simplify fully 12x^{2} y/3x^{2}[

Answer:

x=2

Step-by-step explanation:

-13x-11=-37                             Original equation

-13x=-26                                 Add 11 to both sides

x=2                                         Divide both sides by -13

Answer:

85.4567

Step-by-step explanation:

Its the circle of life yeah yeah and it moves us all.

The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.

A financing model is a planned, institutionalized strategy for creating a steady income stream to sustain an organization's core services and operations. Nonprofits need funding because it enables them to make investments in their operations and increase their overall effect. Securing funding is crucial to keeping your organization operational because nonprofits frequently rely on grants to assist with operational costs. Grants of all kinds are available to nonprofit organizations.

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The step that is the part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10 and (E) 0 = x2 – 9x + 20.

To find the step that is the part of the process of algebraically solving the given system of equations:

That would be:

(C) 4x – 10 = x2 – 5x + 10  ( y = 4x - 10 is substituted for y).

Proof:      

(E) 0 = x2 – 9x + 20  (liked terms are grouped and simplified).

Proof:      

Solving:

Therefore, the step that is part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10.

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The complete question is given below:
Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? Check all that apply.

(A) y = x2 + 5x + 10

(B) y + 5x = x2 + 10 + 4x – 10

(C) 4x – 10 = x2 – 5x + 10

(D) 0 = x2 – 9x

(E) 0 = x2 – 9x + 20

(F) One x-value of a solution to the system is 4.

\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{2 +1}{-4 +6} \implies \cfrac{ 3 }{ 2 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +1= \cfrac{3}{2} (x +6) \end{array}}\)

a. The annual rate of change between 1994 and 2005 is -0.0661.

b. The correct answer to part A written in percentage form is - 6.61 %

c. The value of car in the year 2009 will be$9,850.

a. To find the annual rate of change, we can use the formula:

r = (ln(S2/S1)) / (t2 - t1)

where S1 is the initial value, S2 is the final value, t1 is the initial time, and t2 is the final time.

A) Using the values given, we get:

r = (ln(15000/27000)) / (2005 - 1994) ≈ -0.0661

So the annual rate of change (or decrease, in this case) is approximately -0.0661.

b. To convert this to a percentage, we can multiply by 100 and add a percent sign:

r = -0.0661 × 100% ≈ -6.61%

So the correct answer to part A written in percentage form is approximately -6.61%.

c.  To find the value in the year 2009, we need to use the formula:

S = S0 × \(e^{(rt)\)

where S0 is the initial value, r is the annual rate of change (as a decimal), t is the time (in years), and S is the value after t years.

Since we want to find the value in the year 2009 (which is 15 years after 1994), we have:

t = 15

r = -0.0661

S0 = 27000

Substituting these values, we get:

S = 27000 ×\(e^{(-0.0661 x 15)\) ≈ 9844.78

Rounding to the nearest 50 dollars, we get:

S ≈ $9,850

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Since the given planes are 2x − y + z = 9 and x + y − z = 3 intersect.

Therefore, The parametric equations for the line are x = -2t +6/6 , y = - (3 +t)/3 and z = t.

Parametric Equation:

A parametric equation defines a set of quantities according to one or more independent variables called parameters. Parametric equations are often used to represent the coordinates of points that make up a geometric object such as a curve or a surface, in which case the equations together form a parametric representation, or a parametric system, or a parametric (or spelled) object

According to the Question:

Given equations are

2x - y + z = 9

x +  y - z = 3

Let us consider z = t

2x - y + t = 9

x +  y - t = 3

We can write it as

2x - y  = 9 - t             -------------------------- (1)

x +  y  = 3 - t             ------------------------- (2)

Multiply equation (2) by 2 - equation (1):

    2x - y - (2x +2y) = 9 -t - (6- 2t)

⇒   2x - y -2x -2y = 9 - t - 6+ 2t

⇒ -3y = 3 + t

⇒ y = - (3 +t)/3

Let us substitute the value of y in equation (1)

   2x - {-(3 +t)/3} = 9 - t

⇒ 2x - (-3 -t)/3 = 9- t

⇒ 6x - (-3 -t) = 9 - t

⇒ 6x + 3 + t = 9 - t

⇒ 6x -6 = -2t

⇒ 6x = -2t +6

⇒ x = -2t +6/6

Therefore, the parametric equations for the line are x = -2t +6/6 ,

y = - (3 +t)/3 and z = t.

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The value of x is 17

The congruent arcs are (b) PQ and SR

The radius is 12 units

The value of PQ is 4

The length YZ is 19 units

In this question, we make use of the property of congruent sides

So, we have

3x - 24 = x + 10

When evaluated, we have

2x = 34

Divide by 2

x = 17

By the definition of congruent arcs, congruent arcs are arcs that have equal measures

In this figure, the congruent arcs are PQ and SR i.e. (b) PQ and SR

The radius of the circle is calculated as

r² = (25 + r)² - 35²

When expanded, we have

r² = 625 + 50r + r² - 1225

So, we have

50r = 600

Divide both sides by 50

r = 12

In this question, we make use of the property of congruent sides

So, we have

PQ = SR

Where

SR = 4

When evaluated, we have

PQ = 4

The length of YZ in the circle is calculated as

YZ² = (9 + 8)² + 8²

So, we have

YZ² = 17² + 8²

When expanded, we have

YZ² = 289 + 64

So, we have

YZ² = 353

Take the square root of both sides

YZ = 19

Hence, the length YZ is 19 units

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As per the given curvature, the value of PC is 1785.68 and PT is 1787.55

Curvature:

In statistics, curvature means amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.

Given,

PI is at station (20 00), the radius of curvature is 800 feet, and the angle of curvature is 30 degrees.

Here we need to determine the value of PC and PT.

According to the given value, the tangent distance is calculated as,

=> T = 800 x tan (30/2)

=> T = 800 x 0.2679

=> T = 214.32

Now, the value of PC is calculated as,

PC = PI - T

=> PC = 2000 - 214.32

=> PC = 1785.68

And the value of PT is calculated as,

PT =  PC + L

=> PT = 1785.68 + (100 x (30/1600))

=> PT = 1785.68 + 1.875

=> PT = 1787.55

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The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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Answer: Lola will earn $77 as interest.

Step-by-step explanation:

B = P*(1+r)^t is the formula for compound interest .

Where, 'B' is the principal amount after interest earned.

'P' is Principal amount (which here is $70).

'r' is the rate of return or interest rate(which here is 10%).

't' is time period for which account earns interest.(which here is 1 year).

so putting the values we get

70*(1 + 10/100 ) ^ 1           here 10% (=r) is converted from percentage to                   .                                        number after dividing by 100.

Which amount to 70*(1+ 0.1)^1

= 70*1.1

=$77 which is total amount after one year .

Answer:

12

Step-by-step explanation:

To solve this problem you would have to create a system of equations and solve them to find the point of intersection between the two graphs.

Let x equal the amount of muffins and y equal the amount of croissants

Because there was a total of 30 items bought, we can make this expression for our first equation:

x + y = 30

Next, we use the same logic to apply to the total cost for the items:

3.50x + 2.75y = 96.00

If you have a graphing calculator (I used desmos) you can put these two expressions in the calculator and take note of the point of intersection which is (18,12). This point means that 18 muffins and 12 croissants will make both expressions true.

Answer:

270 miles is your answer

Step-by-step explanation:

The absolute change in effective federal income tax from 1940 to 2000 is 15%. This means that the tax rate for the middle class increased by 15 percentage points over this time period.

The absolute change in effective federal income tax from 1940 to 2000 can be calculated by subtracting the tax rate in 1940 from the tax rate in 2000.

To calculate the absolute change in effective federal income tax from 1940 to 2000, we subtract the tax rate in 1940 from the tax rate in 2000:

Absolute change = Tax rate in 2000 - Tax rate in 1940

              = 19% - 4%

              = 15%

Therefore, the absolute change in effective federal income tax from 1940 to 2000 is 15%. This means that the tax rate for the middle class increased by 15 percentage points over this time period.

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The dimensions of a scale drawing of a rectangular flag that is 40 centimeters by 72 centimeters using the scale 1:8 is 4 cm by 7.2 cm. Option C.

This is because a 1:8 scale means that for every actual unit of length, the corresponding length on the scale drawing is 8 times smaller.

Therefore, in order to find the dimensions of the scaled drawing of the flag, we must divide the actual dimensions (40 cm by 72 cm) by 8. The result is 4 cm by 7.2 cm.

It is important to make sure that you use the correct scale when attempting to determine the dimensions of a scaled drawing. If you use a different scale than the one intended, your result will be incorrect.

For example, if you use a 1:4 scale instead of a 1:8 scale, you will end up with a scaled drawing that has dimensions of 20 cm by 36 cm, which is double the correct answer.

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Let's denote the number of miles Charles rode on Tuesday as x.

Since he rode 1.6 miles more on Thursday than on Tuesday, the number of miles he rode on Thursday can be expressed as (x + 1.6). According to the information given, Charles rode a total of 7.6 miles on Tuesday and Thursday. Therefore, we can write the equation: x + (x + 1.6) = 7.6 Combining like terms: 2x + 1.6 = 7.6 Subtracting 1.6 from both sides of the equation: 2x = 6 Dividing both sides by 2: x = 3 So, Charles rode 3 miles on Tuesday. Substituting this value back into the expression for Thursday's mileage: x + 1.6 = 3 + 1.6 = 4.6 Therefore, Charles rode 3 miles on Tuesday and 4.6 miles on Thursday.

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The intensity and the threshold of the noise are illustrations of rates

The decibel measurement of a quiet room is 28

From the graph that completes the question, we have the following point

(Decibel, Intense) = (28,500)

This means that, the decibel measurement is 28

Hence, the decibel measurement of a quiet room is 28

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Answer:

B or 28

Step-by-step explanation:

edge 22

So, the exact acute angle 0 for the given function value is 60°. Therefore, the answer is 60.

A function in mathematics seems to be a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a particular member in the second set (called the range). A function, in other words, receives input from one set and produces outputs from another.

The variable x has been frequently used to represent the inputs, and the changeable y is used to represent the outputs. A function can be represented by a formula or a graph. For example, the calculation y = 2x + 1 represents a functional form in which each value of x yields a distinct value of y.

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Answer:

33 degrees.

Step-by-step explanation: Half of a circle is 180 degrees. If we view the half of circle with angle C on it we can see the other part of the half of circle is 147 degrees. Since we know half a circle is 180 degrees, we subtract our known variable from 180 to get our unknown angle C, 33 degrees.

Answer:

A) (x + 4)(x + 8).

B) (x - 8)(x - 6)

C) (x - 2)(x - 1)

Step-by-step explanation:

a) There are 1540 ways that the teacher can select the three students.

b) The probability that all three students selected are girls is approximately 0.176 or 17.6%.

c) The probability that at least one boy is selected is approximately 0.824 or 82.4%.

a)

To find the number of ways the teacher can select three students out of 22 students (7 boys and 15 girls), we can use the combination formula. The number of ways to select r items from a set of n items is given by:

nCr = n! / (r! * (n-r)!)

where n! represents the factorial of n (i.e., n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1), and r! represents the factorial of r. Applying this formula, we get:

22C3 = 22! / (3! * (22-3)!) = 22! / (3! * 19!) = (22 x 21 x 20) / (3 x 2 x 1) = 1540

Therefore, there are 1540 ways that the teacher can select the three students.

b)

To find the probability that all three students selected are girls, we can use the formula for the probability of an event occurring. Since there are 15 girls and 7 boys, the probability of selecting a girl is 15/22 for the first selection, 14/21 for the second selection (since there are now 14 girls left out of 21 remaining students), and 13/20 for the third selection. Applying the formula, we get:

P(all three are girls) = (15/22) x (14/21) x (13/20) ≈ 0.176

Therefore, the probability that all three students selected are girls is approximately 0.176 or 17.6%.

c)

To find the probability that at least one boy is selected, we can use the complement rule. The complement of selecting at least one boy is selecting all three girls, which we calculated in part (b) to be approximately 0.176. Therefore, the probability of selecting at least one boy is:

P(at least one boy) = 1 - P(all three are girls) ≈ 1 - 0.176 ≈ 0.824

Therefore, the probability that at least one boy is selected is approximately 0.824 or 82.4%.

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Answer:

The file contains the solution to the question

Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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Answer: B

Explanation: The range is a set or a range of y-values of a function. In the graph, the y-value points are -7, -4, 1, 3, and 7. So, the answer is B.

:)

Answer:

the g (7) - value

Step-by-step explanation:

sana maka tulong

Answer:

\(v = \frac{1}{2} a {t}^{2} \\ a = \frac{2v}{ {t}^{2} } \)

'a' can be expressed in terms of 'v' and 't' as -

\($a=\frac{2v}{t^{2} }\)

We have the following expression -

\($v = \frac{1}{2} at^{2}\)

We have to express → a in terms of v and t.

On solving, we get -

Sin(\(2n\pi x\)) = 0.785

Sin(\(2n\pi x\)) = Sin (\(\frac{\pi }{4}\))

2n\(\pi\)x =  \(\frac{\pi }{4}\)

x =  \($\frac{1}{8n}\)

According to the question, we have -

\($v = \frac{1}{2} at^{2}\)

\($a=\frac{2v}{t^{2} }\)

Hence, 'a' can be expressed in terms of 'v' and 't' as -

\($a=\frac{2v}{t^{2} }\)

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9514 1404 393

Answer:

  7x +9y = -1

Step-by-step explanation:

The standard form of the equation for a line is ...

  ax +by = c

where a, b, c are mutually prime integers and a > 0.

We can get this form by multiplying the equation by 9, adding 7x+27.

  y - 3 = -7/9(x +4)

  9y -27 = -7x -28 . . . . . multiply by 9, eliminate parentheses

  7x +9y = -1 . . . . . . . . . add 7x+27 to both sides

_____

The attached graph shows both equations. They are in different colors and textures so you can see they are the same line.

We would expect a rate of return of 6.30% on a 5-year Treasury security, assuming the pure expectations theory is valid and disregarding cross-product terms.

The pure expectations theory suggests that the expected return on a bond with a specific maturity is equal to the average of the current and expected future short-term interest rates over that maturity period. In this case, we are interested in the rate of return on a 5-year Treasury security.

Using the information provided, the current real risk-free rate is 2.50% and the expected future rate of inflation is 3.80%. Therefore, the expected nominal risk-free rate for a 5-year period would be the sum of the real risk-free rate and the expected rate of inflation, which equals 6.30% (2.50% + 3.80%).

According to the pure expectations theory, the expected rate of return on a 5-year Treasury security would be the arithmetic average of the current and expected future short-term interest rates over that 5-year period. Since the Treasury security is a risk-free asset, the expected rate of return would be equal to the expected nominal risk-free rate of 6.30%.

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