Determine whether each relation is a function. If so, provide the domain and range.

Answer:

x =(-8+√-32)/6=(-4+2i√ 2 )/3= -1.3333+0.9428i

Step-by-step explanation:

Answer:

1. g < 8

2. d ≤ 6

Answer:

Step-by-step explanation:

Part A:

Rate of pay for David = [tex]\frac{\text{Change in earnings}}{\text{Change in hours worked}}[/tex]

                                            = [tex]\frac{3700-3200}{140-120}[/tex]

                                            = $25

Part B:

If he worked for number of hours = x

Then the function representing the earning will be,

f(x) = 25x + b

For an ordered pair (120, 3200),

3200 = 25(120) + b

b = 3200 - 3000

b = 200

Therefore, function will be,

f(x) = 25x + 200

Part C:

"Slope = 25" means the rate of change in earnings per hour is $25.

Similarly, y-intercept 'b = 200' will represent the fixed amount earned by David in addition to the per hour earnings.

D. A dashed line is used when the inequality is strict ​( < or > ​)

A linear inequality in two variables is obtained by taking a linear equation in two variables, and replacing the equality sign with any one of the four inequality signs: <,>,=<,>=.

The graphed region of points satisfying the inequality is always half of the plane bounded by the corresponding line.

When the inequality is [tex]\leq[/tex] or [tex]\geq[/tex], the line is included. Otherwise, the line is excluded.

So, A dashed line is used when the inequality is strict ​( < or > ​) is not true about the boundary line in the graph of a linear inequality in two​ variables

Therefore, the correct option is D.

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Answer:

Step-by-step explanation:

Draw a picture! You get a right triangle with vertical leg = 17,000 ft, and you want to find the hypotenuse.

sin(21°) = 17,000/hypotenuse

hypotenuse = 17,000/sin(21°) = 47,437.3 ft

Answer:

21.96 ; 24.72

Step-by-step explanation:

Given that :

Give the equation:

A(t) = 700(1.03)^t

A.)

Average rate of change over the first 4 years ;

(t=0 to t=4)

At t = 0

A(0) = 700(1.03)^0 = 700

A(1) = 700(1.03)^1 = 721

A(2) = 700(1.03)^2 = 742.63

A(3) = 700(1.03)^3 = 764. 9089

A(4) = 700(1.03)^4 = 787.856167

[(721 - 700) + (742.63 - 721) + (764.9089 - 742.63) + (787.856167 - 764.9089)] / 4

= 87.856167 / 4

= 21.96404175

= 21.96

Over the 2nd 4 years :

A(4) = 700(1.03)^4 = 787.856167

A(5) = 700(1.03)^5 = 811.49185201

A(6) = 700(1.03)^6 = 835.8366075703

A(7) = 700(1.03)^7 = 860.911705797409

A(8) = 700(1.03)^8 = 886.73905697133127

[(811.49185201 - 787.856167) + (835.8366075703 - 811.49185201) + (860.911705797409 - 835.8366075703) + (886.73905697133127 - 860.911705797409)] / 4

= 98.88288997133127 / 4

= 24.72

Answer:

5 hours cuz 75 divided by 15 is 5 or 15 x 5 is 75

Answer:

105

Step-by-step explanation:

A straight line is 180 degrees so 180-75=105

Answer:

x= 105 degrees

Step-by-step explanation:

We know that the sum of x and 75 degrees is equal to 180 degrees.

So that means that x= 180-75 or x=105 degrees

Answer:

$22.50

Step-by-step explanation:

3 weeks = 21 days

21 × 1 + 1.50

21 + 1.50

22.50

[tex] \frac{132 }{2?} = 66[/tex]

Answer:

B is the correct answer

Step-by-step explanation:

just did this problem

Answer:

18

Step-by-step explanation:

Answer: 18, 21, 24, 27, 30

Step-by-step explanation:

Answer:

y=-9x+51

Step-by-step explanation:

-9x+45=y-6

add 6 to both sides to get

-9x +51=y

Answer:

x=19

Step-by-step explanation:

2x - 8 = 30

get x by itself by adding 8 to both sides

2x=38

divide by 2

x=19

Answer:

There is no picture... But here is a representation of the inequality on a graph

The graph 2x - 5y < 3 cut the x-axis at the point (3,0) and the y-axis at the point (0,-0.6).

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given inequality is 2x - 5y <3. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

When the inequality 2x - 5y < 3 is plotted on the graph it covers the region which is less than the line 2x - 5y < 3. The graph cut the x-axis at the point (3,0) and the y-axis at the point (0,-0.6).

The graph of the given inequality is attached with the answer below.

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Answer:

Step-by-step explanation:

"a number is multiplied by 7" can be represented by 7x

"25 is added to twice the number" can be represented by 2x+25

7x = 2x+25

5x = 25

x = 5

The number is 5 if  a number is multiplied by 7, the result is the same as when 25 is added to twice the number.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the number is x:

From the problem, we can model a linear equation in one variable.

7x = 2x + 25

5x = 25

x = 5

Thus, the number is 5 if  a number is multiplied by 7, the result is the same as when 25 is added to twice the number.

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Answer:

49c2

Step-by-step explanation:

Answer:

212272.71

Step-by-step explanation:

we have the following equation (for interesting that compound yearly)

PV(1+i)^n

200000(1+.015)^4

212272.71

The total amount of interest Katy will get at the end of 4 years is £12,272.71

The steps are as follow:

p = £200 000

r = 1.5%

n = 4 years

A = p(1+r/100)ⁿ

A = 200000(1+1.5/100)⁴

A = 212,272.71 £

C.I. = A - p

C.I. = 212,272.71 - 200,000

C.I. = £12,272.71

So the  total amount of interest Katy will get at the end of 4 years is £12,272.71

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Answer:19.625

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

Answer:-516

Step-by-step explanation:

Answers:

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

Explanation:

To simplify this, we combine the coefficients. This works because all of the terms have 'x' in them and nothing else (they are all like terms). We can think of this problem as trying to evaluate -12+14-6. This simplifies to -4

So -12x+14x-6x simplifies to -4x

Afterward, we replace x with 129 to get

-4x = -4*129 = -516

Answer: The correct answer is (5, 3)

Step-by-step explanation: I got it right on the exam

(5,3) will make a rhombus.

A Quadrilateral with all sides equal but with nonequal diagonals is know as Rhombus.

Let D have coordinate (x,y)

The length of all the sides of the rhombus is equal.

length of AB = [tex]\sqrt{({2-3})^2 + ({2-4})^2} = \sqrt{1+4} = \sqrt{5}[/tex]

Similarly BD = [tex]\sqrt{({3-x})^2 + ({4-y})^2} = \sqrt{25+{x}^2+{y}^2-6x-8y}[/tex] -------------(1)

CD = [tex]\sqrt{({4-x})^2 + ({1-y})^2} = \sqrt{17+{x}^2+{y}^2-8x-2y}[/tex] -------------(2)

We know BD = CD gives,

[tex]\sqrt{17+{x}^2+{y}^2-8x-2y} = \sqrt{25+{x}^2+{y}^2-6x-8y}[/tex]

By squaring both sides and solving we get,

3y - x = 4 ----------------------(3)

Since BCD is a right-angled triangle,

[tex]{BC}^2 = {BD}^2 + {CD}^2[/tex]  

BC = [tex]\sqrt{10}[/tex]

10 = 5 + [tex]\sqrt{17+{x}^2+{y}^2-8x-2y}[/tex]

8  = [tex]{x}^2+{y}^2-8x-2y[/tex] -------------------(4)

solving equation (3) and (4) we get x = 5 and y = 3

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Answer:

4.6

Step-by-step explanation: