what is the input-output table for the function f(x) = 3x^2-x+4

Answer:

(x - 5)(x - 3)

Step-by-step explanation:

You need two numbers that multiply to 15 and add to 8. There aren't many numbers that will do that.

15 and 1 is one pair of numbers. They multiply to 15 but don't add to 8.

6 and 2 add to 8 but don't multiply to 15.

5 and 3. This in some form is your answer, but handle it carefully.

(x - 5)(x - 3)

The 5 and 3  both have to be minus.

Answer:

(x-3)(x-5)

Step-by-step explanation:

The expression is:

x2 - 8x+15

Break the middle term:

Coefficient of first term will be multiplied by constant

1*15 = 15

Now we have to find out which numbers will be multiplied to get 15

and also by adding those numbers we get the middle term:

3*5=15

3+5 = 8

Now break the middle term:

x^2-3x-5x+15

x(x-3)-5(x-3)

(x-5)(x-3)....

The factors are (x-5)(x-3)....

Answer:

[tex]x^{4}[/tex] - 10x³ + 37x² - 60x + 36

Step-by-step explanation:

Given

(x - 3)²(x - 2)² ← expand each factor using FOIL

(x - 3)² = x² - 6x + 9

(x - 2)² = x² - 4x + 4

We now have the product

(x² - 6x + 9)(x² - 4x + 4)

Each term in the second factor is multiplied by each term in the first factor, that is

x²(x² - 4x + 4) - 6x(x² - 4x + 4) + 9(x² - 4x + 4) ← distribute each parenthesis

= [tex]x^{4}[/tex] - 4x³ + 4x² - 6x³ + 24x² - 24x + 9x² - 36x + 36

Collect like terms

= [tex]x^{4}[/tex] - 10x³ + 37x² - 60x + 36

Answer:

Factored form...

Step-by-step explanation:

Foil out (x-4)(x+2)=16

First: x*x=[tex]x^{2}[/tex]

Outer: 2*x=2x

Inner: -4*x = -4x

Last: -4*2 = -8

Combine them all:

[tex]x^2+2x-4x-8=16[/tex]

Simplify:

[tex]x^2-2x-8=16\\x^2-2x-24=0[/tex]

What multiplies together to make -24 but adds together to make -2?

Lets list the factors of -24 to decide:

1 x -24

2 x -12

3 x -8

4 x -6

-6+4 = -2

Therefore...

[tex](x-6)(x+4)=0[/tex]

Answer:

3rd statement

Step-by-step explanation:

Lets go through the choices and see.

The first one says:

The equation x – 4 = 16 can be used to solve for a solution of the given equation.

If we solve this we get x=20. I just added 4 on both sides.

Is 20 a solution thr original equation? Let's check. We need to replace x with 20 in

(x – 4)(x + 2) = 16 to check.

(20-4)(20+2)=16

(16)(22)=16

16 times 22 is definitely not equal to 16 so the first statement is false.

Lets check option 2:

The standard form of the equation is

x2 – 2x – 8 = 0.

So lets put our equation in standard form and see:

(x – 4)(x + 2) = 16

Foil is what we will use:

First: x(x)=x^2

Inner: (-4)x=-4x

Outer: x(2)=2x

Last: -4(2)=-8

Add together to get: x^2-2x-8. We still have the equal 16 part.

So the equation is now x^2-2x-8=16. Subtracting 16 on both sides will put the equation in standard form. This gives us

x^2-2x-24=0. This is not the same as the standard form suggested by option 2 in our choices.

Checking option 3:

This says:

The factored form of the equation is

(x + 4)(x – 6) = 0.

So we already put our original equation in standard form. Lets factor our standard form and see if is the same as option 3 suggests.

To factor x^2-2x-24, we need to find two numbers that multiply to be -24 and add to be -2. These numbers are 4 and -6 because 4(-6)=-24 and 4+(-6)=-2. So the factored form of our equation is (x+4)(x-6)=0 which is what option 3 says. So option 3 is true.

Let's go ahead and check option 4: It says: One solution of the equation is x = –6. This is false because solving (x+4)(x-6)=0 gives us the solutions x=-4 and x=6. Neither one of those is -6. *

* I solved (x+4)(x-6)=0 by setting both factors equal to zero and solving them for x. Like so,

x+4=0 or x-6=0.

Answer:

15 - n/3 = 20

n = -15

Step-by-step explanation:

Decreased means subtract

15 -

quotient means divide

15 - n/3

Is means equals

15 - n/3 = 20

To solve subtract 15 from both sides

15-15 - n/3 = 20-15

-n/3 = 5

Multiply each side by -3

-3 * (-n/3) = 5*-3

n = -15

[tex]\huge{\boxed{y=-3x+4}}[/tex]

Slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] represents the slope and [tex]b[/tex] represents the y-intercept.

Substitute in the values. [tex]\boxed{y=-3x+4}[/tex]

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case the slope (m) is -3 and the y-intercept (b) is 4

Your equation is:

y = -3x + 4

Hope this helped!

~Just a girl in love with Shawn Mendes

Set up an equation:

Numerator is the top number and denominator is the bottom number in a fraction.

(6x)^5 / d = 36

(6x)^5 can be rewritten as 6^5x^5

6^5x^5 / d = 36

Raise 6 tot he power of 5:

7776x^5 /d = 36

Multiply both sides by d:

7776x^5 = 36d

Divide both sides by 36:

d = 7776x^5 / 36

d = 216x^5

Answer:

6^(32)

Also I don't see your choices.

Step-by-step explanation:

I'm going to apply this law of exponents: (x^a)^b=x^(a*b).

It justs says to multiply the exponents in this case so we have 6^(-8*-4)=6^(32).

Answer:

It would be 1/6^32

Step-by-step explanation:

Answer:

Given a function f(x), the function f(x) + k will be translated k units down if k<0. In this case, if we want to produce a vertical translation by 4 units down of the function f(x) = 2x, therefore the new function is:

f(x) = 2x - 4.

Now, we can graph the function like we normally do. Attached you will find the graph made with the help of a graphing calculator.

Answer:

6

Step-by-step explanation:

362/60

362 is the miles per hour

60 is the minutes in an hour

Answer:

The measure of minor arc BC is 176°

Step-by-step explanation:

we know that

The semi-inscribed angle is half that of the arc it comprises.

so

∠B=(1/2)[minor arc BC]

substitute

88°=(1/2)[minor arc BC]

minor arc BC=176°

mayor arc BC=360°-176°=184°

Answer:

Martha and George Washington had no children together, but they raised Martha's two surviving children. In 1773 her daughter Patsy died when she was 16 during an epileptic seizure. John Parke "Jacky" Custis left King's College that fall and married Eleanor Calvert in February 1774.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

16 un.

Step-by-step explanation:

In right triangle ABC:

m∠C = 90°;

m∠BAC = 2m∠ABC;

BC = 24;

AL is a bisector of angle A.

The sum of the measures of all interior angles in triangle  is always 180°, then

In right triangle the leg that is opposite to tha angle 30° is half of the hypotenuse. This means that

By the Pythagorean theorem,

Let AL be the angle A bisector. By bisector property,

Use the Pythagorean theorem for the right triangle ACL:

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Answer:

AL=24 cm

Step-by-step explanation:

We are given that a triangle ABC,

[tex]m\angle C=90^{circ}[/tex]

[tex]m\angle BAC=2m\angle ABC[/tex]

BC=24 cm

AL is angle bisector

We have to find the value of AL

Let [tex]m\angle ABC=x[/tex]

In triangle ABC

[tex]m\angle BAC+m\angle ABC+m\angle ACB=180^{\circ}[/tex]

[tex]2x+90+x=180[/tex]

[tex]3x=180-90[/tex]

[tex]3x=90[/tex]

[tex]x=\frac{90}{3}=30[/tex]

[tex]m\angle ABC=30^{\circ}[/tex]

[tex]m\angle BAC=2\times 30=60^{\circ}[/tex]

AL is a bisector of angle A

Then [tex]m\angle CAL=30^{\circ}[/tex]

BL=LC=12 cm

In triangle ACL

[tex]sin\theta =\frac{perpendicular side }{hypotenuse}[/tex]

[tex]sin30^{\circ}=\frac{12}{AL}[/tex]

[tex]\frac{12}{AL}=\frac{1}{2}[/tex]

[tex]AL=12\times 2=24 cm[/tex]

Hence, AL=24 cm

Answer:

1. D y = 8

2. C y = −8

Step-by-step explanation:

1.

Both points have y-coordinate 8, so the line is horizontal.

A horizontal line has equation

y = k

where k is the y-coordinate of all of its points.

The y-coordinate of all points on this line is 8.

Answer: y = 8

2.

A line with 0 slope is a horizontal line. All points on a horizontal line have the same y-coordinate.

A horizontal line has equation

y = k

where k is the y-coordinate of all of its points.

The y-coordinate of the given point is -8, so all points must have -8 as the y-coordinate.

Answer: y = -8

The equation of a line through two given points can be found using the point-slope form. A slope of 0 indicates a horizontal line.

To find the equation of a line that contains the points (0, 8) and (8, 8), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Here, (x1, y1) represents one of the points and m represents the slope. Since the y-coordinates of both points are 8, we can see that the line is horizontal. Therefore, the equation of the line is y = 8.

For the second question, a slope of 0 indicates a horizontal line. The equation of a horizontal line is y = b, where b is the y-coordinate of any point on the line. Since our point is (0, -8), the equation of the line is y = -8.

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Answer:

[tex]\large\boxed{(n^3)^2\times(n^5)^4=n^{26}}[/tex]

Step-by-step explanation:

[tex](n^3)^2\times(n^5)^4\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(n^{3\cdot2})\times(n^{5\cdot4})=n^{6}\times n^{20}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=n^{6+20}=n^{26}[/tex]

Answer:

I would recommend using algebraic methods.

Step-by-step explanation:

Of course, guess and check takes a long time and is not very time efficient. If you're graphing it by hand, it'll take time and get tedious, and using algebraic methods will probably give you the most accurate answer. If you have access to a graphing calculator or graphing website like Desmos, then I would suggest using the program to check the answers you got using the algebraic methods.

Hope this helped :)

Answer:

iii) Use algebraic methods

Step-by-step explanation:

There are various method of finding an accurate solution to a system of linear equations.

They are i) graphing method:  ii) algebraic method:  iii) Matrices method:

iv) determinant method:  v) guess method vi) Cramer's rule etc

Guess and check is not reliable because guess is possible only for integers or  numbers with 1 or 2 decimals. SOmetimes guess may give unreliable results.  And every time after the guess, checking and verifying will be time consuming and laborious

Graphing the lines may be accurate but writing tables for each line, choosing scales and drawing lines to find points of intersection may be time consuming.

Algebraic methods using are easy to understand, reliable, and less time consuming but 100% accuracy. There are a number of ways in algebraic method also such as substitution, elimination or cross

Answer:

$2322.59

Step-by-step explanation:

Given

mortgage amount=$470,000

Interest rate annually=4.6%

Time=30 years

Monthly payments=?

Formula to apply

[tex]M=\frac{P(1+r)^n*r}{(1+r)^n-1}[/tex]

where

M=monthly payment for the mortgage

P=Principal amount =$470,000

i=rate per month=4.6÷12=0.3833%

n=30×12=360

Applying the formula

[tex]M=\frac{P(1+r)^n*r}{(1+r)^n-1} \\\\\\M=\frac{470000(1+0.004)^{360}*0.004 }{(1+0.004)^{360} -1} \\\\\\M=\frac{7452.235}{3.209} =2322.59[/tex]

Answer: I need a picture off the pool and measurements.

Step-by-step explanation: I need this in order to figure out the problem and give you a helpful answer.

Answer:

Width or length

Step-by-step explanation:

Cavalieri's Principle states that in two solids with equal altitude, if the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal.

So, if Bailey's pool section is half her friend's pool, then the new volume would be half of the original.  To do that, she can half width or length

Answer:

93

Step-by-step explanation:

A quadrilateral's 4 angles add to 360 degrees

70 + 92+<1 + 105 = 360

Combine like terms

267 + <1 = 360

Subtract 267 from each side

267-267 + <1 = 360-267

<1 = 93

Answer:

93

Step-by-step explanation:

OK it's simple...

The interior angles of ANY quadrilateral (a shape with 4 sides) add up to 360.

So all you have to do is add up the angles you already know (70+92+105=267) and subtract that from 360. (360-267).

Answer:

[tex]y=\frac{1}{30}(x-7)+1.5[/tex]

2.8 million is what we get in 2047

Step-by-step explanation:

Ok I see the following given in 2007, the medium salary is 1.5 million and in 2013 the medium salary is 1.7 million.

It says let x=7 represent 2007 so that means x=13 would represent 2013.

It also says y is in millions so y=1.5 means 1.5 million and y=1.7 means 1.7 million.

So we have these points that we need to find a line for:  (7,1.5) and (13,1.7).

The slope can be found by using the slope formula given two points.  This looks like this (y2-y1)/(x2-x1).

I like to line the points up and subtract then put 2nd difference over 1st difference.

Let's do that.

(13, 1.7)

-(7, 1.5)

-----------

6       .2

The slope is .2/6 or 2/60 (after multiplying top and bottom by 10) or 1/30 (after dividing top and bottom by 2)

So point slope form for this line is [tex]y-1.5=\frac{1}{30}(x-7)[/tex].

To get the point slope form for this line I just entered my m (the slope) and point (x1,y1) I knew on the line (like (7,1.5) ). Point slope form is [tex]y-y_1=m(x-x_1)[/tex].

So adding 1.5 on both sides of  [tex]y-1.5=\frac{1}{30}(x-7)[/tex] gives me  [tex]y=\frac{1}{30}(x-7)+1.5[/tex]

So now it says what is the medium salary in 2047 I believe. So we are going to plug in 47.

This gives us

[tex]y=\frac{1}{30}(47-7)+1.5[/tex]

[tex]y=\frac{1}{30}(40)+1.5[/tex]

[tex]y=\frac{4}{3}+1.5[/tex]

[tex]y=2.833333333333333333333333[/tex]

So 2.8 million

Answer:

* The equation of the median of the trapezoid is 10x + 6y = 39

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) , (x2 , y2) is

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

- The mid point of the line whose end point are (x1 , y1) , (x2 , y2) is

  [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

- The standard form of the linear equation is Ax + BC = C, where

  A , B , C are integers and A , B ≠ 0

- The median of a trapezoid is a segment that joins the midpoints of

 the nonparallel sides

- It has two properties:

# It is parallel to both bases

# Its length equals half the sum of the base lengths

* Lets solve the problem

- The trapezoid has vertices R (-1 , 5) , S (! , 8) , T (7 , -2) , U (2 , 0)

- Lets find the slope of the 4 sides two find which of them are the

 parallel bases and which of them are the non-parallel bases

# The side RS

∵ [tex]m_{RS}=\frac{8-5}{1 - (-1)}=\frac{3}{2}[/tex]

# The side ST

∵ [tex]m_{ST}=\frac{-2-8}{7-1}=\frac{-10}{6}=\frac{-5}{3}[/tex]

# The side TU

∵ [tex]m_{TU}=\frac{0-(-2)}{2-7}=\frac{2}{-5}=\frac{-2}{5}[/tex]

# The side UR

∵ [tex]m_{UR}=\frac{5-0}{-1-2}=\frac{5}{-3}=\frac{-5}{3}[/tex]

∵ The slope of ST = the slop UR

∴ ST// UR

∴ The parallel bases are ST and UR

∴ The nonparallel sides are RS and TU

- Lets find the midpoint of RS and TU to find the equation of the

 median of the trapezoid

∵ The median of a trapezoid is a segment that joins the midpoints of

   the nonparallel sides

∵ The midpoint of RS = [tex](\frac{-1+1}{2},\frac{5+8}{2})=(0,\frac{13}{2})[/tex]

∵ The median is parallel to both bases

∴ The slope of the median equal the slopes of the parallel bases = -5/3

∵ The form of the equation of a line is y = mx + c

∴ The equation of the median is y = -5/3 x + c

- To find c substitute x , y in the equation by the coordinates of the

  midpoint of RS  

∵ The mid point of Rs is (0 , 13/2)

∴ 13/2 = -5/3 (0) + c

∴ 13/2 = c

∴ The equation of the median is y = -5/3 x + 13/2

- Multiply the two sides by 6 to cancel the denominator

∴ The equation of the median is 6y = -10x + 39

- Add 10x to both sides

∴ The equation of the median is 10x + 6y = 39

* The equation of the median of the trapezoid is 10x + 6y = 39

Answer:

The fraction of all shapes are circle is 3/4 (18/24)

Step-by-step explanation:

* Lets explain how to solve the problem

- There are white and black circles

- There are white and black squares

- The ratio of the number of white shapes to the number of black

  shapes is 5/1

∴ The total of the ratio of the all shapes is 5 + 1 = 6

∴ The ratio of the number of the white shapes to the number of all

   shapes is 5/6

∴ The ratio of the number of the black shapes to the number of all

   shapes is 1/6

- The ratio of the number of white circles to the number of white

  squares is 3/1

∴ The total of the ratio of the white shapes is 3 + 1 = 4

∴ The ratio of the number of the white circles to the number of white

   shapes is 3/4

∵ The ratio of the number of the white shapes to the number of all

   shapes is 5/6

∴ The ratio of the number of the white circles to the number of the all

   shapes = 3/4 × 5/6 = 15/24

- The ratio of the number of black circles to the number of black

  squares is 3/1

∴ The total of the ratio of the black shapes is 3 + 1 = 4

∴ The ratio of the number of the black circles to the number of black

   shapes is 3/4

∵ The ratio of the number of the black shapes to the number of all

   shapes is 1/6

∴ The ratio of the number of the black circles to the number of the all

   shapes = 3/4 × 1/6 = 3/24

- The ratio of the number of the circles to the number of the all shapes

  is equal to the sum of the ratio of the white and the black circles to

  the number of all shapes

∴ The ratio of the number of the circle to the number of all shapes is

   15/24 + 3/24 = 18/24 ⇒ divide up and down by 6

∴ The fraction of all shapes are circle is 3/4

Answer:

A = 2000 e^(0.03 t)

The account will have $2255  after 4 years

Step-by-step explanation:

* Lets talk about the compound continuous interest

- Compound continuous interest can be calculated using the formula:

  A = P e^rt

# A = the future value of the investment, including interest

# P = the principal investment amount (the initial amount)

# r = the interest rate  

# t = the time the money is invested for

- The formula gives you the future value of an investment,  which is  

  compound continuous interest plus the  principal.  

- If you want to calculate the compound interest only, you need

 to deduct the principal from the result, So, your formula is:

 Compounded interest only = Pe^(rt)  - P

* Now lets solve the problem

-  Ira invests $2,000 in an account

∵ P = $ 2000

- That account has an interest rate of 3%

∵ r = 3/100 = 0.03

- It is compounded continuously

∵ The equation of the compounded continuously is A = P e^rt

∴ A = 2000 e^(0.03 t)

- We want to find the money in the account after 4 years

∵ t = 4

∴ A = 2000 e^(0.03 × 4) = $2254.99 ≅ $2255

* The account will have $2255  after 4 years

Answer: 1/6

Step-by-step explanation: There are 9 marbles in total. There are 3 red marbles out of 9, and the fraction is 3/9, simplified to 1/3. Since the marble is not being replaced, there are now 8 marbles. 4 of the 8 marbles are blue. The fraction is 4/8, simplified to 1/2. Multiply the fractions.

1/3 x 1/2 = 1/6

There’s a 1/6 chance.

Answer:

The Solution set is (x,y){(2,5)}

Step-by-step explanation:

The given equation is:

  6x+4y=32

 -6x+4y=8

We will use the elimination method:

By this method we will eliminate the variable x.

6x+4y=32

-6x+4y=8

________

      8y=40

Divide both the sides by 8

8y/8=40/8

y=5

Now substitute the value of y in equation 2:

-6x+4y=8

-6x+4(5)=8

-6x+20=8

Move the constant value to the R.H.S

-6x=8-20

-6x= -12

Divide both the terms by -6

-6x/-6 = -12/-6

x= 2

The Solution set is (x,y){(2,5)}....

Answer:

The radius C) of a circle centered at the origin measures the distance from the origin to any point on the circle

Final answer:

The radius of a circle centered at the origin is the distance from the origin to any point on the circle, represented by the equation x² + y² = r².

Explanation:

The radius of a circle centered at the origin measures the distance from the origin to any point on the circle. When we consider the set of all points (x, y) at a fixed distance r from the origin, the equation x² + y² = r² represents a circle of radius r.

This equation is derived using the Pythagorean theorem. The radius is not to be confused with the circumference, which is the distance around the circle, or the y-coordinate, which is simply the vertical position of a point. The radius squared (r²) refers to the square of the length of the radius.

Answer:

60,000/ -30,000 (read explanation)

Step-by-step explanation:

8% of 10,000 is 800, 800 x 50(years) = 40,000, 100,000 -40,000 = 60,000, I believe you meant 100,000, cause if not, the answer is -30,000

Hope this helped

[tex]\bf \stackrel{\textit{y-intercept}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})}\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-1)}{1-0}\implies \cfrac{1+1}{1}\implies \cfrac{2}{1}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=2(x-0) \\\\\\ y+1=2x\implies \stackrel{\textit{general form}}{-2x+y+1=0}[/tex]

To find the equation of the line with a y-intercept of -1 and passing through the point (1,1), you first determine the slope (which is 2), leading to the slope-intercept form: y = 2x - 1. Then convert this to the general form: -2x + y + 1 = 0.

The general form of the equation of a line is Ax + By + C = 0 where A, B, and C are constants.

To write the equation of a line with a given point (1,1) and a y-intercept of -1, we'll start with the slope-intercept form of the equation, which is y = mx + b. We know that the y-intercept b is -1.

Next, we need to find the slope m, which is the change in y over the change in x. Using the point (1,1), we calculate the slope as (1 - (-1)) / (1 - 0) which equals 2.

Therefore, the slope-intercept form of our line is y = 2x - 1.

To convert this to general form, rearrange the terms and change the equation to have a 0 on one side: -2x + y + 1 = 0.

This is the general form of the equation of the line with the given conditions.

Answer:

0.5

Step-by-step explanation:

there are 26 black cards

26/52=

0.5

Answer:

0.5

Step-by-step explanation:

A deck of cards has 52 cards. Out of which 26 are red and 26 are black. The black cards are further divided into two suits.

So,

total sample space = n(S) = 52

Let A be the event that the drawn card is a black card

Then,

n(A) = 26

So, the probability of A will be:

[tex]P(A) = \frac{n(A)}{n(S)}\\ = \frac{26}{52}\\ =\frac{1}{2}\\ =0.5[/tex]

Hence the theoretical property of drawing a black card is 0.5 ..

Answer:

Step-by-step explanation:

We have a triangle 45° - 45° - 90°.

Sides are in the ratio 1 : 1 : √2 (look at the picture).

If [tex]BC=12\sqrt2[/tex] then [tex]AB=(12\sqrt2)(\sqrt2)=(12)(2)=24[/tex]

Used [tex](\sqrt{a})(\sqrt{a})=a[/tex]

Answer:

Jamal is 12 and his mother is 36

Step-by-step explanation:

12 times 3 is going to be 36. Then after 12 years, Jamal will be 24 and Jamal's mother will be 36+12 which is 48. Comparing 24 to 48, 48 is double 24 which means that 48 is two times greater than 24, (putting it in terms of the question).

Answer:

Jamal is 12 and his mom is 36

Step-by-step explanation:

If Jamal is 12 right now and you multiply that by three, you get 36. But since he's going to be half of her age in 12 years. So if you add 12 to 12 you get 24 for Jamal and if you add 12 to 36 you get 48 for his mom. This makes her age exactly double Jamal's age.