Answers
To determine if expressions are equivalent, we simplify them or substitute variables with actual values to see if they yield the same result. We simplify by eliminating terms where possible, grouping like terms, and applying mathematical operations.
Explanation:Without the original mathematical expressions, it's difficult to provide direct answers to your question. Normally, we determine whether expressions are equivalent by simplifying them using algebraic rules or substituting variable with actual values to see if they produce the same results.
For example, the expressions 2(3 + 5) and 6 + 10 are equivalent because they both simplify to 16. We identify equivalent expressions by simplifying which includes eliminating terms where possible, grouping like terms, and applying mathematical operations.
Ultimately, the exact process may vary depending on the complexity and specific form of the expressions in question.
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The expressions equivalent to [tex]$\sqrt[3]{128}^x$[/tex] are (c) [tex]$(4 \sqrt[3]{2})^x$[/tex] and (d) [tex]$\left(4\left(2^{\frac{1}{3}}\right)\right)^x$[/tex] due to their compatible structures with the original expression.
To determine which expressions are equivalent to [tex]$\sqrt[3]{128}^x$[/tex], let's simplify the given expression first:
[tex]\[\sqrt[3]{128}^x = 2^x \times \sqrt[3]{2}^x\][/tex]
Now, let's compare this with the provided options:
a. [tex]$128^{\frac{x}{3}}$[/tex] - Not equivalent.
b. [tex]$128^{\frac{3}{x}}$[/tex] - Not equivalent.
c. [tex]$(4 \sqrt[3]{2})^x$[/tex] - Equivalent, as [tex]$4 = 2^{\frac{3}{2}}$[/tex].
d. [tex]$\left(4\left(2^{\frac{1}{3}}\right)\right)^x$[/tex] - Equivalent, as [tex]$2^{\frac{1}{3}} = \sqrt[3]{2}$[/tex].
e. [tex]$(2 \sqrt[3]{4})^x$[/tex] - Not equivalent.
Therefore, the expressions (c) [tex]$(4 \sqrt[3]{2})^x$[/tex] and (d) [tex]$\left(4\left(2^{\frac{1}{3}}\right)\right)^x$[/tex] are equivalent to [tex]$\sqrt[3]{128}^x$[/tex].
Related Questions
What is the measure of each interior angle for a regular polygon with 30 sides?
Answers
5040/30=168 degrees in each interior angle
What geometric formula relates the radius of a circle to its area?
Answers
r = radius
[tex] A = \pi r^{2} [/tex]
The geometric formula for the radius of a circle to its area will be;
A = πr²
Where, A is area of circle , r is radius of circle.
What is Circle?
Circle is a closed two dimensional figure in which the set of all points in the plane is equidistance from the center of circle.
Let radius of a circle = r
And, Area of a circle = A
Then, The geometric formula for the radius of a circle to its area will be;
A = πr²
Thus, The geometric formula for the radius of a circle to its area will be;
A = πr²
Where, A is area of circle , r is radius of circle.
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There are 8 pencils in package.how many packages will be needed for 28 children if each child get 4 pencils
Answers
28 children need pencils
Each child gets 4 pencils
28x4 = 112 (pencils needed)
112/8 = 14 packages needed.
Find the difference quotient please
Answers
[tex]f(x) = \frac{x}{x+6} [/tex]
Answers:
[tex]f(a) = \frac{a}{a+6} [/tex]
[tex]f(a+h) = \frac{a+h}{a+h+6} [/tex]
[tex] \frac{f(a+h)-f(a)}{h} = \frac{6}{(a+h+6)(a+6)} [/tex]
Explanation:
[tex]f(a+h)-f(a) = \frac{(a+h)(a+6)-a(a+h+6)}{(a+h+6)(a+h)} \\ = \frac{a^{2}+6a+ah+6h-(a^{2}+ah+6a)}{(a+h+6)(a+6)} \\= \frac{6h}{(a+h+6)(a+6)} [/tex]
[tex] \frac{f(a+h)-f(a)}{h} = \frac{6}{(a+h+6)(a+6)} [/tex]
An urn contains six chips, numbered 1 through 6. two are chosen at random and their numbers are added together. what is the probability that the resulting sum is equal to 5?
Answers
Final answer:
The probability of drawing two chips from an urn numbered 1 through 6 such that their sum is 5 is 4/15, since there are four favourable outcomes (1,4), (2,3), (3,2), and (4,1) out of the total 15 possible combinations.
Explanation:
The question involves calculating the probability of drawing two chips from an urn, each numbered 1 through 6, such that their sum equals 5. To solve the problem, let's consider all possible combinations of two different chips that can be drawn at random:
(1, 4)(2, 3)(3, 2)(4, 1)There are 4 favourable combinations that result in a sum of 5. As each chip can be drawn only once, the total number of pairs can be given by the combination formula C(n, k) = n! / (k!(n-k)!)), where n is the total number of chips and k is the number of chips drawn. In this case, C(6, 2) = 6! / (2!4!) = 15, and so there are 15 possible pairs that can be drawn from our urn.
Therefore, the probability of getting a sum of 5 is the number of favourable outcomes divided by the total number of outcomes, which is 4 favourable combinations divided by 15 possible combinations, resulting in a probability of 4/15.
You have 2 types of bread, 3 types of meat, and 2 types of cheese. How many different sandwiches can you make if each sandwich has 1 type of bread, 1 type of meat, and 1 type of cheese?
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Which temperature conversion is correct? °c = k - 273 k = 273 x °c k = °c - 273 °c = k + 273?
Answers
Answer: The formula to convert kelvin to degree celsius is:
°C=K-273
First option: °C=K-273
how can i turn 7/2 into a decimal
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half of 6 is 3 as you need 2 lots of 3 to make six
half of 1 is 0.5 as you need 2 lots of 0.5 to make 1
therefore 3 + 0.5 is 3.5.
you need 2 lots of 3.5 to make 7
[tex] \frac{7}{2} \cdot \frac{5}{5} = \frac{35}{10} [/tex]
Or, as a mixed number:
[tex]3 \frac{5}{10} [/tex]
If you're familiar with how to read decimal values, "3 and 5 tenths" can be written in decimal form as 3.5.
What is the area of the trapezoid shown? (1) angle a = 120 degrees (2) the perimeter of trapezoid abcd = 36?
Answers
Neither statement alone is sufficient to determine the area of the trapezoid.
Explanation:The area of a trapezoid can be found using the formula:
Area = (1/2) * (sum of parallel sides) * height
To find the area of the trapezoid, we need the lengths of the parallel sides and the height.
(1) The given angle does not provide information about the lengths of the sides, so it is not sufficient to find the area.
(2) The perimeter of the trapezoid does not directly give information about the lengths of the sides, so it is also not sufficient to find the area.
Therefore, neither statement alone is sufficient to determine the area of the trapezoid.
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Please help guys!!
What set of transformations is performed on LMNO to form L'M'N'O'?
A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin
A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin
Answers
Answer:
Its b and can you give me the brainlist
Step-by-step explanation:
Why is it incorrect
Answers
[tex]\bf \cfrac{|3v-1|}{5}\ge 4\implies |3v-1|\ge 20\implies \begin{cases} +(3v-1)\ge 20\\ -(3v-1)\ge 20 \end{cases}\\\\ -------------------------------\\\\ +(3v-1)\ge 20\implies 3v-1\ge 20\implies 3v\ge 21\implies v\ge \cfrac{21}{3} \\\\\\ \boxed{v\ge 7}\\\\ -------------------------------\\\\[/tex]
[tex]\bf -(3v-1)\ge 20\implies -3v+1\ge 20\implies -3v\ge 19 \\\\\\ \stackrel{\textit{negative division, the sign changes}}{v\le \cfrac{19}{-3}}\implies \boxed{v\le -\cfrac{19}{3}}\\\\ -------------------------------\\\\ 7\le v\le -\cfrac{19}{3}[/tex]
What shape has 4 congruent sides but is not a square?
Answers
What has 6 wheels and flies ?
Answers
Answer:
A garbage truck
Step-by-step explanation:
Sarah washes cars at the car wash. She makes $8.25 per hour and earns $30 in tips per day. Give an expression that Sarah could use to calculate her daily earnings.
Answers
equations: y=8.25x+30
x= hours
y= total amount of money
you would need to multiply 8.25 by the number of hours worked (x) and then add the tips
so it would be A. 8.25x+30
what is sin 30?......
Answers
Answer:
The correct option is D) [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
we need to find sin 30° with the reference of provided figure
Since, [tex] sin\theta=\frac{perpendicular}{hypotenuse}[/tex] .....(1)
In fig , perpendicular is 1 and hypotenuse is
now put [tex]\theta=30\degree[/tex] in (1)
[tex] sin\theta=\frac{1}{2}[/tex]
Hence, The correct option is D) [tex]\frac{1}{2}[/tex]
If a six sided die is tossed two times and '3' shows up both times, the probability of a '3' on the third trial is
Answers
If a six sided die is tossed two times and '3' shows up both times, the probability of a '3' on the third trial is [tex]\frac{1}{6}[/tex]
Given :
A six sided die is tossed two times and '3' shows up both times
'3' shows up both the times .
When the dice is rolled third time. there are 6 possibilities comes up
In the third trial , we have six possibilities 1,2,3,4,5,6
Out of six possibilities , the chance of getting '3' is only once
So, the probability of a '3' on the third trial is [tex]\frac{1}{6}[/tex]
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Can somebody help me please?
Answers
Write an equation that represents a vertical translation 7 units down of the graph of g(x)=|x|
Answers
Translation involves changing the position of a function.
The equation that represents the new function is: [tex]\mathbf{g'(x) = |x| - 7}[/tex]
The parent function is given as:
[tex]\mathbf{g(x) = |x|}[/tex]
The rule of translating a function down is:
[tex]\mathbf{(x,y) \to (x,y-h)}[/tex]
Where: h is the number of units translated down
i.e. h = 7
So, we have:
[tex]\mathbf{g'(x) = g(x) - h}[/tex]
Substitute [tex]\mathbf{g(x) = |x|}[/tex]
[tex]\mathbf{g'(x) = |x| - h}[/tex]
Substitute 7 for h
[tex]\mathbf{g'(x) = |x| - 7}[/tex]
Hence, the required function is: [tex]\mathbf{g'(x) = |x| - 7}[/tex]
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The equation that represents the given situation is g(x) = |x|-7
To write an equation that represents a vertical translation 7 units down of the graph of g(x) = |x|, we need to modify the original function accordingly.
A vertical translation can be represented by adding or subtracting a constant to the function. In this case, since we are translating the graph downward by 7 units, we subtract 7 from the original function:
g(x) = |x| - 7
Thus, the equation that represents this vertical translation is g(x) = |x| - 7.
This results in each point on the graph of g(x) = |x| shifting 7 units downward, creating the new graph of g(x) = |x| - 7.
Find the values of x and y.
a. x=44, y=66
b. x=46, y=44
c. x=90, y=44
d. x=90, y=46
Answers
m<BAC = 180 - 2(46) = 180 - 88
y = 88/2 = 44
x = 180 - (44+46) = 180 - 90 = 90
answer
c. x=90, y=44
whats the chance to not get 33% chance 3 times in a row
Answers
Simplify the expressions. (use only positive exponents in your answers.) (a) (9x4)(-9x-3) = incorrect: your answer is incorrect.
Answers
36(-9x-3)
-324x-108
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what is solution of 7v-(6-2v)=12 show work
A -3.6
B -2
C 2
D 3.6
Answers
9v-6=12
9v=18
v=2
40% of a certain number is 80 what is that number ?
Answers
40/100(x)=80
x=200
Your answer is 200.
A red kangaroo can cover 40 feet in 1 jump. How many feet can the red kangaroo cover in 12 jumps.
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Find the value of a.
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a = 18
6a - 2a = 83 - 11
4a = 72
a = 72/4
a = 18
Factor the expression:
30x^3-5x^2-18x+3
PLZ SHOW YOUR WORK
Answers
30x^3 -5x^2 turns into 5x^2(6x-1)
-18x+3 turns into -3(6x-1)
we can then combine them to get (5x^2-3) (6x-1)
What is surface area
Answers
2 * 3.61 * 11 = 79.42
Area of the front and back =
2 * (2 * 3) = 12
Total Area = 91.42 cm
simplify
(-6i)(-7-6i)-(7i)(3-2i)
Answers
(-6i)(-7-6i) becomes 42i + 36i^2, or 42i -36
-(7i)(3-2i) becomes -[21i - 14i^2], or -[21i + 14]
Combine these two products.
42i-21i -36 -14
21i - 50 (answer)
Raul is selling coupon books. He started with 50 coupon books and has already won a prize for selling at least 10 coupon books. The total amount of money Raul will make from selling x coupon books is represented by a function.
f(x)=20xf(x)=20x
What is the practical domain of the function if Raul sells 50 coupon books?
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Closest integer to the square root 75
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Thus the nearest integer is 9
Hope this helps :)
√64 = 8
√81 =9
think it should be 9 it's closer