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2 years ago

Solve each of these equations. Explain or show your reasoning.

Mathematics

1 answer:

Svetlanka [38]2 years ago

4 0

$2(x+5)=3x+1 \\2x+10=3x+1 \\-x=-9 \\x=9$

$3y-4=6-2y \\5y=10 \\y=2$

$3(n+2)=9(6-n) \\3n+6=54-9n \\12n=48 \\n=\frac{48}{12}=4$

Hope this helps.

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Why is (x-3) NOT a factor of x3+2x2-5x-6

ivolga24 [154]

As the expression is not equal to zero on x=3, x-3 is not a factor of given expression

Step-by-step explanation:

Given expression is:

$x^3+2x^2-5x-6$

We have to check if x-3 is a factor of given expression

In order for x-3 to be a factor of expression, we have to put x-3 = 0 => x=3 in expression.

If the expression is zero at x=3 then x-3 is a factor of expression otherwise not.

So putting x=333 in expression

$=(3)^3+2(3)^2-5(3)-6\\= 27+2(9) - 15-6\\= 27+18-15-6\\= 45-21\\=24 \neq 0$

As the expression is not equal to zero on x=3, x-3 is not a factor of given expression

Keywords: Polynomials, expressions

Learn more about polynomials at:

#LearnwithBrainly

8 0

3 years ago

Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished. Write an

marissa [1.9K]

Answer:

equation: p=15m+10

p=pages

m=months

amount of pages after 5 months: 85

Step-by-step explanation:

You know Clara already has 10 pages, and that 15 will be written per month. Therefore, the equation is p=15m+10

To find the answer for 5 months simply substitute m

15(5) + 10

75+10

85=total pages

3 0

2 years ago

Read 2 more answers

Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62° F. Sally's temperature can be described by z =

irina1246 [14]

Answer:

Sally's temperature is 97.27 °F.

Step-by-step explanation:

All the information given in the question tells us that the human body temperatures are normally distributed with a population's mean = 98.20°F and a standard deviation = 0.62°F.

The question gives us Sally's temperature in a z-score. We have to remember that the standard normal distribution is a particular case of a normal distribution where the mean = 0 and the standard deviation = 1.

Using the standard normal distribution, we can determine every probability associated with a normal distribution "transforming" the raw scores, coming from normally distributed data, into z-scores.

A z-score gives us the distance from the population's mean and is in standard deviation units. So, a z = 1.5 tells us that the value is 1.5 standard deviations above the mean. Conversely, a z = -1.5 tells us that the raw score is also 1.5 standard deviation from the mean, but in the opposite direction, that is, below the mean.

The formula for a z-score is as follows:

$\\ z = \frac{x - \mu}{\sigma}$ (1)

Where

$\\ x\;is\;the\;raw\;score$ .

$\\ \mu\;is\;the\;population\;mean$ .

$\\ \sigma\;is\;the\;population\;standard\;deviation$ .

Then to find x (or the raw score, that is, Sally's temperature), we need to solve the formula (1) for it to finally solve the question.

Then

$\\ \mu = 98.20^\circF$ °F

$\\ \sigma = 0.62^\circF$ °F

$\\ z = -1.5$

Thus (with no units)

$\\ -1.5 = \frac{x - 98.20}{0.62}$

$\\ (-1.5*0.62) = x - 98.20$

$\\ (-1.5*0.62) + 98.20 = x$

$\\ x = (-1.5*0.62) + 98.20$

$\\ -0.93 + 98.20$

$\\ x = 97.27$ °F

Thus, Sally's temperature is $\\ x = 97.27$ °F (rounding the answer to the nearest hundredth).

8 0

3 years ago

Read 2 more answers

An equation of a number and 25 equals to the sum of 141 and 159 divided by 2

Mamont248 [21]

Answer:

25 = 141 + 159/2

Step-by-step explanation:

5 0

3 years ago

Rhombus A has a base of 7 inches and an area of 35 square inches. Rhombus B has a base and height that are three times the base

STALIN [3.7K]

For rhombus A:
base = 7 in
area = 35 in²

Area of rhombus = b * h
⇒ 35 = 7 * h
⇒ h = 35/7
⇒ h = 5 in

Rhombus B:
height = 3*5 = 15 in
base = 7*3 = 21 in
Area = 15 * 21 = 315 in²

Area of rhombus B is 9 times area of rhombus A. When the dimensions are increased to 3 times the initial dimension, area became 9 times.

8 0

3 years ago

Read 2 more answers