The Expression [tex](3p^{3} q)^{\frac{3}{4} }[/tex] in radical form is [tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]
What is Expression?An expression is a combination of numbers, operator and variables.
The given expression is [tex](3p^{3} q)^{\frac{3}{4} }[/tex]
We know that
[tex]a^{\frac{p}{q} } =\sqrt[q]{a^{p} }[/tex]
So let us use same form to solve the given expression to radical form.
[tex](3p^{3} q)^{\frac{3}{4} }[/tex]=[tex]\sqrt[4]{(3p^{3} q)^{3} }[/tex]
Simplify the terms in root,
=[tex]\sqrt[4]{(3^{3}p^{3.3}q^{3} }[/tex]
=[tex]\sqrt[4]{27p^{9}q^{3} }[/tex]
[tex]\sqrt[4]{27p^{4}p^{4}pq^{3} }[/tex]
=[tex]p.p\sqrt[4]{27pq^{3} }[/tex]
=[tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]
Hence the Expression [tex](3p^{3} q)^{\frac{3}{4} }[/tex] in radical form is [tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]
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Tony is now three years older than howard. five years ago the sum of their ages was 59. now, tony is
The Tony age and Howard age be 36 and 33 respectively.
It is required to find the age of tony.
What is age?The amount of time during which someone or something has lived or existed. The length of time that a person has lived or a thing has existed.
Given:
Let Howard age=x
Tony age=x+3
Before 5 year we have,
Howard age=x-5,
Tony age=x+4-5=x-1
Some of there age=59
According to given question we have,
x-5+x-1=59
2x-6=59
2x=65
X=65/2
x=32.5
The age can't be fraction or decimal so we take 33.
Howard age=33
Tony age=33+3=36
Therefore, the Tony age and Howard age be 36 and 33 respectively.
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When the Citizens United decision was handed down, a flood of corporate cash was expected to enter the political system. The ruling did result in more corporate and union spending, but far less than anticipated because__________.?
The measure of each interoir angle of a regualr polygon is 144 . how many sides does this polygon have
Assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of $26,000 and a standard deviation of $5000. what is the cutoff salary for teachers in the bottom 10%?
Tasha earns $400 per week plus a commission of 10% on her weekly sales. Each week she saves of her earnings. In the expression , what does the expression 400 + 0.1s represent in this situation?
the amount Tasha saves each week
the amount Tasha earns each hour
Tasha's weekly commission
Tasha's weekly earnings
Answer:
its D
Step-by-step explanation:
The price of a set of kitchen cabinets is $1,500 in January. In February, the price is increased by 10%. After not selling, the price is reduced by 5% in March. What is the price in March?
The cost of an oil change is $21.95. The markup rate is 65%. What is the selling price?
A student earned 37 out of 50 points on the last test. What percent correct did the student earn?
The length of a side of an equilateral triangle is 12. find the length of the altitude
Final answer:
To calculate the altitude of an equilateral triangle with side length 12, divide the side by 2 and multiply by [tex]\(\sqrt{3}\)[/tex] giving an altitude of approximately 10.3923 units.
Explanation:
To find the length of the altitude of an equilateral triangle with a side length of 12, you can use the Pythagorean theorem. The altitude of the equilateral triangle creates two 30-60-90 right triangles. The altitude is the longer leg in this case, and the side of the triangle is the hypotenuse. In a 30-60-90 triangle, the longer leg (altitude) is [tex]\(\sqrt{3}\)[/tex]times the shorter leg (half of the side of the triangle).
First, divide the side of 12 into two to get the shorter leg of the right triangle, which is 6. Then, multiply 6 by \(\sqrt{3}\) to find the length of the altitude. This results in:
[tex]\(6 \times \sqrt{3} = 6\sqrt{3} \approx 10.3923\)[/tex]
Therefore, the altitude of the equilateral triangle is approximately 10.3923 units long.
The great pyramid in Egypt was built around 2560 BC over the years it has lost 30 feet of height off its top and is now 451 feet tall. Find the original height of the great pyramid
How is interest similar to sales tax in markup
To find the value of an expression is called
The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 2. What percent of the class is boys?
work out the height of a parallelogram with a base of 10m and an area of 60m2
divide this polynomial:
(x^2-6x-20) divided by (x+2)
* if someone would be able to tell me how to divide this it would be very MUCH appreciated
Which ordered pair is a solution to this equation? 2x+3y=16 A.) (11, 1)
B.) (7,2)
C.) (5,2)
D.) (3,2)
5,2 is the answer, this is such easy question my baby brother could do it easy
Matt has a block. He uses one of the flat surfaces of the block to trace a triangle. What type of solid figure is Matt's block?
The types of 3D objects on which one face is triangular are triangular prism, triangular-based pyramid, and square-based pyramid so Matt's solid figure can be anyone among the three.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given,
Matt used a 3D block to draw a triangle on the paper.
Now in order to draw a triangle there are three types of 3D objects that can be used,
01) Triangular prism,
02) Triangular-based pyramid
03) Square-based pyramid
Hence "The types of 3D objects on which one face is triangular are triangular prism, triangular-based pyramid, and square-based pyramid so Matt's solid figure can be anyone among the three".
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I need help solving 206x12
A patchwork blanket is made up of 10 identical squares.Liam has made 14 squares,Raj has made 12 squares and Gemma has made 15 squares.How many patchwork blankets have they made between them ?
Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – 4. Her graph is shown below. What are the solutions of –x2 + 4x = x – 4? A.–5 and 0
B.–5 and –1
C.–1 and 4
D.0 and 4
Answer
C.–1 and 4
Explanation
Solving the equations y = –x² + 4x and y = x – 4
–x² + 4x = x – 4
x² - 4x + x = 4
x² - 3x = 4
x² - 3x + (3/2)² = 4 + (3/2)²
(x - 3/2)² = 4 + 9/4
= 6.25
x - 3/2 = √6.25 or x - 3/2 = -√6.25
x = 2.5 + 1.5 x = -2.5 + 1.5
= 4 = -1
4.624 to the nearest 10m
The value of the decimal number 4.624 to the nearest 10 places is 4.6
What is rounding off the numbers?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.
Given decimal number is 4.624. The rounding off is:-
4.624 = 4.6 at 10 places
Therefore, the value of the decimal number 4.624 to the nearest 10 places is 4.6
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can u please give me an answer best gets the brainliest
How many sides does a polygon have if the sum of interior angles is 11700
Which of the following statements about bullying is true? A. Children will independently learn positive behaviors as they mature B. Bullying is not harmful. C. Bullying is just a phase and children will grow out of it. D. Types of bullying include physical, verbal, emotional, and cyberbullying.
Types of bullying include physical, verbal, emotional, and cyberbullying about bullying is true. Correct option is D.
Option D is the correct statement. Bullying can take various forms, and the four main types of bullying are physical (e.g., hitting, pushing), verbal (e.g., name-calling, teasing), emotional (e.g., spreading rumors, excluding someone), and cyberbullying (bullying that takes place online or through digital means). It is essential to recognize and address these different types of bullying to create a safe and supportive environment for children and prevent harm.
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Shirley measures the thickness of a piece of cardboard with a ruler that has centimeter and inch markings. Which of the following is most likely the value that Shirley measures?
3 inches is most likely what she measures because the ruler only has inches and centimeters so inches would be more logical
1. Find the length (distance) of segments AB, CD, and EF.
AB =
CD =
EF =
2. Find the midpoint of segments AB, CD, and EF.
AB =
CD =
EF =
3. Find the slope of the segments AB, CD, and EF.
AB =
CD =
EF =
Answer:
1) AB=7 CD=3 EF=[tex]3\sqrt{5}[/tex] 2) [tex]M_{AB}=\frac{-1}{2},2[/tex] [tex] \\ M_{EF} =(\frac{5}{2}-3)[/tex] \\ [tex] \\ M_{EF} =(\frac{5}{2}-3)[/tex] 3) AB not inclined CD not inclined EF 6/5
Step-by-step explanation:
1) We can use the Distance Formula to answer the 1st. question.
But in the first case AB I'd rather doing it intuitively because it is a straight line parallel to the x-axis
AB
A(-4,2) and B(3,2)
In this segment, also parallel we can calculate the length as |-4|+|3|=7 since both have the same y coordinate.
Using the Distance formula to check it:
[tex]D=\sqrt{(3--4)^{2}+(2-2)^{2}}\\D=\sqrt{49}\\D=7[/tex]
CD
C(-4,-1) D(-4,-4)
Similar to the first one but this time with different y coordinates.
The length will be calculated by subtracting the absolute values for y:
|-4|-|-1|=4-1 = 3
Using the Distance formula to check it:
[tex]D=\sqrt{(-4--1)^{2}+(-4--4)^{2}}\\D=\sqrt{9}\\D=3[/tex]
EF
E (1,-1) F(4,-5)
In this case there's no straight line.
So right to the Distance Formula:
[tex]D=\sqrt{(-5-1)^{2}+(4-1)^{2}}\\ D=\sqrt{36+9}\\D=\sqrt{45}\\D=3\sqrt{5}[/tex]
2) To find the Midpoints we need to calculate the Mean of these two points.
AB
A(-4,2) and B(3,2)
[tex]M_{AB} =\frac{-4+3}{2},\frac{2+2}{2}\\M_{AB}=\frac{-1}{2},2[/tex]
CD
C(-4,-1) D(-4,-4)
[tex]M_{CD} =\frac{-4-4}{2} ,\frac{-1-4}{2} \\M_{CD} =(0,\frac{-5}{2})[/tex]
EF
E (1,-1) F(4,-5)
[tex]M_{EF} =\frac{4+1}{2} ,\frac{-1-5}{2} \\ M_{EF} =(\frac{5}{2}-3)[/tex]
3) To find the Slope let's calculate the quotient of a difference between y-coordinates over x-coordinates of two given points.
[tex]m_{AB}=\frac{2-2}{3--4}=\frac{0}{7}=0[/tex]
AB is not inclined.
CD
C(-4,-1) D(-4,-4)
[tex]m_{CD}=\frac{-4--1}{-4--4}=\frac{-3}{-4+4}=\frac{-3}{0}[/tex]
Not Defined for all Real Set of Numbers
The line CD is not inclined.
EF
E(1,-1) F(4,-5)
[tex]m_{EF}=\frac{-5-1}{4--1}=\frac{6}{5}[/tex]
The line EF has a slope of 6/5
Problem page a light bulb consumes 2400 watt-hours per day. how many watt-hours does it consume in 3 days and 6 hours?
Final answer:
The light bulb consumes 7800 watt-hours in 3 days and 6 hours, calculated by summing the daily consumption over three days and additional energy consumed in 6 hours.
Explanation:
To calculate the energy consumption in watt-hours, we first understand that the light bulb consumes 2400 watt-hours in one day. To find out how much it consumes in 3 days and 6 hours, we multiply the daily consumption by the number of days and then add the consumption for the additional 6 hours:
Energy consumed in 3 days = 2400 watt-hours/day imes 3 days = 7200 watt-hours
Energy consumed in 6 hours = (2400 watt-hours/day) / (24 hours/day) imes 6 hours = 600 watt-hours
Adding these two amounts gives us the total energy consumption in the specified time:
Total energy consumption = 7200 watt-hours + 600 watt-hours = 7800 watt-hours
Therefore, the light bulb consumes 7800 watt-hours in 3 days and 6 hours.
Write a compound inequality to represent all of the numbers between -4 and 6.
Answer:-4 < x < 6
Step-by-step explanation:
the number of peaches, p, is three less than half the number of grapes, g. which expression represents the number of peaches in terms of the number of grapes
A.g/2-3
B.2g-3
C.g-3/2
D.3g-2
peaches = 3 less than one half the number of grapes
so from the written problem you can get:
p=1/2g-3
1/2g is the same as g/2
so answer is A. p= g/2-3
ed is using the recipe shown to make fruit salad he wants to use 30 diced stawberries in his vruit sald how many bananas apples and pears should ed use in his fruit sald
Answer:
4
Step-by-step explanation: