Darlene wrote this proof of the identity (x + y)2 - (x - y)² = 4xy. Which of the
following is a justification for Step 5 of her proof?
Step 1: (x + y)2-(x - y)² = (x+y)(x + y) - (x-y)(x-y)
Step 2: (x+y)(x+y) - (x - y)(x - y) = (x² + xy + xy + y²) - (x² - xy - xy + y²)
Step 3: (x² + xy + xy + y²) - (x² - xy - xy + y²)(x² + 2xy + y²) - (x² - 2xy + y²)
Step 4: (x² + 2xy + ²) - (x²2²-2xy + ²) = x² + 2xy + y² - x² + 2xy-j²
Step 5: x2 + 2xy + y2-x² + 2xy-y²= 4xy

Answer:

2√3

Step-by-step explanation:

√12 =

√4 * √3 =

√2^2 * √3 =

2 * √3 =

2√3

https://brainly.com/question/16800358

Answer:

We can write 12 as 4 + 4 + 4, or 4 ∙ 3. So, create three squares that each have two columns and two rows.

a series of 3 squares, each composed of 4 smaller squares

so √12 =√4 x 3 = √4 x √3 = 2√3

Step-by-step explanation:

a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

Learn more about initial principal here:

https://brainly.com/question/26100282

#SPJ11

Answer:

the first one

Step-by-step explanation:

Answer:

4/6 of a book in an hour

Step-by-step explanation:

1/6 = 1/4

1/4 x 4/1 = 1

1/6 x 4/1 = 4/6

Bam! UwU

Lol Hope This Helps !

Answer:

is that for social studeies

Step-by-step explanation:

Answer:

-45

Step-by-step explanation:

5 *-1 *-3= 15

4 *-3 *4= -48

3 *4 *-1=-12

15 -48 -12= -45

Answer:

TOP LEFT

Step-by-step explanation:

Answer:

Your answer would be

X^2-7

Step-by-step explanation:

Hope it helps .

Good luck .

Answer:

92.75

Step-by-step explanation:

tenth spot is to right of decimal round up or down depending on the next number

Answer:

Step-by-step explanation:

ima a braintlest

There are 7.0874 grams in a quarter of an ounce

In the context of drug measurements, a "quarter" is often used to refer to a quarter of an ounce. One ounce is equal to 28.3495 grams. Therefore, a quarter of an ounce would be:

1/4 x 28.3495 = 7.0874 grams

So there are 7.0874 grams in a quarter of an ounce.

It's important to note that the term "quarter" is not a standard unit of measurement and is often used in the context of illegal drug transactions. It's always a good idea to use standard units of measurement, such as grams or milligrams, when measuring any substance for scientific or medical purposes.

Therefore, one quarter is 7.0874 grams

Learn more about quarter of an ounce here

brainly.com/question/30403498

#SPJ4

They are both factors of 15x-10 because 5(3x-2)=15x-10

factor x factor=product.

In this case 15x-10 is the product

The weighted average of a data set is 36.

Here,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

We have to find the weighted average of a data set.

What is Weighted Average?

Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set.

Now,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

The weighted average is given by the formula;

\(x = \frac{f_{1} x_{1} + f_{2} x_{2}+ f_{3} x_{3}+ ...... f_{n} x_{n}}{f_{1} +f_{2} + f_{2}}\)

Hence,

The weighted average of a data set;

x = 20 x 3 + 40 x 5 + 50 x 2 / 3+5+2

x = 360/10 = 36

Hence, The weighted average of a data set is 36.

Learn more about the weighted average visit:

https://brainly.com/question/18554478

#SPJ4

The values that would represent those having type O blood are between 000 and 449, inclusive (Option 3).

The given study states that 45% of Americans have type O blood. This means that out of 100 individuals, 45 would have type O blood. When using a random number generator producing three-digit values from 000 to 999, we can determine which values represent those having type O blood.

Since 45% of Americans have type O blood, it implies that the probability of an individual having type O blood is 0.45. The random number generator produces equally likely values from 000 to 999, where each value has a probability of 1/1000.

To find the values representing those having type O blood, we need to consider the range of values that corresponds to the 45% probability. The inclusive range between 000 and 449 (Option 3) represents the values that have a probability less than or equal to 0.45. Therefore, the values between 000 and 449, inclusive, would represent those having type O blood.

To learn more about probability visit:

brainly.com/question/30034780

#SPJ11

An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 27 - 4(n - 1).

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ = a₁ + (n - 1)d

Where:

From the information provided, we have the following parameters:

First term, a₁ = 27

Second term, a₂ = 31

Next, we would determine the common difference as follows:

Common difference, d = a₂ - a₁

Common difference, d = 31 - 27

Common difference, d = 4.

Substituting the parameters into the mathematical expression, we have;

aₙ = 27 + (n - 1)(4)

aₙ = 27 - 4(n - 1).

Read more on arithmetic sequence here: brainly.com/question/24989563

#SPJ1

To find the critical value needed to construct a confidence interval for the population mean, we need to know the level of confidence and the sample size.

However, the information you provided only states "level" and "sample size," without specifying their values. Additionally, you mentioned that the population standard deviation is unknown.

In general, the critical value is determined based on the desired level of confidence and the sample size, and it depends on the distribution of the data (e.g., normal distribution, t-distribution). For a normal distribution and when the population standard deviation is unknown, the critical value is usually determined using the t-distribution.

To calculate the critical value, we need to know the level of confidence and the sample size (degrees of freedom for the t-distribution). With these details, we can use statistical tables or software to find the corresponding critical value.

Know more about critical value here:

https://brainly.com/question/30168469

#SPJ11

Answer:

C

Step-by-step explanation:

Looking at the graph, we can see that the graph crosses the y-axis at y=2.

Hence, our y-intercept should be 2.

Therefore, we can eliminate A.

We also notice that the graph is downwards sloping.

Therefore, our slope is negative.

So, we can eliminate B.

Therefore, our answer must be C.

Answer:

C

Step-by-step explanation:

I have the same question and my answer was right

Answer:The system 150x+400y=1950 and x = y+2 could be used to determine the number of small boxes and large boxes ordered where x represents the number of small boxes and y represent the number of large boxes.

Step-by-step explanation:

Answer:

Let s = the number of small boxes purchased

Let l = the number of large boxes purchased

100s + 350l= 2400

s+l= 9

the standard deviation of the sample means:

σ(x) = σ/\(\sqrt{n}\)

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement text annotation indicator, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. In fact, this also holds true even if the population is binomial, provided that min(np, n(1-p))> 5, where n is the sample size and p is the probability of success in the population. This means that we can use the normal probability model to quantify uncertainty when making inferences about a population mean based on the sample mean.

For the random samples we take from the population, we can compute the mean of the sample means:

μ (x) = μ

and the standard deviation of the sample means:

σ(x) = σ/\(\sqrt{n}\)

To learn more about central limit theorem:

https://brainly.com/question/18403552

Answer:

y = 7 is the same as y = 0x + 7 in slope intercept form

                            slope m= 0 parallel to x-axis

A line to the x-axis (or to a line parallel to x-axis) will be parallel to the y-axis (perpendicular to x-axis)

Equation of y-axis is x=0

this line passes through (2,9) means the line parallel to y-axis has x-coordinate =2

so, equation of this line is x=2

Step-by-step explanation:

Based on the given information, where the Reproducibility result is 5% and the Repeatability result is 50%, it indicates that the majority of the variation in the measurement system is due to the repeatability component rather than the reproducibility component.

Re-examine and possibly revise the handling of the part to be measured: If the interaction between the operator and the part is identified as a significant source of variation, addressing this issue by re-evaluating and improving the part handling process can help reduce repeatability errors.

Investigation into the instrument: Validating the proper functioning and accuracy of the measuring instrument is crucial. An investigation should be conducted to ensure that the instrument is calibrated correctly and operating within acceptable specifications.

More training for the operators: Providing additional training and guidance to the operators can help improve their skills and reduce variations introduced by human factors. This includes ensuring they follow standardized measurement procedures, properly handle the equipment, and interpret the results accurately.

To know more about Reproducibility,

https://brainly.com/question/32341463

#SPJ11

The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).

The slope-intercept formula is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation in the question

2x - y = -3

First, we solve form for y and reorder in slope intercept form.

2x - y = -3

Subtract 2x from both sides

2x - 2x- y = -3 - 2x

- y = -3 - 2x

Divide each term by -1

y = 3 + 2x

Reorder in slope intercept form

y = 2x + 3

To find the y-intercept, replace x with zero and solve for y

y = 2(0) + 3

y = 3

Therefore, the y-intercept is 3.

Learn more about equation of line here: brainly.com/question/2564656

#SPJ1

Answer:

y = -3/4 x + B

Step-by-step explanation:

B is the translation of the line across y-axis

Answer:

y = -1/2x + 1/2

Step-by-step explanation:

perpendicular lines have slopes that are opposite signs and reciprocal

therefore, use m=-1/2 and point (9, -4) to complete the equation by finding 'b' (the y-intercept)

-4 = -1/2(9) + b

-4 = -9/2 + b

-4 + 9/2 = b

-4 + 4 \(\frac{1}{2}\) = b

b =  \(\frac{1}{2}\)

The inverse of g' (-1/5) is -15625 / 4^{5/4}.

To find g' (-1/5), we first need to find g(x) which is the inverse of f(x). To do this, we start by setting y = f(x) and solving for x.
y = f(x) = {x^7} / {x^4 + 4}

Multiplying both sides by x^4 + 4, we get:
y(x^4 + 4) = x^7

Expanding the left side, we get:
y(x^4) + 4y = x^7

Substituting u = x^4, we get:
yu + 4y = u^(7/4)

Rearranging and solving for y, we get:
y = (u^(7/4)) / (u + 4)

Substituting back u = x^4, we get:
y = (x^7) / (x^4 + 4)

Thus, g(x) = (x^7) / (x^4 + 4).

Now, to find g'(-1/5), we need to take the derivative of g(x) and evaluate it at x = -1/5.

Using the quotient rule, we get:
g'(x) = [7x^6(x^4+4) - x^7(4x^3)] / (x^4+4)^2

Substituting x = -1/5, we get:
g'(-1/5) = [7(-1/5)^6((-1/5)^4+4) - (-1/5)^7(4(-1/5)^3)] / ((-1/5)^4+4)^2

Simplifying and expressing in exact form, we get:
g'(-1/5) = [-(4/3125)^(3/4)] / (4/3125)^2 = -1 / (4/3125)^{5/4} = -15625 / 4^{5/4}

Know more about inverse here:

https://brainly.com/question/3831584

#SPJ11

Explanation:

The initial expression is:

To know the value of m, we need to solve the equation for m, so adding 7 to both sides of the equation, we get:

Then, we can multiply both sides by 4, so:

Step-by-step explanation:

Probability Density Function(PDF) is a statistical

expression that defines a probability distribution for a descrent random variable as opposite to a continuous random variable.

Answer:

U ARE A QUEEN

Step-by-step explanation:

HAY BESTIE

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

for such more question on measure of arc

https://brainly.com/question/25716982

#SPJ8

Answer:

44, -60, 4

Step-by-step explanation:

8(5) + 4 ---- 40 + 4 ---- 44

8(-8) + 4 ---- -64 + 4 ---- -60

8(0) + 4 ---- 0 + 4 ---- 4