The graph below represents which system of inequalities?

graph of two infinite lines that intersect at a point. One line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line. The other line is solid, and goes through the points 1, 1, 2, negative 1 and is shaded in below the line.

Answer:

x = 20

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

let's take a peek, we have two fractions, let's get the LCD of all fractions, in this case the LCD of 2 and 5, hmmmm that'd be 10.

now, let's multiply both sides by the LCD of 10 to do away with the denominators and proceed.

[tex]\bf \cfrac{x}{2}+\cfrac{2x}{5}=18\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{x}{2}+\cfrac{2x}{5} \right)=10(18)}\implies 5x+4x=180 \\\\\\ 9x=180\implies x=\cfrac{180}{9}\implies x=20[/tex]

Answer: median

Step-by-step explanation: Statistical Mathematics

7, 10, 16, 21, 26, 30, 40, 43

Here we have an even number of the data entries so we get two values in the mid.

Now take the average of those mid values:

Answer:

y = 3x-9

Step-by-step explanation:

y = -1/3 x +2

The slope is -1/3

We want a line perpendicular to it

Perpendicular lines have negative reciprocal slopes

The new slope is -(-3/1) = 3

We have a slope  m=3 and a point (5,6)

We will use point slope form to find the line

y-y-1 = m(x-x1)

y-6 = 3(x-5)

In slope intercept form

Distribute

y-6 = 3x-15

Add 6 to each side

y-6+6 = 3x-15+6

y = 3x-9

Answer: Option D

D. 0.92

Step-by-step explanation:

The correlation coefficient "r" is a number between -1 and 1 that indicates how related are two variables X and Y.

The stronger the nearest correlation is, the value of r a -1 or a 1.

A negative correlation indicates that when X increases Y decreases.

A positive correlation indicates that when X increases Y increases.

A correlation close to zero implies that there is very little correlation of the variables. When this happens, the points are scattered in the graph.

In this case you can see in the graph that the points are not scattered, but aligned. You can also observe that when X increases Y increases also.

This allows us to conclude that the correlation is strong and positive. Therefore the correct option is option D.

[tex]r = 0.92[/tex]

Answer:

x = e^2 = 7.39

Step-by-step explanation:

We have been given the logarithmic equation;

6+In x=8

The first step is to subtract 6 on both sides of the equation;

6 + ln x - 6 = 8 - 6

ln x = 2

We then introduce the exponential function, since the exponential function and the natural log function are inverses of each other;

[tex]e^{lnx}=e^{2}\\\\x=e^{2}=7.38906[/tex]

Answer:

Step-by-step explanation:

6 + ln(x)  = 8

ln(x) = 8 - 6

ln(x) = 2

x = [tex]e^{2}[/tex]

x = 7.38905609893

x = 7

She is 3 years older than her brother and has (x+3) in the equation means that x is being used as her brothers age. (She is adding 3 to her brothers age)

The answer is Amy's brother's age.

Answer:

B

Step-by-step explanation:

Answer:

3/11

Step-by-step explanation:

A ratio for 3 cups to 8 cups is written as 3:8.

To turn this into a fraction, you must put the first number over the sum of both numbers.

3/3+8

3/11

To find the other two vertices of the square given two points, create a diagonal line between the two points. The y-coordinate for the other two vertices will be the same as the given points, and the x-coordinate can be found by adding or subtracting the distance between the two given points from the x-coordinate of one of the given points.

The other two vertices of the square can be found by creating a diagonal line from one given vertex to the other. The slope of this diagonal line is zero, indicating that it is a horizontal line. Since the other two vertices should be equidistant from the given points, the y-coordinate for both vertices would be the same as the given points, which is 2. To find the x-coordinate of one of the vertices, we can add the distance between the two given points (4) to the x-coordinate of one of the given points (-3), resulting in the x-coordinate of one of the other vertices being 1. Likewise, to find the x-coordinate of the other vertex, we can subtract the distance between the two given points from the x-coordinate of one of the given points, resulting in the x-coordinate of the other vertex being -7.

https://brainly.com/question/33821777

#SPJ2

[tex]\bf \textit{Half-Angle Identities} \\\\ sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 75\cdot 2\implies 150\qquad \qquad \qquad \cfrac{150}{2}\implies 75 \\\\[-0.35em] ~\dotfill\\\\ sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{1-cos(150^o)}{2}}\implies sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{1-\left( -\frac{\sqrt{3}}{2} \right)}{2}}[/tex]

[tex]\bf sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{1+\frac{\sqrt{3}}{2}}{2}}\implies sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{\frac{2+\sqrt{3}}{2}}{2}} \\\\\\ sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{2+\sqrt{3}}{4}}\implies sin\left( \cfrac{150^o}{2} \right)=\pm\cfrac{\sqrt{2+\sqrt{3}}}{\sqrt{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill sin\left( \cfrac{150^o}{2} \right)=\pm\cfrac{\sqrt{2+\sqrt{3}}}{2}~\hfill[/tex]

The value of sin75 by using half angle identity is [tex]sin\dfrac{[150^0]}{[22]}=\pm\dfrac{\sqrt{2+\sqrt{3}}}{2}[/tex]

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

Value of sin75 by using half angle identity is calculated as:-

Half angle identity for is,

[tex]sin\dfrac{\theta}{2}=\pm\sqrt{\dfrac{1-cos\theta}{2}[/tex]

[tex]\dfrac{\theta}{2}=\dfrac{150}{2}[/tex]

[tex]sin\dfrac{150}{2}=\pm\sqrt{\dfrac{1-cos150}{2}[/tex]

[tex]sin \dfrac{150}{2}=\pm\sqrt{\dfrac{{1+\dfrac{\sqrt{3}}{2}}}{2}[/tex]

[tex]sin \dfrac{150}{2}=\pm\sqrt{\dfrac{2+\sqrt{3}}{4}[/tex]

[tex]sin\dfrac{[150^0]}{[22]}=\pm\dfrac{\sqrt{2+\sqrt{3}}}{2}[/tex]

Hence, the value of sin75 is [tex]sin\dfrac{[150^0]}{[22]}=\pm\dfrac{\sqrt{2+\sqrt{3}}}{2}[/tex].

To know more about Trigonometry follow

https://brainly.com/question/24349828

#SPJ5

Answer:

Option B is correct

Step-by-step explanation:

Given:

f(x) = -20x^2 +14x +12 and

g(x) = 5x - 6

We need to find f/g and state its domain.

f/g = -20x^2 +14x +12/5x - 6

Taking -2 common from numerator:

f/g = -2(10x^2 - 7x - 6) / 5x -6

Factorize 10x^2 - 7x - 6= 10x^2 - 12x +5x -6

Putting in the above equation

f/g = -2(10x^2 - 12x +5x -6)/ 5x -6

f/g = -2(2x(5x-6) + 1 (5x-6)) / 5x-6

f/g = -2 ( (2x+1)(5x-6))/5x-6

cancelling 5x-6 from numerator and denominator

f/g = -2(2x+1)

f/g = -4x -2

The domain of the function is set of all values for which the function is defined and real.

So, our function g(x) = 5x -6 and domain will be all real numbers except x = 6/5 as denominator will be zero if x=5/6 and the function will be undefined.

So, Option B is correct.

ANSWER

-4x-2; all real numbers except x=6/5

Option B is correct.

EXPLANATION

The given functions are:

[tex]f(x) = - 20 {x}^{2} + 14x + 12[/tex]

We factor to get,

[tex]f(x) = - 2(10 {x}^{2} - 7x - 6)[/tex]

Split the middle term:

[tex]f(x) = - 2(10 {x}^{2} + 5x - 12x - 6)[/tex]

[tex]f(x) = - 2(5x(2{x} + 1)- 6(2x + 1))[/tex]

[tex]f(x) = - 2(2{x} + 1)(5x - 6)[/tex]

and

[tex]g(x) = 5x - 6[/tex]

[tex]( \frac{f}{g} ) = \frac{f(x)}{g(x)}[/tex]

[tex]( \frac{f}{g} ) = \frac{ - 20x + 14x + 12}{5x - 6}[/tex]

where 5x-6≠0

x≠6/5

[tex]( \frac{f}{g} ) = \frac{- 2(2{x} + 1)(5x - 6)}{5x - 6}[/tex]

Cancel the common factors to get,

[tex]( \frac{f}{g} ) = - 2(2{x} + 1)[/tex]

[tex]( \frac{f}{g} ) = - 4{x} - 2[/tex]

Answer:

The solution was solved correctly by Keith

The solutions of the equation are x=-5,x=-12

Step-by-step explanation:

we have

[tex]x^{2}+17x+72=12[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}+17x=12-72[/tex]

[tex]x^{2}+17x=-60[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]x^{2}+17x+8.5^{2} =-60+8.5^{2}[/tex]

[tex]x^{2}+17x+72.25 =12.25[/tex]

Rewrite as perfect squares

[tex](x+8.5)^{2}=12.25[/tex]

square root both sides

[tex](x+8.5)=(+/-)3.5[/tex]

[tex]x=-8.5(+/-)3.5[/tex]

[tex]x=-8.5(+)3.5=-5[/tex]

[tex]x=-8.5(-)3.5=-12[/tex]

The solution was solved correctly by Keith

The solutions of the equation are x=-5,x=-12

Answer:

The first box is Keith and the second box is -5,-12

Step-by-step explanation:

Answer:

[tex]x_1=i\sqrt{7}[/tex]

[tex]x_2=-i\sqrt{7}[/tex]  

Step-by-step explanation:

Given the equation [tex]x^2=-11+4[/tex], you need to solve for the variable "x".

You can follow this steps:

Step 1: you need to make the addition indicated in the equation:

[tex]x^2=-7[/tex]

Step 2: Apply square root to both sides of the equation:

[tex]\sqrt{x^2}=\±\sqrt{-7}[/tex]

[tex]x=\±\sqrt{-7}[/tex]

Step 3: Since [tex]i=\sqrt{-1}[/tex], then you need to rewrite it as:

[tex]x=\±i\sqrt{7}[/tex]

Therefore the solutions are:

[tex]x_1=i\sqrt{7}[/tex]

[tex]x_2=-i\sqrt{7}[/tex]

Answer:

D

Step-by-step explanation:

Use the formula for the volume of a cylinder.

[tex]V=\pi r^2h[/tex]

Plug in the values we know.

[tex]V=\pi6^2*9 \\ \\ V=36\pi*9 \\ \\ V=324\pi[/tex]

The volume of the cylinder given will be 324π.

The volume of a cylinder is calculated by using the formula:

Volume = πr²h

where,

r = radius = 6 inches.

h = height = 9 inches

Volume = πr²h

Volume = π × 6² × 9

Volume = π × 36 × 9.

Volume = 324π

Learn more about volume on:

https://brainly.com/question/12129530

A scale factor of 2 means the dimensions are multiplied by 2.

15 x 2 = 30

8 x 2 = 16

Answer:

259 divided by 170,000 gives you the % 259 is out of 170,000 which is .0015. Move the decimal two spaces to the right to get the actual commission rate=.15%

Answer:

C

Step-by-step explanation:

ln 1 = 0, so f(1) = 0 + 2 = 2.  So we need to find a graph that passes through (1, 2).  Only graph C fits.

The graph of the function f(x) = In x + 2 is the graph b

The parent function for the natural log function is f(x) = ln(x).

To transform the graph of f(x) = ln(x) to the graph of f(x) = ln(x) + 2, we perform the following transformation:

Vertical Shift:

The graph is shifted two units upward.

This is because adding 2 to the output of the function has the same effect as shifting the graph two units upward.

So, the graph of f(x) = In x + 2 is b

Rread more about transformation at

https://brainly.com/question/31898583

#SPJ2

Final answer:

To find the correct product of (5x − 11)² , apply the squaring of a binomial formula to get an expanded form 25x² − 110x + 121.

Explanation:

The student is asked to find the correct product of the expression (5x − 11)² . To solve this, we can apply the squaring of a binomial rule, which is an application of the distributive property (also known as the FOIL method for binomials). According to this rule, the square of a binomial (a − b)² is equal to a² − 2ab + b² .

Substituting 5x for a and 11 for b, we get:

(5x)² = 25x²  (the square of the first term)

2 × 5x × 11 = 110x (double the product of the two terms)

11² = 121 (the square of the second term)

Putting it all together:

(5x − 11)² = 25x − 110x + 121

This is the expanded form of the given expression.

Answer:

3²

Step-by-step explanation:

Add the indices together

3⁸ ₓ 3⁴ = 3¹²

3² ₓ 3⁸ = 3¹⁰

Now we minus the indices since we are dividing

3¹² - 3¹⁰ = 3²

Answer: 170

Step-by-step explanation:

Based on the problem, you know that this corporation listed their sales in 100s as 1,700. This means that, to calculate their actual volume in thousands, you need to multiply 1,700 by 100 and divide the product by 1,000.

Let be "x" their actual volume in thousands.

Therefore, applying the corresponding procedure, you get that the value of "x" is the following:

[tex]x=\frac{(1,700)(100)}{(1,000)}\\\\x=\frac{170,000}{1,000}\\\\x=170[/tex]

Final answer:

To find the corporation's sales volume in thousands from a base of '100s', one needs to multiply 1,700 by 100 and then divide by 1,000, resulting in a sales volume of 170 thousand shares.

Explanation:

The question asks us to convert a corporation's sales figure from 100s to thousands. The listed sales are 1,700 in 100s, which means the sales are 1,700 × 100 shares. To convert this number into thousands, we divide by 1,000 because there are 1,000 units in one thousand.

Thus, the calculation would be:

Multiply 1,700 by 100 to get the total sales in shares.

Divide the result by 1,000 to convert it into thousands.

(1,700 × 100) / 1,000 = 170,000 / 1,000 = 170.

Therefore, the actual volume of sales in thousands is 170.

Answer:

Could be C) or D) None of these, 29688.05cm^2

Step-by-step explanation:

Did the question to round off to any numbers?

Formula for cylinder's T.S.A: 2 π r h + 2 π r^2

Diameter= 2 x radius

Radius = 70cm / 2 = 35cm

Height -> need to convert m to cm -> 100cm

Substitute these values into the formula:

2 x π  x 35 x 100 + 2 x π x (35)^2 = 29688.05cm^2

Answer:

Q = 25°

Step-by-step explanation:

Given

cos(Q + 60) = 0.0872, then

Q + 60 = [tex]cos^{-1}[/tex] (0.0872 ) = 85° ( nearest degree )

Q = 85° - 60° = 25°

Answer:

the answer is A.

Step-by-step explanation:

that is a good good question

Answer:

C. 43.72

Step-by-step explanation:

just took it on edge

Answer:  $277.91

Step-by-step explanation:

The average of the 2 highest salaried quarters is:

[tex]\dfrac{\$13,500+\$12,775}{2}=\dfrac{\$26,275}{2}=\$3,137.50[/tex]

Divide that by 26 (weeks) to find out her average weekly salary:

[tex]\dfrac{\$3,137.50}{26}=\$505.29[/tex]

Multiply that by 55% (0.55) to calculate her weekly unemployment benefit:

[tex]\$505.29(0.55)=\$277.908[/tex]

Round to the nearest penny --> $277.91

[tex]3(2 + x) \\ = 6 + 3x \\ = 3x + 6[/tex]

Yes it is because three times two is six and three times x is three x hope this helps

Angle 4: 64.76 degrees because vertical angles are equal to each other

Angle 6: 180-64.76= 115.24 degrees.

I forget the names of these rules lol

<4 is also 64.76 because alternate interior angles are congruent

<6 is the same-side interior angle to <4 so they are supplementary angles. 180 - 64.76 = 155.24 degrees.

<6 is 155.24 degrees

Answer:

The possible values of n are -0.5 and -3.5

Step-by-step explanation:

Analyze two cases

1) n-(-2)=1.5

Solve for n

n+2=1.5

n=1.5-2

n=-0.5

2) -2-n=1.5

n=-2-1.5

n=-3.5

see the attached figure

Answer:-0.5,-3.5

Step-by-step explanation:i did this

Hello There!

First, we are give the problem which is 2,624/4

 0 6 5 6

4 2 6 2 4

− 0      

 2 6    

− 2 4    

   2 2  

 − 2 0  

     2 4

   − 2 4

       0

ANSWER IS 656

Answer:

1) x = 5√(1-sin^2t)

2) y = = -2+3t

Step-by-step explanation:

1)

Given rectangular equation:

x^2/25 + y^2 =1

Parametric equations y=-sint and x=?

Find parametric equation for x

Substituting value of y =-sint in given rectangular equation, we get

x^2/25 + (-sint )^2 =1

x^2/25 + sin^2t =1

x^2 + 25sin^2t = 25

x^2 =25 - 25sin^2t

taking square root on both sides

x= √(25 - 25sin^2t)

  = √25(1-sin^2t)

   = 5√(1-sin^2t)

2)

Given rectangular equation:

y=-3x+4

Parametric equations x=2-t and y=?

Find parametric equation for y

Substituting value of x=2-t  in given rectangular equation, we get

y= -3(2-t) +4

 = -6+3t+4

 = -2+3t !

Answer:

y = x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x is in this form

with slope m = 1 and c = 0

• Parallel lines have equal slopes, thus

y = x + c ← is the partial equation of the parallel line

To find c substitute (2, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = x + 2 ← equation of parallel line

The equation of the line parallel to y = x and passing through the point (2, 4) is y = x + 2.

In mathematics, two lines are said to be parallel if they have the same slope. The given line is y = x, and because its slope is 1 (the coefficient of x), the line we're looking for, which is parallel to this, will also have a slope of 1.

To find the equation of a line with a given slope that passes through a certain point, we use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the point. Substituting 1 for m, and the given point (2, 4) into this equation gives us y - 4 = 1(x - 2), which simplifies to y = x + 2, the equation of the line we were seeking.

https://brainly.com/question/35689521

#SPJ2

Answer:

A is the answer

Step-by-step explanation:

(0, -5):

-5 = 2(0) - 5 >>>   -5 = -5

-5 = (0)^2 - 5 >>>   -5 = -5

(2, -1):

-1 = 2(2) - 5 >>>   -1 = 4 - 5 >>>   -1 = -1

-1 = (2)^2 - 5 >>>   -1 = 4 - 5 >>>   -1 = -1

The solutions of the given set of equations are (0, -5) and (2, -1) so option (A) will be correct.

The equation is a combination of variable and constant. Which could be in addition multiplication or subtraction.

Given y = 2x -5 and y = x² - 5

By putting the y value into another equation

2x -5 = x² - 5

x² - 2x = 0

x(x - 2) = 0

x = 0 and x = 2.

Now y corresponding to x = 0 is y = -5 and corresponding to x= 2 is y = -1.

Hence the possible set of coordinates among the options are (0, -5) and (2, -1).

For more information about the system of equations.

https://brainly.com/question/13038733

#SPJ2