What is the value of (−13)4

Answer:

[tex]f^{-1}(x)=\dfrac{3-x}{5-x}, \quad \{x|x\neq 5\}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\dfrac{5x-3}{x-1}[/tex]

As the given function is a rational function, the domain and range are restricted.

f⁻¹(x) is the notation for the inverse of the function.  

The inverse of a function is a reflection in the line y = x.

To find the inverse of the given function, swap f(x) for y:

[tex]\implies y=\dfrac{5x-3}{x-1}[/tex]

Rearrange the equation to isolate x:

[tex]\implies y(x-1)=5x-3[/tex]

[tex]\implies xy-y=5x-3[/tex]

[tex]\implies 3-y=5x-xy[/tex]

[tex]\implies 3-y=x(5-y)[/tex]

[tex]\implies x=\dfrac{3-y}{5-y}[/tex]

Swap the x for f⁻¹(x) and the y for x:

[tex]\implies f^{-1}(x)=\dfrac{3-x}{5-x}[/tex]

The range of the function is the domain of the inverse function.

Therefore, the domain of the inverse function is restricted:

32/3

Step-by-step explanation:

5 = 3(x-9)

5 = 3x - 27

5 + 27 = 3x

32 = 3x

x = 32/3

Answer:

x = 15

Step-by-step explanation:

since the sides are bisected, the inner line is parallel to the largest side.

8x+9 + 5x-24 = 180

The compound interest is quaterly then answer is $266,022.2639 and when it is in continuously then answer is $275,579.4095

Quarterly compounding is what?

Compounding quarterly is the term used to describe the amount of interest that is earned on a quarterly basis on a savings account or investment where the interest is also reinvested. As most banks offer interest income on the deposits, which compounds quarterly, this information is useful in computing the fixed deposit income. It can also be used to figure out any revenue from money market instruments or other financial products that pay quarterly income.

What Does Constant Compounding Mean?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. While this is not attainable in practice, the concept of continually compounded interest is crucial in finance. Given that most interest is compounded on a monthly, quarterly, or semiannual basis, this is an extreme example of compounding.

a) A = P(1 + r/n)nt  

P = $25000

r = 12% = 0.12

t = 20 years

n = 4

A = 25000(1 + 0.12/4)(4)(20)

A = $266,022.2639  (Answer)

b) A = Pert

P = $25000

r = 12% = 0.12

t = 20 years

A = 25000e(0.12)(20)

A = $275,579.4095   (Answer)

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Answer:

if the selling price of the radio is Arya 4321 and loss e79 find the cost price of the radio

For the given roots and point, the polynomial is:

p(x) = (62/72)*(x + 3)²*(x - 2)²*(x + 2)

We know that a polynomial with leading coefficient a and the roots:

x₁, x₂, ..., xₙ

Can be written as:

p(x) = a*(x - x₁)*...*(x - xₙ)

Here we have the roots:

-3, -3, 2, 2, -2

Then we can write:

p(x) = a*(x + 3)*(x + 3)*(x - 2)*(x - 2)*(x + 2)

p(x) = a*(x + 3)²*(x - 2)²*(x + 2)

Now we also know that our polynomial passes through (0, 62), then:

p(0) = 62 = a*(0 + 3)²*( 0 -2)²*(0 + 2)

62 = a*9*4*2

62/(9*4*2) = a

62/72

then the polynomial is:

p(x) = (62/72)*(x + 3)²*(x - 2)²*(x + 2)

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For every 4 beef cattle there is 3 dairy cattle. For 24 dairy cattle there will be 32 beef cattle as per the given ratio of 3:4.

An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls). The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two things.

Here,

a. No for every 4 beef cattle there is 3 dairy cattle.

b. 4/3=x/24

x=4*24/3

x=32 beef cattle

There are 3 dairy cattle for every 4 beef cattle. According to the stated ratio of 3:4, there will be 32 beef cattle for every 24 dairy cattle.

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The minimum age of Johnny is 21 as calculated by linear inequality.

Let Johnny 's age be x.

hence bobby's age = (x+5)/2

Now the sum of their ages is over 66 years.

So we will set an inequality to find the minimum age of Johnny.

x + (x+5)/2 > 66

or, 2x + x + 5 > 66

or, 3x > 61

or, x > 20 1/3

Therefore age cannot be fraction hence the minimum age of Johnny is 21 years.

In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On that number line, size comparisons between two numbers are typically done. Different notations can be used to represent various kinds of inequalities, including:

A is smaller than b, as shown by the symbol a < b.

When the expression a > b is employed, it means that a is greater than b.

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The plan that fits to Landyn's budget is plan B

What is percentage and how to calculate it?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%." Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. Two methods exist for calculating a percentage. By adjusting the fraction's denominator to 100 and applying the unitary approach.

We are given that Landyn's current monthly net pay is $560

And he does not wish to spend more than 10% of his current net pay

That means not more that $56

Now we are given 3 choices

Out of which the third one is more than 60 hence this rules out the third option. Now the first option the value is 55+55(0.005) which again is more than $56

Consider the option B)

50 + 50(0.05)

= 52.5

Which is less than $56

Hence, The plan that fits to Landyn's budget is plan B

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The five number from the box plot is presented as follows:

A box and whisker plot shows five things of a distribution, listed as follows:

The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.

The data set's maximum value.

These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.

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The Sample space for number greater than 3= {4, 5, 6}

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

A number cube with faces labeled from 1 to 6 will be rolled once.

so, Sample Space = { 1, 2, 3, 4, 5, 6}

sample space for number greater than 3= {4, 5, 6}

Thus, the probability is 3/6 or 1/2.

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The true statement when the frozen yogurt stand charges per ounce of frozen yogurt purchased is B. Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.

In the scenario, the total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.

In this case, it is important to note that Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.

For example, for 2 ounces, this will be:

= 0.45f + 1

= 0.45(2) + 1

= 0.9 + 1

= $1.9

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Answer:

-1,-2,0

Step-by-step explanation:

n(2-3)

1st term=n(2-3)

substitute value

1(2-3)=-1

2nd term=2(2-3)=-2

3rd term=3(3-3)=0

The picoseconds that are there in 6 minutes is 3.6 × 10^14.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

In this case, picosecond is one trillionth of a second. If one trillionth = 1 × 10^12

The seconds in 6 minutes will be:

= 60 × 6

= 360 seconds

= 3.6 × 10^2

The picoseconds in 6 minutes will be:

= 1 × 10^12 × 3.6 × 10^2

= 3.6 × 10^14

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Answer:

Step-by-step explanation:

AC is the diagonal of the parallelogram ADCB.

q is half of AC, therefore:

Substitute values and solve for x:

Find the length of AC:

Answer:

a) velocity

b) displacement

Using the formula, the real of z is 2 and the linear form of z is [tex](x-2)(x^2+2x+4)[/tex].

In the given question,

The given expression is z=x^3−8

We can given expression as [tex]x^3-8=(x)^3-(2)^3[/tex]...............(1)

We have to find the real root of the z.

We also have to find the z as a product of linear terms.

To solve the given expression using the formula

[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

If we compare equation 1 to the [tex]a^3-b^3[/tex].

After compare we get a=x and b=2

Now the linear form of the given expression is

[tex]z=(x)^3-(2)^2[/tex]

[tex]z=(x-2)(x^2+2x+(2)^2)[/tex]

Simplifying

[tex]z=(x-2)(x^2+2x+4)[/tex]

Now the real root of of z;

x-2=0

x=2

Hence, the real of z is 2 and the linear form of z is [tex](x-2)(x^2+2x+4)[/tex].

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The arithmetic mean of the numbers is -6 11/15

Arithmetic mean is often referred to as the mean or arithmetic average. It is calculated by adding all the numbers in a given data set and then dividing it by the total number of items in that set.

therefore, arithmetic mean= sum of items/ no of items

The average of numbers,7, 17, 1/3 ,-2/5, -12 ,7, - 121, 49,-16,-9and 4 is obtained by adding the numbers to together and dividing the result by the total frequency.

The sum of the numbers is 7 +17 +1/3-2/5 -12+7 - 121+ 49-16-9+ 4= -1111/15

the total number of items in the set is 11

therefore arithmetic mean = -1111/15÷ 11

= -1111/15×1/11

=-101/15

= -6 11/15

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Answer:

-4

Step-by-step explanation:

When answering questions like these first, combine like terms you get 3x+5 =3x+8, Subtract 5 from both of the sides you get 3x=3x+3 remove 3x from both sides and you got 0=3 this is a contradicting statement meaning no solution ∅

B) Distribute first, 3x + 2 -x  = x + 3 + 3x +4

2, Combine the like terms 2x - 1 = 7 + 4x

3, Isolate variable and constants 2x = 8 + 4x

3(1) Cont- Isolation -2x = 8

Thus divide both side by -2 giving us -4

The image of point (2,0) after the transformation involving the dilation and the rotation is given as follows:

(0, -1).

The first transformation applied to the point is a dilation, which multiplies the coordinates of the point by the scale factor.

The point has these following coordinates:

(2,0).

The scale factor of the dilation is:

k = 1/2 = 0.5.

Then each coordinate of the point is multiplied by 0.5, hence:

Hence the coordinates are:

(1,0).

The rule for a rotation of 270º clockwise around the origin is:

(x,y) -> (y,-x).

Then:

Thus the coordinates of the image are given as follows:

(0, -1).

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Perimeter of triangle BCF is 19.24 units. Area of triangle BCF is 15 [tex]units^{2}[/tex].

Distance formula = [tex]\sqrt{(x1-x2)^{2}+(y1-y2)^{2} }[/tex]

Perimeter = a + b + c

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

      s = [tex]\frac{a+b+c}{2}[/tex]

Given, B(3,2), C(1,-2), F(-3,5).

BC = a  = [tex]\sqrt{(3-1)^{2} +(2+2)^{2} }[/tex]

            = [tex]\sqrt{2^{2} +4^{2} }[/tex]

            = [tex]\sqrt{4+16}[/tex]

            = [tex]\sqrt{20}[/tex]

            = 4.47 units

CF = b = [tex]\sqrt{(1+3)^{2} +(-2-5)^{2} }[/tex]

           = [tex]\sqrt{4^{2} +7^{2} }[/tex]

           = [tex]\sqrt{16+49}[/tex]

           = [tex]\sqrt{65}[/tex]

           = 8.06 units

BF = c = [tex]\sqrt{(3+3)^{2} +(2-5)^{2} }[/tex]

           = [tex]\sqrt{6^{2} +3^{2} }[/tex]

           = [tex]\sqrt{36+9}[/tex]

           = [tex]\sqrt{45}[/tex]

           = 6.71 units

Perimeter = a + b + c

                = 4.47 + 8.06 + 6.71

                = 19.24 units

s = [tex]\frac{a+b+c}{2}[/tex]

 = [tex]\frac{19.24}{2}[/tex]

 = 9.62

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

        = [tex]\sqrt{9.62(9.62-4.47)(9.62-8.06)(9.62-6.71)}[/tex]

        = [tex]\sqrt{9.62*5.15*1.56*2.91}[/tex]

        = [tex]\sqrt{224.91}[/tex]

        = 14.99

        ≈ 15  [tex]units^{2}[/tex]

Hence, perimeter is 19.24 units and area is 15  [tex]units^{2}[/tex].

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₁₁C₈ * ₄C₃ as related to permutations is ₁₁P₈ / 8! * ₄P₃ / 3!

The term combination refers to a method of choosing where order does not matter. an instance forming 3 letter word from ABC. the combination is ₃C₃ = 1

In permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6

All the items above are different permutations however for combination they are same.

The difference mathematically is dividing by the number of arrangements

₃C₃ = 3! / (3!(3-3)!) = 3! / (3!* 0!) = 3! / 3! = 1

₃P₃ = 3! / (3-3)! = 3! / (0!) = 3! / 1 = 3! = 6

Therefore ₃C₃ = ₃P₃ / 3!

similarly

₁₁C₈ * ₄C₃ = ₁₁P₈ / 8! * ₄P₃ / 3!

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The equation of the parabola exists y = 3/80(x - 20)² - 15

In the coordinate plane, a parabola exists algebraically represented using the standard equation. A parabola's general equation exists written as,

y = a(x - h)² + k

where (h, k) signifies the vertex.

y² = 4ax is the typical equation for a normal parabola.

substitute the values in the above equation, we get

y = a(x - 20)² - 15

simplifying the above equation, we get

0 = a(0 - 20)² - 15

0 = 400a - 15

a = 15/400

a = 3 / 80

Therefore, the equation of the parabola exists y = 3/80(x - 20)² - 15.

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Answer:

d. -15

Step-by-step explanation:

f(x) = 3x - 9, when x = -2

Input -2 into the function for x and solve:

f(-2) = 3(-2) - 9

f(-2) = -15

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The total number of movies that the students saw is 105.

I got the answer by adding all of the values that the students saw. So I add 14,10,16,15...etc. which gives me the total of 105.

If the fuel efficiencies of each of the cars that week is  20 gallons of gas and  25 gallons of gas.

Let x represent the gallons consumed by car 1

Let y represent gallons consumed by car 2

Formulate an equation:

30x+40y = 1600      equation 1

x+y = 45                equation 2

Substituting equation  2 into equation 1,

30x+40(45-x) = 1600

30x+ 1800-40x = 1600

-10x+1800 = 1600

-10x = -200

Divide both side by -10x

x = -200/-10

  x = 20

Substitute value of x into equation 2

x+y = 45

20+y = 45

     y = 25

Hence,

Car 1 consumes 20 gallons of gas and Car 2 consumes 25 gallons of gas.

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The slope of the line that is perpendicular to y is m=6/7.

What do you mean by slope?

A number used to define a line's direction and steepness in mathematics is called the slope or gradient of the line.

The slope is denoted by m,

m = slope

According to the data in the given question:

We have to determine the slope of line that is perpendicular to y,

y=6/7x+2

For the slope, we need follow this equation, where m is slope,

y=mx+b............(1)

In the given question,

m=6/7

Therefore, the slope of the line is m=6/7.

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