What is the following quotient? ^3sqrt60/^3sqrt20
Answers
The quotient ^3√60 / ^3√20 simplifies to 2.
To simplify the quotient ^3√60 / ^3√20, we can apply the rules of exponents for radicals.
Let's start by simplifying the individual cube roots:
^3√60 = ^3√(2^2 × 3 × 5) = 2^2 × ^3√(3 × 5) = 2^2 × ^3√(15).
Similarly,
^3√20 = ^3√(2^2 × 5) = 2 × ^3√5.
Now we can rewrite the original quotient using these simplified forms:
^3√60 / ^3√20 = (2^2 × ^3√15) / (2 × ^3√5).
Since we have the same cube root in the numerator and denominator, we can cancel them out:
^3√60 / ^3√20 = (2^2 × ^3√15) / (2 × ^3√5) = 2^2 / 2 = 4 / 2 = 2.
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Related Questions
Solve for j - 1/3 = j/4 - 10/3
Answers
The value of j is equal to -4
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here: j - 1/3 = j/4 - 10/3
j-j/4 = -10/3+1/3
j = -3/0.75
j=-4
Hence, The value of j is equal to -4
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Pls help step by step (special right triangles)
Answers
Value of base and hypotenuse of triangle are 9√3 and 18 respectively.
Define right triangleA right triangle is a triangle with one interior angle measuring 90 degrees, known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are known as the legs of the right triangle. The length of the hypotenuse can be found using the Pythagorean theorem, that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
Height of triangle=9
Base of triangle=y
Hypotenuse of triangle=x
Using trigonometric ratio
Sin30°=Height/Hypotenuse
½=9/x
x=18
Cos30°=Base/hypotenuse
√3/2=y/18
y=9√3
Hence, value of base and hypotenuse of triangle are 9√3 and 18 respectively.
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Solve for measure of angle a.
55°
a = [?]°
25° ат
![Solve for measure of angle a.55a = [?]25](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/CxjJWzaGBUWoTwV9U4OFAhpLhwGjl7KX.png)
Answers
Check the picture below.
![Solve for measure of angle a.55a = [?]25](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/r7Vl2sCCZI9Ir0qw1EubCc6i2RQyoR8E.png)
The prime factorisation of √169 is?
Answers
Answer:
Square root of 169 by Prime factorization is 13×13
Answer:
13*13
Hope this helped!
Need answer asap.......
Answers
Answer: For this one, I'll use y=mx+b because that equation make the most sense in this scenario.
A) X is the number of hours, and 15, or b is the tip
B) y= 30x + 15.
Have a great day!
Stay safe and healthy!
Happy holiday seasons!
May I please have brainliest?
which of the points shown below given by the equation y=x
Answers
Answer:
I believe its D
Step-by-step explanation: X and Y are both -3
Rewrite the function by completing the square.
h (x)=x^2+3x−18
Answers
Answer: (x+6)(x-3)
Step-by-step explanation:
y=x^2+3x-18
(x+6)(x-3 )
A certain type of kickboard scooter comes in silver, red, 2
or purple with wheel sizes of 125 millimeters or 180
millimeters. Determine the total number of color-wheel size combinations.
(This is probability and I’m having such a hell of a time figuring it out pls help)
Answers
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.
Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:
Total combinations = Number of color options × Number of wheel size options
Total combinations = 4 colors × 2 wheel sizes
Total combinations = 8
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
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How long it will take 2000$ to double if it is invested at 6% interest compounded semi annually
Answers
Answer:
Number of year = 11.725 year (Approx.)
Step-by-step explanation:
Given:
Amount invested = $200
Interest rate = 6% (compounded semi annually)
Future value = 2 x Amount invested
Find:
Number of year
Commutation:
Future value = 2 x Amount invested
Future value = 2 x 200
Future value = $400
Number of year (Semi-annual) = 2n
Interest rate (Semi-annual) = 6% / 2 = 3%
So.
A = P[1+r]ⁿ
400 = 200[1+3%]²ⁿ
2 = [1.03]²ⁿ
n = 11.725 year
Number of year = 11.725 year (Approx.)
solution of equation x^2-2x=-2
Answers
Answer:
\(x=1\pm i\)
Step-by-step explanation:
The given equation is :
\(x^2-2x=-2\\\\x^2-2x+2=0\)
The above equation is a quadratic equation whose solution can be given by :
\(x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\)
Here,
a = 1, b = -2 and c = 2
So,
\(x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(1)(2)} }{2(1)}\)
So,
\(x=1+i,1-i\\\\x=1\pm i\)
So, the solution of the equation is \(1\pm i\).
How are triangleABC and triangle ADE related? How do you know pls explain.
Answers
Triangle ABC and ADE are similar triangles
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.
It has been shown that angles in ABC and ADE are equal.
To show that the ratio of corresponding sides are equal
6/12 = 8/16 = 10/20
The ratios all give a value of 1/2
Therefore we can say that the triangles ABC and ADE are similar.
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What is 1/4=y/12 can't figure it out i believe its 3/12
Answers
1/4 ✕ 12
12/4
Y = 3
9514 1404 393
Answer:
y = 3
Step-by-step explanation:
You are correct that ...
1/4 = y/12 = 3/12
This means y = 3, the numerator of the fraction with 12 as the denominator.
__
In the original equation, you can get there by multiplying both sides of the equation by 12 (the denominator under y).
12(1/4) = 12(y/12)
12/4 = (12/12)y . . . . simplify a bit
3 = y
Boxers in the nineteenth century used their bare fists. In modern boxing,
fighters wear padded gloves. How do gloves protect the brain of the boxer from
injury?
Answers
Answer:
boxers get injured but it is good to have some security on your fist and for those who do do boxing it's nice to have some security
O
X
y
X
y
X
y
X
y
0
2
0
0
-1
0
1
0
5
2
113
1
2
2
8
4
WIN
3
3
4
11
2.5 -2.5-7.5 -12.5
6
W/W
5
6
Select all table’s that represent proportional relationship between x and y
Answers
All tables that represent proportional relationship between x and y are:
B. table B.
E. table E.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)
Constant of proportionality, k = 1.
Therefore, the required linear equation is given by;
y = kx
y = x
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Using log evaluate 3^x=10
Answers
Answer:
x ≈ 2.09590327429
Step-by-step explanation:
You want the solution to 3^x = 10 using logarithms.
LogsTaking logarithms of both sides of the given equation, we have ...
x·log(3) = log(10)
Dividing by the coefficient of x gives ...
x = log(10)/log(3)
x ≈ 2.09590327429
__
Additional comment
If the logarithm to the base 10 is used, then this becomes ...
x = 1/log₁₀(3)
The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.
For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.
<95141404393>
The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).
Taking the log of both sides, we get:
log(3^x) = log(10)
Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:
x * log(3) = log(10)
Next, we can divide both sides of the equation by log(3) to isolate the variable x:
x = log(10) / log(3)
Using a calculator, we can evaluate the right side of the equation:
x ≈ 1.46497
Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
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The three paths intersect in pairs at the points A, B, and C.
Answers
Answer:
Not a complete question... Sorry
express each ratio as a fraction in simplest form .3km to 500m
Answers
300m:500m
(/100)
3:5
3+5=8
0.3km= 3/8
500m= 5/8
what is the solution to -3/8x-11=4
Answers
Answer: -40
Step-by-step explanation:
Answer:
-1/40
Step-by-step explanation:
-3/8x -11+11=4+11
-3/8x=15
-3/8x x=15x
-3/8=15x
15x/15= -3/8/15
x=-1/40
Hope this helps!^^
Given the function f(x) = 3x ^ 2 - x + 6 , what is f(- 2) ?
Answers
Answer:
f(x) = 3x2 + 5 and y = 3x2 + 5
Step-by-step explanation:
Multiply.
(2x+6)²
NEED ANSWER ASAPP
Answers
Answer:
4x² + 24x + 36
Step-by-step explanation:
(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36
Please can someone who knows the right answer help me? From a group of 5 boys and 3 girls, a boy and a girl will be selected to attend a conference. In how many ways can the select be made?
Answers
The selection can be made in 15 different ways, taking into account the distinct combinations of a boy and a girl from the given group of 5 boys and 3 girls.
To determine the number of ways a boy and a girl can be selected from a group of 5 boys and 3 girls to attend a conference, we can use the concept of combinations.
The number of ways to choose one boy from 5 boys is 5C1, which is equal to 5. Similarly, the number of ways to choose one girl from 3 girls is 3C1, which is equal to 3.
To select one boy and one girl, we need to multiply the number of ways to choose a boy and a girl together. Using the multiplication principle, we multiply the number of choices for each category: 5C1 * 3C1 = 5 * 3 = 15.
Therefore, there are 15 ways to select a boy and a girl from the given group to attend the conference.
Each combination represents a unique pair consisting of one boy and one girl. For example, if the boys are labeled as B1, B2, B3, B4, and B5, and the girls are labeled as G1, G2, and G3, the possible pairs could be (B1, G1), (B1, G2), (B1, G3), (B2, G1), (B2, G2), and so on, up to (B5, G3).
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Is 604,892 divisible by 4?
Answers
Answer:
yes it is 604892÷4=151,223
2c-10<3c-9 solve the following inequality
Answers
Answer:
\(c > -1\)
Step-by-step explanation:
\(2c-10 < 3c-9\\-10 < c-9\\-1 < c\\c > -1\)
How do you write 2/5 as a percentage
Answers
Answer:
40%
Step-by-step explanation:
To convert a decimal to a fraction, multiply it to 100
\(\frac{2}{5} \times 100\)
\(=\frac{2}{5} \times \frac{100}{1}\)
\(=\frac{2\times100}{5\times1}\)
\(=\frac{200}{5}\)
\(=40\)
Therefore, \(\frac{2}{5}\) is 40%
Step-by-step explanation:
Explanation:
To get 25 as a percent, we need the denominator to be 100 .
Now that we have a denominator equal to 100 , just look at the numerator and that's your percent.
40%
.40.
.4 or 0.4.
Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answers
Using the table, we can see that the loan increases by a factor of 1.058 after 1 year and by a factor of 1.058/1.045 = 1.0124 after 2 years. Thus, we have:
1.058 = (1 + r/n)^(n*1)
1.0124 = (1 + r/n)^(n*2)
Dividing the second equation by the first, we get:
1.0124/1.058 = (1 + r/n)^(n*1)
Taking the nth root of both sides, we get:
(1 + r/n) = (1.0124/1.058)^(1/n)
Solving for r, we get:
r = n * [(1.0124/1.058)^(1/n) - 1]
We don't know the value of n, but we can make an educated guess that it's either 1 or 2, since the loan is increasing by roughly 5.8% per year. If we try n = 1, we get:
r = 1 * [(1.0124/1.058)^(1/1) - 1] = -0.0427
This is clearly not the correct answer, since the interest rate cannot be negative. If we try n = 2, we get:
r = 2 * [(1.0124/1.058)^(1/2) - 1] = 0.0574
This is a reasonable answer, since it's close to the observed increase in the loan value of 5.8% per year. Therefore, the rate of interest per annum is 5.7% to 1 d.p.
(b) Using the formula for compound interest, we can find the value of the loan 10 years after it starts:
A = P * (1 + r/n)^(n*t) = 2500 * (1 + 0.0574/1)^(1*10) = £4,745.60 (to the nearest 1p
Answer:
25000
Step-by-step explanation:
A circle has a radius of 30 cm and a central angle that measures 312 degrees. Find the length of the arc defined by this central angle
Answers
The length of the arc defined by the central angle of 312 degrees is 26π cm.
The formula for the arc length of a circle is given by:
L = (θ/360) × 2πr
where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.
Substituting the given values, we get:
L = (312/360) × 2π(30)
L = (26/30) × π × 30
L = 26π cm
Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.
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Find the area of parallelogram RSTU.
Answers
\(\huge\sf\blue{Solution:-}\)
Here is a Parallelogram RSTU.
Given,
Height = 16.5 inches
Base = 15.3 inches
★Area of Parallelogram is = Base × Height
So, Area = 15.3 × 16.5 => 252.45 inches² or 252.5 inches²
________________________________________
Answer:
252.5
Step-by-step explanation:
{Be careful}
The area: \(15.3\times16.5\times\frac{1}{2}\times2\)
\(=252.5\) inches²
I hope this helps you
:)
What percent of 15 is 45?
Answers
Answer:
Step-by-step explanation:
let the number be x %
according to the question the equation is
x% of 15=45
x/100*15=45
15x=45*100
x=4500/15
x=300
therefore x=300%
The difference between 12 and ten times a number is -28
Answers
Answer:
4Step-by-step explanation:
\(n-\text{the number}\\\\12-10n=-28\qquad|\text{subtract 12 from both sides}\\\\12-12-10n=-28-12\\\\-10n=-40\qquad|\text{divide both sides by (-10)}\\\\\dfrac{-10n}{-10}=\dfrac{-40}{-10}\\\\\boxed{n=4}\)
Which model shows a ratio of 1 white to 2 blue?
