evaluate numerical expression . Be sure to use the order of operations rules. ​

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.

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Answer:

x=-1 or x=7

Step-by-step explanation:

|x−3|=4

x-3=-4 or x-3=4

x=-1 or x=7

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:

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

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.

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To find an equivalent ratio, multiply both the numerator and denominator of the given ratio by the same number. In this case, multiplying both 1 and 26 by 2 gives us an equivalent ratio of 2:52.

To find an equivalent ratio, we can multiply or divide both the numerator and denominator of the given ratio by the same number. In this case, we can multiply both the numerator and denominator of the ratio 1:26 by 2 to get an equivalent ratio. Therefore, the equivalent ratio is 2:52.

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.

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:

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

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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:

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

Answer:

1 1/3

Step-by-step explanation:

(5/6 x 1/1) + (1/2 x 2/3) + ?

the answers to that are 5/6 and 3/6 so

5/6 + 3/6 = ???

5 + 3/ 6 = 8/6

8 divided by 2/ 6 divided by 2 = 4/3

so divide the numerator and denominator 4 divided by 3

then convert that to a mixed number

1 1/3

Answer:

13/16.

Step-by-step explanation:

1/2 = 8/16 so:

5/16 + 1/2

= 5/16 + 8/16

= 13/16 (answer).

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:

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

[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

Answer:

7

Step-by-step explanation:

Since the triangle is right we can use the cosine ratio to find IR

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{IR}{TR}[/tex] = [tex]\frac{IR}{14}[/tex]

Cross- multiply

IR = 14 × cos60° = 14 × 0.5 = 7

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

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: 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:

[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:

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).

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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:

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 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

Final answer:

The equation y = -x² - 2x + 3 can be expressed in vertex form as y = -(x + 1)² + 4.

Explanation:

The equation y = -x² - 2x + 3 can be expressed in vertex form as:

y = -(x + 1)² + 4

To convert the equation to vertex form, we need to complete the square. Here are the steps:

Factor out a common negative from the first two terms: y = -1(x² + 2x) + 3

Take half the coefficient of x (-2/2 = -1) and square it: (-1)² = 1

Add the squared value inside the parentheses and subtract it outside: y = -(x² + 2x + 1) + 3 - 1

Simplify: y = -(x + 1)² + 2

The vertex form of the equation is y = -(x + 1)² + 4.

Answer:

(3,-3)

Step-by-step explanation:

An ordered pair is written with X first, then Y (X,Y).

X is the left and right axis Y is the up and down axis.

The dot is at X = 3 and Y = -3

It would be written as (3,-3)

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:

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:

see explanation

Step-by-step explanation:

Given

T= 2π[tex]\sqrt{\frac{L}{g} }[/tex]

Square both sides

T² = 4π² [tex]\frac{L}{g}[/tex] ( divide both sides by 4π²

[tex]\frac{T^2}{4\pi ^2}[/tex] = [tex]\frac{L}{g}[/tex]

Multiply both sides by g

L = [tex]\frac{gT^2}{4\pi^2 }[/tex]

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

15 x 2 = 30

8 x 2 = 16