What is the image of the point ( − 1 , 2 ) after a rotation of 270 counterclockwise about the origin?

Answer:

261

Step-by-step explanation:

The value of  [tex]f^{-1}(-7)[/tex] is given by -57/8.

Given that:-

f(x) = (x + 1)/(x + 8)

We have to find the value of [tex]f^{-1}(-7)[/tex].

Let f(x) = y

Hence,

[tex]f^{-1}(y) = x[/tex]

Now, we will find the inverse of the given function.

Hence, we can write,

y = (x + 1)/(x + 8)

We can rewrite it as:-

y = (x + 8 - 7)/(x + 8) = (x + 8)/(x + 8) - 7/(x + 8) = 1 - 7/(x + 8).

1 - y = 7/(x + 8)

x + 8 = 7/(1 - y)

x = 7/(1 - y) - 8

x = 7/(1 - y) - 8(1 - y)/(1 - y)

x = (7 - 8(1 - y))/(1 - y)

x = (7 - 8 + 8y)/(1 - y)

[tex]f^{-1}(y) = \frac{(8y - 1)}{( 1 - y)}[/tex]

Replacing y with x in the above equation, we can write,

[tex]f^{-1}(x) = \frac{(8x - 1)}{( 1 - x)}[/tex]

The above equation is the inverse of the function.

Putting x = -7 in the above equation, we get,

[tex]f^{-1}(-7) = \frac{(8(-7) - 1)}{( 1 - (-7))}[/tex]

= (-56 - 1)/ (1 + 7) = - 57/8

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y=-4x + 3

EXPLANATION

Given:

y = -4x + 5

To find the equation which represent a line that is parallel to the above, all we need to do is to oserve their slope.

Using a unique properties that states : slope of parallel lines are equal.

Observe that comparing the equation y =-4x + 5 with y=mx + b

slope = m= -4

From the option given, the only equation when compared with y=mx + b that has a slope of -4 is y=-4x + 3.

Therefore, the equation which represent a line that is parallel to y=-4x + 5 is y=-4x + 3

Ek, this is the solution:

Step 1: Let's review the information provided to us to answer the problem correctly.

Sales of the new toy = 2,000 per day

Price of the toy when sales are 2,000 per day = $ 6

Ther

The interpretation of the transformation of the given functions are;

f([tex]x + \frac{1}{4}[/tex]) means translated by 1/4 units to the left.

f(x) + 1/4 means that f(x) is translated by 1/4 units upwards

There are different ways of function transformations such as translation, reflection, dilation, compression e.t.c

Now, the function written can be said to translated by 1/4 units to the left . This is because when we translate a function by say "a" units to the left, we are simply going to add a units to the x - variable.

To translate a graph upwards, it simply means we will add the number of units to the function; for example, f (x) + 3 moves the graph of the function f (x) upward by 3 units.

Thus, the given function f(x) + 1/4 means f(x) is translated by 1/4 units upwards

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The number of payments to pay off the loan of $200,000 at 6.3% interest, compounded monthly is 315 monthly payments.

Using the compounding format for determining the monthly payments, the number of periods for the periodic payments can be computed.

In this situation, we used the online finance calculator to determine the number of payments.

Compounding accumulates the interest on a loan and adds it to the principal for computing subsequent interest.

At the end of the period, the balance is made up of the principal and compounded interest.

I/Y (Interest per year) = 6.3%

PV (Present Value) = $200,000

PMT (Periodic Payment) = $-1300

FV (Future Value) = $0

Results:

N (# of periods) = 314.854

Sum of all periodic payments = $-409,309.97

Total Interest $209,309.97

Thus, you are likely to make 315 monthly payments to settle the loan.

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The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985

Probability is what has the potential to happen. This area of math examines how random events happen. A value between 0 and 1 is used to express it. In order to anticipate the possibility of events, probability has been introduced to mathematics. The degree of likelihood that something will happen can be used to define probability. This fundamental theory of probability, which is also applied to the probability distribution, can be used to estimate the likelihood of the results of a random experiment. We must first determine the total number of alternatives in order to determine the likelihood that a specific event will occur.

Given that : He or she did not have the disease. The individual actually had the disease No positive 9 , negative 133 Yes Positive 140 ,Negative 18 .

                      Yes              No

Positive :          140            9

negative :         18              133

P = [tex]\frac{Someone get positive }{he not had the disease}[/tex]

= [tex]\frac{140}{142}[/tex]

=0.985

The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985

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Answer:

If you have earned 20 points, this means you have passed 25 levels.

Step-by-step explanation:

25 =  5 (20/4)

Shop work on the customer's computer for 5.5 hours.

Given,

Charge is flat fee of $ 10.95

and, then $24.50 per hour.

And, to find the number of hours if customer paid $147.90.

Now, According to the question:

Let shop work on computer for x hours .

Then, Amount paid = 10.95 + 24.90x

So, if customer paid $147.90

then, 147.90 = 10.95 + 24.90x

24.90x = 147.90 - 10.95

24.90x = 136.95

x = 136.95/ 24.90

x = 5.5

Hence, Shop work on the customer's computer for 5.5 hours.

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The finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes in Rocket Run 5k.

The formula for calculating the z-score is;

z = (x - μ)/σ

x = sample size

μ = mean of the sample

σ = standard deviation of the sample

The given values are-

μ =  57 minutes

σ = 8 minutes

Probability = 20% = 0.20

Find the z-score from the negative z table for 0.20

z score = -0.84

Put the values in z formula and find x.

z = (x - μ)/σ

-0.84 = (x - 57)/8

Simplifying;

x = -6.72 + 57

x = 50.28 minutes

Thus, finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes Rocket Run 5k.

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Rewrite the limit as

[tex]\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = \lim_{x\to0} \frac{5x}{\sin(5x)} \cdot \lim_{x\to0} \frac{\cos(5x)}5[/tex]

Then using the known limit,

[tex]\displaystyle \lim_{x\to0} \frac{\sin(x)}x = 1 \implies \frac1{\lim\limits_{x\to0}\frac{\sin(x)}x} = \lim_{x\to0}\frac x{\sin(x)}=1[/tex]

it follows that

[tex]\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = 1 \cdot \frac{\cos(0)}5 = \boxed{\frac15}[/tex]

The measure of the vertically opposite angle ∠A = 136°

From the given question;

∠A and ∠B are vertical angles.

Thus, ∠A = ∠B

The values are given as;

∠A = (2x +26)°

∠B = (3x − 29)°

Equating both;

(2x +26)°  =  (3x − 29)°

Simplyfying;

2x + 26 = 3x − 29

3x - 2x = 26 + 29

x = 55

Put the value of x in ∠A = (2x +26)°

∠A = (2x +26)° = 2x55 +26

∠A = 136°

Thus, the measure of the vertical angle ∠A = 136°.

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Question 14

[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]

Question 15

[tex]\binom{15}{6}=\frac{15!}{9!6!}=5005[/tex]

Using the normal distribution, the upper boundary, in inches, of a symmetric and centered interval of the sample averages with n = 167 that are within 0.92 standard deviation s of the mean is of:

67.21 inches.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering samples of 167, with the mean and standard deviation of the population given in the problem, the parameters are given as follows:

[tex]\mu = 66.9, \sigma = 4.33, n = 167, s = \frac{4.33}{\sqrt{167}} = 0.335[/tex]

The desired height is X when Z = 0.92, because it is 0.92 standard deviations from the mean and we want the upper limit, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

0.92 = (X - 66.9)/0.335

X - 66.9 = 0.92 x 0.335

X = 67.21 inches.

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Using multiplication of matrices, it is found that the values of a and b are given as follows:

To multiply matrices, we multiply the rows of the first matrix by the columns of the second matrix.

Hence, the element of the row 1 and column 1 of the product matrix is given by the multiplication of the row 1 of the first matrix by the column 1 of the second matrix, then:

3(-1) -2(2) + a(3) = 5

-3 - 4 + 3a = 5

3a = 12

a = 4.

The element of the row 2 and column 2 of the product matrix is given by the multiplication of the row 2 of the first matrix by the column 2 of the second matrix, then:

4(3) - 1(b) + 2(-2) = 2

12 - b - 4 = 2

8 - b = 2

b = 8 - 2

b = 6.

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Answer:

16

Step-by-step explanation:

112/7=16, 16x4=64, 16x3=48, 64-48=16

1.4 repeating as a simple fraction is 13/9

Simple fraction is a fraction with whole number as the numerator and denominator. The top term is called numerator and the bottom term is called denominator.

Decimal number is a number that consist of one whole number and a fractional part and those are  separated by a decimal point

The repeating decimal = 1.4444

Consider the value x = 1.4444

Then multiply 10 on both side of the equation

We get

10x = 14.444

Subtract x from the 10x

10x-x = 14.444-1.4444

Subtract the like terms in the equation

9x = 13

Move 9 to the right hand side

x = 13/9

Hence, 1.4 repeating as a simple fraction is 13/9

The complete question is

1.4 repeating as a fraction in simplest form

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The equivalent value to 2.76 is C. two and nineteen twenty-fifths.

An equivalent value is an amount or numerical expression possessing the same value as the other.

Equivalent values are expressed as equations, using the equation symbol (=).

Equations are a class of the properties of mathematical expressions, including numbers and variables.

Two and nineteen twenty-fifths = 2¹⁹/₂₅.

When expressed as a decimal, 2¹⁹/₂₅ = 2.76.

Thus, 2.76%, 27.6%, or twenty-five over nineteen are not equivalent values of 2.76 but 2¹⁹/₂₅.

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The equation of the line that has the given features is y = -1/3x - 4

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

From the question, the given parameters are

Slope, m = -2

y-intercept, c = 9

As a general rule:

A linear equation is represented as

y = slope * x + y-intercept

This can be rewritten as

y = mx + c

Next, we substitute the known values in the above equation

So, we have the following equation

y = -2x + 9

The above equation cannot be further simplified

So, we have

y = -2x + 9

However, it can also be expressed as

y = 9 - 2x

Hence. the linear equation is y = -1/3x - 4

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Possible question

What is the equation of a linear equation that has the following features

Y-intercept 9 and slop -2

The value of x is 1 , -5 and y is 3 , -3

A[tex]x^{2}[/tex] + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilized in a wide variety of situations. You may be surprised to learn that a quadratic equation accurately predicts a rocket's trajectory after launch. Additionally, a quadratic equation is useful in many fields, including physics, engineering, astronomy, etc.

Given that : the linear-quadratic system of equations is y = [tex]x^{2}[/tex] +5x - 3 and y -x=2 .

y = [tex]x^{2}[/tex] +5x - 3 .....(i)

y = 2+ x.....(ii)

put the value of y in equation i

2 + x = [tex]x^{2}[/tex] +5x - 3

[tex]x^{2}[/tex] +4x - 5 = 0

[tex]x^{2}[/tex] +(5-1)x - 5 = 0

x(x + 5) -1(x + 5) = 0

(x -1)(x + 5)=0

x=1

x=-5

now put value of x in equation ii

y = 2+ x.....(ii)

y = 3 (when x = 1)

y = -3(when x = -5)

The value of x is 1 , -5 and y is 3 , -3

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The table representing the exact values of y from the function is attached below.

In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The sets X and Y are referred to as the function's domain and codomain, respectively.

The given function is of the form y = 2x .

Now let us find the respective values of y for the given values of x.

At x = -2

y = 2x = 2 × (-2) = -4

At x = -1

y = 2x = 2 × (-1) = -2

At x = 0

y = 2x = 2 × (0) = 0

At x = 1

y = 2x = 2 × (1) = 2

At x = -2

y = 2x = 2 × (2) = 4

Therefore the table to represent this y-values of the function is [tex]\begin{table}[]\begin{tabular}{lllll} & & & & \\ & & & & \\ & & & & \\ & & & & \end{tabular}\end{table}[/tex][tex]\begin{table}[]\begin{tabular}{ll} & \\ & \\ & \\ & \\ & \end{tabular}\end{table}[/tex]attached below.

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Answer:

I hope this helps. Four is greater than six times a number t in inequality form is 4 › 6 * t

⇒Plug in places the given values in the expression x-2c and simplify

given that x=3 and c =-3

⇒[tex]=(3)-2(-3)\\=3+6\\=9[/tex]

The expression evaluated at the given variables is equal to 9.

In a case whereby Apollo Spas services 298 hot tubs and each hot tub needs 175 mL of muriatic acid,number of liters of acid that are needed for all of the hot tubs is 52.15 litres.

The unit conversion can be described as the changing of bone unit to another.

We can calculate the number of liters of acid that are needed as (298 * 175)= 52150ml

This can be converted to liter by dividing  52150ml by 1000 which  can be done as (52150ml/1000) = 52.15 litres of acid.

Therefore, the  liters of acid are needed for all of the hot tubs can be expressed as the 52.15 litres

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Let the Length of the rectangle be l and the width of the rectangle be w

The width of a rectangular field is 3 meters less than its length, this can be represented as

w = l - 3

Given the perimeter = 58meters

Perimeter of the rectangle = 2(l + w)

58 = 2(l + l-3)

58 = 2(2l - 3)

58 = 4l - 6

58 + 6 = 4l

64 = 4l

4l = 64

l = 64/4

l = 16

w = l - 3

w = 16 - 3

w = 13

Hence, the length of the rectangle is 16 meters while the width is 13 meters.

Answer:

Slope-intercept form is given as y = mx + c where m is the slope and c is the y-intercept.

Since slope = 2, equation is y = 2x + c.

Substitute (-1,2) into the equation to find c.

2 = 2(-1) + c

c = 4

Hence, equation is y = 2x + 4

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.

Any two ordered pairs can be used to create a solution set on a graph by connecting them with a straight line. Thus, any point along this graphed line would be included in the solution set.

There is only one solution that holds true for both equations if the equations' graphs cross. There are no solutions that hold for both equations if the equations' graphs do not meet (for instance, if they are parallel).

The answer for this graph is -4.

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Answer:

[tex]x = \frac{20}{91}[/tex]

Step-by-step explanation:

Since this is a proportion, first you need to cross multiply.

[tex]\frac{20}{7}[/tex] × [tex]\frac{2}{25}[/tex] = [tex]\frac{40}{175}[/tex]

[tex]\frac{26}{25} x = \frac{40}{175}[/tex]

Now multiply both sides by the reciprocal of 26/25 which is 25/26.

[tex]\frac{25}{26} (\frac{26}{25} )x=\frac{40}{175} (\frac{25}{26} )\\[/tex]

Cancel on the right side, 25 and 175, by 25.  Then cancel 40 and 26 by 2.

[tex]x = \frac{20}{7} (\frac{1}{13} )[/tex]

[tex]x = \frac{20}{91}[/tex]