Which products result in a difference of squares? select three options. (x minus y)(y minus x) (6 minus y)(6 minus y) (3 x z)(negative 3 x z) (y squared minus x y)(y squared x y) (64 y squared x squared)(negative x squared 64 y squared)
Answers
The three (3) products that resulted in a difference of squares are:
(3 + xz)(-3 + xz) (y² - xy)(y² + xy)(64y² + x²)(-x² + 64y²)How to determine the difference of squares?In Mathematics, the standard form for a difference of two (2) squares is given by a² - b² = (a + b)(a - b).
(3 + xz)(-3 + xz) = (3 + xz)(xz -3)
(3 + xz)(xz -3) = 3xz - 9 + x²z² - 3xz.
(3 + xz)(xz -3) = x²z² - 9
Therefore, x²z² - 9 ≡ a² - b²
(y² - xy)(y² + xy) = y⁴ + xy³ - xy³ - x²y²
(y² - xy)(y² + xy) = y⁴ - x²y²
Therefore, y⁴ - x²y² ≡ a² - b².
(64y² + x²)(-x² + 64y²) = (64y² + x²)(64y² - x²)
(64y² + x²)(-x² + 64y²) = 4096y⁴- 64y²x² + 64y²x² - x⁴
(64y² + x²)(-x² + 64y²) = 4096y⁴ - x⁴
Therefore, 4096y⁴ - x⁴ ≡ a² - b².
Read more on difference of squares here: https://brainly.com/question/24673551
Answer:
Step-by-step explanation:
Related Questions
One year, sales increased by 15%. The following year sales increased by 18%. Calculate the overall percentage increase in sales.
Answers
Answer:
35.7%
Step-by-step explanation:
Sales increase in Year 1
Let the original sales be xSales has increased by 15%Therefore, new sales will be :Original sales + Original sales x 15%⇒ x (1 + 15%)⇒ x (1 + 0.15)⇒ x (1.15)⇒ 1.15xSales increase in Year 2
From Year 1, it has increased by 18%New sales will be :Year 1 sales + Year 1 sales x 18%⇒ 1.15x (1 + 18%)⇒ 1.15x (1 + 0.18)⇒ 1.15x (1.18)⇒ 1.357xOverall Increase
Year 2 sales - Original sales / Original sales1.357x - x / x0.357x / x0.357Decimal to % ⇒ x 100%0.357 x 100%35.7%Let the sales be known as "a".
Given statement:
One year, sales increased by 15%.
This can be written as:Year 1 = a + (a × 15%)Step-1: Evaluate the percentage⇒ Year 1 = a + (a × 15%)⇒ Year 1 = a + (a × 15/100)Step-2: Multiply the terms inside the parentheses⇒ Year 1 = a + (a × 15/100)⇒ Year 1 = a + (15a/100)Step-3: Open the parentheses⇒ Year 1 = a + (15a/100)⇒ Year 1 = 100a/100 + 15a/100Step-4: Add the like terms;⇒ Year 1 = 100a/100 + 15a/100⇒ Year 1 = 115a/100Next year (Year 2):Given statement:
The following year sales increased by 18%.
This can be written as:Year 2 = Year 1 + (Year 1 × 18%) Step-1: Substitute the amount of sales in year 1:⇒ Year 2 = Year 1 + (Year 1 × 18%) ⇒ Year 2 = 115a/100 + (115a/100 × 18/100)Step-2: Simplify the fractions in the parentheses:⇒ Year 2 = 115a/100 + (115a/100 × 18/100)⇒ Year 2 = 115a/100 + (23a/20 × 9/50)Step-3: Multiply the fractions in the parentheses:⇒ Year 2 = 115a/100 + (23a/20 × 9/50)⇒ Year 2 = 1150a/1000 + (207a/1000)Step-4: Open the parenthesis:⇒ Year 2 = 1150a/1000 + (207a/1000)⇒ Year 2 = 1150a/1000 + 207a/1000Step-5: Add the fractions:⇒ Year 2 = 1150a/1000 + 207a/1000⇒ Year 2 = 1357a/1000Overall percentage increase:Formula:
Overal percentage increase = (Sales in year 2 - Original sales) × 100
Step-1: Substitute the values in the equation:⇒ Overal percentage increase = (Sales in year 2 - Original sales) × 100⇒ Overal percentage increase = (1357a/1000 - a) × 100Step-2: Simplify the expression in the parentheses:⇒ Overal increase = (1357a/1000 - a) × 100⇒ Overal increase = (1357a/1000 - 1000a/1000) × 100⇒ Overal increase = (357a/1000) × 100Step-3: Open the parentheses and simplify:⇒ Overal increase = (357a/1000) × 100⇒ Overal increase = 357a/10 ⇒ Overal increase = 35.7aStep-4: Determine the overal increase in percentage:⇒ Overal increase = 35.7a⇒ Overal percentage increase = 35.7%Therefore, the overal increase in percent is 35.7%.
Two angles are complementary.The larger angle is 30 degrees more than 4 times the smaller
angle find the measure of each angle
Define variables
Answers
Answer:
Step-by-step explanation:
Remark
2 angles are complementary means that 2 angles add up to 90°. That is the guiding princeple behind the problem.
Givens
Let the smallest angle = x
Let the largest angle = 4x + 30
Equation
4x + 30° + x = 90° Combine like terms on the left
Solution
5x + 30 = 90 Subtract 30 from both sides.
5x + 30 - 30 = 90 - 30 Combine
5x = 60 Divide both sides by 5
5x/5 = 60/5
x = 12
Answer
smallest angle = 12Larger angle = 4*12 + 30 = 78Please help me. I am struggling. Question is in image.
Answers
Answer:
a = -15 when you add -28 f by 13 f
b -51 f lower if you subtract st Louis by chicago
Ten friends played slot machines in Las Vegas. Their average loss was $60 and the standard deviation of the loss was $10. What does the standard deviation of $10 mean
Answers
Using it's concept, it is found the standard deviation of $10 means that most students spent within $10 of the mean of $60 on the slot machines.
What is the standard deviation of a data-set?The standard deviation is given by the square root of the sum of the differences squared of each observation and the mean, divided by the one less than the number of values.It represents by around how much the distribution varies around the mean.Hence, in this problem, the standard deviation of $10 means that most students spent within $10 of the mean of $60 on the slot machines.
More can be learned about standard deviation at https://brainly.com/question/24754716
Match the numbers in column one with the square roots in column two
Answers
Answer:
1..c
2..h
3..g
4..e
5..b
6..d
7..a
Pam signed up for a new gym. She had to pay a $45 sign-up fee and will pay dues of $30 each month for 6 months. Which expression tells you the total cost of Pam's 6-month gym membership? 45+(30times6) or (45+30)times6
Answers
Answer:
45 + (30*6)
Step-by-step explanation:
Aida bought a costume box containing 50 costumes for $300. She sold all of the costumes and made a $250 profit. She sold all of the costumes for the same price. Use the equation 50c-300=250, where c is the selling price of each costume. What was the selling price of one costume in dallars?
Answers
Answer:$11
Step-by-step explanation: 50c - 300= 250
Add 300 to both sides
Divide both sides by 50
Ignore the chosen answer mark thing I clicked on it by accident
Answers
Answer:
It's the one you clicked!
Step-by-step explanation:
It is 22.5 or 22 [tex]\frac{1}{2}[/tex]
because
5/2 simplified is 2.5
2.5 x 9 = 22.5
hope this helps :)
what is p to the power of 2
Answers
Answer:
It really depends if there is more work with this, but of it is just p to the power of two. it would be p².
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Click twice to plot each segment.
Click a segment to delete it.
Answers
Answer: You d u m b. -3/4
Step-by-step explanation:
pls help this is past due and I have no idea on how to do it
Answers
Answer:
42.3
Step-by-step explanation:
Substitute in values[tex]3.6\times (3)+4.5\times (7) = 10.8+31.5=42.3[/tex]Using side lengths only, could the triangles be similar?
Answers
Answer:
Option A
Step-by-step explanation:
Step 1: Compare the sides
We can see that it was rotated in a way where Y is similar to R, X is similar to Q, and Z is similar to S.
[tex]\frac{SQ}{XZ }\neq \frac{QR}{XY} \neq \frac{RS}{YZ}[/tex]
[tex]\frac{0.5}{1}\neq \frac{1}{1.5}\neq \frac{1.5}{2}[/tex]
[tex]0.5\neq 0.6667\neq 0.75[/tex]
Answer: Option A
A rectangle measures 4 3/4 inches by 1/3 inches . What is the area ?
Answers
Answer:
A = [tex]\frac{1}{4}[/tex] in²
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = lb ( l is the length and b the breadth ) , then
A = [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{3}[/tex] ( cancel 3 on numerator/ denominator )
= [tex]\frac{1}{4}[/tex] × 1 = [tex]\frac{1}{4}[/tex] in²
. The ratio of the measures of the sides of a
triangle is 4:7:5. If the perimeter of the
triangle is 128 yards, find the length of the
longest side.
Answers
Step-by-step explanation:
4+7+5=16
128:16=8
8*7=56 yards
What is the area, in square feet, of the shape below?
Answers
Answer:
17.4 ft²
Step-by-step explanation:
The formula to find the area of a triangle:
1/2 x b x h, where b is the base and h is the height.
1) Substitute the given values into the formula and solve it.
= 1/2 x 6 x 5.8
= 1/2 x 34.8
= 17.4
Answer:
Area= 17.4 ft²
Step-by-step explanation:
The formula of the area of any triangle is given by: A = [tex]\frac{b*h}{2}[/tex]
where A: area of the triangle
b: base of the triangle
h: height of the triangle
in this figure we have:
b= 6ft
h= 5.8ft
A= [tex]\frac{6 * 5.8}{2}[/tex] = [tex]\frac{34.8}{2}[/tex]=17.4 ft²
HOPE THIS HELPS :)
complete the function table and write the function rule
Answers
Answer:
6 and -22
Step-by-step explanation:
See attached image.
The function rule for the linear function is y = y = x - 12
The missing values are: x = 6; and y = -22.
What is a Linear Function Rule?Where, m is the average rate of change, and b is the initial value when x is 0, therefore, a linear function rule is given as, y = mx + b.
Find m and b using the table of values given.
Using (32, 20) and (14, 2):
Average rate of change (m) = change in y / change in x = (20 - 2)/(32 - 14)
Average rate of change (m) = 18/18 = 1.
Find b by substituting m = 1 and (x, y) = (14, 2) into y = mx + b
2 = 1(14) + b
2 = 14 + b
2 - 14 + b
-12 = b
b = -12
Write the rule of the linear function by substituting m = 1 and b = -12 into y = mx + b
y = 1(x) + (-12)
y = x - 12
Find the missing values on the table
Fourth Row: when y = -6
-6 = x - 12
-6 + 12 = x
x = 6
Last Row: when x = -10
y = -10 - 12
y = -22
Therefore, the function rule for the linear function is y = y = x - 12
The missing values are: x = 6; and y = -22.
Learn more about linear function rule on:
https://brainly.com/question/4025726
Find the equation of the line shown (first to do gets brainlist)
Answers
Answer:
y = -2x + 9
Step-by-step explanation:
You go shopping and buy shoes for $112 if the tax is 7%
Answers
I dont know how to delete a answer and i got it wrong apparently so sorry
The tax you would pay:
112*(7/100)=7.84$
Your total:
112-7.84=104.16$
Please help! Will mark brainlyest.
Answers
PLSS HELP
I NEED THIS ASAP
Find angle relationship and solve for X!!
(WILL GIVE BRAINLIEST)
Answers
Answer:
Same side exterior anglesx = 15Step-by-step explanation:
The indicated angles are same side exterior angles since located on the same side of the transversal and exterior to parallel lines.
Same side exterior angles are supplementary, so their sum is 180.
Solve the following equation for x
7x + 3 + 4x + 12 = 18011x + 15 = 18011x = 165x = 165/11x = 15Angles are supplementary as they are same side exterior angles
7x+3+4x+12=18011x+15=18011x=165x=15Which one is the correct answer, a b c d
Answers
[tex]g(f(x))=\sqrt{\frac{2301+100x^2}{23+x^2} }[/tex]
Step-by-step explanation:[tex]Substitute\ and\ calculate:\\ \downarrow\\ g(f(x))=\sqrt{\frac{2301+100x^2}{23+x^2} }[/tex]
I hope this helps you
:)
The congruence theorem that can be used to
prove ΔΜΝΡ ΔΑΒC is
O SSS.
O ASA.
O SAS.
O AAS.
Answers
Answer:
SAS
Step-by-step explanation:
AB congruent to MN
Angle B congruent to Angle N
BC congruent to NP
Check both triangles
<N=<BPN=BCNB=ABSo
Two sides are equal and their corresponding angles are equal
SAS should be usedSimplify the algebraic expression below. m + m + m + m + m + m − m + m - m = __?
Answers
Answer:
Simplify the following:
m + m + m + m + m + m - m + m - m
m + m + m + m + m + m - m + m - m = 5 m:
Answer: 5 m
Step-by-step explanation:
Answer:
m=5
Step-by-step explanation:
what is 7x7+89 i want to know what the b is to
Answers
Answer:
138
Step-by-step explanation:
According to PEMDAS (explains which operation you do first)
(Parentheses
Exponents
Multiplication or Division
Addition or Subtraction),
1. multiplication comes before addition
2. Even if it was 89+7x7, it would still be 7x7 first.
3. 7x7=49. Add it to 89 and you get 138
In PEMDAS multiplication comes first
49+89
Add (7x7) and 89
The answer is 138
What is the solutior to the equation 5j = 2/3
Answers
Answer:
j = 0.13333333333
j = 4/30
just divide both sides by 5 my friend
Answer these questions it’s for my math! Please do all the days!
Day 1
how many times do you flush the toilet?
how many mins do you shower?
How many mins do you use the kitchen faucet?
How many mins do you use for the bathroom faucet?
How many times do you use the dishwasher?
How many times do you use the laundry machine?
Day 2
how many times do you flush the toilet?
how many mins do you shower?
How many mins do you use the kitchen faucet?
How many mins do you use for the bathroom faucet?
How many times do you use the dishwasher?
How many times do you use the laundry machine?
Day 3
how many times do you flush the toilet?
how many mins do you shower?
How many mins do you use the kitchen faucet?
How many mins do you use for the bathroom faucet?
How many times do you use the dishwasher?
How many times do you use the laundry machine?
Answers
Answer:
Day 1
4 times
8 mins
1 time
0 times
1 time
0 times ( I never use it)
Day 2
2 times
5.30 mins
0 times
2 times
0 times
0 times
Day 3
5 times
0 mins
0 times
2 times
1 time
0 times
Step-by-step explanation:
Hope it helped you
The sections of a spinner are divided into five
equal sections and are lettered A to E. Myla spins
the pointer of the spinner once and rolls a number
cube numbered 1 to 6. What is the probability of
landing on B and rolling an even number?
Answers
Answer: 0.066, or a 6.6% Statistical Probability.
Step-by-step explanation:
When dealing with Statistical Probability, you are attempting to find the theoretical chance of an action occuring.
With the two actions described, one being a wheel with five set outcomes, and a dice with six set outcomes, you can find the probability of random numbers/outcomes by taking
[tex]\frac{1}{6} \\and\\\frac{1}{5}[/tex]
1/6 being number cube, 1-2-3-4-5-6
and
1/5 being spinner. A-B-C-D-E
In the Event, (made up by actions), it is described that The Cube AND Spinner are rolled and spun at random.
Also, The description asks: what is the probability of landing on B and rolling an even number?
So, the 1/6 chance of the dice becomes 1/3, or .33 or 33%.
And, the 1/5 chance for the spinner stays the same, because it is a single unit. So, probability of landing on B is still 1/5, or .2 or 20%.
When two actions are present in an Event, you are to procedurally multiply the outcomes by the decimal percentage, fraction, or actual percentage, to find the chance of occurence.
In this scenario, I used .2 x .33 and got 0.066
Which, equals 6.6%
I found this by multiplying the decimal percentage by 100, to scale the chance on a 100/100 based scale. In this case, the multiplier on the numerator is .066 ... creating 6.6/100, or .066 or 6.6%
Hope this Helped!
What is the equation of the line that passes through the point (1, 3) and is perpendicular to the line 2x + 3y = 15?
Answers
Answer:
first, we need to know the gradient of the line, 2x+3y=15
Gradient of the line is -2/3
from 3y=-2x+15
Y=-2x/3+5
Step-by-step explanation:
new gradient will be 3/2 since the initial gradient is perpendicular to the new one
therefore, considering the general equation of the line, y-y1=m(x-x1)
where y1=3 and x1=1
we can therefore substitute in the values into the above equation
so, y-3=3/2(x-1)
y-3=3x/2-3/2
2y-6=3x-3
2y-3x=-3+6
2y-3x=3
therefore, the equation of the line perpendicular to line 2x+3y=15 is 3x-2y=-3
In which year did Carlos and Andrew have the largest difference in their salaries?
2003
2004
2005
2006
Answers
Answer:
the answer to this is D. 2006
Can anyone solve this today?
Answers
Answer:
C
Step-by-step explanation:
The area of a square is the square of the side length. When the side length x=2.5 cm, the area is the square of that value.
__
A(x) = x²
A(2.5 cm) = (2.5 cm)² = 6.25 cm²
_____
Additional comment
The "square" of a variable is that variable to the second power. The terms 2x or 4x are linear terms with the variable to the first power, do not represent the area of a square.
The equation A(x) = 4x² introduces a multiplier of 4 that is not applicable to the area of a square based on side length. (The formula might be useful if x represents the distance from one side to the center of the square, the radius of an inscribed circle, for example.)