Mathematics College

Which expression is equivalent to..?

Answers

Answer 1

The equivalent expression is the one in the last option:

[tex]\sqrt[10]{y}[/tex]

Which expression is equivalent to the given one?

Here we want to find an expression equivalent to:

[tex](\frac{1}{\sqrt{y} } )^{-1/5}[/tex]

Remember the two rules for exponents that we need to use here:

[tex]x^{-n} = (1/x)^n[/tex]

[tex]x^{1/n} = \sqrt[n]{x}[/tex]

Using the first rule, we can rewrite our expression as:

[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5}[/tex]

Now we can rewrite the root of a root to get:

[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5} = \sqrt[5]{\sqrt{y} } = \sqrt[10]{y}[/tex]

Where in the last step we just multiplied the exponents for the roots, we can see that the correct option is the last one.

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Related Questions

a man is standing on the edge of a cruise ship for animals with his binoculars he sees a seagull at an angle of eleevatuoj of 27 degrees and his binoculars tell him that the seagull is 94 feet away he also notices a dolphin at an angle of deepens ion it 46 degrees and knows that his binoculars eyesight is 44 feet agout lenses level solve for how high the seagull is above sea level and how far the man binoculars are from the dolphin

Answers

The seagull is approximately 47.86 feet above sea level, and the man's binoculars are approximately 46.25 feet away from the dolphin.

Let's denote the height of the seagull above sea level as "h" and the distance between the man's binoculars and the dolphin as "d."

For the seagull:

We have the angle of elevation as 27 degrees and the distance from the man's binoculars as 94 feet.

Using the tangent function, we can write:

tan(27 degrees) = h / 94

Solving for h, we have:

h = 94 × tan(27 degrees)

For the dolphin:

We have the angle of depression as 46 degrees and the distance from the man's binoculars as 44 feet (lenses level).

Using the tangent function, we can write:

tan(46 degrees) = h / d

Solving for d, we have:

d = h / tan(46 degrees)

Now, let's calculate the values:

h = 94 × tan(27 degrees) ≈ 47.86 feet

d = (47.86 feet) / tan(46 degrees) ≈ 46.25 feet

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Find the average value of f(x) = √81 - ² over the interval [0, 9].
Write the exact answer.
fave
1
Hint: The area of a quarter circle is ².
4
Submit Question

Answers

The average value of f(x) over the interval [-14, 14] is 0.

The average value of the function f(x) = 14 - |x| over the interval [-14, 14] we need to use the formula:

[tex]f_{ave[/tex] = (1/(b-a)) × integral(a to b) f(x) dx

a and b are the limits of integration.

a = -14 and b = 14.

So we have:

[tex]f_{ave[/tex] = (1/(14 - (-14))) × integral(-14 to 14) (14 - |x|) dx

Simplifying the integral get:

[tex]f_{ave[/tex] = (1/28) × integral(-14 to 0) (14 + x) dx + (1/28) × integral(0 to 14) (14 - x) dx

Evaluating the integrals get:

[tex]f_{ave[/tex] = (1/28) × [(14x + (x²)/2)|(-14 to 0) + (-14x + (x²)/2)|(0 to 14)]

[tex]f_{ave[/tex] = (1/28) × [(0 + 98) + (-196 + 98)]

[tex]f_{ave[/tex] = (1/28) × 0

f_ave = 0

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32.6 ÷ 1 =
32.6 ÷ 10 =
32.6 ÷ 100 =

Answers

Answer:

32.6

3.26

0.326

Step-by-step explanation:

You could use long division or a calculator to get these quotients (answers to division problems) but, probably you're supposed to see the pattern of how the decimal moves when you divide by 1, 10, 100 (these are powers of 10)

● Divide by 1, decimal does not move

● Divide by 10, the decimal moves left one place

● Divide by 100, the decimal moves left two places

AXYZ AMNL
X
XY =
33°
Y
LA
12
N
124°
N
8
M

Answers

The length of XY in the congruent triangle is 8 units.

How to find the side of congruent triangles?

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

Therefore, the triangle XYZ is congruent to the triangle MNL.

Hence,

ΔXYZ ≅ ΔMNL

Therefore,

XY = MN

XZ = ML

YZ = NL

Hence,

XY = MN = 8 units

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Divide.
>
(6x²+27x+17) = (x+4)
Your answer should give the quotient and the remainder.
Quotient:
Remainder:
X
Ś

Answers

Answer:

Quotient: 6x+3Remainder: 5

Step-by-step explanation:

You want the quotient and remainder from division of (6x² +27x +17) by (x +4).

Synthetic division

Synthetic division of a polynomial by a monic binomial is an easy way to perform the division without a lot of writing. The attachment pretty well describes the process.

The result is a quotient of 6x +3, and a remainder of 5.

Additional comment

A "monic" polynomial is one that has a leading coefficient of 1.

The number at upper left in the synthetic division tableau is the zero of the divisor. Using the negative of the divisor constant means we can add partial products, saving the confusion and error associated with subtraction.

A rectangular sticker has an area of 55 square mm and a perimeter of 32 mm. What are the dimensions of the sticker

Answers

The calculated dimensions of the sticker are 11 mm by 5 mm

How to determine the dimensions of the sticker

From the question, we have the following parameters that can be used in our computation:

shape = rectangle

perimeter = 32 mm

Area = 55 square mm

Represent the dimensions of teh sticker with x and y

So, we have

Area = xy

Perimeter = 2(x + y)

substitute the known values in the above equation, so, we have the following representation

xy = 55

2(x + y) = 32

So, we have

xy = 55

x + y = 16

When x = 11 and y = 5, we have

11 * 5 = 55

11 + 5 = 16

Hence, the dimensions of the sticker are 11 mm by 5 mm

Answers

The area of the triangle is 85 square units

How to find the area of a triangle using vertices?

The area of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by:

A = (1/2) [x₁(y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

Where:

B: (x₁, y₁) = (-8, 3)

O: (x₂, y₂) = (5, 4)

X: (x₃, y₃) = (-7, -10)

A = (1/2) [x₁ (y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

A = (1/2) [-8 (4 – (-10)) + 5(-10 – 3) + (-7)(3 – 4)]

A = (1/2) [-112 - 65 + 7]

A = 85 square units

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[45- (25+8)] X 18 PLS

Answers

By using the BODMAS rule, Where

B stands for the bracket, O stands for of, D stands for division, M stands for multiplication, A stands for addition, and S stands for subtraction

so ,now

[tex][45-(25+8)]*18\\[/tex]

[tex][45-33]*18\\=216\\[/tex]

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Answer:

216

Step-by-step explanation:

[45- (25+8)] X 18 =

assuming the capitalized x is a multiplicationRemember PEMDAS

[45 - (25 + 8)] × 18 =

[45 - 33] × 18 =

12 × 18 =

216

Which answer is an equation in point-slope form for the given point and slope?
point: (-4, 1); slope: 7
Oy+1=7 (x-4)
Oy+1=7 (x+4)
Oy-1=7 (x+4)
Oy-1=7(x-4)

Answers

Answer: C y-1=7 (x+4)

Step-by-step explanation:

Point slope formula

y - y₁ = m ( x - x₁ ) Where m= slope and (x₁ , y₁) is your point

Given:

point: (-4, 1); slope: 7

plug in to formula

y - 1 = 7 (x+4)

A. Determine if (x+2) is a factor of f(x) =x^3-3x^2-7x+6. Explain your reasoning.

Yes (x+2) is a factor of the function, because the remainder is zero.

No (x+2) is NOT a factor of the function, because the remainder is NOT zero.

B. Use division (long or synthetic) and/or factoring to write f(x) =x^3-3x^2-7x+6 in completely factored form, given that (x+2) is a factor of f(x).

select an answer
f(x)=
DNE
X=
Y=

C. Find all the zeros F(X)= x^3-3x^2-7x+6 . NO DECIMALS!

select an answer
y=
x=
DNE
F(X)=

Answers

A) Yes, (x+2) is a factor of the function, because the remainder is zero.

B) All the factor are,

⇒ (x + 2) (x² - 5x + 3)

C) All the zeroes are,

x = - 2

x = (5 ± √13)/2

Given that;

Function is,

⇒ f (x) = x³ - 3x² - 7x + 6

Now, We can check (x + 2) is a factor of function or not as;

If x + 2 is a factor of function, then x = - 2 is satisfy the function.

So, Put x = - 2;

⇒ f (x) = x³ - 3x² - 7x + 6

⇒ f (- 2) = (- 2)³ - 3 (- 2)² - 7 (- 2) + 6

⇒ f (- 2) = - 8 - 12 + 14 + 6

⇒ f (- 2) = 0

Thus, (x + 2) is a factor of the function,

Hence, We can find all the zeroes as;

(x + 2) ) x³ - 3x² - 7x + 6 (x² - 5x + 3

x³ + 2x²

------------

- 5x² - 7x

- 5x² - 10x

----------------

3x + 6

------------

Thus, We get;

⇒ x³ - 3x² - 7x + 6

⇒ (x + 2) (x² - 5x + 3)

Since, x² - 5x + 3 = 0

x = - (- 5) ± √(- 5)² - 4×1×3 / (2×1)

x = (5 ± √25 - 12) / 2

x = (5 ± √13)/2

Thus,

A) Yes, (x+2) is a factor of the function, because the remainder is zero.

B) All the factor are,

⇒ (x + 2) (x² - 5x + 3)

C) All the zeroes are,

x = - 2

x = (5 ± √13)/2

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Please help me with this 10-11

Answers

Answer:

10.) 152 square feet

11.) 85 degrees

Step-by-step explanation: *Feel free to ask for an explanation*

Ur answer would be A.152 sq feet for 10
And ur answe would be A.85 for 11

When rolling two dice, what’s the probability that the outcomes are greater than 9

Answers

Answer:6??

Step-by-step explanation:

Mrs. Kuhn is making a rectangular quilt. Each quilt square will be 4 inches long. In order to buy fabric, she needs to calculate the area of the quilt. What calculation should Mrs. Kuhn make in order to calculate the area?

the sum of the lengths of the four edges of the quilt
the sum of the number of squares in the length and width of the quilt
the product of 4 inches times the sum of the length and width of the quilt
the product of the number of squares in the length and width of the quilt

Answers

Calculation for Mrs. Kuhn's Quilt

-------------------------------------------------------------------------------------------------------------

To calculate the area of her rectangular quilt, Mrs. Kuhn needs to multiply the length and width of the quilt in inches. Since each quilt square is 4 inches long, the calculation for the area of the quilt is:

Area of quilt = Length of quilt x Width of quilt x (4 inches) ^2

Therefore, the correct calculation for Mrs. Kuhn to determine the area of her quilt is the product of 4 inches times the sum of the length and width of the quilt.

Suppose that the new England colonies of the basketball team is equally likely to win a game as not to win it.if 4 colonies games are chosen at random what is the probability that exactly 3 of those games were won by the colonies

Answers

The probability that exactly 3 of those games were won by the colonies is 25%.

We are given that;

Number of colonies= 4

Number of games= 3

Now,

To find the probability of exactly 3 wins out of 4 games, we can use the binomial probability formula1:

P(X = 3) = nCx * p^x * q^(n-x)

where n is the number of trials (4 games), x is the number of successes (3 wins), p is the probability of success (0.5), q is the probability of failure (1 - p = 0.5), and nCx is the combination of n things taken x at a time.

P(X = 3) = 4C3 * 0.5^3 * 0.5^(4-3) P(X = 3) = (4! / (3! * (4-3)!)) * 0.125 * 0.5 P(X = 3) = (24 / (6 * 1)) * 0.0625 P(X = 3) = 4 * 0.0625 P(X = 3) = 0.25

Therefore, by the probability the answer will be 25%.

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or Find the value of the expression 20 − 9 ÷ m × 2 × n for m = 3 and n =

Answers

The value of the expression 20 − 9 ÷ m × 2 × n for m = 3 and n = 2 is 8

How to find the value of the expression

From the question, we have the following parameters that can be used in our computation:

20 − 9 ÷ m × 2 × n

The values of m and n are given as

m = 3 and n = 2

Substitute the known values in the above equation, so, we have the following representation

20 − 9 ÷ 3 × 2 × 2

Evaluate the quotient

So, we have

20 − 3 × 2 × 2

Evaluate the products

So, we have

20 − 12

Evaluate the difference

So, we have

Hence, the value of the expression is 8

Answers

Answer:

79632 cu ft

Step-by-step explanation:

The volume of a rectangular prism is length x width x height. We are given the values 158 ft by 80 ft by 6.3 ft. All we do is multiply all 3 values by each other, (158)(80)(6.3). The answer after multiplying is 79632 cubic feet.

Maliha has 4 gallons of lemonade.
Jazmine has 5 times as much lemonade
as Maliha. How many quarts does
Jazmine have?

1 gallon = 4 quarts

Answers

Jazmine has 80 quarts of lemonade, which is 5 times the amount Maliha has (16 quarts).

We are given that Maliha has 4 gallons of lemonade. To find out how much lemonade Jazmine has, we need to calculate 5 times the amount Maliha has.

To convert the gallons to quarts, we know that 1 gallon is equal to 4 quarts.

Therefore, Maliha has 4 x 4 = 16 quarts of lemonade.

Now, since Jazmine has 5 times as much lemonade as Maliha, we can calculate Jazmine's amount by multiplying Maliha's amount (16 quarts) by 5.

Jazmine's lemonade = 16 quarts x 5 = 80 quarts.

Hence, Jazmine has 80 quarts of lemonade.

This can be understood as follows:

Maliha's 4 gallons of lemonade can be converted to 16 quarts (4 gallons x 4 quarts/gallon). Jazmine, on the other hand, has 5 times as much lemonade as Maliha.

Therefore, we multiply Maliha's amount (16 quarts) by 5 to find Jazmine's amount, which equals 80 quarts.

It's important to note that 1 gallon is equal to 4 quarts, which is a conversion factor used to convert between the two units of measurement.

By applying this conversion factor, we can determine the amount of lemonade in quarts for both Maliha and Jazmine.

In conclusion, Jazmine has 80 quarts of lemonade, which is 5 times the amount of lemonade Maliha has (16 quarts).

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For any positive number b not equal to 1 and any number or variable n,
evaluate the following expression.
blog =

Answers

For any positive number b not equal to 1 and any number or variable n, note that when evaluated, logb(bⁿ) = n.

What is a positive number?

A positive number is any integer that signifies something other than zero. Positive numbers include natural or counting numbers such as 1,2,3,4,5, fractions such as 3/5 or 232/345, and decimals such as 44.3.

Given logb(bⁿ) and b is any positive number, not equal to 1 and n is any number

If Logₓ ([tex]y^{z}[/tex]) = z * logₓ (y)

Then

Log[tex]_{b}[/tex] (bⁿ) = n * Log[tex]_{b}[/tex] (b)

If logₓ(y) = log[tex]_{z}[/tex](y) / log[tex]_{z}[/tex](x)

Then

Log[tex]_{b}[/tex] (b) = log[tex]_{z}[/tex] (b)/log[tex]_{z}[/tex] (b) = 1

Therefore,

Log[tex]_{b}[/tex] (bⁿ) = n * Log[tex]_{b}[/tex] (bⁿ)

= n x 1

= n

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Full Question:

Although part of your question is missing, you might be referring to this full question:

For any positive number b not equal to 1 and any number or variable n, evaluate the following expression.

logb(b^n) =

with logb being the base

x-intercepts of y=x^2+8x+7

Answers

The x-intercepts would be (-1,0) and (-7,0).

Find (f∘g)(5).
f(x)=x+1
g(x)=5x
(f∘g)(5)=

Answers

The value of function (f о g) (5) would be,

⇒ (f о g) (x) = 26

We have to given that;

Functions f and g are,

⇒ f(x) = x + 1

⇒ g(x) = 5x

Now, We can formulate;

⇒ (f о g) (x)

⇒ f (g (x))

⇒ f (5x)

⇒ 5x + 1

At x = 5;

⇒ 5 × 5 + 1

⇒ 25 + 1

⇒ 26

Thus, The value of function (f о g) (5) would be,

⇒ (f о g) (x) = 26

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Write your answer in scientific notation.

Answers

The difference of the expression in scientific notation is 1.2 * 10⁸

Evaluating the expression in scientific notation

From the question, we have the following parameters that can be used in our computation:

(5.6 * 10⁸) - (4.4 * 10⁸)

Factor out 10⁸ from the expression

So, we have

(5.6 * 10⁸) - (4.4 * 10⁸) = (5.6 - 4.4) * 10⁸

Evaluate the difference

(5.6 * 10⁸) - (4.4 * 10⁸) = 1.2 * 10⁸

Hence, the difference of the expression in scientific notation is 1.2 * 10⁸

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What is y and x equal to ?

Answers

The value of the variables will be 90° and 51°, respectively.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The angle at the periphery will be 90 degrees if it is made by the largest chord which is the diameter. Then we have

x = 90°

The sum of the angles of the triangle will be 180 degrees. Then the value of 'y' is calculated as,

39° + x + y = 180°

39° + 90° + y = 180°

y = 51°

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This question has two parts. First, answer Part A. Then, answer Part B. Part A Which statement best explains whether the relation shown in the graph is a function? A U-shaped graph on a coordinate plane. The graph passes through the points (negative 4, 4), (negative 2, negative 2), (0, negative 4), (2, 2), and (4, 4).

Answers

The relation shown in the graph is not a function because it violates the vertical line test.

We have,

The relation shown in the graph is not a function because it violates the vertical line test.

The vertical line test states that for a relationship to be a function, every vertical line drawn on the graph should intersect the graph at most once.

However, in this case, the U-shaped graph intersects the vertical line at multiple points, such as (-2, -2) and (2, 2).

Therefore, the relation does not meet the criteria of a function.

Thus,

The relation shown in the graph is not a function because it violates the vertical line test.

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Find the sum of -17x,-15x,-2x

Answers

-17x + (-15x) + (-2x) = -17x-15x-2x = -34x

10. Find the area of this kite. 6 2 2 7 Answers 26 units² 13 units² 13√2 units² 1343 units2

Answers

The area of the given kite is,

⇒ A = 26 units²

Now, In this case we have that the area of the kite is given by the area of two triangles,

And, the triangles share the same base with length,

2 + 2 = 4.

And, One of the triangles has height of 6 and the other has height of 7.

So, the total area of kite is,

A = 1/2 × 4 × 6 + 1/2 × 4 × 7

A = 12 + 14

A = 26 units²

Therefore, The area of the given kite is,

⇒ A = 26 units²

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Which coordinate is a zero of the function defined by 3x^2 – 15x – 18?

Answers

Answer:

[tex]3 {x}^{2} - 15x - 18 = 0[/tex]

[tex] {x}^{2} - 5x - 6 = 0[/tex]

[tex](x + 1)(x - 6) = 0[/tex]

x = -1 or x = 6

The coordinates of the zeroes are (-1, 0) and (6, 0).

18/6+5e-0.1x
Let f(x) =
What is f(6)?
Enter your answer in the box rounded to the nearest tenth.

Answers

The value of the function [tex]\rm f (x) = \frac{18}{6} + 5e^{-0.1x}[/tex] at x = 6 will be 5.744.

Given that:

Function, [tex]\rm f (x) = \frac{18}{6} + 5e^{-0.1x}\ \ or \ \ f (x) = 3+ 5e^{-0.1x}\\[/tex]

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The value of the function at x = 6 is calculated as,

[tex]\rm f (x) = 3+ 5e^{-0.1\times 6}\\\\f (x) = 3+ 5e^{-0.6}[/tex]

Simplify the equation further, then we have

f(x) = 3 + 5 · 0.5488

f(x) = 3 + 2.744

f(x) = 5.744

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A submarine is 42 feet belpw rhe surface of water .a shark directly above the submarine is 19 feet below the surface of the water.how many feer above the submarine is to the shark

Answers

The number of feet above the submarine is the shark is 23 feet.

Given that, a submarine is 42 feet below the surface of the water and shark is 19 feet below the surface of the water.

Here, location of shark = 42-19

= 23 feet

Therefore, the number of feet above the submarine is the shark is 23 feet.

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"Your question is incomplete, probably the complete question/missing part is:"

A submarine is 42 feet below the surface of the water a shark directly above the submarine is 19 feet below the surface of the water how many feet above the submarine is the shark.

On a test that has a normal distribution, a score of 30 falls three standard deviations below the mean, and a score of 60 falls three standard deviations above the mean. Determine the mean of this test.

Answers

The mean of the test is 45.

Let's use the formula for z-score:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the raw score, μ is the mean, and σ is the standard deviation.

For the first score of 30, we know that it falls three standard deviations below the mean:

-3 = (30 - μ) / σ

Simplifying this equation, we get:

-3σ = 30 - μ

μ = 30 + 3σ

For the second score of 60, we know that it falls three standard deviations above the mean:

3 = (60 - μ) / σ

Simplifying this equation, we get:

3σ = 60 - μ

μ = 60 - 3σ

Now we can set these two equations equal to each other, since they both equal μ:

30 + 3σ = 60 - 3σ

6σ = 30

σ = 5

Now we can plug this value of σ back into one of the equations for μ:

μ = 30 + 3σ

μ = 30 + 3(5)

μ = 45

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on the importance of setting Comment on in the novel

Answers

The setting of a novel is important because it provides the reader with context on the time, place, and environment that the story takes place in.

Why is setting important ?

It aids in setting the tone, showcasing personalities and tensions, and offering hints about the story's message.

One can establish an ambiance or emotional tone in a novel by means of its setting. One illustration can be seen in the book "The Great Gatsby" authored by F. Scott Fitzgerald uses the backdrop of the Jazz Age to generate a feeling of splendor and exhilaration.

The rapid tempo of the book mirrors the busy lives led by the characters, while the opulent festivities and luxurious habits of the affluent are employed to cultivate an air of indulgence and debauchery.

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The full question is:

On the importance of setting in the novel, comment on how it can be used to create a sense of realism, atmosphere, and meaning?

Other Questions