Which of the following is equal to m^5/2, for all value of m?

(a) |-9| + 6 = 9 + 6 = 15

(b) |-9 + 6| = |-3| = 3

Answer: a is more than 1 but less than 2

Step-by-step explanation:

b > 1

0 < [tex]\frac{1}{b}[/tex] < 1

0 + 1 < 1 + [tex]\frac{1}{b}[/tex] < 1 + 1

1 < 1 + [tex]\frac{1}{b}[/tex] < 2

So 1 < a < 2

maybe try using the 2 and dropping the decimal

Answer:

b.  -x + y = 0

Step-by-step explanation:

Direct variation:

Direct variation means "y varies directly as x”:

[tex]y \propto x \implies y=kx[/tex]

where k is the (non-zero) constant of variation.

To determine which of the given equations represents a direct variation, isolate y for each and compare with the direct variation equation.

Equation a

[tex]y=\dfrac{4}{3}x-2[/tex]

This is not a direct variation equation as there is an addition of -2.

Equation b

[tex]-x+y=0[/tex]

[tex]\implies y=x[/tex]

This is a direct variation equation where the constant of variation is 1.

Equation c

[tex]xy=8[/tex]

[tex]\implies y=\dfrac{8}{x}[/tex]

This is not a direct variation equation as y is inversely proportional to x.

Equation d

[tex]y=14[/tex]

This equation does not include the variable x, and so is therefore not a direct variation equation.

If y varies inversely with x then the line must be linear and increasing

And the y intercept must be 0 in y=mx+c

#1

c=-2

#2

Yes

#3

No

#4

Parallel to x axis no direct variation

Using the concept of vertical and horizontal asymptotes, it is found that the function will have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1 for a = -1 and m = 1.

In this problem, the function is:

[tex]f(x) = \frac{2x^m}{x + a}[/tex]

It has a vertical asymptote at x = 1, hence:

x + a = 0

1 + a = 0

a = -1

It has a horizontal asymptote at y = 2, hence:

[tex]\lim_{x \rightarrow \infty} f(x) = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x + a} = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x} = 2[/tex]

[tex]2^{m-1} = 2[/tex]

Then, since we want to simplify, the exponents at the numerator and the denominator have to be equal, hence m = 1.

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Answer:

20

Steps-by-step explanation:

sorry mistake

Answer:

12

Explanation: I just counted them! :) and there was 6 in the middle and on the outside so 6 + 6 = 12! :)

The true average strain in a way that conveys information about precision and reliability is 27.314.

Given that sample size is 20, mean is 26%, standard deviation is 3.4, confidence level is 95%.

We have to calculate the true average strain in a way that conveys information about precision and reliability.

We have to use t test in our problem because sample size is less than 30.

Weknow that,

t=x bar-μ/s[tex]\sqrt{n}[/tex]

where μ is sample mean,

s is sample standard deviation.

Degree of freedom=n-1

=20-1

=19

T value at 95% confidence interval=1.7281

put the values in the formula of t given above.

1.7291=x bar-26/3.4/[tex]\sqrt{20}[/tex]

1.7291=xbar-26/3.4/4.47

1.7291= x bar-26/0.76

1.7291*0.76=x bar-26

1.314=x bar-26

x bar=26+1.314

x bar=27.314

After rounding it will be 27.31

Hence the true average strain in a way that conveys information about precision and reliability is 27.31%.

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The correct option is (2)  [tex]\frac{8}{5}[/tex] and (3)  [tex]\frac{1}{6}[/tex].

The factor of equation  f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

The rational root theorem, also referred to as the rational zero theorem, is a potent mathematical technique used to identify all potential rational roots of polynomial equations of order 3 and above.

For the given polynomial, the roots are given as;

[tex]$$P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}$$\\ \\$\pm \frac{\text { factors of } a_{0}}{\text { factors of } a_{n}}$.[/tex]

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.

Out of the given options, only   [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex] can be written in the form:  

[tex]\begin{aligned}&\frac{8}{5}=\frac{\text { a factor of } 8}{\text { a factor of } 60} \\&\frac{1}{6}=\frac{\text { a factor of } 8}{\text { a factor of } 60}\end{aligned}[/tex]

Therefore, the rational roots of polynomial f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

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The complete question is-

Which is a factor of f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8? use the rational root theorem to help you find your answer.

Answer:

-2y= -23-15

-2y=-38

-y= -38/2

-y=19 proved

Pairs of triangles appear to be congruent are :

Triangles 2 and 3. Option B

Triangles 2 and 4. Option D

Triangles 3 and 4. Option E

Congruent triangles can be defined as the pairs of triangles with same measurement

Triangles 2 and 3 :

After observing triangles 2  and  3  it appears that triangle  is congruent to triangle  .

Option C

Triangles 2 and 4

After observing triangles 2  and 4   it appears that triangle 2 is congruent to triangle 4 .

Option D

E. Triangles 3 and 4

After observing triangles 3  and 4. They are congruent

Option E

Hence, Option B, D and E are correct of the triangles

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Answer:

Triangles 3 and 4
Triangles 1 and 4
Triangles 1 and 3

Step-by-step explanation:

if this is wrong tell me so i can edit the answer, but this is what i got

Answer:

[tex]\huge\boxed{\sf 81x^4 - 16y^4}[/tex]

Step-by-step explanation:

= (3x - 2y)(3x + 2y)(9x² + 4y²)

= [(3x)² - (2y)²] (9x² + 4y²)

= (9x² - 4y²)(9x² + 4y²)

Using the above formula again

= (9x²)² - (4y²)²

[tex]\rule[225]{225}{2}[/tex]

The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of sine and cosine will be always less than a unit.

In a unit circle, the radius of the circle represents the hypotenuse of the triangle. Since the hypotenuse is the largest side of the triangle, the ratio of the perpendicular to the hypotenuse and the base to the hypotenuse both will be less than the hypotenuse, therefore, 1. Hence, the value of sine and cosine will be always less than a unit.

In construction, we use trigonometry. For figuring areas of triangular shapes, similar to many concepts and phenomena in mathematics.

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Answer:

Distributive property

Step-by-step explanation:

In order to solve this equation we first need to distribute 3 into 2y+5, we use the distributive property to do this.

Answer:

24

Step-by-step explanation:

3x4x2=24

When finding the answer to this problem, you times all of the options by each other.

Answer:

a = (9,8)

b=(10,6)

c=(4,3)

Step-by-step explanation:

basically, you just take the original coordinates and add the translation to it.

so a was -1,6 so just at 10 to -1 as they are x coordinates nad add 2 to 6 because they are Y coordinates and you just do it for all of the points.

Total possible outcomes are 312

We need to find that if you roll a 6-sided die and draw a card from a deck of 52 cards,what are total possible outcomes

Probability is a measure of the possibility that an event will occur. Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it. Probability can range from 0 to 1, where 0 means an event is impossible and 1 means a certain event

An outcome is the result of an event that depends on probability. Probability refers to the likelihood that something will happen, and an event can have more than one possible outcome.

Enumeration of possible outcomes is the process of determining the number of possible outcomes for an event. There are various methods to carry out this process. The best way to calculate the number of possible outcomes of an event depends on the type of event and the structure of the event

If a 6-sided die and draw a card from a deck,

then each side has total possible outcome 52

so, total number of possible outcomes for 6 - sided dice are 52 * 6

= 312

Hence total number of possible outcomes are 312

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CD is the perpendicular bisector of another line AB which can be proven below.

Perpendicular bisector is a line that divides another line into two equal halves in such a way that it creates an angel of 90°.

To proof that CD is the perpendicular bisector of another line AB the following is carried out;

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Answer:

heres what i got

Step-by-step explanation:

2.  definition of a perpendicular bisector

5. reflexive property of congruence

11. definition of square root

Answer:

We have,

According to given figure.

PQ=PR(giventhat)

QS=SR(Bydefinationofmidpoint)

PS=PS(Commonline)

Then,

ΔSPQ≅ΔSPR   (BY congruency S.S.S.)

Hence, PS bisects ∠PQR by definition of angle bisector.

Answer: SA = 445.05

Step-by-step explanation:

Step-by-step explanation:

Well first let's find the derivative in using the power rule

h'(t) = (-4.9)t + 157

h'(t) = -9.8t + 157

we can see from the image above that the maximum height is 1452.602 so that is the answer to the second question.

h'(1452.602) = -9.8(1452.602) + 157

h' = 14,078.500

Answer:

[tex]BC=5\sqrt{2}[/tex], [tex]AC=5\sqrt{4}[/tex]

Step-by-step explanation:

In a 45-45-90 relation triangle the two shortest sides will have equal length, meaning:

[tex]BC=5\sqrt{2}[/tex]

To find the hypotenuse we must multiply the shortest side by [tex]\sqrt{2}[/tex], both sides are equal so it doesn't matter which we multiply.

[tex]AC=5\sqrt{2} \sqrt{2} \\AC=5\sqrt{4}[/tex]

The distance between the helicopter and the first home is 369. 87 m

The distance between the helicopter and the first home can be found using sine law,

Therefore,

180 - 72 - 49 = 59 degrees.

Hence,

420 / sin 59 = A / sin 49°

where

A  = distance form the first home to the helicopter.

cross multiply

420 sin 49 = A sin 59°

A = 420 sin 49 / sin 59

A = 316.978023694 / 0.8571673007

A = 369.869339199

A = 369. 87 m

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The number of minutes it take to complete the same job if sandy and randy work together than if sandy works alone is 18mins.

According to this question, Sandy rakes and bags the leaves on her front lawn in 30 mins while Randy does the same job in 20 mins.

To calculate the time it will take both of them to work together, we use the following expression;

1/30 + 1/20 = 1/x

x = 12mins

Therefore, it will take 30 - 12 = 18 mins, to complete the same job if sandy and randy work together than if sandy works alone.

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A rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."

By critically observing the given function, we can logically deduce that it is an exponential function. Also, the initial value of this exponential function is 1 with a growth factor is 12.

For instance, we have:

At x = -1

y = 12^(-1)

y = 1/12

At x=0

y = 12^(0)

y = 1

At x = 1

y = 12^(1)

y = 12

In conclusion, a rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."

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[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]=[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]

Therefore,

125 = 5³

27 = 3³

Hence,

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} }[/tex]

Hence,

Both cube root are the same now,

Therefore, we have to add them together.

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

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Answer:

D. The slope is -2. The y-intercept is (0,3)

Step-by-step explanation:

You can use any two points.

Let's use the first two points: (0, 3), (2, -1)

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (-1 - 3)/(2 - 0)

slope = -4/2

slope = -2

The y-intercept occurs when x = 0. For x = 0, y = 3, so the y-intercept is 3 which means the point (0, 3).

Answer: D. The slope is -2. The y-intercept is (0,3)

The median of the list of numbers is 7

The number is given as:

9.5, 4.4, 8.1, 2.9, 9.2, 3.2, 9.4, 7, 2.5

Rearrange the numbers in ascending order

2.5, 2.9, 3.2, 4.4, 7, 8.1, 9.2, 9.4, 9.5

The median is the middle number.

The middle number here is 7

Hence, the median of the list of numbers is 7

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Answer:

1.11

Step-by-step explanation:

The amount I'll have in two years at the growth rate described is; $1.21x.

Since it follows that the savings grow by 10% each year, it can be concluded that the growth factor is; 110% = 1.1

Hence, in two years, we have;

= $x × (1.1)²

= $1.21x.

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Answer:

1.21x

Step-by-step explanation:

on rsm it says its correct