Find the value of m in each equation below. Justify your answer.
(x^m × x^2)^3 (k^3)^5 = x^21k^15
Answers
i) [tex]x^a \cdot x^b=x^{a+b}[/tex] (so, when we multiply 2 exponents of the same base, we add the exponents)
ii) [tex]({x^a})^b=x^{a \cdot b}=x^{ab}[/tex]
thus,
[tex](x^m \cdot x^2)^3=({x^{2m}})^3=x^{2m \cdot3}=x^{6m}[/tex]
by first applying property i) then property ii)
also, [tex]({k}^3)^5=k^{15}[/tex], by property ii)
So we have:
[tex]({x^m \cdot x^2})^3 \cdot({k}^3)^5=x^{21} \cdot k^{15}\\\\x^{6m}\cdot k^{15}=x^{21} \cdot k^{15}[/tex],
now we only have to compare the exponents.
6m must be equal to 21,
thus m=21/6=7/2
Answer: m=7/2
Related Questions
Ethan wrote the number four million,three hundred five thousand, seven hundred sixtu-two as 4,350,762.Describe and correct his error.
Answers
A bus service drives passengers between Milwaukee and Chicago every day. They travel from city to city eight times each day. The distance between the two cities is 89 miles..In February there are 28 days. The company's budget allows for 28,000 total miles for February. Do you think the budget is reasonable? Explain
Answers
to the budget
Answer:
Yes the budget is reasonable.
Step-by-step explanation:
A bus service drives passengers between Milwaukee and Chicago every day for eight times each day.
The distance between the two cities is 89 miles.
So, total distance covered per day = [tex]89\times8=712[/tex] miles.
Total distance covered in 28 days = [tex]28\times712=19936[/tex] miles.
As give, The company's budget allows for 28,000 total miles for February.
So, yes the budget is reasonable, as it is less than 28000.
What times what equals 0.59??
Answers
2 can go into .590 .295 times.
One of the multiple answers is:
4 x 0.1475= 0.59
The library charges $0.75 a day for overdue videos and $0.12 a day for overdue books. Emily pays a total of $3.48 in late fees. How many days late were the items?
Answers
Add $0.75 to $0.12 you get $0.87
Divide $3.48 by $0.87 you get 4
A decimal that contains digits that continue forever in a pattern is called a(n) ____ decimal
Answers
7.9 * 10^7 +6.58*10^6=
Answers
Angie is wrapping a present for her best friend. The box is 16 inches long, 12 inches wide, and 3 inches high. How many square inches of wrapping paper does Angie need for her present
Answers
Since we're not looking for the Volume, we'd just multiply one variable by another, for instance:
Bottom = Length * Width
x = 16 * 12 | 16 * 12 = 192
Left = Length * Height
x = 16 * 3 | 16 * 3 = 48
Front = Width * Height
x = 12 * 3 | 12 * 3 = 36
Now that we know 3 of the sides, we then multiply each by 2 since there's another side to this box(in other words, we'd be adding both sides together, multiplying it by 2 still gives you the same answer though).
Bottom + Top, or Bottom * 2
192 + 192 = 384 | or | 192 * 2 = 384
Left + Right, or Left * 2
48 + 48 = 96 | or | 48 * 2 = 96
Front + Back, or Front * 2
36 + 36 = 72 | or | 36 * 2 = 72
Adding these together gives you the answer you're looking for. ^ ^
384 + 96 + 72 = 552
So, the answer should be that Angie needs 552 square inches of wrapping paper for her present. I hope that helped, have a great rest of your day!
| | Ghostgate (Alter) | |
Container A is 13 inches by 19 inches. by 25 inches.Container B is 13 inches by 13 inches by 31 inches.In cubic inches,how much greater is the volume of Container A.
Answers
volume of container A = 13*19*25 = 6175 in^3
volume of container B = 13*13*31 = 5239 in^3
container A is greater by 6175-5239 = 936 in^3 than container B
A rope 25 feet long is cut into 3 pieces. The forest piece is 2x feet long, the second piece is 5x feet long, and he third piece is 4 feet long.
a. Write and solve and equation find x.
b. Find the length of the first and second piece
Answers
7x + 4 = 25
7x = 25 - 4
7x = 21
x = 21/7
x = 3
(b) first piece = 2x....= 2(3) = 6 ft <=
second piece = 5x....= 5(3) = 15 ft <=
The science department buys the equipment shown in the table they bought all three items this year and how many years will they have had by all three items again
Answers
MIcroscopes Every 5 years
Safety goggles Every 4 years
Test Tube Every 2 years
It would take 20 years for them to buy these three items at the same time.
We simply need to find the LCM or least common multiple of the 3 items using the number of years.
Microscopes - 5 years → 5, 10, 15, 20
Goggles - 4 years → 4, 8, 12, 16, 20
Test tubes - 2 years → 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
What value represents a number 10 times as great as 581,000?
Answers
Find three consecutive even numbers that have a sum of 36
Answers
x + (x +2) + (x +4) = 36
Solving:
3x + 6 = 36
3x = 30
x = 10
10,12,14
Hope this helps!
a male lion needs as much as 15 pounds of food each day or 105 pounds of food each week.how much does a lion need in one year.
I'm just checking i have the answer i just want to check thx
Answers
If a male lion eats 15 pounds of food each day or 105 pounds each week, it would need about 5460 pounds of food in a year. We arrive at this by multiplying the weekly amount (105 pounds) by the number of weeks in a year (52 weeks).
Explanation:The question is asking how much food a male lion needs in a year if it eats 15 pounds of food each day, or 105 pounds per week. If we want to know how many pounds of food a lion needs for an entire year, we would need to multiply that weekly amount by the number of weeks in a year. There are 52 weeks in a year. So, we take 105 pounds of food per week and multiply it by 52.
Calculation: 105 × 52 = 5460
So, a male lion needs about 5460 pounds of food in a year.
Learn more about Multiplication here:https://brainly.com/question/35502092
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record the product 8x43 using expanded form to help
Answers
Write two multiplication expressions that have a product of 20,000.
Answers
5,000x4=20,000
8,000•2.5 = 20,000
The product of a non zero rational number and a irrational number is always sometimes or never irrational
Answers
Hope this helps!
Students use a balance to determine the mass of a marble in 7.5 G of graduated bottle contains 10 milliliters of water when the marble is carefully lowered into the granulated bottle and is completely covered with water the volume of the water containing the marble has increased to 12.5 ml what is the density of the marble
Answers
Denisty of the marble = mass / volume = 7.5 / 2.5 = 3 grams/millimeter.
Answer:
3 g/ml
Step-by-step explanation:
After the marble was introduced into the graduated bottle, the volume change from 10 ml to 12.5 ml, this means that 12.5 - 10 = 2.5 ml is the volume occupied by the marble.
The mass of a marble is 7.5 g.
Density is defined as follows:
density = mass / volume =
Replacing with the measures:
density = 7.5/2.5 = 3 g/ml
Tell me whether the expressions in each pair are equivalent... Please i beg Someone to answer this!
1. 6m+1 and 1x6+m
2. 9y and 9+y
3. mp+nq and mq+np
4. -(5-q) and 9-5
5. 8-4c and 4c-8
6. 3(5+z) and 15+2
Pls put down your answer in form!
Answers
1\4 15\100 is it >,<, or =
Answers
25/100 > 15/100
hope this helps
Multiply 8.88x10 to the 4th power. Explain the shift of the digits and the change in the value of each digit
Answers
Chloe wants to cut a 37 in. piece of ribbon into three pieces. The second piece is to be 2 in. longer than the first, and the third piece is to be 3 in. longer than the second. How long will each of the pieces be?
Answers
1st piece = x
2nd piece = x+2
3rd piece = x+2+3 = x+5
37 = x +x+2 + x+5 =
37 = 3x+7
30=3x
x = 30/3 = 10
1st piece = 10 inches
2nd piece = 10+2 = 12 inches
3rd piece = 10+5 = 15 inches
Approximate √39 to the nearest whole number
Answers
√36 < √39 < √49
6 < √39 < 7
√39 ≈ 6
Identify the rate that does not belong with the other three. Justify your response
4.5 feet per second
112.5 in 25 seconds
86.4 feet in 18 seconds
54 feet in 13 seconds
Answers
The other three are similar because they are all in the unsimplified format of distance in a period of time, while the first one is just a simplified rate that could be used to multiply easily.
What is the product of 5 + 2i and 7 + 3i?
Answers
1) 5-2i or 5-2
2) 7-3i or 7-3
I'm learning about Equivalent systems of equations, please help!
Answers
First let's solve for the teacher's:
-2x+5y=10
-3x+9y=6
Solve by substitution (I think elimination might be easier to do for this one, but I don't really remember 100% sorry!)
Isolate the x (or y) variable in the first equation
-2x+5y=10
-2x=10-5y
[tex]x= \frac{10-5y}{-2} [/tex]
Substitute x into the next equation and solve for y
-3(10-5y/2)+9y=6
3*10-5y/2+9y=6
(multiply both sides by 2)
3(10-5y)+18y=12
30-15y+18y=12
30+3y=12
3y=-18
y=-6
Substitute in x
x= -10-5(-6)/2
x=-20
TEACHER'S ANSWER (-20,-6)
GOKU
x-3y=-2
-2x+5y=-7
Do the same as above
Solve for x
x-3y=-2
x=3y-2
Plug in
-2(3y-2)+5y=-7
4-6y+5y=-7
4-y=-7
-y=-11
y=11
x=(3(11)-2)
x=31
GOKU'S ANSWER (31, 11)
SELINA:
-5x+14y=16
-3x+9y=12
One last time!! :)
-5x+14y=16
-5x=16-14y
x=(16-14y)/-5
-3(-(16-14y/5)+9y=12
3*16-14y/5+9y=12
3*16-14y+45y=60
48-42y+45y=60
48+3y=60
3y=12
y=4
x=-(16-14(4))/5
x=8
SELINA'S ANSWER
(8,4)
So neither Goku or Selina got the same answer as the teacher
The teacher's system is
-2x + 5y = 10
-3x + 9y = 6
To find the system that equals to the teachers solution, we must solve all three of them. (Yeah good luck)
Let's start solving the teacher's system
We need to solve -2x + 5y = 10 for x
-2x + 5y = 10
-2x = 10 - 5y
Divide both sides by -2
-2x/-2 = (10-5y)/-2
x = 5/2 y - 5
Now we need to substitute 5/2 y -5 for x in -3x +9y = 6
We gonna replace 5/2 y -5 by x
-3x + 9y = 6
-3(5/2 y - 5) + 9y = 6
Simplify both sides (I used a calculator)
3/2 y + 15 = 6
3/2 y = 6 - 15
3/2 y = -9
To find y, we need to divide both sides by 3/2
3/2 y/3/2 = -9/3/2 (I used a calculator)
y = -6
It easier to find x since we already find y
So, let's find x by substitute -6 for y in x=5/2 y - 5
What does that mean? We gonna replace the value of y which is -6 everywhere we find y (I hope it makes sense)
x = 5/2 y - 5
x = 5/2 (-6) - 5 (use a calculator)
x = -20
Therefor,
x = -20 and y = -6
This is the teacher's solution so we gonna solve the others and see what they have :)
----------------------------------------------
Selina's system
-5x + 14y = 16
-3x + 9y = 12
So, we need to solve -5x + 14y = 16 for x
-5x + 14y = 16
-5x = 16 - 14y
Divide both sides by -5
-5x/-5 = (16 - 14y)/-5
x = 14/5 y + -16/5 (It looks messy here)
To continue, we need to substitute 14/5 y + -16/5 for x in -3x + 9y = 12
-3x + 9y = 12
-3( 14/5 y + -16/5) + 9y = 12
Simplify both sides
3/5 y + 48/5 = 12
3/5 y = 12 - 48/5
3/5 y = 12/ 5
To find y, we just need to divide both sides by 3/5
3/5 y/3/5 = 12/5/3/5 (cancel 5, then divide 12 by 3 = 4)
y = 4
We gonna use the value of y to find x
We gonna do that by substitute 4 for y in x = 14/5 y + -16/5
x = 14/5 y + -16/5
We gonna replace y by 4
x = 14/5 (4) + -16/5 (used a calculator)
x = 8
Therefore,
x = 8 and y = 4
So, Selina system doesn't equal to the teacher's system.
-----------------------------------
Goku's system
again, I used the same steps to solve all of them.
x - 3y = -2
-2x + 5y = -7
We need to solve x - 3y = -2 for x
x - 3y = -2
x = -2 + 3y
I prefer to let the unknown value leads, so it will be
x = 3y - 2 (it still the same thing :) )
Substitute 3y - 2 for x in -2x + 5y = -7
-2x + 5y = -7
-2(3y - 2) + 5y = -7
-6y + 4 + 5y = -7
-y + 4 = -7
-y = -7 - 4
-y = -11
We cannot leave the y with a negative sign, so we must divide both sides by -1
-y/-1 = -11/-1
y = 11
To find x, we need to substitute 11 for y in x = 3y - 2
x = 3y - 2
x = (3)(11)-2
x = 33-2
x = 31
Therefore,
x = 31 and y = 11
Goku's answer doesn't equal to the teacher's answer.
------------------------------------------
Answer : Neither Goku or Selina
I hope I helped!
10 friends go out to lunch and order 9 large pizzas. The friends divide the pizzas evenly. Find how much pizza each friend got as a decimal
Answers
Hope I helped :)
Kevin is 14 inches taller than George. The difference between Kevin and Richard is two inches less than between Richard and George. Kevin at 6'6" is the tallest. How much tall are Richard and George?
Answers
6.6-1.2= 5'4 george
richard is 6'0
Richard is 6'1" and George is 5'11" tall.
To calculate Richard and George's heights, we start with Kevin being 6'6" and 14 inches taller than George, meaning George is 5'4".
The difference between Kevin and Richard is 2 inches less than between Richard and George, making Richard 6'1" and George 5'11".
Solve for x. 3x−82=x−6
20 Points
Answers
3x-82 = x-6
subtract 1 x from each side
2x -82 = -6
add 82 to each side
2x = 76
divide both sides by 2
x = 76/2 =38
x = 38
Check:
3(38)-82 = 38-6
3*38 = 114, 114-82 =32 and 38-6 = 32 32 = 32 TRUE
In which expressions of the exponent be multiplied
Answers
The function g(x) = –3x2 – 36x – 60 written in vertex form is g(x) = –3(x + 6)2 + 48. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –3x2 – 36x – 60? The graph of f(x) = x2 is made narrower. The graph of f(x) = x2 is shifted right 6 units. The graph of f(x) = x2 is shifted down 48 units. The graph of f(x) = x2 is reflected over the y-axis.