Find the domain and range of the relation graphed below. Write your answers in interval notation.

The truth set for each predicate are:

a) d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}

b) d ∈ {  1, 2, 3, 6}

c) x ∈ { [-2, -1] U [1, 2]}

d) x ∈ {-2, -1, 1, 2}

We only need to find the sets of values such that the statements are true.

a)

We want to find vales of d, such that d is an integer, and 6/d is an integer.

Here the possible values of d will be:

d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}

Which are all the factors of 6, so all these integers divide 6.

b) Same as before, but this time the domain is a positive integer, so now the truth set will be:

d ∈ {  1, 2, 3, 6}

c) We want to find real values of x such that:

1 ≤ x² ≤ 4

If we apply the square root to the 3 sides, we get two inequalities:

-√1 ≥ x ≥ -√4

√1 ≤ x ≤ √4

Simplifying:

-1  ≥ x ≥ -2

1  ≤ x ≤ 2

So the truth set is:

x ∈ { [-2, -1] U [1, 2]}

c) Same as before, but now we only have integer solutions, so the truth set is:

x ∈ {-2, -1, 1, 2}

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Answer:

Step-by-step explanation:

Solve -6 < 2x + 4 ≤ 16

To solve for x, we need to simplify the statement.

let's get rid of the 4 that is added to 2x.

do that by subtracting 4 on all sides (3 sides).

-6 - 4 < 2x + 4 - 4 ≤ 16-4

We get: -10 < 2x ≤ 12

Now, let's get rid of the 2 that gets multiplied to x.

do that by dividing all sides by 2.

-10 : 2 < 2x : 2 ≤ 12 : 2

We get: -5 < x ≤ 6

X = {-4,-3,-2,-1,0,1,2,3,4,5,6}

Hope I helped!

Answer:

D

Step-by-step explanation:

You do 180-125 to find the angle (because its a straight line) and then you get 55, then you have a right angle so you have 90 and then you do:

55+90+p=180

and then you get

145 +p=180

180-145=35

p=35

Substituting into the formula [tex]d=\frac{m}{v}[/tex],

[tex]19.32=\frac{m}{0.5}\\\\m=\boxed{9.66 \text{ grams}}[/tex]

Answer:

[tex]11 - 2 {}^{3} [/tex]

[tex]11 - 8[/tex]

[tex]3[/tex]

The expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)

The most fundamental of curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. From a geometric perspective, it may be compared to a prism with a circle as its basis.

Given the volume of a cylinder is given by the formula V = 3.14r^2h, where r is the radius of the cylinder and h is the height and suppose a cylindrical cane has radius (x+8) and height (2x+3)

We have to find expression which represents the volume of the cane

So as per given,

r = x+8

h = 2x + 3

v = πr²h

v = π(x+8)²(2x+3)

v = π(x²+64+16x)(2x+3)

v = π(2x³+128x+32x²+3x²+192+48x)

v = π(2x³+35x²+176x+192)

v = π2x³+π35x²+π176x+π192

Hence the expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)

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Answer :

10.5 miles

Given :

7 miles in 50 mins

Step-by-step explanation :

Calculate how many miles in 1 minute :

Divide both by 50 :

7/50 miles in 1 minute

To work out 75 minutes we multiply both by 75 :

75 × 7/50 =

10.5

Therefore our final answer is 10.5 miles

Hope this helped and have a good day

The reflected function is g(x) = √(-x).

And the correct option is the third one.

Remember that for a function f(x), a reflection across the y-axis gives:

g(x) = f(-x).

In this case, the original function was:

f(x) = √x

Then we have:

g(x) = √(-x).

So we can only evaluate this function in values of x such that:

x ≤ 0.

Then the correct option is:

"On a coordinate plane, a graph starts at (0, 0) and goes to the left through (negative 4, 2)."

As when we evalute g(x) in -4, we get:

g(-4) =  √(-(-4)) = √4 = 2

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Answer:

C

Step-by-step explanation:

Using translation concepts, the sequence that is used to obtain the translated image is:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

For all the vertices, the transformations follow the given pattern:

In the step (x,y) -> (-x,y), the function is reflected over the y-axis. Then, in step (-x,y) ->  (-x + 1, y), the function is shifted right one unit.

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Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9 ( divide through by 9 )

x + y = 1 ( subtract x from both sides )

y = 1 - x

Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9

First, take 9x to the right side.

9y = 9 - 9x

9y = 9 ( 1 - x )

Divide both sides by 9.

y = 1 - x

According to the information in the table, it can be inferred that the trend of the results is positive but does not have an exact linear fit (option B).

To calculate the average of the results we must add all the results and divide the result by the number of years as shown below.

Additionally, to identify if the trend is positive or negative, we must see if the results increase or decrease year after year. From the above, it is possible to infer that it is a positive trend.

On the other hand, it can be stated that it does not have an exact linear fit because the increase is not constant each year.

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Answer: -21

Step-by-step explanation:

Let the number be x.

Then, this means 2(x+8)+5=x.

Answer:

Step-by-step explanation:

You want the domain and range of the function y = √(x -7) +1.

The domain is the horizontal extent of the graph. The graph of the given function extends to the right from x=7, which is included in the solution set.

The domain is x ≥ 7.

The range is the vertical extent of the graph. The graph of the given function extends upward from y=1, which is included in the solution set.

The range is y ≥ 1.

Answer: domain: 7

range: 1

Step-by-step explanation:

The domain of the graph is [-3, 2) and the range is (-4, 5]

From the given graph, we have the following highlights:

Open circles are represented with () while closed circles are represented with []

Hence, the domain of the graph is [-3, 2) and the range is (-4, 5]

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The equation would be  y+ 3/8x+9/4.

Lets try to explain in the further steps to calculate the equation,

Slope formula: (y₂ - y₁) / (x₂ - x₁)

First, plug in these values of the two given points.

[tex]= > (-5+2) / (4+4)\\= > -3/8[/tex]

Slope = -3/8

To find the equation of the line, (y- y1) = m* (x-x1)

So by putting the values into the above equation we get,

[tex]= > (y-4) = -3/8(x+5)\\= > y-4 = -3/8x - 15/8\\= > y + 3/8x + 4 - 15/8\\= > y + 3/8x + 9/4[/tex]

Hence the equation is [tex]y+ 3/8x+9/4.[/tex]

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Answer:

[tex]\huge\boxed{\sf 4x + 8}[/tex]

Step-by-step explanation:

= 4(x + 2)

Distribute

= 4x + 8

[tex]\rule[225]{225}{2}[/tex]

Using a linear function, we have that:

Given that, the percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5% in 1995.

Linear functions are those whose graph is a straight line. The standard form of the linear function is f(x)=y= mx + b. A linear function has one independent variable and one dependent variable.

Where, m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0 and can also be interpreted as the initial value of the function.

The percentage in 1980 is considered as the initial amount, so b = 58.8. In 15 years, the percentage decreased from 58.8% to 50.5%, hence the slope is given by: m = (50.5 - 58.8)/15 = 0.5533.

Thus, the percentage in t years after 1980 is P(t) = 58.8 - 0.5533t.

Now, t + 1980, for which P(t) = 47.

So, P(t) = 58.8 - 0.5533t

47 = 58.8 - 0.5533t.

0.5533t = 11.8.

t = 11.8/0.5533

t = 21.3.

1980 + 21 = 2001, so the percentage will be 47% during the year 2001.

Now, 2005 is 25 years after 1980, so the percentage is P(25), given as follows: P(25) = 58.8 - 0.5533x25 = 44.97%.

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Answer:

10 in base 3

Step-by-step explanation:

3 in base 10 =   10 in base 3

Answer:

4

Step-by-step explanation:

10xyz/40xyz

the xyz would cancel out

leaving 10/40.

10/40 would then simplify to 1/4 (divide by 10)

1/4

The reciprocal of 1/4 is 4

To check:

1/4 * 4 = 1

Answer:

7

4

Step-by-step explanation:

The actual values are shown on the given graph as blue points.

The line of regression is shown on the given graph as the red line.

From inspection of the graph, in the year 2000 the actual rainfall was 43 cm, shown by point (2000, 43).  It appears that the regression line is at y = 50 when x is the year 2000.

⇒ Difference = 50 - 43 = 7 cm

In 2000, the actual rainfall was 7 centimeters below what the model predicts.

From inspection of the graph, in the year 2003 the actual rainfall was 44 cm,  shown by point (2003, 40).  It appears that the regression line is at y = 40 when x is the year 2003.

⇒ Difference = 44 - 40 = 4 cm

In 2003, the actual rainfall was 4 centimeters above what the model predicts.

Were you not given a diagram?

The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)

Given 4c + 5 ≠ 0 and c is a real number, what is the multiplicative inverse of 4c + 5

The expression is given as:

4c + 5

The multiplicative inverse of an expression x is 1/x

This means that:

The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)

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Answer:

1/90

Step-by-step explanation:

Comment

To begin with, there are 10 tiles.. You draw one and don't replace it. Then you draw another tile from the 9 that remain.  The job is to figure out the probability of that happening.

You have a 1/10 chance of drawing the M.

But now there are only 9 tiles left and you have a 1 in 9 chance of drawing a T

Solution

P(M,T) = 1/10 * 1/9 = 1 / 90

You have a 1 in 90 chance of getting the two tiles in the order you have specified.

Slope of the given data is 579.88

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.

Here, given data;

            x₁ = 2009                   y₁ = 12078 burger

            x₂ = 2017                    y₂ = 16717 burger

Now, Slope = (y₂ - y₁)/(x₂ - x₁)

         Slope = (16717 - 12078) / (2017 - 2009)

         Slope = 4639 / 8

         Slope = 579.88

Thus, Slope of the given data is 579.88

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Answer:

its wrong answer and question

A quadratic equation is an equation whose leading coefficient is of the second degree. The correct options are A, B, and E.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c. The Roots of the quadratic equation:

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The complete question is:

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot

8(x2 + 2x + 1) = 3 + 1

8(x2 + 2x) = –3

If we simplify the given options, then the option that is correct is,

A.) 8(x² + 2x + 1) = –3 + 8

     8x² + 16x + 3 = 0

B.) 8x² + 16x + 3 = 0

[tex]x = \dfrac{-16\pm\sqrt{16^2-4(8)(3)}}{2(8)}\\\\x = -1 \pm \dfrac{\sqrt{10}}{4}\\\\x = -1 \pm \sqrt{\dfrac{10}{16}}\\\\x= -1 \pm \sqrt{\dfrac{5}{8}}[/tex]

E.) 8(x² + 2x) = –3

8x² + 16x + 3 = 0

Hence, the correct options are A, B, and E.

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The stock worth now, to the nearest cent, is $58.14.

The current worth of stock = initial price of stock+increase in the price of stocks

If you bought stock last year for a price of $66, and it has gone down 13.9% since then,

Let X be the worth of stock;

66 ×  100 = (13.5% + 100%) × X

6600 = 113.5X

X = 6600/113.5

X = 58.14458

X = $58.14

Hence, The stock worth now, to the nearest cent is $58.14.

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