The simplified form of the expression [tex]\sqrt{p^5q^{10}}[/tex] is p²q⁵√p, obtained by separating and simplifying the square roots of the individual factors.
The expression [tex]\sqrt{p^5q^{10}}[/tex] can be simplified by separating the square roots of the individual factors and simplifying each one individually.
First, let's rewrite the square root of the entire expression:
[tex]\sqrt{p^5}[/tex] = p²√p because we are taking the square root of p to the fifth power which results in p squared and the square root of p remaining.[tex]\sqrt{q^{10}}[/tex] = q⁵ because q to the tenth power is a perfect square, and taking the square root gives us q to the fifth power.Therefore, the simplified form of [tex]\sqrt{p^5q^{10}}[/tex] is p²q⁵√p.
A 12 pack of soda is roughly $3.75. What is the cost per can of soda?
Find the area of a rectangle with a length of (4x^2) and a width of (x+6)
When ordering a student desk priced at $69.00, the shipping charges are 6%. What is the total cost of the desk?
I need help on this please
Peter makes $7,000 a month plus some extra commission he makes 6% of everything he sells if Peter sold $55,000 of jewelry this month what his salary this month
Mary has been $50 to spend on T-shirts from an online store. there is $10 shipping and handling fee and each t-shirt cost $5 which inequality represents the number of t-shirts s Mary can buy the answer choices are 5S + 10 greater than equal to 50, 5S + 10 less than equal to 50, 10s + 5 greater than equal to 50, 10s - 5 greater than equal to 50, 5S - 10 greater than equal to 50
a disk jockey wants to select five songs from a new CD that contains 12 songs. How many ways can a disc jockey choose 5 songs
Solve the system of equations algebraically 5x - 3y = 6 6x - 4y = 2
Answer:
[tex]x=9[/tex] and [tex]y=13[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to solve our given system algebraically.
[tex]5x-3y=6...(1)[/tex]
[tex]6x-4y=2...(2)[/tex]
From equation (1), we will get:
[tex]x=\frac{6+3y}{5}[/tex]
Upon substituting this value in equation (2), we will get:
[tex]6(\frac{6+3y}{5})-4y=2[/tex]
[tex]\frac{36+18y}{5}-4y=2[/tex]
[tex]\frac{36+18y}{5}-\frac{5*4y}{5}=2[/tex]
[tex]\frac{36+18y-20y}{5}=2[/tex]
[tex]\frac{36-2y}{5}=2[/tex]
[tex]\frac{36-2y}{5}*5=2*5[/tex]
[tex]36-2y=10[/tex]
[tex]36-36-2y=10-36[/tex]
[tex]-2y=-26[/tex]
[tex]\frac{-2y}{-2}=\frac{-26}{-2}[/tex]
[tex]y=13[/tex]
Upon substituting [tex]y=13[/tex] in equation (1), we will get:
[tex]5x-3(13)=6[/tex]
[tex]5x-39=6[/tex]
[tex]5x-39+39=6+39[/tex]
[tex]5x=45[/tex]
[tex]\frac{5x}{5}=\frac{45}{5}[/tex]
[tex]x=9[/tex]
A sandwich shop offers the following toppings. How many two topping sandwiches can you make? -lettuce -tomato -bacon -cheese -mustard
A) 8
B) 10
C) 12
D) 20
Please include steps or explain how you got your answer! :)
The correct answer is: B) 10
Step 1:
To calculate the number of two-topping sandwiches you can make from the given toppings, you can use the combination formula:
[tex]\[C(n, k) = \frac{n!}{k!(n-k)!}\][/tex]
Where:
- [tex]\(n\)[/tex] is the total number of toppings available (5 in this case).
- [tex]\(k\)[/tex] is the number of toppings you want to choose (2 in this case).
- [tex]\(C(n, k)\)[/tex] represents the number of combinations.
Step 2:
Substituting the values:
[tex]\[C(5, 2) = \frac{5!}{2!(5-2)!}\][/tex]
[tex]\[C(5, 2) = \frac{5!}{2!3!}\][/tex]
[tex]\[C(5, 2) = \frac{5 × 4}{2 × 1}\][/tex]
[tex]\[C(5, 2) = \frac{20}{2}\][/tex]
[tex]\[C(5, 2) = 10\][/tex]
So, you can make [tex]\(10\)[/tex] two-topping sandwiches from the given toppings.
The music teacher has a list if 128 students who have signed up for music classes. The music teacher can register 6 students in each class. What is the LEAST number of classes needed for all the students to be registered in a class?
How many different ways can a family visit Philadelphia, Baltimore, and Washington? 3 6 12
Answer:
Answer is 6 ways
Step-by-step explanation:
Given that a family wants to visit three different places as Philadelphia, Baltimore, and Washington.
We have to find the number of ways these three can be visited.
Here this is a question of permutation since order matters.
There are 3 cities and these can be visited in 3P3 ways =3!
=3x2x1 =6 ways
There are in total 6 different ways that the family can visit three different places as Philadelphia, Baltimore, and Washington.
Solve for e.
9e^2f=49
e=±√7f/3
e=±7√f/3
e=±7√f/3f
e=±√7f/3f
QM Q6.) Write the slope-intercept equation of the function f whose graph satisifies the given conditions.
In a right triangle, if the measures of the other two angles are 2x – 5 and 3x + 10, what are the measures of these two angles?
A. 30° & 60°
B. 29° & 61°
C. 50° & 40°
D. 51° & 39°
Answer: B. 29° & 61°
Step-by-step explanation:
Hey can you please help me posted picture of question
1¼ gallons equals how many pints?
Answer:
10 pints
Step-by-step explanation:
There are 8 pints in a gallon, so ...
(1.25 gal) × (8 pt/gal) = 10 pt
Hey can you please help me posted picture of question
Find the sum of the first 10 terms for the sequence {21, 63, 189, . . . }.
5.2 × 1010
620,004
206,661
2730
The sum of the first 10 terms for the sequence given is 620,004.
What is Geometric sequence?A geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given is a geometric sequence, 21, 63, 189, . . . we need to find the sum of the first 10 terms,
Sum of n terms of GP = aₙ = arⁿ-1 / r-1,
a₁ = 21
r = 3
So,
a₁₀ = 21 × 3¹⁰-1 / 3-1
a₁₀ = 21 × 29,524
a₁₀ = 620,004
Hence the sum is 620,004.
Learn more about geometric sequence, click;
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write (-5,2) and (-5,6) in standard form [if you can describe how to do this for the future]
Mr zucco baked a total of 270 cupcakes and muffins. After ue sold 1/3 of the cupcakes and baked 18 more miffins, he had twice as many cupcakes as muffins. How many cupcakes and muffins did mr. Zucco bake to begin with?
i need help with this
The height of a free falling object at time t can be found using the function, h(t) = - 12t2 + 36t. Where h(t) is the height in feet and t is the in seconds. Find the time when the object hits the ground
Hey can you please help me posted picture of question
A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $41,949.00 each year, and $28,826.00 for each person employed for the year. For the next year, the company projects that labor costs will total $1,483,249.00. How many people does the company intend to employ next year?
Answer:
50
Step-by-step explanation:
Let
x = number of employees each yeary = labor costsThe relationship between x and y can be represented through a linear equation.
y = a . x + b
where,
a is the slope
b is the y-intercept
The slope represents the cost per each person employed, that is, a = $28,826.00/person.
Then,
y = ($28,826.00/person) . x + b
Even if no person is hired (x = 0), there is a fixed cost of $41,949.00 (y = $41,949.00).
$41,949.00 = ($28,826.00/person) . 0 + b
b = $41,949.00
The final equation is
y = ($28,826.00/person) . x + $41,949.00
If the company will spend $1,483,249.00 (y = $1,483,249.00.),
$1,483,249.00 = ($28,826.00/person) . x + $41,949.00
1,441,300 = ($28,826.00/person) . x
x = 50 person (50 people)
The company intends to employ 50 people next year.
£54 in the ratio 5:4
The base of a triangular prism is an equilateral triangle with a perimeter of 15in. If the height of the prism is 4in, find the surface area.
Use technology to determine an appropriate model of the data. (0,0), (1,3), (2,4), (3,3), (4,0)
f(x) = – x2 + 4x
f(x) = x2 - 4x
f(x) = - x2 + 4x - 1
f(x) = x2 - 4x + 1
Answer:
Option A.
Step-by-step explanation:
To determine an appropriate model of the data each data should satisfy the expression.
For function 1. f(x) = -x² + 4x
Now for each point
f(0) = 0 , f(1) = 3, f(3) = 3 and f(4) = 0
therefore the given points lie on the function.
For option 2
f(0) = 0, f(1) = -3, f(2) = -4, f(3) = -3 and f(4) = 0
Therefore points do not lie on the function.
For Option 3.
f(0) = -1, f(1) = 2, f(2) = 3, f(3) = 2 and f(4) = -1
Therefore the points do not satisfy the expression.
For option 4.
f(0) = 1, f(1) = -2, f(2) = -3, f(3) = -2 and f(4) = 1
Therefore, the points do not satisfy the expression.
Option A. is the correct option.
Find the sum: (x5 - 3x4 + x2 - 4) + (5x4 + 3x2 + 2x + 1). Enter your answer as a polynomial in descending order below, and use the caret (^) for exponents. For example, you would write as 4x^2.
An open box with a square base should be constructed. the bottom, should be constructed from a heavy duty cardboard that cost $3 per square inches and the sides from a medium duty cardboard that cost $2 per square inches. if the volume of the box must be 120 cubic inches, what should be the dimensions of the box in order to minimize the cost for the material?
Identify the problem with the following poll.
A recent poll asked 82 college students 7 questions about their experience at college. When asked their age only 58 responded.
correlation and causality
loaded questions
nonresponse
self interest