Answer:
[tex]p^2\sqrt[4]{27pq^3}[/tex]
Step-by-step explanation:
[tex](3p^3q)^\frac{3}{4}[/tex]
To get radical form , remove the fractional exponent
[tex](a^m)^n=a^{mn}[/tex]
multiply the exponent 3/4 inside the parenthesis
[tex]3^\frac{3}{4} p^{3 \cdot \frac{3}{4}} q^\frac{3}{4}[/tex]
[tex]3^\frac{3}{4} p^{\frac{9}{4}} q^\frac{3}{4}[/tex]
[tex]\sqrt[4]{27} \cdot p^2\sqrt[4]{p} \cdot \sqrt[4]{q^3}[/tex]
[tex]p^2\sqrt[4]{27pq^3}[/tex]
The radical form of the expression [tex]\rm \left (3p \times 3q \right )^{\frac{3}{4}}[/tex] will be [tex]\left ( 3\sqrt{3} \right ) \left (\sqrt[4]{p^3q^3} \right )[/tex].
How do convert the exponent into the simplest radical form?If the power of the variable "a" is b/c. Then the simplest radical form of the expression will be
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
[tex]\rm \left ( a \right )^{\rm \frac{b}{c}} = \rm \sqrt[\rm c]{\rm a^b}[/tex]
The expression is given below.
[tex]\rm \rightarrow \left (3p \times 3q \right )^{\frac{3}{4}}[/tex]
We know that (ab)ⁿ = aⁿ × bⁿ. Then the expression will be
[tex]\rm \rightarrow \left (3^{\frac{3}{4}} \times p^{\frac{3}{4}} \times 3^{\frac{3}{4}} \times q^{\frac{3}{4}} \right )[/tex]
Simplify the expression in the radical form. Then we have
[tex]\rm \rightarrow \left (3^{\frac{3}{2}} \times p^{\frac{3}{4}} \times q^{\frac{3}{4}} \right )\\\rightarrow \left ( \sqrt{3^3} \times \sqrt[4]{p^3} \times \sqrt[4]{q^3} \right ) \\\rightarrow \left ( 3\sqrt{3} \right ) \left (\sqrt[4]{p^3q^3} \right )[/tex]
The radical form of the expression [tex]\rm \left (3p \times 3q \right )^{\frac{3}{4}}[/tex] will be [tex]\left ( 3\sqrt{3} \right ) \left (\sqrt[4]{p^3q^3} \right )[/tex].
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If h and k are constants and x^2+kx+7 is equivalent to (x+1)(x+h), what is the value of k?
To find the value of k when x^2+kx+7 is equivalent to (x+1)(x+h), we expand (x+1)(x+h), compare coefficients, and deduce that k is 8.
Explanation:If h and k are constants and x^2+kx+7 is equivalent to (x+1)(x+h), we are looking for the value of k. To find k, we expand the right-hand side and then compare coefficients.
Expanding (x+1)(x+h) gives us x^2+hx+x+h, which simplifies to x^2+(h+1)x+h.
Comparing this to x^2+kx+7, we can see that k must be equal to h+1.
Since there is no h term in x^2+kx+7, we infer that h must be equal to 7. Consequently, k=h+1 which leads us to k=7+1.
Therefore, the value of k is 8.
Select all the expressions that cannot be factored using intergal coefficients and intergal constants
A. X^2 + 5x + 3
B. 25 - 20x + 4x^2
C. -2x^2 + 7x - 3
D. 2x^2 - 5x + 4
Paige measured 4/9 cup of onions, 3/4 cup of celery, and 2/7 cup of carrots. How many cups of vegetables did Paige measure out for her vegetable soup?
Answer:
Step-by-step explanation:
1) Make all the fractions have the same denominator.
- To do that you need to find the LCM (least common denominator) of 4, 9, and 7.
(look at image 1)
-Then apply the number you multiply the original denominator by to the original numerator
(look at image 2)
-Add the fractions together
(look at image 3)
Point a and point b are placed on a number line point a is located -20 and point b is 5 less then point a .which statement about paint b is true
Find the following measure for this figure.
Volume =
A. 275π cubic units
B. 91 2/3π cubic units
C. 36 2/3π cubic units
What does the notation f prime of x mean?
Final answer:
The notation f'(x) represents the derivative of the function f with respect to x, signifying the rate of change of the function or the slope of the tangent to its curve at a specific point.
Explanation:
The notation f prime of x, often written as f'(x), represents the derivative of the function f with respect to x. This concept is a fundamental part of calculus, which deals with the rate at which quantities change. The derivative f'(x) is the instant rate of change of the function f(x) at a particular value of x, or the slope of the tangent line to the curve f(x) at that point.
For example, if f(x) = x2, then the derivative f'(x) would equal 2x, as the rate of change of x2 with respect to x is 2x. This means that for every unit increase in x, the value of x2 increases by an amount corresponding to 2x.
The derivative can also be understood in the context of physics, where it might represent things like velocity, which is the derivative of position with respect to time. Regardless of the context, f'(x) is about understanding how a function changes at a specific point.
Mrs. Decker walks for 30 minutes each day as often as possible. What is an equation that relates the number of days d that Mrs. Decker walks and the number of minutes m that she spends walking?
I need help with estimating and 920,026-535,722
The given difference of two numbers which we have to estimate is
920,026-535,722
Actual Difference=384,304
→Estimation Using Ones
920,030-535,720=384,310
→Estimation Using Tens
920,000-535,700=384,300
Estimation using Tens is Closer to Actual Difference.
So, Answer=384,300
456 students participated in Switch Day. The students raised money for charity so that the principal would approve of the day. If the total amount money raised was 912, and each student brought in the same amount of money, how much did each student raise?
Write the equation of the line that passes through (2, 4) and has a slope of –1 in point-slope form.
The other person is correct i just did the test
1. The perimeter of a rectangular garden is 690 ft. The short sides are each 55 ft. long. What's the length the other 2 sides? Which equation models the situation?
a) 55+2x=690
b) 55+x=690
c) 2(55)+2x=690
d) 55(x-2)=690
2. Two boys took turns driving home. Will averaged 52 miles per hour. Jim averaged 44 miles per hour and drove 2 hours longer than Will. X is the Will time drove, with D being the length of the trip in miles. The trip was 352 miles. If Jim's equation was 44(X+2)=D-52X. Which equation models the situation?
a) 143
b) 209
c) 238
d) 191
Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth. 5x+2y=7 -2x+6=9
Answer:
The y-coordinate of the solution is approximately 7.2.
Explanation:
To solve the system of equations:
1. [tex]\( 5x + 2y = 7 \)[/tex]
2. [tex]\( -2x + 6 = 9 \)[/tex]
We'll start by solving the second equation for [tex]\( x \):[/tex]
[tex]\[ -2x + 6 = 9 \][/tex]
Subtract 6 from both sides:
[tex]\[ -2x = 9 - 6 \][/tex]
[tex]\[ -2x = 3 \][/tex]
Divide both sides by -2:
[tex]\[ x = -\frac{3}{2} \][/tex]
Now that we have the value of [tex]\( x \)[/tex], we can substitute it into the first equation to find [tex]\( y \):[/tex]
[tex]\[ 5x + 2y = 7 \][/tex]
[tex]\[ 5(-\frac{3}{2}) + 2y = 7 \][/tex]
[tex]\[ -\frac{15}{2} + 2y = 7 \][/tex]
Add [tex]\( \frac{15}{2} \)[/tex] to both sides:
[tex]\[ 2y = 7 + \frac{15}{2} \][/tex]
[tex]\[ 2y = \frac{14}{2} + \frac{15}{2} \][/tex]
[tex]\[ 2y = \frac{29}{2} \][/tex]
Divide both sides by 2:
[tex]\[ y = \frac{29}{4} \][/tex]
Now, let's convert the fraction into a decimal rounded to the nearest tenth:
[tex]\[ y \approx 7.2 \][/tex]
24 golf balls and 18 golf clubs how many bundles of golf balls and clubs can she make with nothing left over
24 -18 = 6
24/6 =4
18/6 =3
6 bundles with 4 balls and 3 clubs each
Complete the solution of the equation. Find the value of y when x equals 15.
3x ‒ 8y = 5
y= ?
I hope that helps!
60/5(7-5)=2
I got 24, but some other people got 6.
60/5(7-5) - P
60/5(2) - M/D (left to right)
12(2) - M/D (left to right)
=24
determine which equations below when combined with the equation 3x - 4y equals two or form a system with no solutions. choose all that apply.
1. 2y=1.5x-2
2. 2y=1.5-1
3. 3x+4y=2
4. -4y+3x=-2
The correct answers are:
1. 2y=1.5x-2 ; and 4. -4y+3x=-2.
Explanation:
Using the first equation, we have the system
[tex]\left \{ {{3x-4y=2} \atop {2y=1.5x-2}} \right.[/tex]
The second equation can be written in standard form just as the first one. To do this, we will subtract 1.5x from each side:
2y = 1.5x-2
2y-1.5x = 1.5x-2-1.5x
-1.5x+2y = -2
This makes our system
[tex]\left \{ {{3x-4y=2} \atop {-1.5x+2y=-2}} \right.[/tex]
To solve this, we will make the coefficients of x the same; we do this by multiplying the bottom equation by 2:
2(-1.5x+2y=-2)
-3x+4y=-4
This gives us the system
[tex]\left \{ {{3x-4y=2} \atop {-3x+4y=-4}} \right.[/tex]
We solve this by adding the two equations:
[tex]\left \{ {{3x-4y=2} \atop {+(-3x+4y=-4)}} \right. \\\\\\0+0 = -4\\0=-4[/tex]
There is no solution to this.
For the second system, we will follow the same process, subtract 1.5x from each side of the second equation:
2y=1.5x-1
2y-1.5x = 1.5x-1-1.5x
-1.5x+2y = -1
To make the coefficients of x the same, multiply the second equation by 2:
2(-1.5x+2y=-1)
-3x+4y=-2
We will add the two equations to solve:
[tex]\left \{ {{3x-4y=2} \atop {+(-3x+4y=-2)}} \right. \\0+0=0\\0=0[/tex]
This means that the equations are of the same line and there are infinite solutions.
For the third system, the coefficients are already the same. We will cancel by subtracting the bottom equation from the top:
[tex]\left \{ {{3x-4y=2} \atop {-(3x+4y=2)}} \right. \\\\-4y-4y=2-2\\-8y=0\\\frac{-8y}{-8}=\frac{0}{-8}\\y=0[/tex]
Since we have a value for y, this has a solution.
For the last system, we will rearrange the second equation with the x term in front:
3x-4y=-2
Now we will subtract this from the first equation:
[tex]\left \{ {{3x-4y=2} \atop {-(3x-4y=-2)}} \right. \\-4y--4y=2--2\\0=4[/tex]
This has no solution.
9/5 times a number plus 6 is 51 ?
PLEASE HELP!!!! The measure of an angle is x. The sum of the measure of this angle and an angle with twice the measure is the measure of an obtuse angle. Given the range of possible measures for the larger angle
What is the exact value of sin30
For what values of x would the rectangle have a perimeter of at least 242?
a.9 or less
b.12 or less
c.12 or greater
d.25 or less
The ratio of red to blue m7m's in a jar is 5:7. if there are 108 m&m's in the jar, how many are red
Solve the equation for the indicated variable :
Item 15 The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone. The formula for the surface area S of a right cone is S=πr2+πrl,S=πr2+πrl, where r is the radius of the base and l is the slant height. Find the height of the cone.
Final answer:
The height of the cone is equal to the slant height plus 1.
Explanation:
To find the height of the cone, we can use the formula for the surface area of a cone: S = πr^2 + πrl, where r is the radius of the base and l is the slant height. Since the problem states that the surface area is equal to the volume, we can set S equal to V and solve for h, the height of the cone.
Here's the step-by-step calculation:
S = V
πr² + πrl = V
πr² + πrl = πr²h
πr² + πrl - πr²h = 0
Combine like terms: πr²(1 - h) + πrl = 0
Divide both sides by πr to solve for h: 1 - h + l = 0
Subtract l from both sides: 1 - h = -l
Subtract 1 from both sides: -h = -l - 1
Multiply both sides by -1 to solve for h: h = l + 1
So, the height of the cone is h = l + 1.
three times a number plus 16
The phrase 'three times a number plus 16' translates to '3x + 16' in mathematical terms, where 'x' represents any number.
Explanation:The phrase 'three times a number plus 16' can be converted into an algebraic expression. In mathematical terms, 'a number' is usually represented by the letter 'x'. 'Three times a number' can be written as '3x'. 'Plus' is represented by the '+', so 'three times a number plus 16' is written as '3x + 16'.
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The area of a rug is 36 square feet. the length of the rug is 5 feet longer than the width. what is the width of the rug?
what is 25+120-10x=10x-35=
twenty five is the quotient of a number y and 3.5
The Porters’ food, clothing, and medical expenses are not fixed expenses. Explain what type of expense they are, and why.
Food, clothing, and medical are variable expenses because they occur regularly but can change from month to month.
The Porters’ food, clothing, and medical expenses are variable expenses.
A fixed expenses are the expenses that are constant and doesn't change while the variable expenses are those that are not fixed since they change.In this case, Porters’ food, clothing, and medical expenses are variable expenses since they can change every month.Read related link on:
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Find the rate of change of the surface area of a sphere with respect to the radius r. what is the rate when r = 6?
Final answer:
The rate of change of the surface area of a sphere with respect to its radius is 8πr. For a sphere with a radius of 6, this rate is 48π square units per unit of radius.
Explanation:
The surface area S of a sphere is given by the formula S = 4πr², where r is the radius of the sphere. To find the rate of change of the surface area with respect to the radius, we need to differentiate the surface area formula with respect to r. This calculation gives us dS/dr = 8πr. When r = 6, the rate of change, or the derivative evaluated at this radius, is dS/dr = 8π(6) which equals 48π.
So, the rate of change of the surface area of a sphere with respect to its radius when r = 6 is 48π square units per unit of radius.
Make the following conversion.
0.075 m = _____ cm
0.075 m is 7.5 centimeters.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement.
Given that, convert 0.075 m into cm
We know that, 1 meter = 100 centimeters
0.075 meter = [(100) × 0.075] centimeter
0.075 meter = (100 × 0.075) centimeter
= (100 × 75/1000) centimeter
= (7500/1000) centimeter
= (75/10) centimeter
= 7.5 centimeter.
Hence, 0.075 m is 7.5 centimeters.
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