How can you transform the equation 8x - 10 + 10 + 4x = -10 + 6x + 6x + 10 into the form of a = a, where a is a number, to show that the equation has an infinite number of solutions? Select all that apply.

A. by adding 12x to both sides of the equation and then simplifying

B. by subtracting 8x to both sides of the equation and then simplifying

C. by subtracting 12x from both sides of the equation then simplifying

D. by subtracting 20 from both sides of the equation then simplifying

E. by dividing 6x from both sides of the equation and then simplifying

Answer:

20% off

Step-by-step explanation:

22-17.60=4.4

(5)4.4=22

Answer:

bottom right

Step-by-step explanation:

bottom right

After simplifying the expression we get: 12√6

Given, √864

Take the LCM of the given number:

864 = 2×2×2×2×2×3×3×3

Minimize the terms:

= √4×4×2×9×3

Reduce the terms:

= √16×9×2×3

multiply the terms:

= √144×2×3

= 12√6

Hence after simplifying we get the answer as 12√6

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The zeros of the function f(x) = x³ + 9x² + 20x  is :

0, 5 ,4

Steps to solve quadratic equation:

Check your answer by plugging it into the original equation.

Given function,

f(x) = x³ + 9x² +20x

take x common from f(x),

=> x(x² + x - 20) = 0

=> x(x² + 5x + 4x + 20) = 0

=> x( x + 5 ) + 4 ( x +5 ) = 0

=> (x + 5)  ( x + 4 ) = 0

=> x -5 = 0 or x -4 = 0

=> x = 5 and x = 4 .

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Answer:

A

Step-by-step explanation:

below is the parent function graphed and according to the chart we move the graph down 2 units and reflect it over the x axis and a is the only option

The equation for the linear function f(x) is f(x) = 2 / 7 x - 10 / 7

The linear function is f(x)

f(-2) = - 2 and f(5) = 0

Therefore, let's find the equation for the linear function f(x):

A linear function is a function that represents a straight line on the coordinate plane.

Therefore, linear function is represented as follows:

y = mx + b

where

Hence,

-2 = m(-2) + b

0 = 5m + b

b = -5m

Therefore,

m(-2) + - 5m = -2

-2m - 5m = -2

-7m = -2

m = 2 / 7

Therefore,

b = - 5 (2 / 7)

b = - 10 / 7

Hence,

f(x) = 2 / 7 x - 10 / 7

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y = -1/5x +1/2 linear function has the same slope .

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

First solve for the slope

m =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m=[tex]\frac{0-\frac{3}{5} }{\frac{1}{2} -\frac{1}{5} }[/tex]

m = [tex]\frac{-1}{5}[/tex]

Look for the linear equation with the same value of m after determining the slope (parallel equation).

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Time can be used to quantify, contrast, or even rank the length of events or the gaps between them. To complete the cooking at 2:00 PM, George needs to start his cooking at  12:30 PM.

Time can be defined in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be calculated, compared, or even ordered utilizing time.

Given time needed for each meals are;

Turkey = 70 min

Pumpkin pie = 17 min

Rolls = 30 sec

coffee = 45 sec

Total time = 87 min 75 sec

                = 1 hour 27min 75 sec

So in order to complete the cooking at 2:00 PM, George needs to start his cooking at  12:30 PM.

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Answer:

3/7

Hope this helps!

Have a good day :).

The number of ways that 5 players can be selected from the 11 eligible players is; 462 ways

The number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth is; 120 Ways

We are given that In a soccer match;

A tie at the end of two overtime periods leads to a "shootout" with five kicks taken by each team from the penalty mark.

Each kick must be taken by a different player

Now, to find the number of ways that 5 players can be selected from the 11 eligible players, we will use combination to get;

11C5 = 11!/(5! * (11 - 5)!)

= 11!/(5! * 6!)

= 462 ways

Now, if we care about order or position, we will use permutation to get the number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth;

5P5 = 5!/(5 - 5)

= 120 Ways

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Dilate figure A with center o and scale factor 2

What is transformation?
The transformation, or f: X → X, is the name given to a function, f, that maps to itself. The pre-image X becomes the picture X following the transformation. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.
Example: A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.

We know that re-sizing an item uses a transition called dilation.
In the figure the dimensions of the figures differ by a factor of 2.
Thus, dilation of figure A by a factor of 2 shows figure A is similar to Figure B

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Written in Slope Intercept Form:

[tex]y=-\frac{5}{4} x-14[/tex]

Hope this helps! If so, please lmk! Thanks and good luck!

The relation which is a function among the answer choices is; A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.

A function is a relation in which each element of the domain is associated with exactly one element of the codomain.

A relation can be tagged a function if it describes that there should be only one output (y - value) for each input ( x - value). Put simply, a function is a kind of relation (defined by a set of ordered pairs) in which case, it ensures that every x-value is associated with only one y-value.

On this note, since the relation described in the first answer choice is such that every x-value is associated with only one y-value as it is a parabola (quadratic function), it is termed a function.

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Answer:

This video provides an example of how to determine the original price of an item given the discounted price and the percent mark

Step-by-step explanation:

Given that P is a point on the perpendicular bisector, l, of MN, we have proved that PM = PN because By the definition of reflection, point P is the image of itself and point N is the image of N.

We are given :

P is a point on the perpendicular bisector, l, of MN.

Now, we want to prove that PM = PN

A Reflection is a transformation in which the figure is the mirror image of the other. Every point is a mirror reflection of itself .

By the definition of reflection, we can deduce that point P is the image of itself , and point N is the image of M .

The line l acts as a Line of symmetry or axis of reflection.

Now, in transformations, we know that reflections preserve length and as a result, PM = PN.

Therefore, we will conclude that point N is the image of M .

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Answer: Point M

Step-by-step explanation:edge 2023

An equation of the line in point-slope form is y = 6x + 50.

y = y₁ = m(x -x₁) is the equation of a straight line, where m is the slope and (x₁, y₁) are the coordinates at a given point on the line (see slope-intercept form). When you know the slope and another point on the line, the point-slope form of a linear equation is most helpful for locating a point on a line. When two other points are known, it can also be used to locate a point on a line.

Given,

y₂ = 200

y₁ = 230

x₂ = 30

x₁ = 25

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Slope = [tex]\frac{230-200}{30-25}[/tex]

Slope = [tex]\frac{30}{5}[/tex]

Slope = 6

Equation:

y - y₁ = m(x - x₁)

y - 200 = 6(x - 25)

y - 200 = 6x - 150

y = 6x + 50

An equation of the line in point-slope form is y = 6x + 50.

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The mean = 0.2,  variance = 0.03226 and Standard deviation = 0.1796

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given:

level            x

1             0.419

2            0.276

3            0.225

4            0.068

5            0.012

So, mean = (0.419+ 0.276 + 0.225+ 0.068 + 0.012)/5

mean = 0.2

level          x        (x- mean)       (x- mean)²        

1             0.419        0.219            0.0479  

2            0.276       0.076            0.0057

3            0.225        0.025         0.000625

4            0.068       -0.268         0 .0718

5            0.012        -0.188          0.0353

So, variance = 0.032265

standard deviation = √(variance)

Standard deviation = √(0.032265)

Standard deviation = 0.1796

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Answer:

You cant use the distributive property because it is when the equation is like this: ax(b+c) so if it was 11x(5+0) you would multiply the 5 by 11 by itself and multiply 0 with 11 then you add them and get 55. I hope that helps :)

Step-by-step explanation:

Answer:

the ratio is 6.5 : 1.5

Step-by-step explanation:

it asks "what is the ratio of time spent studying in math to studying for English?"

ratio uses the ":" mark. also you put the parts like this:

first part : second part

the parts can be found by looking for the "to" as indicated bold in the question

the first part of the ratio it asks is the "time spent studying in math" in hours which is 6.5

the second part of the ratio it asks is the "time spent studying in English" in hours which is 1.5

so the answer is:

6.5 : 1.5

Answer:

Ratio of time spent studying in math to studying for English

[tex]\large \text{$=\dfrac{13}{3}$ }[/tex]

Step-by-step explanation:

What is a ratio?
We use ratios to compare two numeric quantities or quantities with the same units

Basically a ratio of one quantity x to another quantity y can be expressed in the following ways, all read as the ratio of x to y

x/ y

x to y

x : y

The most useful way of representing a ratio is by using the fractional form because it can be used in determining other quantities

In this problem you spend 6.5 hours/week  studying for math and 1.5 hours/week studying for English

Since both units are the same (hours/week) we can compute the ratio as

[tex]{\dfrac{\text{Number of hours studying math}}{\text{Number of hours studying English}}\\\\= \dfrac{6.5}{1.5}\\\\[/tex]

We can simply this fraction as follows

Multiply both numerator and denominator by 10

[tex]= \dfrac{65}{15}\\\\[/tex]

Divide both sides by 5

[tex]\dfrac{65 \div 5}{15 \div 5}\\\\= \boxed{\bold{\dfrac{13}{3}\\\\}}[/tex]

This is the same as 13:3 or 13 to 3

(Be careful what is the numerator and what is the denominator.
If the question had asked for the ratio of hours studying English to hours studying Math then the ratio would be 1.5/65 = 15/65 = 3/13)

The equation of the line passing through points (-2, 5) can be written as follows

Equation of a straight line is an equation of the form y = mx + c, where

The slope is the gradient which is the ratio of the difference in the y direction to the difference in x direction.

given that the equation of the line is x + 3y = 7

rewriting the equation gives

y = -x/3 + 7/3

hence the slope is -1/3, and this is equated with the formula for slope

[tex]\frac{y-y_{1} }{x-x_{1} }=-\frac{1}{3}[/tex]

substituting the values for points  (-2,5)  and cross multiplying gives

3 (y - 5) = - ( x - -2)

y - 5 = - (x + 2 ) /3

y - 5 = -x/3 - 2/3

y = -x/3 - 2/3 + 5

y = -x/3 + 13/3

Rewriting the equation of the line in standard form is done as follows

y = -x/3 + 13/3

3y = -x + 13

x + 3y = 13

The equations are gotten from substitution the values to the formula for slope and substituting. Rearranging the equation gives the equation in slope intercept form and in standard form.

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Answer:

Bottom left

Step-by-step explanation:

The figure that looks like <-------------------------> is a line

Top left *------------------------* is a segment

Bottom right is a ray *---------------->

Top right is a * point or dot

I hope this helps!

The dimensions of the fenced-in area is

either length = 35 yards and width = 80 yards ,  

or length = 40 yards and width = 70 yards .

In the question ,

it is given that

the total length of the fence = 150 yards

let L be the length of the area to be fenced

let B be the width of the house

Given that one side of the area is fenced using the back side of the house

So, the perimeter of the area to be fenced is 2L+B

equating both the perimeter we get

2L+B=150

B=150-2L       ....(i)

Given the area fenced-in portion = 2800 yards

also the fenced-in portion area = L×B

hence

L*B=2800

Substituting the values of B from equation(i) , we get

L*(150-2L)=2800

150L - 2L² = 2800

2L² - 150L + 2800 = 0

simplifying further , we get

L² - 75L + 1400 = 0

L² -40L -35L +1400 = 0

L(L-40) -35(L-40) = 0

(L-35)(L-40) = 0

So , L = 35 yards or L = 40 yards

Using L = 35 yards , we get B = 150-2(35) = 80 yards

and using L =40 yards , we get B = 150-2(40) = 70 yards .

Therefore , The dimensions of the fenced-in area is

either length = 35 yards and width = 80 yards   ,

or length = 40 yards and width = 70 yards   .

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The modal mark is 16.because as we can see there are two 15, two 13,one 14, two 17 and three 16.

The most appropriapriate choice for factorization will be given by-

[tex](x^2+12+4x)(x^2+12-4x)[/tex] is the required factorization.

What is factorization?

The process of breaking an algebraic expression into product of different factors is called factorization.

Here,

The factorization of [tex]x^4+8x^2+144[/tex] has been shown below-

[tex]x^4+8x^2+144[/tex]

[tex](x^{2} )^2 + 24x^2 +144 -16x^2\\(x^{2} )^2 + 2\times x^2\times 12+ 12^2-16x^2\\(x^2+12)^2 - (4x)^2\\(x^2 + 12+4x)(x^2+12-4x)[/tex]

This is the required factorization

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The solution of the equation is x = 5.

The equation is written as follows:

- 94  = -2 (8x + 7)

The variable to be found as variable x.

A variable is a number represented with a letter in an equation.

Hence,

- 94  = -2 (8x + 7)

open the bracket on the right side of the equation

-94 = - 16x - 14

add 14 to both sides of the equation

-94 = - 16x - 14

-94 + 14 = - 16x - 14 + 14

-80 = - 16x

divide both sides by -16

x = -80 / -16

x = 5

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Answer:

32% or 31.82%

Step-by-step explanation:

so total = 11 billion and export + ethanol = about 3.5 billion so the probability is 3.5/11 or 35/110 which, as a percent, can be written as 32% or more accurate, 31.82% so this is answer

The slope of the line is [tex]\frac{2}{3}[/tex]

The increase divided by the run is the slope. By examining the rise and run, you can infer the slope of a line from its graph. A line has the property that its slope remains constant throughout.

Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.

The slope of the line is [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex]

⇒ [tex]\frac{-7-(-5)}{9-6}[/tex]

⇒ [tex]\frac{-7 + 5}{ 3} = \frac{2 }{3}[/tex]

Thus m = 2/3

Similarly in second case : [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex]

⇒ [tex]\frac{-15 - (-11)}{ 21 - 15}[/tex]

⇒ [tex]\frac{4}{6}[/tex]

= 2/3

Thus the slope of the given table is 2/3

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Answer:

  $1258.09

Step-by-step explanation:

You want the monthly annuity payment that will let you withdraw $150,000 per year forever from an account earning 8% after 30 years.

In order to withdraw an amount "forever," the withdrawal amount must be equal to the interest earned by the account.

  I = Prt

  150,000 = P(0.08)(1)

  P = 150,000/0.08 = 1,875,000

The value of an ordinary annuity is given by the formula ...

  A = P(12/r)((1 +r/12)^(12t) -1) . . . . . where P is the monthly payment, and r is the annual interest rate earned over a period of t years.

Using the values we know, we can find P:

  1875000 = P(12/0.08)((1 +0.08/12)^(12·30) -1) = 1490.359449P

  P ≈ 1258.09

You would need to deposit $1258.09 each month.

__

Additional comment

The formulas used here assume that the deposits and withdrawals occur at the end of the month.