Find the inverse function of y=
x - 7 divided by 4

Answer:

20.15

Step-by-step explanation:

Answer:

20.15

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Geometric series converge if |r| < 1.

A) r = 3

B) r = 1/2

C) r = -4

D) r = 2

Only B has |r| < 1.

The converging sequence of geometric progression is given by the relation A = 1 + 1/2 + 1/4 + 1/8 ... where the common ratio r = 1/2

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

A = 1 + 1/2 + 1/4 + 1/8 ...

Now , the common ratio r of the GP is

r = second term / first term

On simplifying , we get

r = ( 1/2 ) / 1

r = 1/2

So , when | r | < 1 , the GP is a converging series

Hence , the GP is converging series

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The rule for the transformed function is g(x) = -x² - 4, thus, the correct option is c

We can see that f(x) is the quadratic function:

f(x) = x²

Notice that function g(x) opens downwards, then we have a reflection over the x-axis, so we have:

g(x) = -x²

And also, the vertex is at y = -4, so we have a translation down of 4 units, then we have:

g(x) = -x² - 4

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Distance = 1 1/2 miles = (1x2+1) /2 = 3/2 miles

Time = 1/5 hour

Speed rate = Distance / time

Replacing:

To divide we can multiply by the inverse of the second fraction:

Speed rate = 3/2 x 5/1 = 15/2 miles per hour

Answer:

4 x 5 = 20

7 x 5 = 35

the cost per ticket is constant because the two numbers are both multiplied by five in order to get the main cost of the tickets

Step-by-step explanation:

The cost of each pound of grass seed is $6.

A graph of the solution for the cost of each pound of grass seed is shown below.

In order to determine the cost of each pound of grass seed, we would assign a variable to the cost of each pound of grass seed and then translate the word problem into an algebraic linear equation.

Let the variable x represent the cost of each pound of grass seed.

Since Lori bought 3.6 pounds of grass seed and she was charged $22.90, including a tax of $1.30, an algebraic linear equation that best represent this situation is given by;

3.6x + 1.30 = 22.90

3.6x = 22.90 - 1.30

3.6x = 21.60

x = 21.60/3.6

x = $6.

In conclusion, we would sue an online graphing calculator to plot the solution for the cost of each pound of grass seed as shown in the image attached below.

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Answer:

The correct answer is D

Step-by-step explanation:

In order for a relation to be a function, every input for x can only have one output. Therefore, D is the correct answer.

Answer:

D

Step-by-step explanation:

A function is a relation where every input has only 1 output.

Inputs are the x's and outputs are the y's.

Answer a is missing an input.  You have (,0)  The first number is missing.

B is not a function because the input -2 has to outputs 2 and 4.

C is not a function because the input 0 has two outputs 5 and 4

\((\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{5}}} \implies \cfrac{-7 -1}{3 -5} \implies \cfrac{ -8 }{ -2 }\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{4}(x-\stackrel{x_1}{5})\)

\(y-1=4x-20\implies y=4x-19\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

Answer:

a. How much will she have to pay back at the end of the 1 year?

Answer: $540

b. How much interest does she have to pay?

Answer: $40

Step-by-step explanation:

Simple interest for any amount p is given by

SI = p*r*t/100

where r is the annual rate rate of interest

t is the time

____________________________________________

Given

p= $500 (loan taken)

r = 8%

t = 1 year

SI = 500*8*1/100 = 40

Thus, $40 is the interest charged in a year.

Total money paid at the end of one year = loan taken  + interest charged

                                                                    = $500 + $40

                                                                    = $540

a. How much will she have to pay back at the end of the 1 year?

Answer: $540

b. How much interest does she have to pay?

Answer: $40

The aprent function is:

and the new function is:

This is related as follows:

The new function is relfected about the x axis, then it is translated 5 units to the left and 2 units up.

This is shown in the following graph:

where the red graph is f(x) and the blue one is j(x).

Now, the vertex of the original function is the origin; whereas for the second function is in the point (-5,2).

subtracting (c ^ 2 - 4c + 7) from (7c ^ 2 - 5c + 3) would give 6c² - 9c -4

Given the expressions as

(c ^ 2 - 4c + 7)

(7c ^ 2 - 5c + 3)

We are to substract expression 2 from expression 1

In doing this, we need to know the BODMAS rule ( bracket, of, division, multiplication, addition and subtraction). This would help in finding the solution

(7c ^ 2 - 5c + 3) -  (c ^ 2 - 4c + 7)

Expand the bracket

7c² - 5c + 3 - c² - 4c + 7

collect like terms

7c²- c² - 5c - 4c + 3 - 7

Add or substract the like terms

6c² - 9c -4

Thus, subtracting (c ^ 2 - 4c + 7) from (7c ^ 2 - 5c + 3) would give 6c² - 9c -4

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Answer:6c^2-c-4

Step-by-step explanation:

(7c^2-5+3)-(c^2-4c+7)

7c^2-5c+3-c^2+4c-7

Rearrange the terms

7c^2-c^2-5c+4c+3-7

Combine like terms

6c^2-c-4

Answer:

First Option

Step-by-step explanation:

6 divided by 2 = 3 per notebook

Answer:

The store charges $3 per notebook.

The store charges $15 for 5 notebooks.

The graph of the new function would be less steep than the original one but would not be shifted up or down or left or right.

Thus, the correct option is: It would be less steep.

In mathematics, a graph is a visual representation of a set of objects where some pairs of the objects are connected by links. The objects, which are usually represented by points, are called vertices or nodes, and the links, which are usually represented by lines or arcs, are called edges.

The original function y = 5x + 1 has a slope of 5, which means that for every 1 unit increase in x, y increases by 5 units.

The new function y = 2x + 1 has a slope of 2, which is less steep than the slope of the original function.

However, the y-intercept of both functions is the same, which is 1.Therefore, the graph of the new function would be less steep than the original one but would not be shifted up or down or left or right.

Thus, the correct option is: It would be less steep.

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Answer:

  $700 for a chair and a table

Step-by-step explanation:

Let t and c represent the price of a table and a chair, respectively. The given relations are ...

  10c = 4t

  15c +2t = $4000

Divide the first equation by 2 and substitute for 2t:

  5c = 2t

  15c +5c = $4000

  20c = $4000

  c = $200

  t = 5c/2 = 5($200)/2 = $500

The total price of a chair and a table is ...

  $200 +500 = $700 . . . . price of a chair and a table

Answer:

7:01

29%

Doyan of low

Shiman 1-R-1

Flous 1-1 Gambe 1-4-20

12 dual purpose

Martins 1-2-3 Flores 1-2, 1-3, 14

Gamba 2-1-5

Custand 1-4, 2-1

Conditions " humanitarian groups Salahiel 1-1-1, 1-1-2, 1-2-3 1-R-5, 2-L-2, 2-L-3, 2-14, 2-1-5, 2-RI

Flores 1-30

Munting 1-2-4

Gumbon 1-1-3 CDP 1-1-3

Status oppose ending 742 Montoya 1-1, 1-2, 1-3

federal courts challenge

Gamboa 1-R-2 Custom 1-7

CDP 1-L-36, 1-2-4

de Vogue 1-2-1, 2-1-5, 2-L-6

7 expulsions at boders

root causes textul Amer.

Cop 1-L-34, 1-1-2, 1-R-4

Border Report 1-2

CDP 1-R-2, 1-R-3 Montoya 1-8

Custarda 2-2

=

CLOSE

Hopes this helps :)

If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.

The rational zero theorem is used to determine the rational roots of a polynomial function.

Rational Zero Theorem statement:-

The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients

f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,

p is a factor of the constant a₀,

q  is a factor of the leading coefficient an,

and p and q are relatively prime.

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Answer:

Volume is 339.12 cubic units

Step-by-step explanation:

\({ \tt{volume = \pi {r}^{2} h}}\)

» r is radius

» h is height

\({ \tt{v = 3.14 \times ( {3)}^{2} \times (12)}} \\ { \tt{v = 3.14 \times 108}} \\ { \underline{ \tt{ \: \: v = 339.12 \: \: units {}^{3} } \: \: }}\)

The length of the longer wire is 82 feet.

Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.

We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.

In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:

cos(θ) = adjacent/hypotenuse = 16/L

Given that cos(θ) = 8/41, we can substitute this value into the equation:

8/41 = 16/L

To solve for L, we can cross-multiply and solve for L:

8L = 41 * 16

L = (41 * 16)/8

L = 82

Therefore, the length of the longer wire is 82 feet.

In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.

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Answer:

5 units

Step-by-step explanation:

to find out the answer for this you must first find the distance between 7 and 4 and then 6 and 10

then you would square them and then add them

lastly you would take the square root of that and youd have your answer

so

7 - 4 = 3

6 - 10 = -4 (just use 4)

3^2 + 4^2 = 9  + 16 = 25

then you take the square root of this

sqrt(25) = 5

that is your answer

To solve this problem, you will use the Distance Formula to find the distance between two coordinate points.

The Distance Formula is defined as follows:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

We must title our points by the standard coordinate naming system:

\((x_1, y_1) \ \text{and} \ (x_2, y_2)\)

Therefore, our points can be labeled:

Now, substitute the known values as the variables in the Distance Formula:

\(d=\sqrt{(4 - 7)^2 + (10 - 6)^2}\)

You must know the BPEMDAS acronym, which stands for:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Simplify the expression using BPEMDAS:

\(d=\sqrt{(-3)^2 + (4)^2}\)

Remember that when a number is raised to the 2nd power, it is the same thing as multiplying the number by itself:

\(-3\times-3 = 9\)

\(4\times4=16\)

Simplify further by removing the parentheses:

\(d=\sqrt{9+16}\)

Compute the additive operation:

\(d=\sqrt{25}\)

The number that is placed inside of a square root symbol (or a radical symbol) is referred to as the radicand.

In this situation, the radicand is 25.

To simplify the radicand, you may either use a calculator to compute the result, or you can determine which number raised to the 2nd power will result in a final answer of 25.

In this case, we can determine that 5² will result in a final answer of 25.

\(5^{2} = 25\)

The final answer is 5 units.

Answer:

No solution is posible from the information provided

Step-by-step explanation:

Answer:

1. B

2. C

3. 8, 36

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer:

B

Step-by-step explanation:

==========================================================

Explanation:

There are 170 million martians surveyed, note the "170" in the bottom right hand corner.

Of this total, there are 48 million who have completed 4 (or more) years of college. Refer to the bottom of the "4 or more" column.

This must mean that 170 - 48 = 122 million martians have not completed 4 or more years of college. This figure of 122 is effectively the sum of nearly everything in the bottom row, except for the 48 and the 170. In other words, 27+51+44 = 122.

We divide the values 122 over 170, and reduce fully, to get the answer we're after.

122/170 = (2*61)/(2*85) = 61/85

This can be thought of as "if we had 85 million people total, then 61 million of them did not complete 4 or more years of college".

Side note: 61/85 = 0.7176 = 71.76% approximately

The probability that a randomly selected martian, has not completed four years (or more) of college is P = 0.72.

We want to find the probability that a randomly selected martian over the age 25, is not completed over 4 years of studies.

In the table, we can see that we have a total of 170 Martians.

Of these 170, only 48 have completed more than 4 years of college.

Then: 170 - 48 = 122 have not completed 4 years or more.

Then the probability that a randomly selected martian has not completed 4 years or more of college is:

P = 122/170 = 0.72

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The average speed formula is given by:

\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)

Let's calculate the total distance first. The car travels 120 miles from point A to point B, and then returns the same distance. Therefore, the total distance is \(\displaystyle\sf 2 \times 120 = 240\) miles.

Now, let's calculate the total time. The time taken to travel from A to B can be calculated using the formula \(\displaystyle\sf \text{Time} = \frac{\text{Distance}}{\text{Speed}}\).

For the journey from A to B:

\(\displaystyle\sf \text{Time}_1 = \frac{120}{30} = 4\) hours

For the return journey from B to A:

\(\displaystyle\sf \text{Time}_2 = \frac{120}{40} = 3\) hours

The total time for the round trip is the sum of the individual times:

\(\displaystyle\sf \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4 + 3 = 7\) hours

Now, we can calculate the average speed:

\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{240}{7} \approx 34.29\) miles per hour.

Therefore, the average speed for the round trip is closest to 34.29 miles per hour.

The Circle Sector Area correct answer is: O n(30in)2

To calculate the area of the sector in the circle, you would typically use the formula:

Area = (θ/360) * π *\(r^2\)

where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

From the options you provided, the correct choice would be:

O n(30in)2

This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)

Therefore, the Circle Sector Area correct answer is: O n(30in)2

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For the grapes he paid 5.695 and the cherries 10.005. The cherries cost him $4.64 extra, which is the correct answer.

3 x 1.45 = 4.35

1.45 x .2 = .29

4.35 +.29 = 4.64

A cherry is a fruit that is a fleshy drupe that is produced by numerous plants in the genus Prunus. Prunus avium and Prunus cerasus, two species with sweet and tart varieties, respectively, are cultivars from which commercial cherries are produced.

Cherries have a low calorie count and are packed with fiber, vitamins, minerals, nutrients, and other healthy elements. A, C, and K vitamins are provided. Potassium, magnesium, and calcium are also present in each fruit with a long stem. Beta-carotene, an antioxidant, and choline, a necessary nutrient, are also brought by them.

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