Which expression is equivalent to rootindex 3 startroot startfraction 10 x superscript 5 baseline over 54 x superscript 8 baseline endfraction endroot? assume x not-equals 0.
The equivalent expression of the given expression (10^5 / 54x^8)^1/3 would be equal to 5^(1/3) / 3x.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
The expression is given as
[tex](10x^5 / 54x^8)^{1/3}\\\\(5 / 27x^3)^{1/3}\\\\5^{1/3}/ (27x^3)^{1/3}\\\\5^{1/3} / 3x[/tex]
This is the simplest form of expression.
Thus, the equivalent expression is 5^(1/3) / 3x.
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Answer:
D
i did the test
What are the zeros of the following function?
a) 2 and and -3
b) 2 and 3
c) 3 only
d) -3,2 and 3
Answer:
a
Step-by-step explanation:
"Zeroes" of the function are where the graph crosses the x- axis at -3 and 2
Explain, using an example, that there can be two logarithmic expressions, logₓ₁M and logₓ₂N such that x1≠ x2 and M ≠ N, but logₓ₁M = logₓ₂N.
For all [tex]\log_{x_{1}} M[/tex] there is a [tex]\log_{x_{2}}N[/tex] such that [tex]N = M^{\frac{1}{\log_{x_{2}} x_{1}} }[/tex]. The logarithmic expression log ₂ 8 is equivalent to the logarithmic expression log ₃ 27.
How to find equivalent logarithms
Logarithms are trascedental function, that is, a function that cannot be described algebraically.
Let suppose we know that [tex]\log _{x_{1}} M = \log_{x_{2}} N[/tex] such that x₁ ≠ x₂. We proceed to prove that for all [tex]\log_{x_{1}} M[/tex] there is a [tex]\log_{x_{2}} N[/tex] by logarithm properties below:
[tex]\log_{x_{1}} M[/tex] Given[tex]\frac{\log_{x_{2}}M}{\log_{x_{2}}x_{1}}[/tex] Base change[tex]\frac{1}{\log_{x_{2}}x_{1}} \cdot \log_{x_{2}} M[/tex] Associative property[tex]\log_{x_{2}} M^{\frac{1}{\log_{x_{2}} x_{1}} }[/tex] [tex]n\cdot \log a = \log a^{n}[/tex][tex]N = M^{\frac{1}{\log_{x_{2}} x_{1}} }[/tex] ResultFor example, let suppose that x₁ = 2, M = 8 and x₂ = 3, then the value of N is:
[tex]N = 8^{\frac{1}{\log_{3} 2} }[/tex]
N = 27
Thus, for all [tex]\log_{x_{1}} M[/tex] there is a [tex]\log_{x_{2}}N[/tex] such that [tex]N = M^{\frac{1}{\log_{x_{2}} x_{1}} }[/tex]. The logarithmic expression log ₂ 8 is equivalent to the logarithmic expression log ₃ 27.
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will give brainliest if right!!! pls helppp
Answer:
i think B is the answer
What is the missing term?
Please draw it on a piece of paper
Step-by-step explanation:
Here is the example you can take idea from it.
James studied for his test. He started studying at 3:20 p.m. and studied for 2 hours
and 15 minutes. What time did he finished studying?
Answer:
5:35
Step-by-step explanation:
since he started at 3:20 , to find when he ended you add the 2 hours to that, which gives you 5:20. but, you still have the fifteen minutes which you just add to 5:20, giving you 5:35.
Question 9 (1 point)
(03.01 LC)
What is the length of the unknown side of the right triangle? (1 point)
х
7
24
Оа
7
Ob
24
Ос
25
Od
31
Apply Pythagorean theorem
x²=24²+7²x²=576+49x²=625x=√625x=25Answer:
25 units
Step-by-step explanation:
Since this triangle is a right triangle, we can use pythogoras theorem to calculate the unknown side length (x). The pythogoras theorem states that the (longest side)² is equivalent to (Side)² + (Side)².
Let the longest side be "c" and the other side lengths be "a and b".
⇒ Pythogoras theorem formula: c² = b² + a²
If this statement is proven false, then the triangle shown is not a right triangle. Now, let's use the formula to determine the missing side length.
Let "c" be "x" and the other side lengths be "7 and 24 (as stated in image)"
⇒ c² = b² + a²⇒ x² = 7² + 24²SImplify both sides as needed.
⇒ x² = 49 + 576⇒ x² = 625Take square root both sides as needed.
⇒ √x² = √625⇒ x = 25 unitsThe measure of x is 25 units.
1=7/10x
solve the equation
Answer:
I hope it's 1=7/10x because if so it's gonna be
Step-by-step explanation:
X = 10/7
Answer:
1=7/10x
1=0.7x
divide 0.7 on both sides
x=1.4285 = x=1.43
Science!
In the process of combustion, a fuel such as coal undergoes _________________.
Answer
Burning of coal undergoes combustion reaction. Combustion reaction is a type of reaction in which chemical species experiences oxidation by undergoing a reaction with the oxidizing agent which results in the emission of energy in the form of heat. It is an exothermic process.
Step-by-step explanation:
If there are 20 lollipops and 40 candy bars for a gift bag, fill out all of the possible ratios of lollipops to candy bars that could be made
Answer:
20:40
Step-by-step explanation:
The required ratio of lollipops to candy bars is 1:2.
Given that,
There are 20 lollipops and 40 candy bars for a gift bag, fill out all of the possible ratios of lollipops to candy bars that could be made is to be determined.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Total number of lollipops = 20, in a bag
Total number of candy bars = 40, in a bag
The ratio of lollipops to a candy bar in a bag,
Ratio = number of lollipops/number of candy bars
Ratio = 20 / 40
Ratio = 1 / 2
Ratio = 1:2
Thus, the required ratio of lollipops to candy bars is 1:2.
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Solve for the product of 2 4/5 x 4/6
Answer:
28x/15
Step-by-step explanation:
Sophia wants to foster creativity in her organization. She finds an online training program that claims to teach people how to approach workplace challenges in a more creative way. Sophia is skeptical but decides to give it a try. She randomly selects 40 employees and randomly assigns half of them to complete the online training program (n
The type of test that will be required in the organization is a two samples test assuming unequal variance.
What is a hypothesis?It should be noted that a hypothesis simply means a statement of expectation that will be tested by research.
From the complete question, the type of test that will be required in the organization is a two samples test assuming unequal variance. This is performed on the data of two random samples.
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Need some help please.
Applying the rules of exponents, the letter answers that form the code are: MATH IS NOT JUST ANOTHER FOUR LETTER WORD.
What are the Rules of Exponents?Some of the rules of exponents to be applied are as follows:
[tex]x^0 = 1\\\\x^m \times x^n = x^{(m + n)}\\\\x^{-m} = \frac{1}{x^m} \\\\x^m \div x^n = x^{(m - n)}\\\\[/tex]
What are Equivalent Expressions?If two expressions have the same value, both are said to be equivalent expressions.
1. [tex]3^2 \times 3^{-5} = 3^{2 - 5}\\\\[/tex]
[tex]3^-3 = \frac{1}{3^3} = \frac{1}{27}[/tex]
Answer: H
2. 3³/6² = 27/36 = 3/4
Answer: R
3. [tex]\frac{3^2}{3^5} = 3^{2 - 5} = 3^{-3]} = \frac{1}{3^3} = \frac{1}{27}[/tex]
Answer: M
4. 7²/7² = 49/49 = 7° = 1
Answer: J
5. 8^-2 = 1/8² = 1/64
Answer: A
6. (4²)(4³) = 4^(2 + 3) = [tex]4^5[/tex]
Answer: L
7. (3²)³ = 3²*³ = [tex]3^6[/tex]
8. 4° × 4^-1 = 1 × 1/4 = 1/4
Answer: E
9. [tex]\frac{(2^4)^3}{(2^7)(2^5)} = \frac{2^{12}}{2^{12}}[/tex] = 1
Answer: U
10. [tex](3^2)^{-1} = 3^{-2}[/tex]
Answer: I
11. [tex]1^{98}[/tex] = 1
Answer: D
12. [tex]y^{10} \div y^5 = y^{10 - 5} = y^5[/tex]
Answer: F
13. [tex]8^{-2} \times 8^4 = 8^{(-2 + 4)}[/tex] = 8² = 64
Answer: S
14. [tex]2^{-3} \times 3^{-2} =[/tex] 1/2³ × 1/3² = 1/8 × 1/9 = 1/72
Answer: O
15. [tex]\frac{3^2}{3^2} = 3^{2-2} = 3^0 = 1[/tex]
Answer: N
16. [tex](\frac{1}{2} )^{-1} = (2^{-1})^{-1}[/tex] = 2
Answer: T
Thus, applying the rules of exponents, the letter answers that form the code are: MATH IS NOT JUST ANOTHER FOUR LETTER WORD.
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Find the value of x. Round to the nearest tenth. 1.4ft 2.1 ft 2x x = [ ? ]ft
Perpendicular projected from center of a circle to its chord bisects it. The value of the x for this case is: x = 1.565 ft approximately.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
What is the relation between line perpendicular to chord from the center of circle?If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or |AC| = |CB|
For this case, consider the diagram below.
The line OC divides AB in half.
Since it is given that:
Length of AB = |AB| = 2x ft,
therefore, we get:
|AC| + |CB| = 2x
|AC|+|AC| = 2x (as |AC|=|CB|)
therfore, we get: |AC| = x feet = |CB|
Now,as the triangle OBC contains a right angle, we can use Pythagoras theorem, and therefore, we get:
[tex]|OB|^2 = |OC|^2 + |CB|^2\\2.1^2 = 1.4^2 + x^2\\x^2 = 4.41 - 1.96\\x = \sqrt{2.45} \approx 1.565 \: \rm ft[/tex]
(took positive root as 'x' represents measurement of length, which is a non-negative quantity).
Thus, the value of the x for this case is: x = 1.565 ft approximately.
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PLS HELP No links pls and Ty<333!!!
A circle's diameter is 8 centimeters.
What is the circle's area (use 3.14 for pi and round to the nearest
tenth)?
Answer:
Formula for the area of a circle;
A = π[tex]r^{2}[/tex]
Where 'π' represents pi(22/7 or 3.14), and 'r' stands for the radius being squared.
But, we are given a diameter instead of a radius.
So to find the radius of the diameter we must find 1/2(half) of the diameter:
Diameter/2 = Radius
Plug in what we know:
D/2 = R
8/2 = R
4 = R, 4 is our radius.
Now we use this radius in our formula;
A = π[tex]r^{2}[/tex]
A = 3.14(4^2) ← (The symbol ' ^ ' means to the power of.)
A = 3.14(16)
A = 50.24 centimetres is the area for this circle.
please help me thanks so much
Answer:
Vertically opposite angles
Answer:
B) Vertical angles (congruent)
Step-by-step explanation:
Hope this helps!
HELP! WILL GIVE BRAINLEST! On the unit circle, an arc of length 2 subtends an angle, β. What is the radian measure of β?
Answer:
2 rad
Step-by-step explanation:
Given :
arc length = 2 mradius of a unit circle = 1 mFormula
l = rβ⇒ β = l/rSolving for β
β = 2/1β = 2 radLillian just got hired for a new job and will make $34,000 in her first year. Lillian
was told that she can expect to get raises of $3,500 every year going forward. How
much money in salary would Lillian make in her 20th year working at this job?
Answer: $104,000
Step-by-step explanation:
34,000+20x(3500)
34,000+70,000
HELP ME I DONT DO MATH
Answer:
alright where's the question
The period of a function is 4
How many cycles of the function occur in a
horizontal length of 12pie?
DONE
Hence total cycles:-
12π/4π3cyclesAnswer is 3
The required there are 3π cycles of the function in a horizontal length of 12π.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
If the period of a function is 4, that means the function completes one cycle every 4 units of horizontal distance.
To find out how many cycles occur in a horizontal length of 12π, we need to divide 12π by the period of the function, which is 4:
Number of cycles = (12π) / 4
Simplifying the expression, we get:
Number of cycles = 3π
So, there are 3π cycles of the function in a horizontal length of 12π.
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pls help i thought i understood it but it was incorrect the first time
Subtraction property of equality
====================================================
Reason:
We subtract 18 from both sides to go from 4x+18 = 78 to 4x = 60
So we use the aptly named subtraction property of equality.
In general that rule is if a = b, then a-c = b-c
The numbers of days 12 friends went camping during the summer are 6, 2, 0, 10, 3, 6, 6, 4, 12, 0, 6, and 2. Use the number line to identify the correct least value, first quartile, median, third quartile, and greatest value of the data.
Question 2
The range of the data is
.
If a person runs 1/3 mile in 1/9 of an hour what is the unit rate per hour
Answer:
3 miles per hour
Step-by-step explanation:
he runs 1/3 mile in 1/9 of an hour
then
he runs (we multiply both sides by 9)
9×(1/3) mile in 9×(1/9) of an hour
then
he runs
(9/3) mile in (9/9) of an hour
then
he runs
3 mile in 1 hour
Lilly is placing an order for r bags of rice for her sushi restaurant. The market charges $15.70 per bag of rice. Which equation represents the total cost, t , of Lilly's order?
At a construction job for a museum, 9 painters were tasked with painting the interior. These painters made up 55% of the painting crew, so how many painters in all worked on this job? Round your answer to the nearest whole number if necessary.
(I will mark brainliest if you give the answer+explanation)
Answer:
16
Step-by-step explanation:
First, you can create a ratio:
Number of people/percentage of total
So 9 being 55% of the painting crew would be:
[tex]\frac{9}{0.55}[/tex], because we are trying to find the total number of painters, you can create another fraction where x is the numerator (number of people) and the denominator is 1 (or 100% of the painters). [tex]\frac{x}{1}[/tex]
Because these fractions are proportions of the same thing, we can set them equal to each other.
[tex]\frac{9}{0.55} =\frac{x}{1}[/tex], cross multiplying gives:
9=0.55x
Dividing both sides by 0.55 gives:
x=(around) 16
guys can anyone please help me on this , i don’t understand!!
Answer:
The correct answer would be Option A; all real numbers
Hope this helps!
Can someone hepl me solve this it is importaint thank you so much ?
4/7x5/3x3/4=?
Answer:
5/7 is the answers for the question
What is the volume of a right cylinder with a radius of 4m and a height of 4m?
Question 8 options:
256π m3
8π m3
16π m3
64π m3
volume of cylinder: π * radius² * height
=============
⇒ π * 4² * 4
⇒ π * 16 * 4
⇒ 64π
Thus the volume of cylinder is 64π cm³
Question :-
What is the volume of a right cylinder with a radius of 4 m and a height of 4 m?Answer :-
The volume of a right cylinder is 64π m³.[tex] \rule{180pt}{4pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{4 \: m}}\put(9,17.5){\sf{4 \: m}}\end{picture}[/tex]
Solution :-
As per provided information in the given question, we have been given that the Radius of a cylinder is 4 m. The height of a cylinder is 4 m. We have been asked to find the volume of a right cylinder.
To calculate the volume of a right cylinder, we will apply the formula below :-
[tex] \bigstar \: \: \: \boxed{ \sf{ \: \: Volume_{(Cylinder)} = \pi r^2 h \: \: }}[/tex]
Substitute the given values into the above formula and solve for Volume :-
[tex]\sf:\implies Volume_{(Cylinder)} = \pi r^2 h[/tex]
[tex]\sf:\implies Volume_{(Cylinder)} = \pi \times (4 \: m)^2 \times 4 \: m [/tex]
[tex]\sf:\implies Volume_{(Cylinder)} = \pi \times 16 \:m^2 \times 4 \: m [/tex]
[tex]\sf:\implies Volume_{(Cylinder)} = \pi 64 \: m^3[/tex]
[tex]\sf:\implies\bold{Volume_{(Cylinder)} = 64\pi \: m^3}[/tex]
Therefore :-
The volume of a right cylinder is 64π m³.[tex]\\[/tex]
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Have a great day! <33
Can someone help me quick please ?
Let's look at the answer choices to see what the questions wants us to do with the data
⇒ essentially they compare Carol's mean or median to herself or to
Anna's mean or media
⇒ therefore we should calculate Carol's mean, median and Anna's
mean, median
Before we start calculating, let's define what is the mean and median
Mean: it is basically the average which is the sum of all numbers in the set divided by the number of numbers in that setMedian: it is the middle number of the set when the set is ordered from lowest to highestLet's calculate:
Carol's mean,median⇒ Carol's data ordered: 20, 30, 45, 60, 70
[tex]Mean = \frac{20+30+45+60+70}{5} = \frac{225}{5}=45\\ \\Median: 45[/tex]
Anna's mean, median⇒ Anna's data ordered: 30, 35, 45, 60, 65
[tex]Mean = \frac{30+ 35+ 45+ 60+ 65}{5} =\frac{235}{5} =47\\\\Median: 45\\[/tex]
Now using the data, let's compare:
first choice: Carol's mean is equal to her median--> correct
second choice: Carol's mean is not greater than Anna's mean--> incorrect
third choice: Anna's median isnot greater than her mean --> incorrect
fourth choice: Anna's mean is not equal to Carol's mean --> incorrect
Hope that helps!