What is the area of the triangle?

Delicious77 [7]

Answer:

independent

Step-by-step explanation:

Since no one else answered, figured you wouldn't mind if I do. :-), and you didn't use any CAPS.

How those two events (even and greater than 9) relate?

independent: YES. Can one happen without the other? Certainly. You see (1,1) is an even number that is not greater than 9. Equally, you see (6,5) which is greater than 9, but is not an even number.

inclusive: No, since there's a least one case where a pair number is not greater than 9. The opposite is also true... at least 1 number > 9 that is not even.

Mutually exclusive: No, since there numbers that are even AND greater than 9 (6,4) for example.

Conditional: No. Does one need the other to happen? Absolutely not.

5 0

2 years ago

The values 10 and 15 are plotted on the number line

Brums [2.3K]

im pretty sure the answer is 0.7

4 0

3 years ago

Read 2 more answers

1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

german

Answer:

Step-by-step explanation:

1.

To write the form of the partial fraction decomposition of the rational expression:

We have:

$\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}$

2.

Using partial fraction decomposition to find the definite integral of:

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx$

By using the long division method; we have:

$x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }$

$- 2x^3 -16x^2-40x$

$x+ 20$

So;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}$

By using partial fraction decomposition:

$\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}$

$= \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}$

x + 20 = A(x + 2) + B(x - 10)

x + 20 = (A + B)x + (2A - 10B)

Now; we have to relate like terms on both sides; we have:

A + B = 1 ; 2A - 10 B = 20

By solvong the expressions above; we have:

$A = \dfrac{5}{2}$ $B = \dfrac{3}{2}$

Now;

$\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}$

Thus;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}$

Now; the integral is:

$\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx$

$\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}$

3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.

Please check to the attached image below for the solution to question number 3.

4 0

2 years ago

Find equation to the given value of the curve x=t^5+1, y=t^6+t, and t=-1. please help I keep getting y=-1.4x and it is incorrect

irakobra [83]

Well for the function of x we have x=t^5+1 and we know t= -1

So you plug in -1 instead of the t and you will get x=(-1)^5+1
Now just resolve that equation to get the value of x

x = (-1)^5+1 = -1+1 = 0 So x=0

Do the same with y and you’ll get y=2

3 0

2 years ago

A cylindrical cup is 10 centimeters in height. When filled to the very top, it holds 500 cubic centimeters of water. What is the

Vladimir [108]

Answer:

4

Step-by-step explanation:

the formula for radius is

$r=\sqrt{\frac{v}{\pi h } }$

so. 500 divided by pi times 10. then square root your final answer. cool. let's get started.

3.14*10 is 31.4, you can do that without thinking.

500/31.4=15.92

$\sqrt{}$ 15.92= 3.99, or just 4

the radius is four.

6 0

3 years ago