Answer:
The expression [tex]9a^{10}+6a^2b^4+b^8[/tex] is equivalent to the given expression.
Step-by-step explanation:
The given expression is
[tex](3a^5+b^4)^2[/tex]
Use algebraic formula:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](3a^5+b^4)^2=(3a^5)^2+2(3a^5)(b^4)+(b^4)^2[/tex]
[tex](3a^5+b^4)^2=3^2(a^5)^2+6a^5b^4+(b^4)^2[/tex]
Use exponent property:
[tex](a^m)^n=a^{mn}[/tex]
[tex](3a^5+b^4)^2=9a^{10}+6a^5b^4+b^8[/tex]
Therefore expression [tex]9a^{10}+6a^5b^4+b^8[/tex] is equivalent to the given expression.
Gina and Danny are playing an addition card game. In the card game, each player takes turns pulling two cards, one at a time, from a deck of cards. If the first card plus the second card is positive, the player keeps those cards. If the answer is zero or negative, the player loses those cards, and the cards go back in the deck.
There are only 10 cards in the deck, which have the following numbers:
(a) If a player gets a first card that is a positive number, what must the second card be in order for the player to keep the cards? Explain your reasoning.
(b) Gina pulls as her first card. What must her second card be in order for her to have a positive answer? List all correct answers and explain why or show your work.
(c) Danny also pulls a as his first card. He pulls a second card and says he has to put the cards back in the deck because he got a negative answer. What card could Danny have pulled? List all correct ans
numbers...
1 2 3 4 5
-1 -2 -3 -4 -5
To meet building codes, a building must have a roof no taller than 74 feet. An architect is designing a museum with a 14 ½ foot ground floor, and 12 foot 3 inch upper floors (including supports) How many floors, including the ground floor, can the building have?
Answer:
Building can have 4 floors.
Step-by-step explanation:
Height of the ground floor is 14.5 foot and height of upper floors = 12 foot 3 inches or 12.25 foot per floor
Let there are x floors in the building.
Total height of the building = 74 foot
Therefore, total height of the building = Height of the ground floor + Height of the upper floors
74 = 14.5 + 12.25x
74 - 14.5 = 12.25x
12.25x = 59.5
x = [tex]\frac{59.5}{12.25}[/tex]
x = 4.9 floors
Therefore, the building can have 4 floors.
find properties to find 4 x 23 x 25
What is the product?
(7.1 x 10^4) x (4.8 x 10^3)
A. 3.408 x 10^7
B. 3.408 x 10^8
C. 3.408 x 10^12
D. 3.408 x 10^13
(7.1 x 10^4) x (4.8 x 10^3) = A. 3.408 x 10^7
az+17=-4z-b solve of z .
[tex]30.76*0.08[/tex]
about how much would it cost to buy 4 CD/MP3 players and 3 MP3 players... CD Players $74.00... MP3 $99.00
I really need help!!
TJ, Max, and Misha are all the same age. The sum of their ages is s years. How old was TJ eight years ago?
Thanks!
Answer:
(s divided by 3)-8
Step-by-step explanation:
It's an expression :>
Simplest form 1/8 x 20=
The simplest form of the given expression is 5/2.
What is simplest form?Expressions are rewritten in a compact and unlike terms-free manner when they are simplified. Expressions are simplified by combining like phrases, resolving any provided brackets, and only leaving unlike terms that cannot be further reduced in the final simplified expression.
The given expression is 1/8 ×20.
Here, 20/8
= 10/4
= 5/2
Therefore, the simplest form of the given expression is 5/2.
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Since a middle school opened, the
girls'
basketball team has had the same record every season. The team has won a total of
84
games while losing only
6
games. Find the constant of proportionality of wins to losses.
The constant of proportionality of the girls' basketball team's record, with 84 wins to 6 losses, is 14.
The constant of proportionality in the context of a basketball team's win-loss record is calculated by dividing the total number of wins by the total number of losses. As the team has won a total of 84 games and lost 6 games, the constant of proportionality is 84 divided by 6, which equals 14. This means that for every loss, the team has approximately 14 wins.
How do you simplify algebraic frations
Find the value of the algebraic expression for the given values of the variables.
x2 − 3y3 + 4z for x = −4, y = −2, z = 6
In a different sixth grade class the ratio of boys to girls is 3:2.how many boys and how many girls could there be in this class?is there more than one possible answer?explain
Show how to solve the problem 378 times 6 using place value with regrouping. Explain how you knew when to regroup
Answer:
2268
Step-by-step explanation:
We have to solve the problem 378 dimes 6 using place value.
Place of 8 in 378 = once
Place of 7 in 378 = Tens
Place of 3 in 378 = Hundred
Now we can write this number as ( 300 + 70 + 8 )
( 300 + 70 + 8 ) × 6 = (300) × 6 + 70 × 6 + 8 × 6
= 1800 + 420 + 48
= 2268
You have $25 to spend at the movie you spent $18.75 on ticket you want to go buy a bag of popcorn with the rest of the money how many bags can you buy in one bag cost $2.50 use the inequality 2.50b + 18.75 <25 where b represents the number of bag of popcorn
What is the coefficient in the expression 2x/7+2
The coefficient of the expression 2x/7 + 2 will be 2/7.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2x/7 + 2
Now,
The coefficient of x is the number which is multiply with the x.
So, The expression is,
⇒ 2x/7 + 2
⇒ (2/7) x + 2
The coefficient of x in the expression is;
⇒ 2/7
Thus, The coefficient of the expression 2x/7 + 2 will be 2/7.
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The midpoint of AB is M (4,2). If the coordinates of A are ( 6,-4) what are the coordinates of B?
The coordinates of point B are calculated using the midpoint formula. Substituting given values for points A and M allows us to find B's coordinates, which are (2, 8).
Explanation:The midpoint of a line segment is calculated using the formula M=(x1 +x2)/2, (y1+y2)/2 where x1 and y1 are the coordinates of the first point and x2, y2 are the coordinates of the second point. Given that the coordinates of point A are (6,-4) and the coordinates of the midpoint M are (4, 2), we can set up the following equations to solve for the coordinates of point B (x2, y2): (6+x2)/2 = 4 and (-4+y2)/2 = 2. Solving for x2 and y2 gives us the coordinates of Point B: (2, 8).
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I have chosen 4 MYSTERY INTEGERS. At least one
is positive and one is negative.
Follow these clues to figure out my integers. BE SURE TO EXPLAIN YOUR
REASONING!
1. The sum of the four integers is (-6)
2. When you order the integers from LEAST to GREATEST the difference of the
middle two integers is (-4) and the sum is 0
3. The quotient when you divide the LEAST integer by the GREATEST is (-3)
4. The product of the two greatest integers is (+6)
what are three ways you can solve a proportion?
In this exercise we have to explain the three possible methods of solving a proportion, as follows:
1) Vertical
2)Horizontal
3)Diagonal
What is proportion?It is the equality between two or more ratios derived from measurements extracted from quantities. When two ratios have the same result, we say they are proportional. If these ratios represent measures of some magnitude, we also say that they are proportional.
So we know that a proportion is given by the equality between two ratios and the resolution process consists of the following situation: “the product of the extremes is equal to the product of the means” or using the eventual cross multiplication.
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a gallon of chocolate milk sells for $3.14. a snack-size bottle of chocolate milk sells for 3 cents per ounce. which is a better buy?
A gallon of chocolate milk will cost less than snack size bottle so it will be better to buy.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.
Another example could be kilo gram to gram.
Given,
1 gallon ↔ $3.14
Since, 1 gallon = 128 ounce and $1 = 100 cents
128 ounce ↔ 314 cents
So,
1 ounce ↔ 2.453 cents
Now,
Snack-size bottle cost ⇒
1 ounce ↔ 3 cents.
Hence " a gallon of chocolate milk is cheap and batter to buy".
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If 3x + 8x + 4x = 6x + 63, then what is 5x + 23?
Benito rune 1/10 of a mile each day. Which shows how to find the number of days it will take for Benito to run 3/5 of a mile
All social science theories of child socialization emphasize:
The school orchestra is creating a cd of their last concert
hello I am in a math 95 class. my names drew and I was looking at a problem having to do with exponential equations .
There were about 1.32 million Hispanic-owned businesses in 2006 and 1.7 million in 2008.
a) Find an exponential model for this data in which t = 0 corresponds to 2006 and the number of businesses is measured in millions. Round computed values to at least 4 decimal places
f(t)=
b) Assuming the model remains accurate, how many million Hispanic-owned businesses will there be in 2024? Round to the hundredth.
million businesses
PLEASE HELP QUICK!!! WILL GIVE BRAINLIEST!
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The number m and 58 are additive inverses.
Drag and drop 58 and m to their correct positions on the number line.
Drag and drop the label “Sum” to the sum of 58 and m.
Answer:
[tex]m=-\frac{5}{8}[/tex]
Step-by-step explanation:
We have been given that the number m and 58 are additive inverses.
We know that two numbers are additive inverses when they add up-to 0.
[tex]\frac{5}{8}+m=0[/tex]
[tex]\frac{5}{8}-\frac{5}{8}+m=0-\frac{5}{8}[/tex]
[tex]m=-\frac{5}{8}[/tex]
Therefore, the additive inverse of [tex]\frac{5}{8}[/tex] would be [tex]-\frac{5}{8}[/tex].
shade the grid to represent the ratio 23\50. Then find the missing number
23\50=__\100
If the perimeter of a square is 3 feet, how many inches long is each side of the square
Jen bought a 5.00 footling. Sales tax is 8%. How much was sales tax
Solve on the interval [0,2pi) : 2 csc x -3 = -5 a- pi/6, 5pi/6 b- 3pi/2 c- 2pi/3, 4pi/3 d- 7pi/6, 11pi/6