Consider the following scenario describing the residents of Charlestown: The list pairs resident's ages with their zip codes.

Does this scenario represent a function?

The equation which is equivalent to -i among the answer choices is; i^(15), option A

It follows from the concept of complex numbers that the representation -i stands for √-1 and on this note, it follows that;

i² = -1

i³ = -i

i⁴ = 1

Hence, it follows that;

i^(15) = i⁴ × i⁴ × i⁴ × i³ = 1 × 1 × 1 × -i = -i.

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The two real values that are not in the domain of the composition are x = 2 and x = -2.

Here we have:

f(x) = 1/x

g(x) = x^2 - 4

The composition is:

f°g = f(g(x)) = 1/(x^2 - 4)

The two values that are not in the domain are the values of x such that g(x) = 0, because we can't divide by zero.

g(x) = 0 = x^2 - 4

4 = x^2

±√4 = x

±2 = x

So g(x) = 0 when x = 2 or x = -2, so these are the two real values that are not in the domain of f°g.

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The value of the washing machine after 6 years with 20% depreciation every year is $78.64.

Depreciation is the practice of subtracting a business asset's cost over a number of years as opposed to just one.

Depreciation is used to adjust the cost of a productive asset with a longer-than-year-long useful life to the income generated by operating the asset. The expense of the asset is typically dispersed across the years that it is utilized.

Calculation for the asset value after depreciation of 20% every year.

The purchasing cost of washing machine is $300.

The rate after 6 years is-

Rate = purchased price×[tex](1-r)^{t}[/tex]

       = 300×[tex](1-0.2)^{6}[/tex]

       = 300×[tex]0.8^{6}[/tex]

       = 78.64

The cost of washing machine after 6 years will be $78.64.

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Using the given information, the percent error is 52%

From the question, we are to calculate the percentage error

From the given information,

Prediction = 23 people

Actual = 48 people

Using the formula,

[tex]Percent \ error = \frac{|Prediction - Actual|}{|Actual|}\times 100\%[/tex]

[tex]Percent \ error = \frac{|23 - 48|}{|48|}\times 100\%[/tex]

[tex]Percent \ error = \frac{|-25|}{|48|}\times 100\%[/tex]

[tex]Percent \ error = \frac{25}{48}\times 100\%[/tex]

Percent error = 52.083%

Percent error ≈ 52%

Hence, the percent error is 52%

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Answer:

[tex]y=\frac{3}{4}x+2[/tex]

Step-by-step explanation:

So when you express a linear function in slope-intercept form it's given in the form of y=mx+b, where m is the slope, and b is the y-intercept. This is because as x increases by 1, the y-value will increase by m (because multiplication), and since the slope is defined as rise/run, the rise will be m, and run will be 1, giving you a slope of m/1 or m. The reason b is the y-intercept, is because whenever the linear function crosses the y-axis, the x-value will always be 0. Meaning that mx will be 0 because m * 0 will equal 0... and that leaves b by it self, so b will determine the y-intercept.

So if you look at the graph, the linear function crosses the y-axis as (0, 2) so the value of b will be 2. This gives you the equation y=mx+2.

Now to calculate the slope, we can take any two points and see how much the rise was and how much the run was. It can also be more formally defined in the equation: [tex]y=\frac{y_2-y_1}{x_2-x_1}[/tex]. So let's take the points (0, 2) and (8, 8). As you can see the x-value increases by 8 or "ran" by 8, and the y-value increased by 6. So the rise over run in this case is 6/8 which can simplified as 3/4. That is the slope. This gives you the complete equation of: [tex]y=\frac{3}{4}x+2[/tex]

Answer:

x = 2

Step-by-step explanation:

The left side would be (3x - 12)
The right side would be (-4x+2)

In an equation, 3x - 12 = -4x+2

Combine all the letters on the left and plain numbers on the right,

3x + 4x = 12 + 2

Note: When you transfer to the other side of the equal sign, the number will change its sign.

Simplify the 3x + 4x = 12 + 2,

                     7x = 14

                      [tex]x=\frac{14}{7}[/tex]

                      x = 2

⊱________________________________________________________⊰

Answer:

Step-by-step explanation:

[tex]\large\begin{gathered} \sf{Simplify \ using \ the \ distributive \ property:} \\ \sf{3(x-4)=2(-2x+1)} \\ \ \sf{3x-12=-4x+2} \\ \rm{Move \ 12 \ to \ the \ right, \ with \ the \ opposite \ sign} \\ \ \sf{ 3x=-4x+2+12} \\ \rm{Move \ -4x \ to \ the \ left, \ wth \ the \ opposite \ sign.} \\ \sf{3x+4x=14} \\ \rm{Collect \ the \ like \ terms} \\ \sf{7x=14} \\ \rm{Divide \ the \ entire \ equation \ by 7.} \\ \sf{\dfrac{7x}{7}=\dfrac{14}{7} \\ \sf{x=2} \ \bigstar \end{gathered}[/tex]

Done!!

⊱______________________________________________________⊰

Answer:

h(x) = 2^(x) - 1.

Step-by-step explanation:

Let's look at each equation:

f(x) = -3x +7, Well as x increases, since it's multiplication, there are "going to be more" -3's, so it's going to be decreasing.

g(x) = -4(2^x). While 2^x is increasing, because "there are going to be more 2's multiplied by each other" as x increases, it's being multiplied by a negative number, so it's actually going to be decrasing

h(x) = 2^(x) - 1. Here's it's going to be increases as x goes towards infinity because "there are going to be more 2's multiplied by each other", and there isn't any negative sign, while there is a negative 1, it's constant, so the overall value will be increasing

Answer:

inverse variation: xy=20

Step-by-step explanation:

Direct Variation is when y increases as x increases and is linear

Inverse Variation is when y decreases as x increases although it's not linear and the x and y has a constant product.

By observing the table, you'll see as x increases, y decreases. You'll also notice a constant product of 20 between x and y. (2 * 10) =  20. (4 * 5) = 20. ( (8 / 1) * (5 / 2) = 40/2 = 20))... and so on. So the function can be represented as xy = 20

Answer:

awnser D is the only function

The graph of the inequality will be B. on a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.

It can be deduced that the coordinates satisfy the equation of the line.

3y = 2x - 12

Divide through by 3.

y = 2/3x - 4.

The slope is 2/3.

In conclusion, the correct option is B.

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Answer:

b

Step-by-step explanation:

The value of P(A and C) is 0.18

From the tree diagram, we have the following probability values:

P(A) = 0.6

P(C) = 0.3

The probability P(A and C) is then calculated as:

P(A and C) = 0.6 * 0.3

Evaluate

P(A and C) = 0.18

Hence, the value of P(A and C) is 0.18

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Using proportions, the percentage change in the cost of manufacturing the kitchen cabinet was a increase of 5.5%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The standard cost is given as follows:

S = 250 + 120 + 60 = $430.

After the increases, the price will be given as follows:

S = 250 x 1.1 + 120 x 1.08 + 60 x 0.82 = $453.8.

The price increased. The percent change, given by the change divided by the initial value, is:

P = 23.8/430 x 100% = 5.5%.

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Answer: Option 2

Step-by-step explanation:

The vertex must have a y-coordinate of 5, so eliminate options 3 and 4.

Also, since there must be a maximum, the coefficient of [tex]x^2[/tex] must be negative. So, eliminate option 1.

This leaves us with option 2.

The volume of the sphere is 2308.4 mm³

From the question, we are to determine the volume of the sphere

The volume of a sphere is given by the formula

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

Where V is the volume

and r is the radius

From the given information,

Diameter, d, of the sphere = 16.4 mm

r = 16.4/2

r = 8.2 mm

∴ [tex]V=\frac{4}{3}\times 3.14 \times 8.2^{3}[/tex]

V = 2308.394

V ≅ 2308.4 mm³

Hence, the volume of the sphere is 2308.4 mm³

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The angle based on the information given about the rail is 163°.

From the information given, the value of angle 2 will be:

17° + x = 180° (angle on a straight line)

Collect like terms

x = 180° - 17°

x = 163°

In this case, it should be noted that angle 1 and 2 are alternate angles. Therefore, angle 1 will be 163°.

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Answer:

A. Scalene

E. Obtuse

Step-by-step explanation:

Obtuse are angles that are greater than 90°

Scalene is not congruent sides.

Answer:

x = 1

y = -2

Step-by-step explanation:

x = 19 + 9y

3x- 3y = 9

________

3(19+9y)-3y=9

y=-2

x=19+9(-2)

x=1

(1,-2)

Answer:

[tex] - x = - 1 - 9y \\ \frac{ - x}{ - 1} = \frac{ - 1}{ - 1} - \frac{9}{ - 1} \\ x = 1 + 9y...(3) \\ 3(1 + 9y) - 3y = 9 \\ 3 + 27y - 3y = 9 \\ 3 + 24y = 9 \\ 24y = 9 - 3 \\ 24y = 6 \\ \frac{24y}{24} = \frac{6}{24} \\ y = \frac{1}{4} \\ \\ \\ \\ x = 9( \frac{1}{4} ) + 1 \\ x = \frac{9}{4} + 1 \\ x = \frac{13}{4} [/tex]

Step-by-step explanation:

ATTACHED IS THE SOLUTION!

Answer:

9

Step-by-step explanation:

Because line PQ and line PR are both tangent to circle S, it would result in them being equal. So first to find PQ, you would have to find the value of variable x. To do this you would set both equations equal to each other and solve

6x - 9 = 2x + 3

-2x       -2x

4x - 9 = 3

    +9   +9

4x = 12

x = 3

Now you have to substitute 3 back into the equation for PQ:

6(3) - 9

18 - 9

= 9

Resulting in PQ = 9, to check your answer, take the value of x (3) and substitute it into PR and you should also get 9

2(3) + 3

6 + 3

= 9

The expected number of pairs of adjacent cards which are both black is  650 / 51

For each pair of cards, the probability that they are both black is 26/52 * 25/ 51 = 25 / 102,

So since there are 52 pairs in the circle, the expected number of pairs which are both black is

25 / 102 * 52 = 650 / 51

Probability is genuinely how probable something is to happen. Every time we're unsure about the final results of an occasion, we can speak approximately the chances of sure results—how probably they're.

The evaluation of occasions governed by chance is referred to as statistics.

A sequence of movements where the outcomes are constantly unsure. The tossing of a coin, deciding on a card from a deck of playing cards, throwing a cube. It's far a single final results of an experiment. Getting a Heads even as tossing a coin is an event.

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The equivalent expression to2-1/y/3+1/y is [tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]

Equivalent expressions are expressions does not look the same but when a value is being replaced with their variable, they end up giving the same result.

From the information given:

We have are to determine the equivalent expression to:

[tex]\mathbf{=\dfrac{(2-\dfrac{1}{y})}{(3+ \dfrac{1}{y})}}[/tex]

So if we multiply both the numerator and the denominator with 1/y, we have:

[tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]

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Answer:

211.68 miles

Step-by-step explanation:

21.6 x 9.8

There are 120 five digit numbers that can be created

The digits are given as:

2, 3, 5, 7 and 8

Since there are no conditions, and the digits cannot be repeated.

Then the number of digits is:

Digits = 5!

Expand

Digits = 5 * 4 * 3 * 2 * 1

Evaluate

Digits = 120

Hence, there are 120 five digit numbers that can be created

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The value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.

The given quadratic expression needs to be expressed using the perfect square method to be of the form (x + b)² + c.

We express the quadratic expression x² + 1300x + 1300 using the perfect square method following these steps:

x² + 1300x + 1300

= x² + 2x(1300/2) + (1300/2)² + 1300 - (1300/2)²

= x² + 2x(650) + (650)² + 1300 - (650)²

= (x + 650)² + 1300 - 422500

= (x + 650)² - 421200.

Comparing this to (x + b)² + c, we get:

b = 650, and c = -421200.

Therefore, the value of c/b = (-421200)/650 = -648.

Therefore, the value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.

The question seems improper. The proper question is:

" The quadratic x^2+1300x+1300 can be written in the form (x + b)^2+c, where b and c are constants. What is c/b?"

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The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

x – 2 = √(2x – 1)

Square on both side, then we have

               (x – 2)² = 2x – 1

         x² – 4x + 4 = 2x – 1

         x² – 6x + 5 = 0

   x² – 5x – x + 5 = 0

x(x – 5) – 1(x – 5) = 0

       (x – 5)(x – 1) = 0

                         x = 1, 5

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

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Answer:

Please review the equation format.  I made an assumption (below) for this answer.

-0.57

Step-by-step explanation:

5x2 45x 24 = 0 is not a quadratic formula,

5x^2 + 45x + 24 = 0 is, however.  Also, it gives -.8.43 as one solution.  The other is −0.569351, or -0.57 to the nearest hundredth.

The other solution of the given quadratic equation would be -0.57

Quadratic Equation

An algebraic equation of the second degree in x is known as a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

The given quadratic equation is,

5x² + 45x + 24 = 0

Here,

a = 5

b = 45

c = 24

Applying the Quadratic Formula

The quadratic formula for the two roots of a quadratic equation is given as,

[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]       ........... (1)

and [tex]x=\frac{-b+\sqrt{b^{2}+4ac } }{2a}[/tex]   ............ (2)

Substituting the values of a, b, and c in equation (1), we get,

x = -8.43

Calculating the Second Root

Now, the other solution can be found by substituting the values of a, b, and c in the equation (2),

[tex]x=\frac{-45+\sqrt{45^{2}+4(5)(24) } }{2(5)}[/tex]

[tex]x=\frac{-45+\sqrt{(2505) } }{10}[/tex]

[tex]x=-0.57[/tex]

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Answer:

x = 4

Step-by-step explanation:

Since they are parallel, we use the formula  

[tex]\frac{part}{part} = \frac{part}{part}[/tex]

[tex]\frac{14}{x} =\frac{7}{2}[/tex]

7x = 28

x = 4

Answer:

A

Step-by-step explanation:

cone volume equals

V=π/3r²h

(1782=π/3r²h) multiplied by 3 to get rid of the denominator

5346=πr²h

cylinder v=πr²h by substitution the volume would be the same as cone 5346

Answer:

your question is wrong, it's not an expression but a quadratic equation. if so your answer will be x=8±2√7

Step-by-step explanation:

by using, completing the square method

x²-16x-4=0

x²-16x=4

x²-16x+(-16×0.5)²=4+(16×0.5)²

x²-16x-8²=4+8²

(x-8)²=68

x-8=√68

x-8=±2√7

so x=8±2√7

please next time write the correct question

The range of the function is f(x) <= 4

The attached graph is the missing piece in the question

The function f(x) is given as:

The above means that, the value of the function do not exceed y = 4

Hence, the range of the function is f(x) <= 4

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