Answer:
m = 8Step-by-step explanation:
Given the expression:
x³(x−y)⁷−y³(x−y)⁷
This can also be written as (x³-y³)(x-y)⁷
(x³-y³)(x-y)⁷= (x-y)⁷ (x³-y³)
Expand (x³-y³)
x³-y³ = (x-y)(x²+xy+y²)
Substitute back into the original expression:
(x-y)⁷ (x³-y³) = (x-y)⁷(x-y)(x²+xy+y²)
(x-y)⁷ (x³-y³) = (x-y)⁸(x²+xy+y²)
(x-y)⁷ (x³-y³) = (x-y)⁸(x²+y²+xy)
Comparing the result with (x−y)^m(x^2+y^2+nxy).
(x-y)⁸ = (x-y)^m
m = 8
Also:
nxy = xy
n = xy/xy
n = 1
Hence the value of m is 8
The value of m is 8
The expression is given as:
[tex]x^3(x-y)^7-y^3(x-y)^7[/tex]
Factor out (x - y)^7 in the above expression
[tex]x^3(x-y)^7-y^3(x-y)^7 = (x^3 - y^3)(x -y)^7[/tex]
Expand out (x^3 - y^3) as the difference of two cubes
[tex]x^3(x-y)^7-y^3(x-y)^7 = (x-y)(x\²+xy+y\²)(x -y)^7[/tex]
Combine the common factors
[tex]x^3(x-y)^7-y^3(x-y)^7 = (x\²+xy+y\²)(x -y)^8[/tex]
Rewrite the expression as:
[tex]x^3(x-y)^7-y^3(x-y)^7 = (x -y)^8(x\²+xy+y\²)[/tex]
The expression format is given as:
[tex](x-y)^m(x^2+y2^+nxy)[/tex]
So, we have:
[tex](x-y)^m(x^2+y2^+nxy) = (x -y)^8(x\²+xy+y\²)[/tex]
By comparison, we have:
[tex]m = 8[/tex]
Hence, the value of m is 8
Read more about expressions at:
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Convert 8% to a fraction/mixed number and a decimal. Select all that apply.
Answer:
hope this helps :)
Step-by-step explanation:
Decimal - 0.008
Simplifed fraction -- 2/25
Answer:
[tex]8\% = \frac{2}{25} in \: fraction \\ 8\% = \frac{8}{100} = 0.08 \: in \: decimal[/tex]
Pls help with math ASAP
Choose ALL answer choices equivalent to the ratio of snails to frogs?
A. 4:3
B: 3:4
C: 9:12
D: 12:9
E: 18:20
F: 27:36
And the picture shows that there are 4 frogs and 3 snails
Now let's assume that you have a newer toilet that uses 6 L per flush, but you are considering upgrading to a dual-flush toilet. If you flush the toilet four times per day, but three of those times you could use the 3 L flush, how many liters of water would you save in 1 year
Answer: 3,285 Liters
Step-by-step explanation:
In the actual case, all your flushes consume 6 L of water.
You flush 4 times per day, then you consume 4 times 6 L per day, this is:
4*6L = 24 L per day.
And in one year there are 365 days, then in one year you consume:
365*24 L = 8,760 L
Now, if you upgrade the toilet, now per day you use:
one time 6 L and 3 times 3 L
Then in day, you use:
1*6 L + 3*3 L = 6L + 9L = 15L
And in the complete year, you will use 365 times that, which is:
365*15 L = 5,475 L
The amount of water that you would save is equal to the difference between the amount that you use in one year with no upgrade (8,760 L) and the amount that you would use in a year if you upgraded your toilet ( 5,475 L)
The difference is:
D = 8,760 L - 5,475 L = 3,285 L
This means that, in this situation, you would save 3,285 liters of water per year if you upgrade your toilet.
Write the ratio 21 wins to 9 losses as a faction in simplest form.
Answer: 7/3
Step-by-step explanation:
Divide both by 3
21/ 3 = 7
9 / 3 = 3
You get 7/3. Hope that helps!
help meh pls! I will give brainleist if correct omgawd pls!
Answer:
5= (1/4)c
Step-by-step explanation:
What is the solution set for this inequality 55 > 7cm + 6
Answer:
Answer:
First, we will substitute x for cm, and then graph the equation to find the solution
Step-by-step explanation:
Therefore, the answer is (7,0)
Two similar polygons are shown below:
Which transformation was performed on PQRS to form P′Q′R′S′?
a. A dilation factor of 2
b. A dilation factor of 4
c. A dilation factor of 1 over 2
d. A dilation factor of 1 over 4
Answer:
a. A dilation factor of 2
Step-by-step explanation:
S'R'/SR = 2/1 = 2
Find the range.
3 -9 7 -1 5 -4 2
Answer: The range is 94.
Hope this helps
Rewrite the function by completing the square. f(x)=x^2−2x+17
Answer:
[tex]f(x) = {x}^{2} - 2x + 17 \\ completing \: squares \\ divide \: the \: sum \: by \: 2 \: and \: the \: result \: to \: the \: {x}^{2} and \: subtract \: it \: from \: the \: product \\ in \: this \: case. \: our \: sum \: is \: 2 \\ f(x) = ({x}^{2} \times \frac{2}{2} ) + (17 - \frac{2}{2} ) \\ f(x) = {(x + 1)}^{2} + (17 - 1) \\ f(x) = {(x + 1)}^{2} + 16[/tex]
First try was incorrect
Ethan sells balloons at the fair. He sells 1810 balloons in 10 hours on
Tuesday and 1086 balloons in 6 hours on Saturday.
What is the constant of proportionality that relates the total number of
balloons sold, y, to the number of hours selling balloons, x?
label optional
x f(x) VX X
X
✓
(x) < > T
Answer: 6.55
Step-by-step explanation:
Hudson wants to ride his bicycle 51 miles this week. He has already ridden 12 miles. If he rides for 6 more days, what is the average number of miles he would have to ride each day to meet his goal?
Evaluate the expression 2 + 23 × 5 - 3.
20
39
37
47
The expression after evaluating results in the number 114.
What is BODMAS Rule?BODMAS rule is the rule used when solving expressions involving more than one operations.
It is the abbreviation of Brackets, Order, Division, Multiplication, Addition, Subtraction, which is the order of the operations to be done.
The expression given is,
2 + 23 × 5 - 3
We have to evaluate the expression in the order of BODMAS.
There are no brackets and orders and division.
Start with the multiplication.
2 + 23 × 5 - 3 = 2 + 115 - 3
Next do the addition.
2 + 115 - 3 = 117 - 3
= 114
Hence the value of the expression given is 114.
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If the ratio of green to yellow marbles is 2:3, what percent of the marbles are yellow?
Answer:
60 yellow marbles
Mandi has $52 and would like to buy some magazines. Each magazine costs $8. How many magazines can Mandi buy? How much more money would she need to buy another magazine?
3 1/2 x 1 1/3
Please explain how to get the answer
Answer: 77/3 or 25.67
Step-by-step explanation:
3 1/2 * 11/3
3 * 2+1=7
7/3 * 11/3
7 * 11= 77
3 stays the same
77/3 or 25.67
Answer:
4 2/3
Step-by-step explanation:
You need to turn the fractions into improper fractions
To do that you multiply the whole number by the denominator and add the numerator, doing that will give you your new numerator, but the denominator stays the same
3 1/2. 3×2 = 6. 6+1=7 3 1/2 = 7/2
1 1/3. 1×3 = 3. 3+1 = 4. 1 1/3 = 4/3
Then multiply both numerator by each other and do the same for the denominators
7×4 = 28
2×3 = 6
28/6
Then simply it
28/6 = 4 2/3
Rise over run (-5,2) and (1,-2)
(4,10) and (-2,-5) slope
Answer/Step-by-step explanation:
6. Given, (-5, 2) and (1, -2):
[tex] \frac{rise}{run} = \frac{y_2 - y_1}{x_2 - x_2} [/tex]
[tex] = \frac{-2 - 2}{1 - (-5)} [/tex]
[tex] = \frac{-4}{6} [/tex]
[tex] = \frac{-2}{3} [/tex]
9. Given, (4, 10) and (-2, -5):
[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_2} [/tex]
[tex] = \frac{-5 - 10}{-2 - 4} [/tex]
[tex] = \frac{-15}{-6} [/tex]
[tex] slope = \frac{5}{2} [/tex]
24 + 7 and 9 * ( 24 + 7 )
Answer:
1. 31
2. 279
Step-by-step explanation:
1. simple addition
2. simple multiplication
I need help on this with solutions please
Answer:
See answers below:
1. AAS2. ASA3. SAS4. HL5. SSS6. ΔABC ≅ ΔDFE7. ΔTRS ≅ ΔTUV8. ΔTRS ≅ ΔSUT9. ΔCAB ≅ ΔFDEWrite 25 x 10in standard form.
Answer:
Step-by-step explanation:
25 x 10=250
standard form is 2.5 x 10²
Find the vertex of the parabola. y = negative 4 x squared + 24 x minus 35 a. ( -3, 1) c. ( 3, 1) b. ( -3, -1) d. ( -1, -3)
Answer:
(3, 1)
Step-by-step explanation:
y = -4x² + 24x - 35
Find the vertex by using the formula:
(h, k) → [tex]\displaystyle \Big [ -\frac{b}{2a}, \ f \Big (-\frac{b}{2a} \Big ) \Big ][/tex]In this problem, we have:
a = -4 b = 24 c = -35Using 24 for b and -4 for a, we can substitute these values into the vertex formula:
[tex]\displaystyle -\frac{b}{2a} \rightarrow -\frac{24}{2(-4)} = \frac{-24}{-8} = 3[/tex]The h-value for the vertex is 3.
Now let's plug 3 back into the standard form equation to solve for the k-value of the vertex.
[tex]-4x^2 + 24x - 35 \rightarrow -4(3)^2+24(3)-35 = -36 + 72 - 35 = 1[/tex]The k-value for the vertex is 1.
The vertex of the parabola is (3, 1).
9 square root 3 divided by 3 square root 3
Answer:
[tex] \frac{9 \sqrt{3} }{3 \sqrt{3} } = \frac{9}{3} = 3 \\ [/tex]
3 is the right answer.
Need help with this one.
Answer:
1. 120
2. 2600
Step-by-step explanation:
6% of 2000 = 120
2000+120(5)
2000+600
=2600
Estimate the product of 2 & 4/11 and 16 & 1/5.
A. about 2 × 16 = 32
B. about 2 × 14 = 28
C. about 3 × 16 = 48
D. about 3 × 14 = 42
Answer:
a
Step-by-step explanation:
Determine what is closer to 2 4/11.
you would- 4/11 to get 2
you would +6/11 to get 3.
So 2 is closer
Do the same with 16 1/5
16 is closer
therefore, it is 2*16=32
(4x5)to the power of 2-6+3=
Answer:
if i understood right..
Step-by-step explanation:
... 2-6+3= 1
4×5= 20
1×20=20
the answer is 20.
I'm sorry if i understood the wrong thing.
Graph the function.
f(x)=−1/5x+4
Use the Line tool and select two points to graph.
Answer:
The coordinates are: (1,3.8), (2,3.6)
Now, plotting these points on graph as shown in figure.
Step-by-step explanation:
We need to graph the function: [tex]f(x)=-\frac{1}{5}x+4[/tex]
For drawing the graph, we need x and y coordinateness.
The can be found as following:
If we put x =1 in the given function, we will get:
[tex]f(x)=-\frac{1}{5}x+4\\Put\:x=1\\f(x)=-\frac{1}{5}(1)+4\\f(x)=-\frac{1}{5}+4\\f(x)=\frac{-1+4*5}{5}\\f(x)=\frac{-1+20}{5}\\f(x)=\frac{19}{5}\\f(x)=3.8[/tex]
So, we get when x =1 f(x) or y = 3.8
Now for finding second point, we put x =2 in the given function
[tex]f(x)=-\frac{1}{5}x+4\\Put\:x=2\\f(x)=-\frac{1}{5}(2)+4\\f(x)=-\frac{2}{5}+4\\f(x)=\frac{-2+4*5}{5}\\f(x)=\frac{-2+20}{5}\\f(x)=\frac{18}{5}\\f(x)=3.6[/tex]
So, we get when x =2 f(x) or y = 3.6
The coordinates are: (1,3.8), (2,3.6)
Now, plotting these points on graph as shown in figure.
You find 1 on x-axis and 3.8 on y-axis for first point (1,3.8)
Similarly You find 2 on x-axis and 3.6 on y-axis for second point (2,3.6)
Look at at pic attached! Pls hurry :( 21 points
Answer:
C option
Step-by-step explanation:
bcz root of 121 is 11. then 2/3 +11 will give you a rational number.
Answer:
2/7 + square root of 121 (the third one)
Step-by-step explanation:
a rational number is a number where if you write it as a fraction, both the numerator and denominator are integers (numbers like 1 and 2 but not like 3.4 or 5.6)
the equation simplified a bit looks like this:
2/7 + 11/1
anddd so all the numbers are integers which means that expression is correct :3
Help please asap thx
Answer:
2 and a half, but it wants it as a mixed fraction which would be 5/2
Step-by-step explanation:
i hope this helped :)
Answer:
5/2.................
Please help me with these questions FAST it's formal and I can't faillllllll!!!!!!,
The school store sells pens for $0.70 each and pencils for $0.30 each. Anthony spent $2.70 to buy a total of 5 pens and pencils.How many pencils
did Anthony buy? ___ pencils
Answer:
Pencils=2
Step-by-step explanation:
Pencils-n
-0.70 - 0.70 = -3.5
0.70p + 0.30 = 2.7
-0.4n = -0.8
-0.4 -0.4
n=2