The binomial expansion of the given expression is:
x³ - y³ - 3x²y + 3y²x
What is a polynomial?
A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.
Depending on the number of terms it can be :
monomialbinomialtrinomialWe solve first by perfect square trinomial, then we apply the distributive property.
(x- y)³ = (x - y)²(x - y)
(x - y)² = x² - 2xy + y²
(x - y)( x² - 2xy + y²)
x³ - 2x²y + y²x - x²y + 2y²x - y³
x³ - y³ - 3x²y + 3y²x
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with the steps as well please
Answer:
Step-by-step explanation:
(i)
[tex]2.014^2-2.012^2=\\(2.014+2.012)(2.014-2.012)=\\4.026*0.002=\\0.008052=\\8.052*10^{-3}[/tex]
(ii)
[tex]12^3+8^3=\\(12+8)(12^2-(12)(8)+8^2)=\\20*(144-96+64)=\\20*112=\\2240[/tex]
(iii)
[tex]9^3-5^3=\\(9-5)(9^2+(9)(5)+5^2)=\\4*(81+45+25)=\\4*151=\\604[/tex]
Determine whether the given measures define 0,1,2 , or infinitely many triangles. Justify your answers.
a=5, b=9, c=6
When only three sides are provided without any information regarding the angle, such as a = 5 m and b = 9 m, c = 6m we can either create no triangle or create an unique triangle. Hence, either 0 or 1 Triangle.
For example :
How many different triangles may be formed with side lengths of 5m,9m and 6 m ?
Create a triangle with the following measurements: 5 meters, 9 meters , and 6meters, by protractor-adjusted to the given length of sides. You have constructed a triangle.
We can only create one triangle here, as no choice can be made in the given length of side as they are prefixed.
This implies that you cannot chose the side length independently. So, only one triangle which is unique will be formed. Hence, 0 or 1 triangle is formed
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The vasquez family visits their grandmother every 3 weeks and hosts a neighborhood party every 8 weeks. every 16th week, the vasquez family takes a day to go hiking. a. after how many weeks will the vasquez family both visit their grandmother and host the neighbor hood party? b. after how many weeks will all three events occur?
Using least common multiple (LCM), the Vasquez family both visit their grandmother and host the neighbor hood party after 24 weeks. After 48 weeks, all three events will occur at the same time.
A common multiple is defined as a whole number, that is a shared multiple of each set of numbers. The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers.
If the Vasquez family visit their grandmother every 3 weeks and host a neighbor hood party every 8 weeks, to know when will these event will occur at the same time, solve for the LCM of 3 and 8.
3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . .
8 : 8, 16, 24, 32, 40, . . .
LCM = 24
Hence, after 24 weeks, both will occur at the same time.
To know when will the three events will occur at the same time, solve for their LCM.
3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, . . .
8 : 8, 16, 24, 32, 40, 48, . . .
16 : 16, 32, 48, . . .
LCM = 48
Hence, after 48 weeks, all three events will occur at the same time.
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(12+6) divided by 3 squared simplified :p
Answer:
The answer is 36
Step-by-step explanation:
12+6=18
18/3=6
6 squared is 36
36 simplified is still 36
Find the distance between each pair of parallel lines with the given equations.
y=-2 x+1 y=-2 x+16
The distance between each pair of parallel lines with the given equations y = -2x+1 and y = -2x+16 is 15 units.
We can find the points passing through the lines.
Hence,
The points passing through the line y = x - 11 are:-
Let x = 0
y = -2(0) +1
(0,1)
and;
Let x = 1/2
y = -2(1/2) + 1 = -1 +1
(-1/2,0)
The points passing through the line y = -2x + 16 are:-
Let x = 0
y = -2(0) + 16 =16
(0,16)
and;
Let x = 8
y = -2(8) + 16 = -16 + 16
(8,0)
Hence, using distance formula, the distance between the parallel lines will be:-
[tex]\sqrt{(16-1)^2+(0-0)^2} = \sqrt{15^2+0}=\sqrt{225} = 15[/tex] units.
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Help wanted! Im I’m desperate need of assistance!
Answer:
-2/5
Step-by-step explanation:
Hi there!
We find slope by using rise over run.
For this problem, identify two points on the line. I'll use (0, 3) and (5, 1).
[tex] m = \frac{{y} - {y} }{ {x} - {x}}[/tex]
You can plug the coordinates into this formula, making sure they stay in the right order. Subtract the first y coordinate from the second y coordinate, and the first x coordinate from the second x coordinate. (Just make sure one point is on the left, and the other on the right).
[tex] \frac{3 - 1}{0 - 5} = \frac{2}{ - 5} [/tex]
2/-5 is the same as -2/5, so that is your answer
If h(x)=|1-7x|, find each value… 23-h(9)
Answer:
-41
Step-by-step explanation:
h(x) = | 1-7x
First, calculate the value for the function for x = -9
h(-9) = |1--7x|
h(-9) = |1+63|
h(-9) = |64|
h(-9) = 64
23-h(-9) = 23-64 = -41
Hope this helps ;0
What types of things have you measured before?
Answer:
1. Room size (length * width) for carpet
2. From window top to floor for curtains
Step-by-step explanation:
Multiply the numbers.
The result of multiplying the numbers 234 x 0.35 is 81.9
How to multiply the numbers?The numbers are given as:
234 and 0.35
Express the numbers in a product expression
So, we have
234 x 0.35
Express 234 as 200 + 34
So, we have
234 x 0.35 = (200 + 34) x 0.35
Expand the bracket
So, we have
234 x 0.35 = 200 x 0.35 + 34 x 0.35
Evaluate the product
So, we have
234 x 0.35 = 70 + 11.9
Evaluate the sum
So, we have
234 x 0.35 = 81.9
Hence, the result of multiplying the numbers 234 x 0.35 is 81.9
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what is multiples of 30 and 45?
Eddie used 9.6 cups of flour to bake 3 cakes. How much flour, on average, did he put in each cake?
Answer: i believe its 3.2 cups per cake
Step-by-step explanation:
9.6 / 3 = 3.2
Solve $2+\frac{1}{6}y=3x+4$
Answer:
[tex]y=18x+ 12[/tex]
Step-by-step explanation:
Given equation:
[tex]2+\dfrac{1}{6}y=3x+4[/tex]
Solve for ySubtract 2 from both sides:
[tex]\implies 2+\dfrac{1}{6}y-2=3x+4-2[/tex]
[tex]\implies \dfrac{1}{6}y=3x+2[/tex]
Multiply both sides by 6:
[tex]\implies 6 \cdot \dfrac{1}{6}y= 6 \cdot3x+ 6 \cdot2[/tex]
[tex]\implies y=18x+ 12[/tex]
How much money will you have if you invest $2200 at 2%/a compounding annually for 30 years?
Answer:
$3,985.00
Step-by-step explanation:
The formula for the amount accrued, A if you invest an amount P at r% compounded annually for n years is given by the formula
[tex]A = P\left(1 + \dfrac{r}{100}\right)^n[/tex][tex]A = P\left(1 + \dfrac{2}{100}\right)^{30} \\\\= P\left(1 + 0.02\right)^{30} \\\\= P\left(1 .02\right)^{30} \\\\= \; \$3,985.00[/tex]
The division by 100 is necessary to allow r% to be reduced to a decimal
So using this formula directly by substituting values gives
Solve for y in terms of x
5x+y=31
Solving for y in terms of x gives y = 31 - 5x
What is the subject of formula?The subject of a formula is defined as the variable that is expressed in terms of the other variables in an equation or given expression.
It is also described as the variable that is being worked out in a given equation.
Given the equation;
5x +y = 31
Let's make 'y' the subject
We have to make 'y' stand alone by taking the other variables or terms over the equality sign, we have
y = 31 - 5x
Thus, solving for y in terms of x gives y = 31 - 5x
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Suppose a total of 15 ounces of medicine is added to the original mixture (so that the total volume is now 25 ounces with 18 ounces of medicine and 7 ounces of water). How much water must now be added so that the mixture has the same proportion of medicine and water as the original mixture?
We have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.
Given,
The quantity of medicine added to the original mixture = 15 ounces
New quantity of medicine in the mixture = 18 ounces
Quantity of water in the mixture = 7 ounces
Total new quantity of mixture = 18 + 7 = 25 ounces
Original quantity of medicine in the mixture = 18 - 15 = 3 ounces
Original quantity of water in the mixture = 7 ounces
Total original quantity of mixture = 3 + 7 = 10 ounces
We have to find the amount of water to add into the new mixture to make the proportion of medicine and water same as the original mixture.
Here,
Proportion of medicine and water in original mixture = 3:7
Quantity of medicine and water in new mixture = 18:7
Now,
18 ÷ 3 = 6
Then, 7 × 6 = 42
So, 42 - 7 = 35
Therefore, we have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.
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what is the area of the triangle below
The area of triangle is 12 square units.
What is the triangle?
Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Given:
The given points are
A=(1,2)
B=(1,8)
C=(5,2)
According to given question we have
By the use of distance formula , we get
[tex]AC=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AC=\sqrt{(5-1)^{2} +(2-2)^{2} }\\\\AC=\sqrt{(4)^{2} +(0)^{2} }\\\\AC=4 units\\\\\\AB=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AB=\sqrt{(1-1)^{2} +(8-2)^{2} }\\\\AB=\sqrt{(0)^{2} +(6)^{2} }\\\\AB= 6 units[/tex]
Area of right triangle(A) is given by:
[tex]Area =\frac{1}{2} base *height[/tex]
where,
base of the triangle =4 units
height of the triangle =6 units.
[tex]Area =\frac{1}{2} base *height\\\\Area =\frac{1}{2}* 4 *6\\\\Area =12 square units[/tex]
Therefore, the area of triangle is 12 square units.
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2(3+6)+6-2=?
Solve the problem step by step
Answer:
13
Step-by-step explanation:
first use PEMDAS= P= Parentheses E= Exponents M= Multiplication D= Division A= Addiction S= Subtraction.
(3+6)+6-2=
9+6-2=
15-2=
13
Add 3+6 which is 9
Add 3+6 which is 9then add 9+6 equal to 15
Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15
Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15boom that's how you do it
Answer:
22
Step-by-step explanation:
Use Pemdas
P means parenthesis so add the numbers in the parenthesis
3 + 6 = 9
2(9) + 6 - 2 =
Next is E, but there are no exponents so now there is M
multiply 2 times 9, you will get 18.
18 + 6 - 2 =
So next is A which is addition, add 18 + 6
18 + 6 = 24.
24 - 2
And lastly, S which is subtraction.
24 - 2 = 22
So the answer is 22
Complete the congruence statements for each pair of congruent figures below
Triangles are congruent if their matching interior angles and sides are all congruent.
What is congruence in math?
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.
Congruent figures: what are they?
Congruent figures have sides that are the same length and angles that are the same measurement. In other terms, two figures are said to be congruent when they are superimposed upon one another. Even when they are flipped or rotated, they perfectly fit on top of one another.What is congruent shapes?
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.Learn more about congruent
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y^2/3 - 5y^1/3 +6=0
Answer:
Solution on Screen
Step-by-step explanation:
It's okay don't worry
4,000 is blank times much as 4
Answer: 1000
Step-by-step explanation:
4000/4
Answer:
1000
Step-by-step explanation:
blank can be written as x. since this is a multiplication problem we need to the opposite of multiplying, which is dividing. rewrite the problem as 4000/4=x
solve by dividing 4000 by 4 to get 1000
Which equation below combines with the equation -4 x+6 y=3 to form a system with an infinite number of solutions?
A. 0.5+x=1.5 y
B. 0.75+2 x=1.5 y
C. 0.5+2 x=1.5 y
D. 0.75+x=1.5 y
To form a system with an infinite number of solutions, the equation -4x + 6y = 3 must be combined with D. 0.75 + x = 1.5 y.
A system of equations is a set of two or more equations which includes common variables.
To form a system with an infinite number of solutions, the lines should be the same or overlapping. These lines must have the same slope and y-intercept. The equations of these lines must be the multiple of one another.
Given the equation -4x + 6y = 3, rewrite this in the form c + ax = by(same as the form of the choices).
-4x + 6y = 3 ⇒ 3 + 4x = 6y
To make 6y into 1.5y, divide both sides by 4.
3 + 4x = 6y ⇒ 0.75 + x = 1.5 y
Hence, the equation -4x + 6y = 3 must be combined with 0.75 + x = 1.5 y to form a system with an infinite number of solutions.
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1 Use the number line to find the coordinate of the midpoint of JP. K L M + -7-6-5-4-3-2-1 0 1 2 3 4 5 6 N P
The coordinate of the midpoint of JP is -1
How to find the coordinate of the midpoint of JP?On the number line, we have the following coordinates
J = -7
P = 5
The coordinate of the midpoint of JP is calculated using
Midpoint = 1/2 * (J + P)
This gives
Midpoint = 1/2 * (-7 + 5)
Evaluate the sum
Midpoint = 1/2 * -2
Evaluate the product
Midpoint = -1
Hence, the coordinate of the midpoint of JP is -1
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14. In science class, students weighed different
amounts of clay. Miguel's weighed
4.361 ounces, Kim's weighed 2.704 ounces,
Simon's weighed 5.295 ounces, and
Victoria's weighed 8.537 ounces.
A. How many ounces of clay did Miguel
and Victoria have in all?
B. How many ounces of clay did Kim and
Simon have in all?
Answer:
A:12.898
B:7.999
Step-by-step explanation:
A: 4.361+8.537
B:2.704+5.295
Is -71 - 43 positive or negative?
Answer:
Negative
Step-by-step explanation:
What is the sum of the finite geometric series?
a. -15+30-60+120-240+480
What is the sum of the finite geometric series?
a. -15+30-60+120-240+480= 315
Given:
a=-15
r= -2
n=6
[tex]S_n=\frac{a(1-r^{n})}{1-r} \\\\S_6=\frac{-15(1-(-2)^{6})}{1+2}\\\\S_6=\frac{-15(1-64)}{3}\\\\S_6=\frac{-15(-63)}{3}\\\\S_6=5*63=315[/tex]
What is a finite geometric series?
A geometric series is a series with a geometrically connected progression.A geometric series is a list of numbers where each number, or term, is found by multiplying the preceding term by a common ratio r.Because there are only a finite number of terms, we refer to this geometric series as a finite geometric series (an infinite geometric series continues on forever.)To learn more about finite geometric series, refer:
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Suppose a local office store has a press that can print 54,000 brochures per hour. How many brochures can be printed during a 3 1 4 hour run?
Answer:
Step-by-step explanation:
Rate: 54000 brochures per hour
Formula: D=RT Distance=Rate x Time (In this case distance is the amount)
(I’m not sure if you meant to type 3 1/4 or 314. I’ll include both)
D=54,000(3 1/4)
Two ways
1. 54,000(3 1/4)=175,500
2. 54,000x3 is 162,000, and 1/4 of 54,000 is 54,000/4=13,500. 162,000+13,500=175,500.
(54,000 x 314 = 16,956,000)
Hope this helps!
Which statements prove that m || n?
Answer:
The first 2 and the 2nd to last equations
Step-by-step explanation:
Angles 8 and 10 are alternate interiors, which would only work if m and n are parallel.
Angles 1 and 9 are congruent angles, which would only work if m and n are parallel.
Angle 1 and 3 are on the same line, so that can't prove it.
m8 and m9 could only add up to 180 if m and n are parallel, which makes this also true.
Angles 7 and 10 add up to 180, but can't be congruent.
the sum of 12 and twice y
Answer:12+2y
Step-by-step explanation:
Answer:
12 + 2y
Hope this helps :)
Step-by-step explanation:
When it says "sum," this means the answer to 2 numbers you add. The first number would be 12, and the other number will be y 2 times. So y plus y equals 2y. The final equation is 12 + 2y.
Which of the following defines workplace politics?
O Choices made according to law
O Beliefs of a person or social group in which they have an emotional investment
O Games played in a workplace environment to achieve status, advancement and money
O Professional standards of conduct, based on moral principles and values, guilding decision-making and actions
Answer:
"Games played in a workplace environment to achieve status, advancement and money"
what is a non-repeating decimal, give examples of nom repeating decimals.
Answer:
Recurring Decimal
Recurring Decimal, also called as repeating decimal, is a decimal number only that consists of digits repeating after a fixed interval after the decimal. For example, 46.374374374..., 5173.838383... etc. Decimals can be classified into different categories depending upon what type of digits occur after the decimal point, whether the digits are repeating, non-repeating, end, or unending (infinite digits after the decimal point).
Examples are
0.6666666666,
1.456456456
Step-by-step explanation:
Set as brainliest
