Find DG.
DE
2x+17
EF
8
FG
2
x + 20

Answer:

write three methods of writing set. Give one example of each methods.

The x axis is labeled as Number of days.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

let x be the  number of days and y be money.

So, the equation is

y = -7x + 150.

Hence, the x axis is labeled as Number of days.

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Step-by-step explanation:

[tex] {x}^{3} + 3x + 1 = 1 = = = > \\ {x}^{3} + 3x = 0 = = = > \\ x({x}^{2} + 3) = 0 \\ x = 0 \: or \\ {x}^{2} + 3 = 0 = = = > \\ {x}^{2} = - 3 = = = > x 1= \sqrt{ - 3} \: or \: i \sqrt{3} \\ x2 = - \sqrt{ - 3} = = = > x2 = - i \sqrt{3} [/tex]

[tex] {x}^{3} + 3x + 1 = 5 = = = > \\ {x}^{3} + 3x - 4 = = = > \\ (x - 1)( {x}^{2} + x + 4) = 0 = = = > \\ x - 1 = 0 = = > x1 = 1 \\ {x}^{2} + x + 4 = 0 = = = > \\ x2 = - 1 + i \sqrt{3} \\ x3 = - 1 - i \sqrt{3} [/tex]

[tex] {x}^{3} + 3x + 1 = 3 = = = > \\{ x}^{3} + 3x - 2 = 0 = = = > x = 0.6[/tex]

The values of the inverse of the function, f(x) = x³ + 3·x + 1, obtained from  graphing of the function are;

a. f⁻¹(1) = 0

b. f⁻¹(5) = 1

c. f⁻¹(3) ≈ 0.59607

An inverse function is a function that reverses the action of another function, such that the inverse function maps the output of the function to the corresponding input.

The inverse of the function can be found by graphing the function, f(x) = x³ + 3·x + 1, using technology and then using inverse or table function to find the values of the inverse functions at the specified points

a. The value of the inverse function, f⁻¹(1), is the x-value, on the graph that corresponds to the point with a y-coordinate of 1.

The graph of the function indicates that at a y-value of 1, x = 0, therefore;

f⁻¹(1) = 0

b. Similarly, the graph indicates that a y-value of 5, x = 1, therefore;

f⁻¹(5) = 1

c. When the y-value = 3, we get;

x³ + 3·x + 1 = 3

x³ + 3·x - 2 = 0

Solving the above equation with an online tool, we get; x ≈ 0.59607

Therefore; f⁻¹(3) ≈ 0.59607

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Parallel lines are those on a plane that do not intersect while perpendicular lines are those that intersect at an angle of 90°.

Parallel lines will never intersect with each other and will maintain the same distance from each other for as long as they are on the same plane.

Perpendicular lines on the other hand will intersect each other and will do so at a 90° angle. An example of such a line is the steps on a ladder which intersect the beam at a 90° angle.

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The expression that represents this inequality must relate both temperatures, then it would look like this: -40°F < x < 140°F.

To express this situation in an inequality we must include the temperature values. Additionally, we must include the greater than (>) or less than (<) symbols to relate the values.

According to the above, the expression would look like this:

Note: This question is incomplete because some information is missing. Here is the information:

A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.

Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form.

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The time it will take the money to reach $8,838.51 is 14years

The formula for calculating compound interest is expressed as:

A = P(1+r)^t

where

P = $6,680

A = $8,838.51?

r = 2% = 0.02

Substitute and calculate the time 't"

8,838.51 = 6680(1+0.02)^t
1.3231 = 1.02^t

t = ln1.3231/ln1.02

t = 14years

Hence the time it will take the money to reach $8,838.51 is 14years

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Using the normal distribution, we have that:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the parameters are given as follows:

[tex]\mu = 57, \sigma = 22, n = 17, s = \frac{22}{\sqrt{17}} = 5.3358[/tex]

Hence:

The probabilities are the p-value of Z when X = 58 subtracted by the p-value of Z when X = 55, hence, for a single movie:

X = 58:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{58 - 57}{22}[/tex]

Z = 0.05.

Z = 0.05 has a p-value of 0.5199.

X = 55:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 57}{22}[/tex]

Z = -0.1.

Z = -0.1 has a p-value of 0.4602.

0.5199 - 0.4602 = 0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.

For the sample of 17 movies, we have that:

X = 58:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{58 - 57}{5.3358}[/tex]

Z = 0.19.

Z = 0.19 has a p-value of 0.5753.

X = 55:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{55 - 57}{5.3358}[/tex]

Z = -0.38.

Z = -0.38 has a p-value of 0.3520.

0.5753 - 0.3520 = 0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.

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Answer:

-8

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

-8/5=(6-(-2))/(x-(-3))

-8/5=(6+2)/(x+3)

-8/5=8/(x+3)

5=-(x+3)

5=-x-3

-x=5+3

-x=8

x=-8

Answer:

V = 9 in^3

Step-by-step explanation

Comment

The formula for a Pyramid of any B is V = B * h / 3. You have to be able to calculate the Base or just be given in it.

In this case the Base is a triangle. So the first thing needed is the area of the base.

Base

Area_triangle = base length * height / 2

Neither the Base length nor the height need to be the same as the B and h used for the volume of the Pyramid

Givens

b = 4 inches

h = 1.5 inches

Area_triangle = 4 * 1.5 / 2

Area_triangle = 2 * 1.5

Area_triangle = 3 inches^2

Solution

Base (triangle) Area = 3

h = 9

V = B * h / 3  

V = 3 * 9 / 3

V = 9 cubic inches

Answer V = 9 in^3

The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively

The table of values is given as:

Savings Lower Limit Upper Limit     Frequency

0-199         0         199                       345

200-399   200   399                         97

400-599   400   599                         52

600-799   600   799                         21

800-999   800   999                         9

1000-1199 1000  1199                         8

1200-1399 1200  1399                      3

Rewrite the table to include the class midpoint and the frequency

x               f

99.5         345

299.5        97

499.5        52

699.5        21

899.5        9

1099.5        8

1299.5        3

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]

Evaluate

[tex]\bar x = 233.331775701[/tex]

Approximate

[tex]\bar x = 233.3[/tex]

Hence, the approximation of the mean is 233.3

The standard deviation is calculated as:

[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]

So, we have:

[tex]\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]

Evaluate

[tex]\sigma = 229.82[/tex]

Hence, the approximation of the standard deviation is 229.82

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Answer:

x

Step-by-step explanation:

I got it right.........

The value of the length of the scaled up rectangle is 12.8 unit.

A rectangle is a polygon with four sides , the opposites are parallel and equal.

It is given in the figure that

A rectangle 4* 8 is scaled up and a new rectangle is formed α * 25.6

Scale factor = 25..6/8 =3.2

The value of the length therefore will be

4 * 3.2 = 12.8 unit

Therefore the value of the length of the scaled up rectangle is 12.8 unit.

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The factors of the function after factorization f(x)=[tex]x^{2} -7x-18[/tex] is (x+2) and (x-9)

Given Function  f(x)=[tex]x^{2} -7x-18[/tex] and we have to find the factors of the given function.

The function whose factors are to be found is   f(x)=[tex]x^{2} -7x-18[/tex]

Factorization means finding various expressions which when together multiplied will give the  function itself. Correct combination can only be found by finding the factors of the function. Without finding factors no one can find the solution of an equation or expression also.

f(x)=[tex]x^{2} -9x+2x-18[/tex]

=x(x-9)+2(x-9)

=(x+2)(x-9)

Hence the  factors which when combine together gives function f(x)=[tex]x^{2} -7x-18[/tex] are (x+2)(x-9).

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Answer:

D: (–∞, ∞); R: [–11, ∞)

Step-by-step explanation:

The domain of a quadratic function is all real numbers, so eliminate the third and fourth options.

Also, since the coefficient of [tex]x^2[/tex] is positive, we know the graph opens up and thus has a minimum.

This means that the first option must be wrong since the range has a maximum, not a minimum.

Therefore, the correct answer is Option 2.

Answer:

D: (–∞, ∞); R: [–11, ∞)

Step-by-step explanation:

I honestly don't know the answer but the other person said this so I'm putting it as my answer ill update this answer when i find out if its right or not.

update I GOT A 100% woop woop

Answer:

y = C/h - 2

Step-by-step explanation:

Equation

C = (2 + y)*h

Solution

C = (2 + y)*h                          Divide by h

C/h = (2 + y)*h/h

C/h = 2 + y                            Subtract 2 from both sides

C/h-2 = 2-2+ y                      Combine

C/h - 2 = y

The shaded area for the inequality y > -3-(5/4)x is given below.

The inequality is the relation between two expressions showing the relationships such as greater than, lower than, greater than equals to, and lower than equals to.

The given inequality is -5x-4y<12

solving this inequality for y

-5x-4y<12

⇒ -4y<12+5x

⇒y > (12+5x)/(-4)

⇒y > -3-(5/4)x

the line y= -3-(5/4)x has y intersection at (0,-3) and  x intersection at (-12/5,0).

The inequality y > -3-(5/4)x show that this will be above the straight line y = -3-(5/4)x as if we put (0,0) in the inequality, the inequality will be 0>-3 which is true that shows that the region contains (0,0).

Therefore the shaded area for the inequality y > -3-(5/4)x is given below.

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Answer:

[tex] \frac{ {3x}^{2} }{x + 5} + \frac{15x}{x + 5} [/tex]

[tex] \frac{3 {x}^{2} + 15x}{x + 5 } [/tex]

3x ( x + 5) /( x + 5).

Answer:

as ABC = 3* DEF

AB = 5

DE = 15 = 5*3

AC = 3

DF = 9 = 3*3

BC = 4

EF = 12 = 4 * 3

Distance from the origin to the points  ≈ 0.41.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

Point A (5, 3, 4) and point B (−4, 2, 6) are located away from the origin (0,0,0), and the points from the origin to this points are expressed as OB - OA where;

Let OB is the distance from the origin to the point B

Let OA is the distance from the origin to the point A

Using the formula for calculating the distance between two points;

OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²

OA = √(4-0)²+(3-0)²+(5-0)²

OA = √(16)+(9)+(25)

OA = √50

OA = 7.071

Similarly;

OB = √(6-0)²+(2-0)²+(-4-0)²

OB = √(6)²+(2)²+(-4)²

OB = √36+4+16

OB = √56

OB = 7.4833

Distance from the origin to the points = 7.4833 - 7.071= 0.4123

Distance from the origin to the points  ≈ 0.41

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Answer:

See below

Step-by-step explanation:

There are 52 weeks in a year, so divide t by 52

= 120 (1.016)^(t/52)

      then the % for one week =   1.016^1/52 = 1.0003  = .03%

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

A relation is a function if each value of x maps onto no more than one value of y.

Answer:

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

[tex]11 - 8[/tex]

[tex]3[/tex]

Answer:

I think YZ 'cause the triangle is iscoceles triangle. As the two sides XY and XZ are equal the longest side is YZ.

Answer:

1699

Step-by-step explanation:

30/100*13000

Then add answer with 1300

eg 1300+399

I hope this explanation helps you.Also You can follow me.

Answer:  Choice A

[tex]\begin{pmatrix}-15 & 59 & -3\\16 & 61 & -83\\-45 & -99 & 106\end{pmatrix}[/tex]

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

Explanation:

In matrix A, the upper left corner is -3

Multiply this with -7 to get  -7*(-3) = 21

So we'll have 21 in the upper left corner of matrix -7A. The other entries will be handled in a similar fashion.

Meanwhile, the upper left corner of matrix B is 9. Multiply this with -4 to get 9(-4) = -36 which is the upper left corner entry of matrix -4B

Combine those products: 21 + (-36) = -15

The number -15 is the upper left corner entry in matrix -7A-4B

This points us to choice A as the final answer.