Determine the range of f(x) = |x + 5|.

Answer: (3,1)

Step-by-step explanation:

The most appropriate choice for distance formula will be given by Length of AC = [tex]\sqrt{72} = 8.5 units[/tex]

What is distance?
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over").

What is distance formula?

Distance formula is used to find the distance between two points.

Let A and B be two points with coordinate [tex](x_1, y_1)[/tex]  and [tex](x_2, y_2)[/tex] respectively

Distance between A and B = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]

Here,

Coordinate of A = (1, 1)

Coordinate of E = (4, 4)

Coordinate of C = (7, 7)

Length of AE =

[tex]\sqrt{(4-1)^2 + (4-1)^2}\\\sqrt{9 + 9}\\\sqrt{18}\\3\sqrt{2} units[/tex]

Length of EC =

[tex]\sqrt{(7-4)^2 + (7-4)^2}\\\sqrt{9 + 9}\\\sqrt{18}\\3\sqrt{2} units[/tex]

Length of AC = Length of AE + Length of EC

= [tex]3\sqrt{2} + 3\sqrt{2} = 6\sqrt{2} units[/tex] =[tex]\sqrt{72} units = 8.5 units[/tex]

Fourth option is correct

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Answer:

its true because standard deviation is the only way out to find any solution

Answer:

300

Step-by-step explanation:

The slope of the given line that runs through the points are:

1. Defined

2. Defined

3. undefined.

An undefined slope of a line can be described as the slope of a vertical line that has no run but only rise. That is, the x-coordinates do not change even though the y-coordinates of the line are changing.

Thus, the change in x-coordinates is always 0.

Slope = change in y / change in x.

a. (5 , − 4) and (0 , 1):

Slope = (-4 - 1)/(5 - 0)

Slope = -5/5 = -1 [the slope is defined]

b. (−1 , 8) and (7 , 10):

Slope = (10 - 8)/(7 -(-1))

Slope = 2/8

Slope = 1/4

c. (-4, 12) and (-4, 5)

Slope = (12 - 5)/(-4 -(-4))

Slope = 7/0 [cannot divide, therefore, the slope is undefined]

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When asked which season they preferred, just 3/10 of the students selected either spring or summer. 2/5 fraction went with summer if 1/10 chose spring.

Given that,

When asked which season they preferred, just 3/10 of the students selected either spring or summer.

We have to find what fraction went with summer if 1/10 chose spring.

To find the fraction we have to add the students selected in spring or summer.

3/10+1/10

Denominator are equal numerator can add

(3+1)/10

By adding

4/10

By doing the division

2/5

Therefore, the fraction is 2/5.

2/5 fraction went with summer if 1/10 chose spring.

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Answer:

(a) The profit function is P(x) = 89x - 90,000.

(b) The company's profit at x=23,000 is 1,957,000.

Step-by-step explanation:

Given,

The cost function of the company is C(x)=90,000 +42x and

The revenue function is R(x) = 47x

where x is the number of radios.

(a)

The company's profit function, P, is from producing and selling x radios is

The formula for profit:

Profit (P) = Revenue (R) - Cost (C)

P = R - C

P = 47x - 90,000 + 42x

P = (47x + 42x) - 90,000

P = 89x - 90,000

For (a), The company's profit function, P, from producing and selling x radios is P = 89x - 90,000

(b)

The radios produced and sold are 23,000

So, x = 23,000

putting x value in the profit function, P

P = 89x - 90,000

P = 89 x 23,000 - 90,000

P =  2,047,000- 90,000

P = 1,957,000

For (b), the company's profit at x = 23,000 is 1,957,000.

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Answer:

-2

Step-by-step explanation:

f(-2) = -(-2) - 4

= 2-4

= -2

Answer:

b=-144

Step-by-step explanation:

b/24=-6

cross multiplication

b=24×-6

=-144

The value for h(-1) is 4

The value for  h'(-1) is 1

Given the tangent line to the graph of y=h(x) at the point (-1,4) passes through (3,6), to get h(-1) and h'(-1), we should calculate the following:

Gradient of the tangent line:

Gradient=change in y axis/change in x axis=Δy/Δx

Using the x and y coordinates (-1,4) and (3,6)

Gradient=(6-4)/(3--1)

             =2/4

            =1/2

Gradient=1/2 or 0.5

Equation of the tangent line:

This should be in the form of y=mx+c, where m is the gradient of the line

We use the gradient and one of the x and y coordinates get the equation of the tangent line

Gradient=change in y axis/change in x axis=Δy/Δx, and gradient was found as 1/2

Δy/Δx=1/2

(y-4)/(x--1)=1/2

(y-4)/(x+1)=1/2

2y-8=x+1

y=(1/2)x+4.5

Equation of the tangent line is y=(1/2)x+4.5 or y=0.5x+4.5

And y=h(x)

So, h(x)=0.5x+4.5

Calculate h(-1), here x=-1:

h(x)=0.5x+4.5

h(-1)=(0.5*-1)+4.5

      =4

h(-1)=4

Calculate h'(-1), x=-1:

Here we get the derivative of the equation of the tangent line h(x)=0.5x+4.5,

h'(x)=0.5x^0+0

h'(-1)=1+0

h'(-1)=1

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Answer:

$38.35

Step-by-step explanation:

take $180 subtract $58.35 that will leave you with $125.65 then subtract $82.80 then that will leave you with $38.35

Given the function:

You know that "P" is the profit for a certain "n" commodity (in units).

You need to find the value of "n" when:

In order to find it, you can follow these steps:

1. Substitute this value into the function:

Then:

2. Divide both sides of the equation by -25:

3. Factor the equation by finding two numbers whose Sum is -12 and whose Product is -45. These are 3 and -15, because:

Then:

4. Set up these two equations:

5. Solving form "n" from each equation, you get:

Since the number of units cannot be negative, the answer is:

Answer 2xy3

Step-by-step explanation: you basic combine 2(x+3) to get 2x + 6

The mean absolute deviation of the amount  $39

What is Mean Absolute Deviation?

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data set. A measure of variance in a data set is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.

Given,

The amount she saved throughout the year

January         96

February       38

March            162

April               65

May                178

June               112

July                57

August           143

September    135

October         104

November     88

December     22

The mean of the data will be = 96+38+162+65+178+112+57+143+135+104+88+22/12

= 1200/12

=100

The mean would be 100

|data - mean value| = 96-100 = 4

38-100 = 62

162-100 = 62

65-100 = 35

178-100 = 78

112-100 = 12

57-100 = 43

143-100 = 43

135-100= 35

104-100 = 4

88-100 = 12

22-100 = 78

Now, sum of |data - mean values| = 468

The mean absolute deviation:

                                       =  sum of |data - mean values| / number of values

                                       = 468 / 12

                                       = 39

Hence, the mean absolute deviation of amounts she saved is $39

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The equation that could be used to find x, the number of bikes the store had originally, is (x-94) = 0.

According to the question,

We have the following details:

Bill has sold 36 bikes and is left with 58 bikes more.

Now, the number of bikes the store had originally is given to be x.

So, we have:

x = Number of bikes sold + Number of bikes left

x = 36+58

x = 94

x-94 = 0 (94 was positive on the right hand side. So, it is negative on the left hand side.)

Hence, the equation that could be used to find number of original bikes in Bill's store is x-94 = 0.

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Answer: 179.07 this is ur answer

Step-by-step explanation:

[tex](\stackrel{x_1}{-15}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{70}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-15)}}} \implies \cfrac{-60}{5 +15} \implies \cfrac{ -60 }{ 20 } \implies - 3[/tex]

[tex]\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}{70}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-15)}) \implies y -70= -3 (x +15) \\\\\\ y - 70 = -3x - 45\implies {\Large \begin{array}{llll} y = -3x+25 \end{array}}[/tex]

The ratio of hexagons to triangles is 2/1.

Given:

In the figure,

Number of hexagons = 4

Number of triangles = 2

We have to determine the ratio of hexagons to triangles.

Ratio = Number of hexagons/Number of triangles

Ratio = 4/2

Reducing it we get,

Ratio = 2/1

Therefore, the required ratio is 2/1.

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The total surface area of the prism is 217 square inches.

In geometry, a prism is a polyhedron with n sides made of polygons, a second base that is a translation of the first base, and n additional faces that must all be parallelograms and connect the effective distribution of the two bases.

The base is a square with area = 49 square inches

Length of 1 side = √49 = 7 inches

Area of the triangular sides is given by the formula (1/2) × base × height

Area of each side

= (1/2) × base × height

= (1/2) × 7 × 12

= 42 square inches.

Total surface area

= 42 × 4 + 49

=217 square inches  

Therefore the total surface area is 217 square inches  

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SOLUTION

The given equatiion is:

To be divided by x-1

set the expression to zero:

Substitute x=1 into the polynomial:

This gives:

Therefore the remainder is -14.

x intercept is x = -12

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

x = 4y - 12

y = 0

x intercept is

x = -12

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The inequality that represents the velocity of an object that has mass of 30 Kg and creates a momentum of at least 15 Kg(m/s) is 15 ≥ 30×v  .

The relation between the mass(m) of an object with momentum(p) and velocity(v)  is given by the equation

p=m × v .

In the question,

it is given that

the mass of the object = 30 Kg

the momentum required is at least 15 Kg(m/s).

let the velocity of the object  " v " .

Substituting values in the formula ,

we get ,

15 = 30×v

the word at least in inequality is represented by " ≥ " .

So , the inequality becomes

15 ≥ 30×v

Therefore , the inequality that represents the velocity of an object that has mass of 30 Kg and creates a momentum of at least 15 Kg(m/s) is 15 ≥ 30×v .

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The integer n = 25 is the only value so that the sector AOB is greater than 20 and less than 30.

In this problem we find the sector generated by line segments OA and OB, where O is the center of the circle and the points A and B are on the circle:

20 < 360 / n < 30

20 · n < 360 < 30 · n

First, we determine the factorial decomposition of 360:

360 = 2³ × 3² × 5

Second, find the value of n associated to each limit of the inequality:

Lower limit

360 = (2² × 5) × (2 × 3²)

360 = 20 × 18

n = 18

Upper limit

360 = (2 × 3 × 5) × (2² × 3)

360 = 30 × 12

n = 12

Third, find the values that are between 12 and 18:

x = 2³ × 3

x = 24

n = 360 / 24

n = 15

The only integer that satisfies the inequality is 15.

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The decimal number 3.16 in the form of the simplest fraction is 79/25.

The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.

Consider the decimal number,

Let x = 3.16

Then,

x = 3.16 = 316/100

The fraction then can be simplified as,

x = ( 158 × 2)/ (50 × 2)

x = 158/50

x = ( 79 × 2)/ ( 25 × 2 )

x = 79/25

Hence, the number 3.16 in the simplest fraction is 79/25.

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Given:

Since ∠GFE is a right triangle, we can conclude:

the sum of the internal angles of a triangle is 180, therefore, for the triangle GHF:

Finally, for the triangle GEF:

Explanation

given

Step 1

a) (f+g) (x)

here we need to find a new function ( f+g) (x), this is the sum of the functions f and g, so to find it just add g(x) to f(x)

hence

so

Step 2

now, we have to evaluate that function for x= 9

so

so

I hope this helps you