

$\boxed{x=\frac{24}{\pi +4}}$

Now let's plug that in for $y=6-\frac{1}2x-\frac{1}4\pi x$ .

Since our final answers are in decimal form and not exact form, we can make our lives a little easier here and just use $x\approx3.36059492$ .

$y\approx6-\frac{1}2(3.36059492)-\frac{1}4\pi(3.36059492)$

<span> $y\approx6-(1.68029746+2.63940507809)$

</span><span> $\boxed{y\approx1.68029746191}$

Let's take our answers for $x$ and $y$ and round to 2 decimal places.

$\boxed{x\approx 3.36\ ft}$

$\boxed{y\approx 1.68\ ft}$ </span>

3 0

3 years ago

What is 9/10 of 50 in simplest form

ankoles [38]

50 /10 = 5

5 * 9 = 45

45 is 9/10 of 50

8 0

3 years ago