Simplify fully 12(x - 2)² /6(x-2)(x + 5) 4​

Answer: your welcome

Step-by-step explanation:

Let x = the certain number

"A certain number was tripled                       3x

"then decreased by 10":        3x - 10

"then doubled":           2*(3x-10)

"Then increased by 2":      2(3x-10)+2

"result was 5 times original number":

   2(3x-10)+2 = 5x

   6x - 20 + 2 = 5x

   6x - 5x = 20 - 2

      x = 18

Check (very important):

Is    2*(3*18 - 10) + 2:= 5*18        ?

     2*(54-10) + 2 = 90    ?

      2*(44) + 2 = 90    ?

         90 = 90    ?yes

The statement that best describes the graph of a proportional relationship with paired points is: A. A straight line can be drawn through all the points, and the line passes through the point (0, 0).

A graph that represents a proportional relationship between two variables can be described as a graph that connects all the given points and goes through the point of origin, (0, 0).

A proportional relationship graph is also a straight line graph. Every point in the relationship are located on the line.

An example of a graph that represents a proportional relationship between two variables is the graph given in the diagram above.

As you can observe, all points are connected by a straight line and it passes through the point of origin, (0, 0).

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Answer:

A = 28

B = 2

C = 29

Step-by-step explanation:

28×2+29 = 85

28+2×29 = 86

The probability of winning the lottery is 6.16*10^(-7).

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Answer:

|-74| = 74

yw:)

hope it helps

The coordinates of RS are R(2, 3) and S(-5, 6)

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

Given:

Segment RS is rotated 90 counterclockwise about the origin

So, When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x).

Also, the coordinates are reflected over y- axis.

So, The coordinates of RS before reflection over y- axis is

R(-3, 2) and S(-6, -5)

Now, the coordinates of RS before rotation is

R(2, 3) and S(-5, 6)

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Answer: $97.5

Step-by-step explanation:

15(4) + 7.5(5) = $97.5

Answer:

97.5

Step-by-step explanation:

got it right

Answer:

Second option $0.2

Step-by-step explanation:

First we can convert 3/8 pounds to oz

since 16oz is in 1 pound

so 3/8 pound will be

3/8*16=6 oz

Then to find unit price per oz

we just take the total cost $1.20 divide by 6

$1.20/6=$0.2

Answer:

9, 9, 9900

Step-by-step explanation:

The option that is an appropriate procedure for this experiment is D. The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if their cholesterol level is lowered.

From the information illustrated, the doctor wants to determine if a new medication for cholesterol is more effective than the previous medication.

In this case, it should be noted that it's important to prevent bias. Therefore, it's important that the doctor randomly assign the 30 patients to the new medication

In conclusion, the correct option is D.

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Answer:

answer is A got it right

Step-by-step explanation:

The value of each letter in the given magic square is a = 30, b = 6 , c = 18 and d = 4.

A magic square is one that has several different integers placed in such a way that the sum or total of the numbers is the same on all of the diagonals, as well as in every row, column, and major diagonal.

Given:

A magic square where all rows, columns, and diagonals sum to the same number.

Sum of the numbers in the diagonal of the magic square,

5 + 17 + 29 = 51

In the first row, the sum of numbers will also be 51

5 + a + 16 = 51

a = 51 - 21 = 30

Similarly, the sum in the first column

5 +  28 + c = 51

c = 51 - 33 = 18

And the sum in the last row,

c + d + 29 = 51

Putting the value of c, we get

18 + d + 29 = 51

d = 51 - 47 = 4

Now to find the value of b the sum of the last column,

16 + b + 29 = 51

b = 51 - 45 = 6

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On an average 9.043 [tex]\times10^{5}[/tex] beats more does the mouse heart beats in a day.

The average human heart beats = 1.037[tex]\times10^5[/tex] times per day.

The approximate average mouse heart beats = 1.008[tex]\times10^6[/tex] times per day.

We have to find the how many beats more does the mouse heart beats in a day.

Since we have to find the more heart beat of mouse comparing to the human heartbeats. So we subtract their heart beat.

The human heartbeats have [tex]10^5[/tex] while mouse heartbeats have [tex]10^6[/tex]. So we first equal the power of 10. After equal the power we can easily find the value of the more heart beat of mouse.

We can write,

The average human heart beats = 0.1037[tex]\times10^6[/tex]

Now,

The more heartbeats of mouse = average mouse heart beats − average human heart beats.

The more heartbeats of mouse [tex]= 1.008\times10^6-0.1037\times10^6[/tex]

The more heartbeats of mouse [tex]=(1.008-0.1037)\times10^{6}[/tex]

The more heartbeats of mouse = 0.9043[tex]\times10^{6}[/tex]

The more heartbeats of mouse = 9.043[tex]\times10^{5}[/tex]

Hence, on an average 9.043[tex]\times10^{5}[/tex] beats more does the mouse heart beats in a day.

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IT MEANS THAT THE X COORDINATE CHANGED BY -4

[tex]x = 6 - 4 \\ x = 2[/tex]

THE NEW COORDINATE OF X IS 2

AND THE Y COORDINATE CHANGED BY +7

[tex]y = - 2 + 7 \\ y = 5[/tex]

THE NEW COORDINATE OF Y IS 5

(2,5)

ATTACHED IS THE SOLUTION

The graph of the line passing through the points (-1,-2) with the slope 6/5 has been plotted

The line passing through the points = (-1,-2)

The slope of the line = 6/5

The slope of the line the change in y coordinates with respect to change in x coordinates of the line

We know

Point  slope form [tex](y-y_{1})=m(x-x_{1})[/tex]

Where m is the slope of the line

Substitute the values in the equation

(y-(-2))= 6/5(x-(-1))

y+2 =  6/5(x+1)

y+2 = (6/5)x+6/5

y = (6/5)x+(6/5)-2

y = (6/5)x+(-4/5)

Draw the graph

Hence, the graph of the line passing through the points (-1,-2) with the slope 6/5 has been plotted

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Let x and y be the number of hours Ryan works on each job respectively. He can work no more that 10 hours a week, it means that the sum of x and y must be less than or equal to 10:

He also need to earn at least $72 a week, which means that the sum of 9 times x and 18 times y must be greater than or equal to 72:

The system of inequalities is:

To graph these inequalities, we have to graph the boundary lines which are x+y=10 and 9x+18y=72, and then shade the region depending on the inequality. For the first inequality which is a less than or equal to, the shaded region must be under the boundary line (which is a continuous line) and for the second one, the shaded region must be above the boundary line (which is also continous).

In this case we only can take the solutions that have positive values of x and y, since Ryan can't work a negative number of hours. For example, one combination that will allow Ryan reach his goal is 5 hours as babysitter and 5 hours at the coffee shop.

The equation that can be derived is [tex]4(x-3)=12[/tex]

Given

Four times the difference of some number and 3 amounts to the quotient of 144 and 12.

Let us say some number is x

Quotient of 144 and 12,

Quotient = [tex]\frac{144}{12}[/tex]

Quotient = 12

Four times the difference of x and 3 is as follows

[tex]4(x-3)[/tex]

Writing this in the form of an equation we get

[tex]4(x-3)=12[/tex]

Hence the equation is obtained, also solving the equation for x

[tex]4x-12=12[/tex]

[tex]4x = 24[/tex]

[tex]x=\frac{24}{4}[/tex]

[tex]x=6[/tex]

Hence the equation for given conditions is obtained.

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Answer:-7\5 IS THE ANSWER TO THAT

Step-by-step explanation:

Answer:

a

2

−

b

2

=

(

a

+

b

)

(

a

−

b

)

where

a

=

7

and

b

=

3

x

.

(

7

+

3

x

)

(

7

−

3

x

)

Step-by-step explanation:

Here, we want to evaluate the given equation

Looking at what is given, the operations performed on both sides are different

The reason is because we have addition on one side and division on the other side

By the addition property of equality, we are supposed to have the same operation performed on both sides

Since it is different, then the two are not equal

The amount of interest to be paid by Destiny on the $1600 loan at 6% rate for 3 years is $288.00.

Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.

The formula calculating simple interest is expressed as;

I = P × r × t

Where P is principal, r is rate and t is time.

Given the data in the question;

First, convert the rate from percent to decimal.

Rate r = 6%

Rate r = 6/100
Rate r = 0.06

Now plug the values into the formula and solve for I

I = P × r × t

I = $1,600 × 0.06 × 3

Interest I = $288.00

Therefore, the interest accumulated by Destiny is $288.00.

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The correct option is d. No extrema, is obtained for the given function.

For the state question,

The function is defined as; f(x) = 2/(3x-5).

To estimated the extrema of the function, first find the critical points.

Differentiate the function with respect to x suing division rule.

f(x) = 2/(3x-5).

f'(x) = 3/(3x-5)²

Now, put the function equals to zero.

f'(x) = 3/(3x-5)² = 0.

3 = 0

But, 3 ≠ 0

Thus, there is no critical point found for the function.

The give function is independent of the value of the x, and thus called the constant function.

Therefore, there is no extrema obtained for the function.

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Answer:

Step-by-step explanation:

Lenght of a rectangle: L

Widht of the rectangle: W

Perimeter of the rectangle: P

length of a rectangle is four times it's width: L = 4W

Perimeter is at most 106: P <= 106

Perimeter is 2L + 2W: P = 2L + 2W

P <= 106

if we use the value of P = 2L + 2W, we can write:

2L + 2W <= 106

Since L = 4W, then we can write this equation:

2L + 2W <= 106

2(4W) + 2W <= 106

8W + 2W <= 106

10W <= 106

W <= 106/10 = 10.6

W <= 10.6

Therefore, the greatest possible value for the width is 10.6

Answer:

10.6

Answer:

to solve for x, you gotta make the two equations equal to each other then you can move the numbers to get the value of x

20x+10=30x-10

20x-30x=-10-10

-10x=-20

x=2

Answer:

x=2

Step-by-step explanation:

if m/A and m/B are equal, to find x, your equation would be 20x+10=30x-10. doing two step equations, you would substract 20x from both sides, making your equation look like 10=10x-10. then you would add 10 from both sides making your equation 20=10x. then you would divide 10x from both sides making x=2.

The probability that the subject​ lied, given that the test yields a positive result is; 81.81%

From the given table, we see that;

Number of people with a positive result who did not lie = 10

Number of people with a positive result who lied = 45

Total number of people with positive results = (10 + 45) = 55

Number of people with a negative result who did not lie = 34

Number of people with a negative result who lied = 12

Total number of people with negative results = (34 + 12) = 46

The probability that the subject​ lied, given that the test yields a positive result is;

Probability = 45/55 = 0.818 = 81.81%

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The correct answer is commutative property of addition.

What is commutative property?

In mathematics, the commutative property states that the sum of the expression does not change by changing the order or position of the numbers. Basically, changing the order does not change the sum.

According to the question, the given equation for the property of identity is as follows: 4 + 5 = 5 + 4

For this equation, the commutative identity property of addition which states that:  a + b = b + a

Therefore, using this property, the given equation can be written as:

4 + 5 = 5 + 4

Hence, the correct answer is commutative property of addition.

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The set of letters in the word 'woodpecker' using the listing (roster) method is {c, d, e, k, o, p, r, w}

From the question, we are to write the set of letters in the given word.

The given word is 'woodpecker'.

We are to write the set using either the listing (roster) method or the set builder notation.

The most concise way of writing the set is by using the listing (roster) method.

The roster method is a way to show the elements of a set by listing the elements inside of bracket.

The set of the letters in the given word is {c, d, e, k, o, p, r, w}

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