Examine the regular pentagon below.

Distribute -x(7x+3).

Natasha_Volkova [10]

Answer:

-7x^2-3x

Step-by-step explanation:

-x * 7x + (-x) * 3

-7xx-3x

-7x^2-3x

5 0

3 years ago

What is the slope of a line that is perpendicular to the line<br> y = 2x – 6?

Zolol [24]

Answer:

The slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

$m$ is the slope

$b$ is the y-intercept

Step 1:

Finding the slope of the given equation

The given equation is

$y = 2x - 6$

comparing with the slope-intercept form of the line equation

The slope of the equation is: m = 2

Step 2:

Determining the slope of the perpendicular line

In Mathematics, a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the other line.

As the slope of the equation is: m = 2

Therefore, the slope of the new perpendicular line:

$-\frac{1}{m}=-\frac{1}{2}$

Hence, the slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.

Important Tip:

The product of the slopes of perpendicular lines is -1.

<u>Verification:</u>

The slope of the given line:

$m_1=2$

The slope of the perpendicular line:

$m_2=-\frac{1}{2}\:\:\:\:$

The product of the slopes is:

$\:m_1\times \:m_2\:=2\times -\frac{1}{2}\:\:=-1$

As the product of the slopes of perpendicular lines is -1, therefore, the lines are perpendicular.

Thus, the slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.

7 0

3 years ago

April invested in a lifetime annuity that begins payments at age 65. Her life expectancy is 89. April invested a $1,000,000 into

Mila [183]

Answer:

Monthly payment is $5970

Step-by-step explanation:

Given : April invested in a lifetime annuity that begins payments at age 65. Her life expectancy is 89. April invested a $1,000,000 into the annuity, which earns 4.4% APR compounded monthly.

To find : what is April's monthly payment amount?

Solution :

Formula of monthly payment

Monthly payment, $M=\frac{\text{Amount}}{\text{Discount factor}}$

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$

Where, Amount = $1,000,000

Rate r= 4.4%=0.044 compounded monthly

$i=\frac{0.044}{12}=0.004$

Time = 89-65=23 years

$n=23\times12=276$

Now, put all the values we get,

$D=\frac{1-(1+i)^{-n}}{i}$

$D=\frac{1-(1+0.004)^{-276}}{0.004}$

$D=\frac{1-(1.004)^{-276}}{0.004}$

$D=\frac{1-0.33}{0.004}$

$D=\frac{0.67}{0.004}$

$D=167.5$

Monthly payment, $M=\frac{\text{Amount}}{\text{Discount factor}}$

$M=\frac{1000000}{167.5}$

$M=5970.1$

Approximately,monthly payment is $5970

4 0

4 years ago

Read 2 more answers

Answer this please correctly for brainliest

Anastaziya [24]

Answer:

The first one

Step-by-step explanation:

Because you mulitply 4 by 5 to get 20

7 0

3 years ago

Read 2 more answers

A quadratic equation ax^2+bx+c=0 has -11 and 4 as solutions. Find the values of b and c if the value of a is 1 (hint, use zero f

Alina [70]

Answer:

b = 7, c = -44

Step-by-step explanation:

If the quadratic equation has the solutions -11 and 4, the two factors are:

$(x+11)(x-4)=0$

Since when we use the zero factor property we get

x+11=0 ⇒ x= -11

x-4=0 ⇒ x=4

Thus, we have used the zero factor property in reverse to find the factorization of the quadratic equation.

Now we develop the multiplications between parenthesis:

$(x+11)(x-4)=0\\x^2-4x+11x-44=0\\x^2+7x-44=0$

So b is the number that accompanies the x: b = 7

and c is the independent number: c = -44

3 0

3 years ago