Expand if necessary,combine like terms (x+2) (x+2)

Given: 2n = m + h, h = n + m, n = 2m is proven below.

Given: a - b = c -d, b = d - 1, c = 6; a = 5 is proven below.

Given: 2n = m + h, h = n + m; Prove: n = 2m

Statements:

2n = m + h (Given)

h = n + m (Given)

2n = m + n + m (Substituting the value of h from statement 2)

2n = 2m + n (Combining like terms in statement 3)

2n - n = 2m (Subtracting n from both sides of statement 4)

n = 2m (Simplifying statement 5)

Reasons:

Statement 1 is given

Statement 2 is given

Statement 3 is obtained by substituting the value of h from statement 2 in statement 1

Statement 4 is obtained by combining like terms in statement 3

Statement 5 is obtained by subtracting n from both sides of statement 4

Statement 6 is obtained by simplifying statement 5

Therefore, n = 2m is proven.

Given: a - b = c -d, b = d - 1, c = 6; Prove: a = 5

Statements:

a - b = c - d (Given)

b = d - 1 (Given)

c = 6 (Given)

a - b = c - d (Repeating statement 1)

a - (d - 1) = 6 - d (Substituting b with d - 1 in statement 4)

a - d + 1 = 6 - d (Expanding the bracket in statement 5)

a + 1 = 7 (Adding d to both sides of statement 6 and simplifying)

a = 6 (Subtracting 1 from both sides of statement 7)

Reasons:

Statement 1 is given

Statement 2 is given

Statement 3 is given

Statement 4 is repeating statement 1

Statement 5 is obtained by substituting b with d - 1 in statement 4

Statement 6 is obtained by expanding the bracket in statement 5

Statement 7 is obtained by adding d to both sides of statement 6 and simplifying

Statement 8 is obtained by subtracting 1 from both sides of statement 7

Therefore, a = 5 is proven.

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Answer:

405 yards

Step-by-step explanation:

Given that,

A company made 1,215 yards of copper wire.

They want to wrap the same amount of wire on each three poles.

3 poles = 1,215 yards of copper wire

1 pole = 405 yards of copper wire

So, each pole will require 405 yards of copper wire.

Step-by-step explanation:

perimeter formula is adding up all the sides

so

5x-40 + 5x-40 + 3x-18 + 3x -18

= 16x -116

Answer:

The answer is A.

Step-by-step explanation:

-2 * -5x is 10x. Negative multiplied by negative is a positve. 5x2 is 10.

3 * -2 is -6. Negative mupltiplied by a positive is negative. 3x2 is 6.

Therefore the 10x-6 is the answer.

Hope you learned something! Have a great day!

The critical value of t with df as 7 is 2.36, and the critical value of t with df as 102 is 2.62

In a hypothesis test, the critical value is a value that is used to decide whether to accept the null hypothesis or not. It is based on the level of significance that was selected, which is the highest likelihood that a Type I error could occur.

a)

On referring to the t-distribution table, which is statistical software, or a calculator to find the critical value of t for a 95% confidence interval with degrees of freedom (df) = 7. The two-tailed confidence level of 0.95 is the essential value. We discover that the crucial value of t for a 95% confidence interval with df = 7 is roughly 2.365 using a t-distribution table or program.

b)

The t-distribution table, statistical software, or a calculator are used in a similar manner to estimate the critical value of t for a 99% confidence interval with df = 102. The crucial value is equal to the 0.99 two-tailed confidence level. The crucial value of t for a 99% confidence interval with df = 102 is roughly 2.62, according to a t-distribution table or computer programme.

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Answer:

Step-by-step explanation:

boody boody

The areas of the sectors are:

For an arc length of 2π, the area of the sector is 6π square units.

For an arc length of 3π, the area of the sector is 9π square units.

For an arc length of 4π, the area of the sector is 6π square units.

For an arc length of π, the area of the sector is 3π/2 square units.

The total circumference of the circle is given by:

C = 2πr = 2π(6) = 12π

The total area of the circle is given by:

A = πr^2 = π(6^2) = 36π

To find the area of a sector, we need to know the central angle θ that defines the arc length. The central angle θ is measured in radians and is related to the arc length s and the radius r by the formula:

θ = s/r

So, the area of the sector is given by:

A_sector = (θ/2π)A

where A is the total area of the circle.

Let's find the area of the sector for different arc lengths:

For an arc length of s = 2π, the central angle is:

θ = s/r = 2π/6 = π/3

The area of the sector is:

A_sector = (π/3)/(2π) * 36π = 6π

For an arc length of s = 3π, the central angle is:

θ = s/r = 3π/6 = π/2

The area of the sector is:

A_sector = (π/2)/(2π) * 36π = 18π/2 = 9π

For an arc length of s = 4π, the central angle is:

θ = s/r = 4π/6 = 2π/3

The area of the sector is:

A_sector = (2π/3)/(2π) * 36π = 12π/2 = 6π

For an arc length of s = π, the central angle is:

θ = s/r = π/6

The area of the sector is:

A_sector = (π/6)/(2π) * 36π = 3π/2

So, the areas of the sectors are:

For an arc length of 2π, the area of the sector is 6π square units.

For an arc length of 3π, the area of the sector is 9π square units.

For an arc length of 4π, the area of the sector is 6π square units.

For an arc length of π, the area of the sector is 3π/2 square units.

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Answer:

a product of 4 times a number(n) minus 8

Step-by-step explanation:

let n be the number

4 times (multiply) a number (n) - 8

Answer:

5

Step-by-step explanation:

for the question, let's make a variable

Assume one number is X and we can get a equation like this:

X + 2X+7 = 22

X + 2X = 22 - 7

3X = 15

X = 5

X=32

A HOPE IT HELP:)

WHEN IF I'M WRONG,CORRECT MY ANSWER:)

Negative linear correlation between variables.

The statement "The more you save (x), the less you spend (y)" suggests a negative linear correlation between the variables x and y. In a negative linear correlation, as one variable increases, the other variable decreases at a constant rate.

In this case, as the amount saved (x) increases, the amount spent (y) decreases. This implies that if someone saves more money, they tend to spend less money. It is important to note that correlation does not necessarily imply causation.

In other words, just because there is a negative linear correlation between the amount saved and the amount spent, it does not mean that saving more money causes people to spend less. There may be other factors that influence both variables. Nonetheless, understanding the nature of the correlation between variables can be useful in making predictions and analyzing data.

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Answer:

(x-y)/z

Step-by-step explanation:

296 hot lunches were sold on Friday.

The number of hot lunches sold on Friday can be calculated by multiplying the total number of hot lunches by the relative frequency on Friday:

Hot lunches sold on Friday = 1,350 * 0.22 = 296

Relative frequency is a measure of the number of times an event occurs in a sample, expressed as a proportion of the total number of events. To find the number of hot lunches sold on Friday, we multiply the total number of hot lunches sold in the week by the relative frequency of Friday. This gives us the number of hot lunches sold on Friday, which is 296 in this case. Understanding relative frequency is important in statistics as it helps to summarize data and understand the distribution of events.

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Answer:

Step-by-step explanation:

Hyhh

Answer:

$1,650 profit

Step-by-step explanation:

It cost $15 to groom one animal, if you groom 95 animals you would do 95 animals x $15 = $1,425 profit. If you groom 110 animals and charge $15 per animal you would do the same equation. 110 animals x $15 =  $1,650. The equation for this problem is the number of animals groomed X the cost to groom one animal.

Hope this helps!

The side length of the square is 1/2 - 1/4(x - 7)^2

To find the side length of the square, we need to first express the perimeter in terms of the side length.

Let s be the side length of the square.

Since a square has four equal sides, the perimeter of the square is given by:

y = 4s

Now, we can express s in terms of y:

s = y/4

Substituting this into the given expression for y:

y = 2 - (x - 7)^2

We get:

s = [2 - (x - 7)^2]/4

Simplifying this equation:

s = 1/2 - 1/4(x - 7)^2

Hence, the side length expression is 1/2 - 1/4(x - 7)^2

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Complete question

The perimeter (y) of a square is y =2 - (x - 7)^2. What’s the side length of the square?

9514 1404 393

Answer:

  Vertex: (-1, 4)

  Maximum: f(-1) = 4

  Increasing: (-∞, -1)

  Decreasing: (-1, ∞)

Step-by-step explanation:

The equation can be written in vertex form by "completing the square."

First factor out the leading coefficient from the x-terms.

  f(x) = -(x² +2x) +3

Then add the square of half the x-coefficient inside parentheses. Add the opposite of that amount outside parentheses.

  f(x) = -(x² +2x +1) +3 +1

Write in vertex form.

  f(x) = -(x +1)² +4 . . . . . . . compare to a(x -h)² +k

You can see that the vertex is (h, k) = (-1, 4), and that the vertical scale factor 'a' is negative. This means the vertex is the maximum and the parabola opens downward.

The function will be increasing to the left of the maximum, decreasing to its right.

__

Vertex: (-1, 4)

Maximum: f(-1) = 4

Increasing: (-∞, -1)

Decreasing: (-1, ∞)

Graph: see attached

Answer:

GCF: (x + 2)(9x + 6)

Step-by-step explanation:

Given the algebraic expression, 9x(x + 2) + 6(x + 2), where the greatest common factor (GCF) must be taken out:

Since (x + 2) are common between the two groups, then we can group 9x and 6 together.

In other words:

= 9x(x + 2) + 6(x + 2)  

= (9x + 6)(x + 2)

If we perform the FOIL method onto (9x + 6)(x + 2), it will result in the following trinomial:

(9x + 6)(x + 2)

= 9x² + 18x + 6x + 12

= 9x² + 24x + 12

In order to see why this works, let's go back to the original problem, as if we're trying to determine the resulting trinomial:

Given:  9x(x + 2) + 6(x + 2)  

Distribute 9x and 6 into the parenthesis:

= 9x² + 18x + 6x + 12

Combine like terms:

= 9x² + 24x + 12    ⇒ As we can see, this trinomial matches our solution.

Therefore, the correct answer is: (x + 2)(9x + 6).  

Answer:

(d/2)^2 pi

Step-by-step explanation:

To find the area of a circle the formula is A=pi times radius sqaured. Since we do not have the radius we need to find it. The radius will always be half the diameter hence the (d/2). This will give us the radius, next is just to complete the area formula by squaring the radius and multiplying it by pi.  i hope this helps :)

The circle's area, in function of it's diameter, is given by:

\(A = \frac{\pi d^2}{4}\)

----------------------

\(A = \pi r^2\)

\(A = \pi r^2\)

\(A = \pi (\frac{d}{2})^2\)

\(A = \pi \frac{d^2}{4}\)

\(A = \frac{\pi d^2}{4}\)

Which is the area of a circle of diameter d.

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The given points are T(3,1) and U(5,3)

The x coordinates of these given points are 3 and 5. Add them up to get 3+5 = 8. Then cut this in half getting 8/2 = 4. This is the x coordinate of the midpoint.

The y coordinates are 1 and 3. They add to 1+3 = 4. Then that cuts in half to get 4/2 = 2. This is the y coordinate of the midpoint.

The midpoint is (4,2)

Effectively, we just used the midpoint formula

\((x_m, y_m) = \left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right)\)

In short: add the corresponding coordinates, then divide by 2.

Answer:

15

Step-by-step explanation:

plug in what we know

2(1+4)-(3-8)

PEMDAS says parenthesis first

2(5)-(-5)

Then multiplication since there are no exponenents

10-(-5)

two negatives makes a posititve

10+5

add

15

Answer:

11

Step-by-step explanation:

First, you simplify the equation. 2x+4-y+8=2x+12-y. Then, you apply x=1 and y=3. 2+12-3=14-3=11

The classification of the compounds according to their functional class: A | Aldehyde

B | Alcohol

C | Ketone

D | Amine

Compound A contains a carbonyl group (C=O) bonded to two alkyl groups (R-). This is the general structure of an aldehyde. Aldehydes are characterized by their strong, sweet odor.

They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound B contains an oxygen atom (O) bonded to two alkyl groups (R-). This is the general structure of an alcohol. Alcohols are characterized by their ability to dissolve other polar compounds, such as water. They are also used in a variety of products, such as solvents, cleaners, and fuels.

Compound C contains a carbonyl group (C=O) bonded to a propyl group (CH3CH2CH2-) and an amino group (NH2). This is the general structure of a ketone.

Ketones are characterized by their strong, sweet odor. They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound D contains a nitrogen atom (N) bonded to three alkyl groups (R-). This is the general structure of an amine. Amines are characterized by their basic properties. They are also used in a variety of products, such as pharmaceuticals, plastics, and fertilizers.

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Answer:

2/3

Step-by-step explanation:

Time it would take Sarah to complete the work in one hour = work completed in 1/4 hours x 4

We are multiplying by 4 because there are 4, 1/4 in an hour

1/4 + 1/4 + 1/4 + 1/4 = 1 hour

\(\frac{1}{6}\) × 4 = \(\frac{4}{6}\)

To transform to the simplest form. divide both the numerator and the denominator by 2

= \(\frac{2}{3}\)

Using the concept of proportion, Gianna will have enough yards to make 18 bows

To solve this problem, we need to apply the concept of proportions.

In order to make 1 bow, she needs 1/5 yard of ribbon

Representing this in an equation form will be;

1 bow = 1/5 yard

18 bow = x yard

cross multiply both sides and solve for x

x * 1 = 18 * (1/5)

x = 3.6 yards

From the above, there will be enough yards to make 18 bows.

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Answer:

aszdxcfgvhbjnk

Step-by-step explanation: