Which expression is equivalent to the following complex fraction?

The answer is 2^(9/10). I did it assuming with the ^5 you mean the 5th root of 4

ANSWER

[tex] {2}^{ \frac{9}{10} } [/tex]

EXPLANATION

The given expression is

[tex] \sqrt[5]{4} \times \sqrt{2} [/tex]

Recall that:

[tex] \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } [/tex]

[tex]\sqrt[5]{ {2}^{2} } \times \sqrt{ {2}^{1} } [/tex]

[tex]\sqrt[5]{ {2}^{2} } \times \sqrt{ {2}^{1} } = {2}^{ \frac{2}{5} } \times {2}^{ \frac{1}{2} } [/tex]

Recall that:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We now apply this property of a exponents to obtain:

[tex]\sqrt[5]{ {2}^{2} } \times \sqrt{2} = {2}^{ \frac{2}{5} + \frac{1}{2} } = {2}^{ \frac{9}{10} } [/tex]

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given y = 5(x + 1) = 5x + 5 ← in slope- intercept form

with slope m = 5

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{5}[/tex], thus

y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (10, 2) into the partial equation

2 = - 2 + c ⇒ c = - 2 + 2 = 4

y = - [tex]\frac{1}{5}[/tex] x + 4 ← in slope intercept form

Multiply all terms by 5

5y = - x + 20 ( add x to both sides )

x + 5y = 20 ← in standard form → D

Answer:

1556.25

Step-by-step explanation:

5 3/16.25×300=1556.25

Answer: 3 field goals, 4 touchdowns

Step-by-step explanation:

The number of field goals and touchdowns of the team score will be 3 and 4, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A football team scored a total of 37 points in a game. The team scored some field goals worth 3 points each and some touchdowns with extra points, each together worth 7 points. The team made 19 more points in touchdowns with extra points than in field goals.

Let 'x' be the number of field goals and 'y' be the number of touchdowns. Then the equations are given as,

3x + 7y = 37        ...1

7y = 3x + 19        ...2

From equations 1 and 2, then we have

14y = 56

y = 4

Then the value of 'x' is calculated as,

7(4) = 3x + 19

28 = 3x + 19

3x = 9

x = 3

The number of field goals and touchdowns of the team score will be 3 and 4, respectively.

More about the solution of the equation link is given below.

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Answer:

There are 286 possible combinations

Step-by-step explanation:

To solve this problem we must use the formula of combinations.

[tex]nCr =\frac{n!}{r!(n-r)!}[/tex]

Where n is the number of players that there are and elect r of them

In this case there are 7 + 6 = 13 players and you choose 10 of them

Then we look for  13C10

[tex]13C10 =\frac{13!}{10!(13-10)!}[/tex]

[tex]13C10 =\frac{13!}{10!*3!}[/tex]

[tex]13C10 =286[/tex]

There are 286 possible combinations

Answer:

I think the answer is  w = 16

Step-by-step explanation:

start by dividing -5 from both sides.

-5w=-80

/

-5

w=-16

Based on the phrase they gave, the inequality would look like this:

[tex]\frac{4-g}{8} >-15[/tex]

[tex]\frac{4-g}{8}\leq-15[/tex]

the quotient(÷) of [the difference(- subtraction) of 4 and a number(g) and 8] is at MOST -15.

since the sign is ≤, this means that the inequality is less than or equal to -15, so -15 is the maximum number for the inequality.

Your answer is the last option

Answer:

(D)

Step-by-step explanation:

I got it right on edge/quiz.

Answer:

60%

Step-by-step explanation:

Sales Price = 100 - 40 = 60%

The sales price is $30.00

Therefore 60% is equal to $30.00

60% = $30

1% = 30 ÷ 60 = $0.50

100% = 5 x 100 = $50

The original price is $50

Percentage of the original price = 30/50 x 100 = 60%

To determine the percentage of students who passed both exams, we first calculate the percentage of students who failed in either subject, then subtract that from 100%. Given that 15% failed in Science, 20% in Mathematics, and that 10% failed in both, we find that 75% of students passed both courses.

In this question, we have to find out the percentage of the candidates that passed in both subjects, Science and Mathematics. The percentages given show the failure rates in Science, Mathematics, and in both. Here, we need to use the concept of sets where we sum the individual percentages and subtract the intersection. It is defined as P(A U B) = P(A) + P(B) - P(A ∩ B).

According to the problem, 15% failed in Science and 20% in Mathematics. So, the candidates failing in any one of the subjects would be 15% + 20% = 35%. However, those who failed in both subjects (i.e., intersection part) is 10%, and double-counted when we added up the individual percentages. Therefore, we subtract this from our earlier total, giving us 35% - 10% = 25%. This implies that 25% of candidates fail in at least one subject.

As for those who pass in both, since we know that the total should be 100%, and we've figured out that 25% failed in at least one subject, thus, those who passed should be the remaining 75%.

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The percentage of those who passed in both the subjects is equal to 85%.

In order to determine the percentage of those who passed in both the subjects, we can use the principle of inclusion and exclusion;

Based on the principle of inclusion and exclusion, we have:

Total percentage of candidates who failed in either Science or Mathematics = A + B - C

Percentage of candidates who passed in both subjects = 100% - (A + B - C)

Percentage of candidates who passed in both subjects = 100% - (15% + 20% - 10%)

Percentage of candidates who passed in both subjects = 100% - 15%

Percentage of candidates who passed in both subjects = 85%.

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Answer: (i think these are right)

experimental: 27.08% theoretical: 50% ?

The deviation of the set of data is 678

Answer:

No, it is not.

Step-by-step explanation:

This is not proportional, however, it is linear

The answer is C. because the train will arrive any minute. This is because an adverb clause is a clause that functions as an adverb, and it modifies or describes a verb, adverb or adjective.

Answer:

it should be 9,8

Step-by-step explanation:

After 3 days Chelsea and Zack earn the same amount for dog sitting.

Equation for Chelsea: y = 3x + 2

Equation for Zack: y = 3x

After how many days they earn the same amount: After 3 days; both Chelsea and Zack earn $9.

the possible solutions of this equation. Is that they are not real.

Answer:

Step-by-step explanation:

6x-2y<10 :  3x -y <5

then :  3x -y -5< 0

given the line : 3x-y-5 = 0

the points is a solution to the system of equalities? 6x-2y<10 Located on the line : 3x-y-5 = 0 and under the x - axis.

[tex]d[/tex] stands for distance.

[tex]

d(J, K)=\sqrt{(7-2)^2+(8-4)^2}=\sqrt{25+16}\approx6.4

[/tex]

[tex]

d(J, L)=\sqrt{(1-2)^2+(-1-4)^2}=\sqrt{1+16}\approx4.12

[/tex]

[tex]d(J, K)>d(J, L)[/tex] therefore the answer is D.

Answer:

new value = $50 × (1 − 0.12)3 = $50 × 0.883 = $34.07.

Step-by-step explanation:

She will need 8 cups of vinegar.

Hope this helps!

Answer: 1:45

Step-by-step explanation: If Tom left his house at 1:00 and it took him 45 minutes to get the pool, adding 45 minutes to 1:00 would make his arrival time 1:45. Therefore, he arrived at the pool club at 1:45. Have a great day!

Answer:

Step-by-step explanation:

The answer is a I am not sure

The relationship described by y = 4x + 4 is not proportional because Option D. the graph does not pass through the origin. The y-intercept is 4, indicating it does not meet the criteria for direct proportionality.

The equation y = 4x + 4 describes a linear relationship between x and y. However, for two quantities to be directly proportional, their relationship must be of the form y = kx, meaning that the graph of their relationship must pass through the origin (0, 0).

In the equation y = 4x + 4, the y-intercept is 4, not 0. Therefore, the graph of this equation does not pass through the origin.

Option D) No, because the graph of the equation does not pass through the origin.

Answer:

f(x) has three real roots and two imaginary roots.

Step-by-step explanation:

Given that three roots of a fifth degree polynomial function f(x) are -2,2 and (4+i).

Now we need to find about which of the given statements describes the number and nature of all roots for this function.

We know that imaginary roots always occur in conjugate pairs.

So if (4+i) is root then (4-i) must also be the root.

So now we have total 4 roots

-2, 2, (4+i) and (4-i).

Degree of the polynomial is 5 so that means 1 root is still remaining. It can't be imaginary as that must be in pairs

So that means 5th root is real.

Hence correct choice is :

f(x) has three real roots and two imaginary roots.

Answer:

2x^2+7x-61

Step-by-step explanation:

The blue triangle is the dilated shape from the red triangle.

The dimensions of the blue triangle are half the red one.

The answer is B)1/2.

Answer:1/2

Step-by-step explanation:

Took the test on edge

Step-by-step explanation:

[tex]\text{Put}\ x=-2,\ x=0\ \text{and}\ x=3\ \text{to the equation}\ y=4^x:\\\\y=4^{-2}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\y=\dfrac{1}{4^2}=\dfrac{1}{16}\\-----------------\\\\y=4^0=1\\-----------------\\\\y=4^3=64[/tex]

A)20

B)History

C)$5

D)yes

The correct answer is A) What is your age because This question is a statistical question because the survey is for people of "various ages." Finding out the ages of the greatest number of people who have not seen the game will help the company develop advertising that will reach and appeal to that group.

Answer:

it's the 2nd one

Step-by-step explanation:

d = 3 + at^2

-3 | -3

d - 3 = at^2

d - 3/a = t^2

√d - 3/a = √t^2

t = √d - 3/a

Step-by-step explanation:

So if segment QS and segment PR are equal then all parts are equal which means segment QT= segment PT, segment TR= segment TS. segment QS id equal to 12 which means segment PR is equal to 12. You get segment TR by subtracting 4.9 from 12. Now you know that segment TR is 7.1 which means that segment TS is 7.1.

You also know that segment PS is equal to segment QR so you know that segment QR is 9cm because segment PS is 9cm.

m∠QPR is 33° because you know that ΔQPR's sum is 180 and you know that ∠PQR is 114° b/c 44+70 is 144, 180-144=66 now you take 66 and divide it by 2 (for the two angles left) that equals 33.

m∠STR is 92°. You know this by taking the base angle in ΔPTQ and multiplying it by two (which now equals 88, the base angle is 44°) and you take this number and subtract it from 180. 180-88=92. 92 is you measure of angle STR.

Answer:

10^5 = 100.000

Step-by-step explanation:

We know that 10^5 = 10 * 10* 10 * 10 * 10 = 100.000.

So, we have that 10^5 = 100.000

For this case we have the following expression:

[tex]10 ^ 5[/tex]

Then, as the exponent is positive, we must move the decimal as many times as indicated by the exponent. In this case, we must move it 5 spaces to the right, that is:

[tex]10 ^ 5 = 100000[/tex]

Answer:

[tex]10 ^ 5 = 100000[/tex]

y = 3(-x - 2)

Any horizontal transformations or reflections you make to y = x must be within the parentheses.

The transformed function is g(x) = -7 [tex]log_6[/tex] (-x) +2

The given base function is

f(x) = [tex]log_6[/tex] (x)

Then we have to find the transformed function.

First of all, the graph of the base function f(x) = [tex]log_6[/tex] (x) is vertically stretched by a factor of 7, then the newly transformed function becomes y = 7[tex]log_6[/tex](x)

Then the graph of y = 7[tex]log_6[/tex](x) is reflected over the x-axis, then the newly transformed function becomes y = -7log6(x)

Then the graph of y = -7[tex]log_6[/tex](x) is reflected over the y-axis, then the newly transformed function becomes y = -7[tex]log_6[/tex](-x)

And finally, the graph of y=7log6(-x) is vertically shifted up by 2 units, then the newly transformed function becomes

y = -7 [tex]log_6[/tex] (-x) +2

which is the required equation for the transformed function.

Answer:

2.5 & 1.1

Step-by-step explanation:

that answer is correct ^