Simplify the rational expression. State any restrictions on the variablen^4-10n^2+24/ n^4-9n^2+18

Answers

Answer 1

Answer:

Answer:

The simplified form is $=((n-2)(n+2))/((n-\sqrt3)(n+\sqrt3))$

The variable n can not be equals to $\pm\sqrt3$ as for these value denominator equals to zero which becomes an indeterminate form.

Step-by-step explanation:

we have to simplify the rational expression and state the restrictions on the variable.

$(n^4-10n^2+24)/(n^4-9n^2+18)$

We can now see that both the numerator and denominator are quadratic trinomials in $n^2.\$

We split the middle terms as follows;

$(n^4-10n^2+24)/(n^4-9n^2+18)=(n^4-6n^2-4n^2+24)/(n^4-3n^2-6n^2+18)$

$=(n^2(n^2-6)-4(n^2-6))/(n^2(n^2-3)-6(n^2-3))$

$=((n^2-4)(n^2-6))/((n^2-6)(n^2-3))$

$=((n-2)(n+2))/((n-\sqrt3)(n+\sqrt3))$

which is the simplified form of given expression.

The variable n can not be equals to $\pm\sqrt3$ as for these value denominator equals to zero which becomes an indeterminate form.

Answer 2

Answer: The answer to the question is n^2-4/n^2-3 n ≠±√6±√3

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What is the solution to the equation?5(8 + 7) = 5 • x + 5 • 7

A.
x = 1

B.
x = 5

C.
x = 7

D.
x = 8

Answers

5(8 + 7) = 5(8) + 5(7) . . . . . . . . (distributive property)
Therefore, x = 8

X=8 completely right.

Lane is 10 times Mels age. If the difference in their age is 27, how old is Mel?

Answers

The answer is 3!

explanation; 3x10 equals 30. the difference is 27 years and 30-3=27!

L = 10M
27 = L - M

27 = 10M - M

27 = 9M

M = 3

L = 10M = 10(3) = 30

Lane is 30 years old
Mel is 3 years old

Ronda Rollins gets a Social Security benefit of $350 per month. Her husband receives a benefit equal to 200 percent of Ronda's benefit. If they take an additional $400 per month from savings, what will their monthly income be?700
750
1,050
1,450

Answers

Answer

Find out the what will their monthly income be .

To proof

Let us assume that the their monthly income be x .

As given

Ronda Rollins gets a Social Security benefit of $350 per month

Her husband receives a benefit equal to 200 percent of Ronda's benefit.

If they take an additional $400 per month from savings .

200% written in the decimal form

$= (200)/(100)$

Than the equation becomes

$x = 350 + 2* 350 + 400$

x = 350 + 700 + 400

x= $1450

Therefore monthly income be $1450 .

Option (D) is correct .

Hence proved

350+(2*350)+400=1450

Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.

Which graph best represents the scenario described?

A coordinate plane graph is shown. The axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 5, decreases to 0.25 comma 2, stays horizontal to 0.6 comma 2, then increases to 0.75 comma 9. The line is horizontal to 1.75 comma 9.

A coordinate plane graph is shown. The axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 0, increases to 0.3 comma 2, increases to 0.5 comma 5, then increases to 0.75 comma 9. The line decreases to 1.75 comma 0, where it touches the axis.

A coordinate plane graph is shown. The x-axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 0, increases to 0.25 comma 5, stays horizontal until 0.5 comma 5, then increases to 0.75 comma 9. The line is horizontal until 1.75 comma 9.

A coordinate plane graph is shown. The axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 5, is horizontal to 0.3 comma 5, increases to 0.5 comma 6, is horizontal to 0.8 comma 6, then increases to 1.75 comma 9

The graph shown represents the funds in Sasha’s checking account over 16 days.

Which description would best explain what was happening to Sasha’s checking account during interval C on the graph?

Sasha deposited her paycheck.

Sasha paid her rent.

Sasha did not withdraw or deposit any money.

Sasha withdrew spending money.

Answers

Part 1: Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.

If we graph this there will be 3 segments because the slope of each segment is Keisha's speed during that interval:

⇒ The middle segment will have no slope,which makes the slope undefined.

⇒ The 1st and 3rd segments will have positive slopes, If a line has a positive slope, variable y always increases when x increases.

Choice A). A coordinate plane graph is shown. The axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 5, decreases to 0.25 comma 2, stays horizontal to 0.6 comma 2, then increases to 0.75 comma 9. The line is horizontal to 1.75 comma 9.

The given graph started that the time is 0, when Keisha begins
running. she is already 5 blocks from home. So this data is incorrect. The graph also states that the line decreases,when she runs toward her home.

Terrible choice.

Choice B). A coordinate plane graph is shown. The axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 0, increases to 0.3 comma 2, increases to 0.5 comma 5, then increases to 0.75 comma 9. The line decreases to 1.75 comma 0, where it touches the axis.

Terrible choice.

Choice C). This is the correct answer. It includes all the information that appears on the given graph, and it matches the given story.

Choice D). A coordinate plane graph is shown. The axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 5, is horizontal to 0.3 comma 5, increases to 0.5 comma 6, is horizontal to 0.8 comma 6, then increases to 1.75 comma 9

Terrible choice.

Part 2 : Sasha withdrew spending money. Meaning : To remove (money) from an account.

The correct answer is the last one.

Q1:
Answer:
A coordinate plane graph is shown. The x-axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 0, increases to 0.25 comma 5, stays horizontal until 0.5 comma 5, then increases to 0.75 comma 9. The line is horizontal until 1.75 comma 9.

Explanation:
First segment: distance and time increases (Keisha ran to Natasha's house)
Second segment: time increases, distance is constans (Keisha stayed at Natasha’s house)
Third segment: distance and time increases (Keisha and Natasha ran to swim practice)
Fourth segment: distance is constans, time increases (Keisha and Natasha stayed on practice).

Q2.
Answer:
Sasha did not withdraw or deposit any money. (During 5 days of the account balance has not changed).

"From the graph of g, state the intervals on which g is continuous. Select all that apply.(-INFINITY, -4]
(-INFINITY, -4)
[-4,-2]
[-4,-2)
[-2,2]
(-2,2)
[2,4]
[2,4)
[4,6]
(4,6)
[6,8]
(6,8)
[8,INFINITY)
(8,INFINITY)"

Answers

Final answer:

Without seeing the graph, it's not possible to give specific intervals where the function g is continuous. However, based on interval notation, round brackets indicate the end points are not included, while square brackets show they are included. Therefore, the function is continuous where the graph does not have gaps, jumps or holes.

Explanation:

Without seeing the exact graph, it's impossible to accurately determine the intervals on which g is continuous. However, in general, a function is said to be continuous over an interval if the graph is unbroken over this interval, without any gaps, jumps, or holes. To determine this from the choices provided, generally you'll need to look at the graph and see where there is an uninterrupted line.

A key thing to note is how the intervals are represented. For instance, an interval like (-Infinity, -4] means that the function is continuous from negative infinity up to and including -4. The round bracket, '( )', means that the end points are not included in the interval, while the square brackets, '[ ]', indicate that they are included.

Learn more about Intervals of Continuity here:

brainly.com/question/35326464

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What two positive real numbers whose product is 50 have the smallest possible sum?

Answers

x * y = 50
y = 50 / x
S = x + y = x + 50 / x
S` = 1 - 50 / x²
1 - 50 / x² = 0
50 / x² = 1
x² = 50
x = √ 50 = 5 √2
y = 50 / 5√2 = 5 √2
Answer:
Those numbers are: x = 5√2 and y = 5√2.

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