Which steps can be used to solve for the value of y?
(2013
(y +57) = 178​

The Simplification of the algebraic expression gives:

a. -2/3x² - (4/15)xy +  (11/4)y²

b. -(12/7)x³ + (20/9)y

Simplification of an algebraic expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression

a. (1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

To simplify this, add or subtract like terms. That is:

(1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

     = (1/3)x² - 3x² - (2/5)xy + (2/15)xy + 2y²  + (3/4)y²

     = -2/3x² - (4/15)xy +  (11/4)y²

b. (2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y

To simplify this, add or subtract like terms. That is:

(2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y = (2/7)x³- 2x³ - (1/3)y + 2y + (5/9)y

                                                    = -(12/7)x³ + (20/9)y

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Answer:

the midpoint is (9,5). hope this helps

Answer:

The best first step would be to multiply the second equation by -2

Step-by-step explanation:

The best first step would be to multiply the second equation by -2

then you would have the following

\(\ \ \ \ \ \ 4x - 5y = 2 \\-2*(2x)+ (-2)*y = (-2)*3\)

and when you multiply it is easy to eliminate because you will get

   \(4x - 5y = 2 \\-4x -2y = 6\)

and if you sum the equations you get

-7y = 8

so that is a single variable equation which is easier to solve.

Step-by-step explanation:

Subtract the 99 from 949 then    divide by 2

949-99= 425 dollars = price of dryer

( then washer is  425 + 99 )

Answer:

10.2

Step-by-step explanation:

Answer:

10.2

Step-by-step explanation:

cos = adj/hyp

cos22 = x/11

11 cos22 = 10.199

Answer:

40 pounds

Step-by-step explanation:

For this situation, you just multiply 8 bags and 5 pounds representing total pounds for 8 bags.

8 times 5 = 40 pounds

The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

\(a_1 = 10, q = -\frac{2}{3}, k = 8\)

The formula for the sum of the first n terms is given as follows:

\(S_n = a_1\frac{1 - r^n}{1 - r}\)

Hence the sum for this problem is given as follows:

\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)

\(S_8 = 5.77\)

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Answer:

6.24

Step-by-step explanation:

41.63-4.19=37.44

37.44÷6=6.24

Given that,

The radius of the circle, r = 7.3 units

To find,

The diameter of the circle.

Solution,

If r is the radius of the circle, then its diameter is given by the relation as follows :

d = 2r

Put the value of r.

d = 2(7.3)

= 14.6 units

So, the diameter of the circle is 14.6 units. Hence, the correct option is (A).

Step-by-step explanation:

1/6

1/6- 1/2 = 1/4

1/4*1/2= 1/8

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Answer:

she is 0 blocks away from home because you said she started at home

Answer:

a) Malavika is 8 blocks west from home

b) Traveled 20 blocks total

Step-by-step explanation:

a) According to a compass: 3 west (left), then 6 east (right) and that puts you at 3 east (right). Then back 11 west (left) puts you at 8 west (left)

b) Add up all blocks traveled: 3 + 6 + 11 = 20

We can solve the quadratic equation using factorization method.

First, let's re-write the equation:

Next, we try to factorize the expression by the left:

Next, we equate each factor to zero to find the value of x

We can conclude that :

We can also do a check by substituting the value of x back into the equation:

Based on the information given, we know that the two triangles have two pairs of congruent angles. This is sufficient to prove that the two triangles are congruent using the AAS (Angle-Angle-Side) postulate. Therefore, the method I would use to prove the two triangles congruent is **AAS**.

Step-by-step explanation:

3^6  = 3 * 3^5

 = 3 * 243 =  729

Answer:

b) local minimum at \(x=\frac{1}{e}\)

c) Graph of the function is convex

Step-by-step explanation:

We are told that \(f'(\frac{1}{e})=0\), which implies there is a turning/stationary point at \(x=\frac{1}{e}\).

Substituting \(x=\frac{1}{e}\) into \(f''(x)\) will tell us if the turning point is a minimum or a maximum:

\(f''(\frac{1}{e})=\frac{1}{\frac{1}{e} } =e>0 \implies \textsf{local minimum}\)

Therefore, statement a) is false and statement b) is true.

If the function has a minimum turning point, then this implies that the curve is convex.  Therefore, statement c) is true.

Extremum = local min and max points.

We have already established that there is a local minimum at \(x=\frac{1}{e}\), therefore statement d) is false.

I know this is not needed for this question, but here are the workings to detemine the equation of the function (I've also attached a graph).  This supports the answers above.

\(\textsf{if} \ f''(x)=\frac{1}{x}\\\\\implies f'(x)=\int f''(x) \ dx \\\\\implies f'(x)=ln|x|+C\\\)

\(\textsf{if} \ f'(\frac{1}{e})=0\\\\\implies ln|\frac{1}{e}|+C=0\\\\\implies -1+C=0\\\\\implies C=1\\\\\)

\(\implies f'(x)=ln|x|+1\\\)

\(\textsf{if} \ f'(x)=ln|x|+1\\\\\implies f(x)=\int f'(x) \ dx\\\\\implies f(x)=xln(x)-x+x+C\\\\\implies f(x)=xln(x)+C\)

Answer:

582.6

Step-by-step explanation:

2/3 x 874 = 582.6

The value of m∠G = 48.6° .

A triangle is a polygon with three sides , angles and vertices.

It is given that

In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°

m∠G = ?

well, using the law of cosines,

GH ² = 9² + 11² - 2(9)(11) cos65°

f = 10.88 ft

now, using the law of sines,

sinG/9 = sin65°/10.88

m∠G = 48.6°

Therefore the value of m∠G = 48.6° .

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Answer:

D.

Step-by-step explanation:

Horror (12) + Comedy (15) = 27

Action(17) + Drama(6) = 23

27 > 23

The statement that is true is a person who will go to this theatre next Friday is more likely to prefer horror or comedy than action or drama.

The probability helps us to know the chances of an event occurring.

\(\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

As is given that the total number of people surveyed is 50, while the table suggests the preferences of the people about the movie.

Therefore, if take the probability of a person watching a horror or comedy movie it will be,

\(\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

\(\rm Probability=\dfrac{\text{Number of people preferring Horror or comedy}}{\text{Total Number of people surveyed}}\\\\Probability = \dfrac{12+15}{50} = 0.54\)

The probability of a person watching an action or drama movie it will be,

\(\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

\(\rm Probability=\dfrac{\text{Number of people preferring Action or drama}}{\text{Total Number of people surveyed}}\\\\Probability = \dfrac{17+6}{50} = 0.46\)

Since the probability of a person watching a horror or comedy movie is more, therefore, a person who will go to this theatre next Friday is more likely to prefer horror or comedy than action or drama.

Thus, the statement that is true is a person who will go to this theatre next Friday is more likely to prefer horror or comedy than action or drama.

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The ratio of the length of the shortest diagonal to the length of the longest diagonal in a regular hexagon is \($\sqrt{3}/2$\). This can also be written as \($\frac{\sqrt{3}}{2}$\).

A hexagon is a six-sided polygon with all angles equal to 120 degrees. In a regular hexagon, all sides are equal in length and all angles are equal. The diagonals of a hexagon are line segments that connect non-adjacent vertices of the hexagon.

A regular hexagon has nine diagonals. The shortest diagonal of a regular hexagon is the one that connects opposite vertices and is equal to the length of a side of the hexagon. The longest diagonal of a regular hexagon is the one that connects opposite vertices and passes through the center of the hexagon.

To find the ratio of the length of the shortest diagonal to the length of the longest diagonal, we need to find the length of the longest diagonal in terms of the length of the shortest diagonal. We know that the length of the shortest diagonal is equal to the length of a side of the hexagon.

We can draw the longest diagonal and form an equilateral triangle by connecting the center of the hexagon to the two endpoints of the longest diagonal. The length of the side of this equilateral triangle is equal to the length of the longest diagonal of the hexagon.

The ratio of the length of the shortest diagonal to the length of the longest diagonal is then equal to the ratio of the side length of this equilateral triangle to the length of the side of the hexagon, which is \($\frac{\sqrt{3}}{2}$\).
Therefore, the ratio of the length of the shortest diagonal to the length of the longest diagonal in a regular hexagon is $\sqrt{3}/2$. This can also be written as \($\frac{\sqrt{3}}{2}$\).

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Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Answer:

A. Margin of error=0.0346

B. Confidence interval=0.4854 to 0.5546

Step-by-step explanation:

A. Computation the margin of error

First step is to calculate the Confidence level using this formula

Confidence level= 1 -α

Where,

α=0.95

Let plug in the formula

Confidence level= 1-0.95

Confidence level= 0.05

Second step is to find Z using this formula

Zα/2

Let plug in the formula

Z= 0.05/2

Z=0.025

Third step is to find the Z score of Z=0.025

Zα/2=1.96

Now let calculate the margin of error using this formula

Margin of error=Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Margin of error=1.96√0.52(1-0.52)/800

Margin of error=1.96√0.52(0.48)/800

Margin of error=1.96√0.2496/800

Margin of error=1.96√0.000312

Margin of error=0.0346

Therefore Margin of error will be 0.0346

B. Computation for the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009

Computation for the boundaries of confidence interval

Using this formula

p- Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52-1.96√0.52(1-0.52)/800

Confidence interval=0.52-1.96√0.52(0.48)/800

Confidence interval=0.52-1.96√0.2496/800

Confidence interval=-0.52-1.96√0.000312

Confidence interval=0.4854

Computation for the boundaries of confidence interval

Using this formula

p+ Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52+1.96√0.52(1-0.52)/800

Confidence interval=0.52+1.96√0.52(0.48)/800

Confidence interval=0.52+1.96√0.2496/800

Confidence interval=-0.52+1.96√0.000312

Confidence interval=0.5546

Therefore the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009 is 0.4854 to 0.5546

josh is 3 years older than 4 times kim's age. the sum of their ages is less than 43. inequality for the situation, then the oldest age kim could be.

4k + 3 < 43

k < 10

We are given that Josh is 3 years older than 4 times Kim's age. We can express this as 4k + 3, where k represents Kim's age. We are told that the sum of their ages is less than 43, so we can write this as an inequality: 4k + 3 < 43. To find the oldest age Kim could be, we can solve this inequality for k. To do this, we subtract 3 from both sides, giving us 4k < 40. Finally, we divide both sides by 4, giving us k < 10. Therefore, the oldest age Kim could be is 10.

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Answer:

\(\textsf{17.} \quad a_n=2(2)^{n-1}\)

\(\textsf{18.} \quad a_n=-729 \left(\dfrac{1}{3}\right)^{n-1}\)

Step-by-step explanation:

To write a rule for the nth term of a geometric sequence, we can use the following formula:

\(\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}\)

\(\hrulefill\)

Given terms:

Substitute the given values into the formula to create two equations:

\(\begin{aligned}a_3=ar^{3-1}&=8\\ar^2&=8\end{aligned}\)

\(\begin{aligned}a_6=ar^{6-1}&=64\\ar^5&=64\end{aligned}\)

To find the common ratio, r, divide the second equation by the first equation to eliminate a:

\(\dfrac{ar^5}{ar^2}=\dfrac{64}{8}\)

  \(\dfrac{r^5}{r^2}=8\)

\(r^{5-2}=8\)

   \(r^3=8\)

   \(r^3=2^3\)

    \(r=2\)

Substitute the found value of r into one of the equations and solve for a:

\(\begin{aligned}a(2)^2&=8\\4a&=8\\\dfrac{4a}{4}&=\dfrac{8}{4}\\a&=2\end{aligned}\)

Therefore, the rule for the nth term of the given geometric sequence is:

\(\boxed{a_n=2(2)^{n-1}}\)

\(\hrulefill\)

Given terms:

Substitute the given values into the formula to create two equations:

\(\begin{aligned}a_4=ar^{4-1}&=-27\\ar^3&=-27\end{aligned}\)

\(\begin{aligned}a_6=ar^{6-1}&=-3\\ar^5&=-3\end{aligned}\)

To find the common ratio, r, divide the second equation by the first equation to eliminate a:

\(\dfrac{ar^5}{ar^3}=\dfrac{-3}{-27}\)

  \(\dfrac{r^5}{r^3}=\dfrac{1}{9}\)

\(r^{5-3}=\dfrac{1}{9}\)

  \(r^{2}=\dfrac{1}{9}\)

   \(r=\sqrt{\dfrac{1}{9}}\)

   \(r=\dfrac{1}{3}\)

Substitute the found value of r into one of the equations and solve for a:

\(\begin{aligned}a\left(\dfrac{1}{3}\right)^3&=-27\\\dfrac{1}{27}a&=-27\\a&=-729\end{aligned}\)

Therefore, the rule for the nth term of the given geometric sequence is:

\(\boxed{a_n=-729 \left(\dfrac{1}{3}\right)^{n-1}}\)

Answer:

i can't not understand sorry

Answer:

this is what I put please put it in your own words

Step-by-step explanation:

1. The title: Oh, the Places You'll Go!

2. Author: Dr. Seuss

3. Publisher: RANDOM HOUSE NEW YORK

4. Some invented words used in the book that you particularly like. Lurches, Slumps, Brains.

5. What the funniest stanza (for verse) in the book is, in your opinion. You have brainss in your head

II. Warm-up

butterfly butterflyfling

bridge bridgeamabob

bill billblingflingaling

III. Type a short, funny story using invented words for as many things as you can.

One day I was riding my horse and then I see carrot kids playing in the pasture and I asked to join them and the said yes.

Answer: You can use this whole paragraph if you want. I don't mind c:

Step-by-step explanation:

I. Independent research: Look up any Dr. Seuss book in your library and type the following information.

The title: The Lorax

Author: Dr. Seuss

Publisher: Random House Children's Books

Truffula Seed

“I am the Lorax. I speak for the trees. I speak for the trees for the trees have no tongues.”

II. Warm-up

1. Mouse

2. House

3. Spouse

III. Type a short, funny story using invented words for as many things as you can.

I went to a house in the woods and it was owned by a bird and a lion. They fed me porridge with crackers then put me down to sleep.

(I don't know what else to put but I hope that's good enough.)

I hope this helps you!! <3

From the statement of the problem we know the following facts about a circle:

- its center is at the point:

- it's tangent to the y-axis.

Using the data above we draw the following graph of the circle:

From the graph, we see that the circle center is at a distance of 1 unit from the y-axis (to which it is tangent), so the circle has a radius:

Replacing the data of the center and the radius in the general form equation of the circle, we get: