Answers
For each number, generate a factor tree. This is where you break a number down into smaller factors in a visual "tree" like style. The idea is to factor down to the prime factors and then you circle the common primes between each number. The values you circle are then multiplied if you circle more than one value in each tree.
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Problem 34
Xiao factored correctly but didn't pull out the GCF. So he didn't factor fully. In the case of 60 and 90, the GCF is 30. This is the largest shared factor between the two values. So we can pull out 30 to get
60+90 = 30*2+30*3 = 30*(2+3)
I'm basically using the distributive property in reverse. You can distribute the 30 back in and get 60+90 again. Notice how the inner stuff 2 and 3 have no factors in common other than 1.
Related Questions
six is greater than or equal to the quotient of a number y and 2.5
Answers
The statement 'six is greater than or equal to the quotient of a number y and 2.5,' can be converted into the inequality 6 >= y/2.5. Solving for y by multiplying both sides by 2.5 gives y <= 15. Therefore, any number y that is 15 or less will satisfy this inequality.
Explanation:The question provided, 'six is greater than or equal to the quotient of a number y and 2.5,' requires manipulation of an inequality in mathematics to find the potential values of y. To represent this in mathematical terms, one could write the inequality as 6 ≥ y/2.5. From here, it is a simple matter of isolating y by multiplying both sides of the inequality by 2.5, which results in y ≤ 15. Therefore, any number y that is less than or equal to 15 satisfies the inequality.
Inequality, Isolating variables and Mathematical terms are vital concepts for understanding and solving problems in algebra.
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At the beginning of the year, Adrian's savings account balance was $28. Each week, he deposits another $15 into that account, and he doesn't spend any of his savings.
Is his savings account balance proportional to the number of weeks since the start of the year?
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Answer:
The given condition is not proportional.
Step-by-step explanation:
At the beginning of the year, Adrian's savings account balance was $28.
Let Adrian invests for 'x' weeks.
So, total amount will becomes :
[tex]28+15x[/tex]
Since 4 weeks = 1 month, it will represent a linear equation only.
Linear functions have a constant rate of change and describe a straight line on a graph. So, this is not proportional.
The given equation is in the form y = mx + b, so its linear. For the equation to be proportional, it should be in the form of y = kx.
How do I solve this?
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A baker decorates 42 cupcakes in 30 minutes. She decorates cupcakes at a constant rate. How many cupcakes can the baker decorate per minute?
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If the baker decorates 42 cupcakes in 30 minutes and you have to find a minute you have to divide 42 by 30 to find your answer which is 1.4 cupcakes a minute.
Hope this helps!
Rewrite as a simplified fraction 1.1 3 =?
Answers
The requried 1.1 3 can be written as a simplified fraction of 44/333.
What is the fraction?A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers. In a fraction, the top number is referred to as the numerator, while the bottom number is referred to as the denominator.
Here,
To rewrite 1.1 3 as a simplified fraction, we can first recognize that the repeating decimal can be represented as a fraction using a geometric series.
Let x = 0.133. Then, we can multiply both sides of this equation by 1000 to obtain
1000x = 133.333...
Next, we can subtract x from 1000x to obtain
999x = 133.333... - 0.133...
Simplifying the right side gives
999x = 133.2
Finally, dividing both sides by 999 gives
x = 133.2 / 999 = 44 / 333
Therefore, 1.1 3 can be written as a simplified fraction of 44/333.
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I am asking the same question again in the hope of finding a more detailed answer. Explain why the two figures below are not similar.
Answers
which of the following is the correct graph of the compound inequality 4p+1>-7 or 6p+3 <33?
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1)4p+1>-7
4p>-7-1
4p>-8
=p>-2
2)6p+3<33
6p<33-3
6p<30
=p<5
therefore p>-2 or p<5
Answer:
set of all real numbers (-∞,∞)
Step-by-step explanation:
Solve each inequality
[tex]4p+1>-7[/tex]
Subtract 1 from both sides
[tex]4p>-8[/tex]
Divide by 4 on both sides
[tex]p>-2[/tex]
[tex]6p+3 <33[/tex]
Subtract 3 from both sides
[tex]6p<30[/tex]
Divide both sides by 6
[tex]p<5[/tex]
[tex]p>-2[/tex] or [tex]p<5[/tex]
The graph is attached below
A)What is the difference between the highest elevation in Alabama and lowest elevation in Louisiana?
B) find the difference between the lowest elevation in New Mexico and the lowest elevation in California.
C) find the difference between the highest elevation in florida and the lowest elevation in California?
D) what is the Difference between the lowest elevation in Alabama and the lowest elevation in Louisiana?
Plzzzz help me
Plz :(:
Answers
Answer:
Part (A) the difference is 2,415 feet.
Part (B) the difference is 3,124 feet.
Part (C) the difference is 627 feet.
Part (D) the difference is 8 feet.
Step-by-step explanation:
Consider the provided table:
Part (A) The difference between the highest elevation in Alabama and lowest elevation in Louisiana.
highest elevation in Alabama is 2,407 and Lowest elevation in Louisiana is –8
Subtract the lowest elevation in Louisiana from the highest elevation in Alabama as shown:
2,407 – (–8 )= 2,407 + 8 = 2,415
So, the difference is 2,415 feet.
Part (B) the difference between the lowest elevation in New Mexico and the lowest elevation in California.
Lowest elevation in New Mexico is 2,842 and the lowest elevation in California is –282.
Subtract the lowest elevation in California from the lowest elevation in New
Mexico as shown.
2,842 – (–282) = 2,842 + 282 = 3,124
So, the difference is 3,124 feet.
C) The difference between the highest elevation in Florida and the lowest elevation in California.
Highest elevation in Florida is 345 and the lowest elevation in California is –282.
Subtract the lowest elevation in California from the highest elevation in Florida as shown.
345 – (–282) = 345 + 282 = 627
So, the difference is 627 feet.
Part (D) The Difference between the lowest elevation in Alabama and the lowest elevation in Louisiana.
Lowest elevation in Alabama is 0 and the lowest elevation in Louisiana is –8.
Subtract the lowest elevation in Louisiana from the lowest elevation in Alabama.
0 – (–8) = 0 = 8
So, the difference is 8 feet.
Lena is going to cover her entire garden with topsoil. The garden is 36 feet long by 22 feet wide. A bag of topsoil costs $3 and covers 300 square feet of area. How much will the topsoil for Lena's garden cost?
Answers
$6.64?
You can do this with the formula length * width
In this case it would be:
36 * 22
Which is equal to 792.
Now, you just want to find how many bags of topsoil she needs.
Since I'm assuming you cannot buy half of a bag of topsoil, she will end up buying extra topsoil, because you can't just cut a bag of topsoil in half and then take some of it, then buy that.
So to have enough, she must buy 3 bags of top soil, which would end up costing $9.
When solving negative one over three (x − 15) = −4, what is the correct sequence of operations?
Multiply each side by negative one over three , subtract 15 from each side
Multiply each side by −3, add 15 to each side
Multiply each side by negative one over three , add 15 to each side
Multiply each side by 3, subtract 15 from each side
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step 1 : multiply both sides by -3, step 2 : add 15 to both sides
because when u multiply both sides by -3, this cancels out the -1/3 on the left side leaving u with : x - 15 = -4 * -3.....x - 15 = 12.....and then u would add 15 to both sides....giving u : x = 12 + 15.....x = 27
What is 0.27% as a decimal
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Which figure does not appear to be congruent to this one?
Answers
Answer:
Choice C is the correct one.Step-by-step explanation:
In the image you can observe that the third choice doesn't appear to be congruent to the given one, beacuse it's smaller.
On the other hand, choice A, B and D, have figures that apparently are the same size and shape to the given one, they were just rotated, which is a rigid transformtion, that is, they just move, their size or shape doesn't shape.
Therefore, the right answer is C figure.
Drag and drop the answer into the box to identify each function as linear, exponential, or neither.
x 2 3 4
f(x) 5.5 7 8.5
x 0 3 6
f(x) 1 8 64
Answers
f(x) 5.5 7 8.5
The first function is linear. When you subtract 5.5 from 7, you get 1.5 and when you subtract 7 from 8.5 you also get 1.5. That's how we know it's a linear function because there's clearly pattern. HOWEVER, if you had 5.5, 7, and 9 that would not be a linear function. Why? Because when you take away 7 from 9 you get 2. In order for it to be a linear function you have to get the same exact number when you subtract.
x 0 3 6
f(x) 1 8 64
The second function is exponential because when you divide you get the exact same number. 8/1 = 8 and 64/8 = 8. So this is exponential. But if you had 72 instead of 64 it would not be an exponential function because there has to be a pattern.
I hope this makes sense. Btw I had this question on my test too and this is correct.
Using function concepts, it is found that:
The first function is linear.The second function is exponential.If the absolute value of the change is always the same, it is linear. If the rate is the same, it is exponential.In the first function:
[tex]8.5 - 7 = 7 - 5.5[/tex]
Absolute value always the same, hence linear.
In the second function:
[tex]\frac{64}{8} = \frac{8}{1}[/tex]
Rate always the same, hence exponential.
A similar problem is given at https://brainly.com/question/24282972
S = 6ab + 4a^3
Make b the subject of the formula
Answers
S = 4 a^3 + 6 a b is equivalent to 4 a^3 + 6 a b = S:4 a^3 + 6 a b = S
Subtract 4 a^3 from both sides:6 a b = S - 4 a^3
Divide both sides by 6 a:Answer: b = S/(6 a) - (2 a^2)/3
The mass of a an atom of helium is 6.65 x 10^−24. Use scientific notation to express the mass of 250 helium atoms.
A) 1.6625 x 10−21
B) 1.6625 x 10−22
C) 1.6625 x 10−24
D) 1.6625 x 10−26
Answers
mass of one helium atom x 250
Express 250 as 2.50.
(6.65 x 10−24)(2.50 x 102)
16.625 x 10−22
Scientific notation is the way of writing a large number between 1 to 10 with a power of 10.
The mass of one atom is 6.65 x [tex]10^{-24}[/tex]
The mass of 250 helium atoms is 1662.5 x [tex]10^{-24}[/tex].
The scientific notation to express the mass of 250 helium atoms is
1.6625 x [tex]10^{-21}[/tex].
What is scientific notation?It is the way of writing a large number between 1 to 10 with a power of 10.
Example:
1.2 x 10² is in scientific notation.
9.1 x 10³ is in scientific notation.
We have,
Mass of one atom of helium = 6.65 x [tex]10^{-24}[/tex]
Mass of 250 atoms of helium:
= 250 x 6.65 x [tex]10^{-24}[/tex]
= 1662.5 x [tex]10^{-24}[/tex]
Now,
We will make 1662.5 into a number between 1 and 10.
1662.5
= (1662.5/1000) x 1000
= 1.6625 x 10³
Now,
= 1.6625 x 10³ x [tex]10^{-24}[/tex]
= 1.6625 x [tex]10^{3 - 24}[/tex]
= 1.6625 x [tex]10^{-21}[/tex]
Thus,
The mass of one atom is 6.65 x [tex]10^{-24}[/tex]
The mass of 250 helium atoms is 1662.5 x [tex]10^{-24}[/tex].
The scientific notation to express the mass of 250 helium atoms is
1.6625 x [tex]10^{-21}[/tex].
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Simplify each of the following expressions to find the length of the tightrope.
a) 5+2+8
b) 7+3+2+(-4)
c) 4+9+3
d) 8+6+2+(-5)
Answers
b) 7+3+2+(-4) =8
c) 4+9+3 = 16
d) 8+6+2+(-5) = 11
b) 7 + 3 + 2 - 4 = 8
c) 4 + 9 + 3 = 16
d) 8 + 6 + 2 - 5 = 11
hope this helps
Which word in the sentence is an intensive pronoun?
Ned himself finished the jigsaw puzzle that he and his sister had started.
A.
he
B.
himself
C.
his
D.
that
Answers
Answer:
b. Himself
Step-by-step explanation:
Yi and Sue play a game. They start with the number $42000$. Yi divides by a prime number, then passes the quotient to Sue. Then Sue divides this quotient by a prime number and passes the result back to Yi, and they continue taking turns in this way.
For example, Yi could start by dividing $42000$ by $3$. In this case, he would pass Sue the number $14000$. Then Sue could divide by $7$ and pass Yi the number $2000$, and so on.
The players are not allowed to produce a quotient that isn't an integer. Eventually, someone is forced to produce a quotient of $1$, and that player loses. For example, if a player receives the number $3$, then the only prime number (s)he can possibly divide by is $3$, and this forces that player to lose.
Who must win this game, and why?
Answers
There are a total of 9 prime number factors of 42000.
That means that the quotient can only be passed 9 times until someone reaches 1.
The person on the 9th turn will lose.
In this case, the person who has the 9th turn is Yi.
Yi is going to lose.
Have an awesome day! :)
Answer:
The first person starting will always lose.
Step-by-step explanation:
First, I will the prime factorization of 42000. After finding the prime factorization of 42000, I will count the number of primes in the prime factorization. After that, we will find which round the person will lose.
Prime Factorization of 42000: 2*2*2*2*3*5*5*5*7
Number of Primes in List: 9
The person losing: The person on the 9th turn will lose.
The person on the 9th turn is Yi. Therefore, no matter how Yi or Sue keeps mixing the order of the numbers, Yi will always lose.
I hope this helps!
Determine the correct scientific notation form of the number. 60,700,000,000
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4ax+by=3 , 6ax+5by=8
Answers
2. x=8-5by/6a
Please Help me I would beg you and 20 points!
Answers
Each fraction is each number of cases divided by the total.
Truck: 63/315 = 1/5
Train: 140/315 = 4/9
Air: 112/315 = 16/45
which of the following is equal to 5 4/9 5.49 5.25 7.25 5.4
Answers
(4/9) ~=0.44444
5+0.4444=5.4444
Round and it becomes
5.4
Answer:
5.4
Step-by-step explanation:
We are given that
[tex]5\frac{4}{9}[/tex]
We have to find the value which is equivalent to given fraction number.
[tex]5\frac{4}{9}=\frac{45+4}{9}[/tex]
[tex]5\frac{4}{9}=\frac{49}{9}[/tex]
When we divide 49 by 9 then we get
[tex]\frac{49}{9}=5.4444[/tex]
It can write as 5.4
Hence, [tex]5\frac{4}{9}=5.4[/tex]
Answer:5.4
Karen runs a print shop that makes posters for large companies. It is a very competitive business. The market price is currently $1.00 per poster. She has fixed costs of $250.00. Her variable costs are $1,500 for the first thousand posters, $1,200 for the second thousand, and then $800 for each additional thousand posters.What is her AFC per poster if she prints 1,000 posters? What is her AVC and ATC?
Answers
So given she prints 1,000 posters: AFC = 250.00/1000 = $0.25
Given she prints 2,000 posters: AFC = 250.00/2000 = $0.125
Given she prints 10,000 posters: AFC = 250.00/2000 = $0.025
ATC = TC / Quantity printed
where TC = FC + Variable C * Quantity printed
If she prints 1000: TC = 250 + 2000*1000 = 2,000,250
ATC = 2,000,250/1000 = 2000.25
If she prints 2000: TC = 250 + 1600*2000 = 3,200,250
ATC = 3,200,250/2000 = 1600.125
If she prints 10000: TC = 250 + 1600*2000 + 1000*8000 ($1000 for each additional poster after 2000) = 11,200,250
ATC = 11,200,250/10000 = 1120.025
Please help me on this one I’m stuck
Answers
hoped this helped ☺
Two planes leave airport at the same time, one traveling south and one traveling west. If three hours later they are 500 miles apart and the plane flying south has traveled 200 miles farther, how far did the one flying west travel?
Answers
Simplify.
43 · 44 / 49
A) 4^16
B) 4^2
C) 1/4^2
D) 1/4
Answers
Answer: The correct option is C.
Explanation:
The given expression is,
[tex]\frac{4^3.4^4}{4^9}[/tex]
Using the exponent rule [tex]a^m.a^n=a^{m+n}[/tex] , we get,
[tex]\frac{4^{3+4}}{4^9}[/tex]
[tex]\frac{4^{7}}{4^9}[/tex]
Using the exponent rule [tex]\frac{a^m}{a^n}=a^{m-n}[/tex] , we get,
[tex]{4^{7-9}}[/tex]
[tex]4^{-2}[/tex]
Using the exponent rule [tex]\frac{1}{a^n}=a^{-n}[/tex] , we get,
[tex]4^{-2}}=\frac{1}{4^2}[/tex]
Therefore, the option C is correct.
At the ice cream shop there are 14 shakes sold for every 6 malts. What is the ratio of malts to shakes?
Answers
The weight of an elephant is 1000 times the weight of a cat. If the elephant weighs 14,000 pounds how many pounds does the cat weigh
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x= weight of the cat
14,000=1,000x
x=14 pounds is what the cat weighs.
Check: 14*1,000= 14,000
write 19/25 as a decimal fist person to answer the question correctly is going to be the brainliest
Answers
19/25 * 4/4 = (19*4) / (25 * 4) = 76 / 100
So now you can just convert this to a decimal, and say 0.76.
if a piece of ribbon is 6 1/4 feet long ,how long is it in inches
Answers
the answer is 75 inches.
a quarter of a foot is 3.
6 * 12 = 72 so 72 inches.
EDIT: 72 + 3 = 75