Which operation results in an expression equivalent to ? 23y^4 - 6y^3 + 35y^2 - 20y
A. Q - P
B. PQ
C. P - Q
D. P + Q
Answers
Answer:
D. P + Q
Explanation:
Given:
P = 8y⁴ + 6y³ + 8y
Q = (5y² - 4y)(3y² + 7)
Required:
Determine which operation will give an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.
SOLUTION:
Perform each operation given to see which of them gives an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.
Q - P:
P = 8y⁴ + 6y³ + 8y
Q = (5y² - 4y)(3y² + 7)
Q - P = (5y² - 4y)(3y² + 7) - (8y⁴ + 6y³ + 8y)
(5y²(3y² + 7) -4y(3y² + 7)) - (8y⁴ + 6y³ + 8y)
(15y⁴ + 35y² - 12y³ - 28y) - (8y⁴ + 6y³ + 8y)
Open parentheses
15y⁴ + 35y² - 12y³ - 28y - 8y⁴ - 6y³ - 8y
Collect like terms
15y⁴ - 8y⁴ - 12y³ - 6y³ + 35y² - 28y - 8y
7y⁴ - 18y³ + 35y² - 36y
Therefore, P - Q does not give us an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.
PQ:
P = 8y⁴ + 6y³ + 8y
Q = (5y² - 4y)(3y² + 7) = (15y⁴ + 35y² - 12y³ - 28y)
PQ = (8y⁴ + 6y³ + 8y)(15y⁴ + 35y² - 12y³ - 28y)
=(8y⁴(15y⁴ + 35y² - 12y³ - 28y) +6y³(8y⁴ + 6y³ + 8y)(15y⁴ + 35y² - 12y³ - 28y) +8y(8y⁴ + 6y³ + 8y)(15y⁴ + 35y² - 12y³ - 28y))
= 120y⁸ . . . . .
Note: You don't need to perform this operation further anymore. It would definitely not give us the equivalent expression we are looking for. The degree of the leading term (120y⁸) is way too greater than the degree of the leading term (23y⁴) of the equivalent expression we are looking for.
Thus, PQ cannot give us an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.
P - Q:
P = 8y⁴ + 6y³ + 8y
Q = (5y² - 4y)(3y² + 7) = (15y⁴ + 35y² - 12y³ - 28y)
P - Q = (8y⁴ + 6y³ + 8y) - (15y⁴ + 35y² - 12y³ - 28y)
Open parentheses
8y⁴ + 6y³ + 8y - 15y⁴ - 35y² + 12y³ + 28y
Collect like terms
8y⁴ - 15y⁴ + 6y³ + 12y³ - 35y² + 8y + 28y
-7y⁴ + 18y³ - 35y² + 36y
Therefore, P - Q cannot give us an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.
P + Q:
P = 8y⁴ + 6y³ + 8y
Q = (5y² - 4y)(3y² + 7) = (15y⁴ + 35y² - 12y³ - 28y)
P + Q = (8y⁴ + 6y³ + 8y) + (15y⁴ + 35y² - 12y³ - 28y)
Open parentheses
8y⁴ + 6y³ + 8y + 15y⁴ + 35y² - 12y³ - 28y
Collect like terms
8y⁴ + 15y⁴ + 6y³ - 12y³ + 35y² + 8y - 28y
23y³ - 6y³ + 35y² - 20y
Therefore, P + Q will result in an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.
The answer is D.
Related Questions
The quadratic function modeling the height of a ball over time is symmetric about the line , where t is time in seconds. Which statement is true about this situation?
A.
The height of the ball is the same after 1 second and 3 seconds.
B.
The height of the ball is the same after 0 seconds and 4 seconds.
C.
The height of the ball is the same after 0.5 second and 5.5 seconds.
D.
The height of the ball is the same after 1.5 seconds and 3.5 seconds.
Answers
Answer:
A. The height of the ball is the same after 1 second and 3 seconds.
Step-by-step explanation:
The quadratic equation function modeling is used to analyze the relationship between variables in the equation. If the ball is at height and t is time then the ball is on symmetric line which will move for initial 1 second then stabilizes at 3 seconds.
4cm
2cm
6cm
Find the area please
Answers
Step-by-step explanation:
ummm where is the pic? like bruh
Answer:
48 cm
Step-by-step explanation:
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-7x = -28
solving one step equations
show your work
Answers
Answer:
x=4
Step-by-step explanation:
-7x=-28
-7 -7
x=4
Divide both sides by -7. A negative divided by a negative will give you a positive. So the answer would be x=4.
Answer:
x=4
you divide both sides by -7 to get the x by itself. -28 divided by -7 is 4.
3
Assignment
♡ Find the product of 419 and 321
Find the product of 326 and 124
③ If a mais pay #354 for a book how mac
alle le gay for 7s boots?
④ The price of a big fan is 8494. How
much will 198 big fans cost?
③ Find the product of 3102 and 480
Dictionary Meaning
② Anounced
Answers
Step-by-step explanation:
1. 419*321=134499
2. 326*124 = 40424
3. 354* 7 = 2478
here mac paid 2478
4. 8494*198= 1681812
here it will cost 1681812
5. 3102*480=1488960
6. announced = to reveal something
What is the slope of the line that passes through the points (-10,8)and (-15,-7)
Answers
Answer:
m = 3
Step-by-step explanation:
Use the slope formula to find the slope m .
Convert 139 pounds to kilograms
Round answer to the nearest tenth.
Conversion table:
1 kilogram = 2.205 pounds
Answers
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Step-by-step explanation:
Is this relation a function? Justify your answer.
10
9
8
7
5
4
3
2
1
1 2 3
5
6 7
8 9 10
O A. No, because two points with the same y value have different x-
values
OB. No, because two points with the same x-value have different y
values
O C. Yes, because every x and y-value is positive,
D. Yes, because the number of x-values is the same as the number of
Answers
Answer:
i don't now
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Their is two point on the x value that is the same but on the y value the points are different.
What similarity rule can be used to prove the triangles are similar . plz help
Answers
Answer:
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Step-by-step explanation:
The length of a rectangle is 4 more than the width. The area is 357 square centimeters.
Find the length and width of the rectangle
Answers
Answer:
17*21 = 357
Step-by-step explanation:
Firstly, set up your equation.
x*(x+4)=357
Multiply X by (x+4)
x^2+4x=357
You then subtract 357 from both sides
x^2+4x-357=0
Simplify using the quadratic formula shown, if you need assistance on solving this equation put it into a online calculator, or photomath as it shows the steps taken to solve it.
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Greta writes a fraction that is greater than 1 and less than 2. Jullo writes a fraction that is greater than 3 and less than 4. Greta and Julio
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The product is greater than 1 and less than 2.
The product is greater than 3 and less than 4.
The product is greater than Julio's fraction
The product is less than Greta's fraction,
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Answers
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Step-by-step explanation:
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Answer:
B-2.5
Step-by-step explanation:
Because the median for the first one is 5 and the median for the second one is 7.5 and 7.5-5=2.5
Y=-6x+15 what is the slope of this function?
Answers
Answer:
slope = -6
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
The line is moving down negatively, and by using rise over run, we can determine that the slope is -6/1
Find Each Sum.
1) (-12)+7=
2) (-10)+(-7)=
3) (-6)+12=
4) 8+7=
5) 3+4=
6) (-45)+9=
Answers
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3) 6
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5) 7
6) -36
Kayla measures a distance of 50 inches. She needs to find the equivalent number of meters. Which conversion factors should she use? Check all that apply.
(A) StartFraction 2.54 centimeters Over 1 inch EndFraction
(B) StartFraction 1 inch Over 2.54 centimeters EndFraction
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(D) StartFraction 100 centimeters Over 1 meter EndFraction
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Step-by-step explanation: :)
Answer:
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Step-by-step explanation:
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3u = 4.8
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Answers
Answer:
U = 1.6
Step-by-step explanation:
Divide 4.8 by 3.
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How much salsa does each person get?
Answers
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Can you please add a step by step
Answers
Answer:
4.8
Step-by-step explanation:
15/6 is 2.5 whitch when divided by 12 is 4.8 so 12 divided by 2.5 is 4.8
Answer:
4.8 meters
Step-by-step explanation:
[tex]\frac{15}{6} = 2.5[/tex] 12 ÷ 2.5 = 4.8 metersI hope this helps!
Write an equation for each of the following phrases or word problems. Solve for the missing variable. a. Two times a number is 16. b. Two plus a number is 28. c. Three is a number divided by 6. d. Samuel is y years old. In 10 years, he will be 27. How old is Samuel? e. A third of a pizza is 400 calories. How many calories in the whole pizza?
Answers
Answer:
2x8=16
2+26=28
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answers
Answer:
a. 0.5 g/cc
Step-by-step Explanation:
Given:
Measurement of rectangular prism = 3 cm × 4 cm × 6 cm
Mass of rectangular prism = 36 grams
Required:
Density of rectangular prism
SOLUTION:
[tex] Density = \frac{Mass}{Volume} [/tex]
Mass = 36 g
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Answers
Answer:
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Step-by-step explanation:
It has a lot of strong beats and the rhythm sounds better than A and C.
Water flows through a pipe at a rate of 8 pints per hour. Express this rate of flow in cups per week.
Answers
Answer:
2,688 cups per week
Step-by-step explanation:
Lets begin by figuring out the pints per week/pints per day. Multiplying 8 times 24, we get our daily total of 192 pints per day. Multiply this by 7 and we get a total of 1344 pints per week. We now must convert these pints into cups, which can be done by multiplying the total amount of pints by 2. 1344 times 2 = 2,688 cups
Can you help me with this one?
Answers
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Answers
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Step-by-step explanation:
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The graph shows the cost C in dollars of W pounds of blueberries a proportional relationship. select all the true statements
A 1 pound of blueberries cost $2.75
B 2.75 pounds of blueberries cost $1
C 5pounds of blueberries cost $15
D 12 pounds of blueberries cost $33
E The point (3,9) is on the graph of the proportional relationship
Answers
Answer:
A, D
Step-by-step explanation:
Cost ($) = C
lbs (Blueberries) = W
One pound of blueberries costs $2.75 because to find how much 1 lb is you need to divide by 6.
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2.75 * 5 is 13.75 (This means C is wrong)
Do the same but with 12 for D
2.75 * 12 is 33, so D is correct
You could do the same method as above for E, but the easier way to do this is to see that the relationship of 3:9 is equal to a 1:3 ratio, which is the same as what the pounds to cost ratio is (which is 1:2.75)
Hope this helps! ^_^
A linear graph is represented by a straight line
The true options are:
A. 1 pound of blueberries cost $2.75 D. 12 pounds of blueberries cost $33The points on the graph are:
[tex]\mathbf{(x_1,y_1) = (0,0)}[/tex]
[tex]\mathbf{(x_2,y_2) = (6,16.50)}[/tex]
The slope (m) of the graph is:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{16.50 - 0}{6-0}}[/tex]
[tex]\mathbf{m = \frac{16.50}{6}}[/tex]
[tex]\mathbf{m = 2.75}[/tex]
The above means that: 1 pound of blueberries costs $2.75
Hence, (a) is true, and (b) is false
Multiply 2.75 by 5, to get the cost of 5 blueberries
[tex]\mathbf{C(5) = 2.75 \times 5=13.75}[/tex]
This means that: (c) is false
Multiply 2.75 by 12, to get the cost of 12 blueberries
[tex]\mathbf{C(12) = 2.75 \times 12=33}[/tex]
This means that: (d) is true
(e) is false, because:
[tex]\mathbf{\frac{9}{3} \ne 2.75}[/tex]
Hence, the true options are: (a) and (d)
Read more about linear graphs at:
https://brainly.com/question/11804653
A store has 2 times as hooded sweatshirt as crewneck sweatshirts. The total number of sweatshirts is 36. How many hooded sweatshirts does the store have?
Answers
Answer:
Answer below
Step-by-step explanation:
It would be 36×2=72
since we're doubl8ng it so there would be 72 hooded sweatshirts
Answer:
24 Hooded Sweatshirts
Step-by-step explanation:
36/3=12
2x12=24 or hooded sweatshirts
1x12=12 or crewneck sweatshirts
12+24=36 total sweatshirts :)
Which of the following numbers is a perfect square?
222
141
196
124
Answers
Answer:
196
Step-by-step explan
How do you do this question?
Answers
Answer:
B
Step-by-step explanation:
This is a ratio of polynomials. As n approaches infinity, an approaches 4n / n⁸ = 4 / n⁷, which is a convergent p-series.
Using Limit Comparison Test:
an = (2 + 4n) / (1 + n²)⁴
bn = 4 / n⁷
lim(n→∞) an / bn = 1
The limit is greater than 0, and bn converges, so an also converges.
Find the Unit Rate.
216 diving students to 12 instructors
Answers
Answer: 216 diving students to 12 instructors = 18 students per instructor.
Step-by-step explanation:
Which of the following numbers is irrational?