Answer:
1) 396
2) 20 1/2
3) 26.6
4) 8x + 56
5) 66 + 6x
6) 8x + 8
Step-by-step explanation:
* Lets explain how to solve the product mentally
# Remember the distributive property can help you to find the product
mentally the distributive property ⇒ a(b + c) = ab + ac
- Lets solve them
1)
- In 9 × 44 we can write 44 as (40 + 4)
∴ 9 × 44 = 9(40 + 4)
∵ 9(40 + 4) = 9 × 40 + 9 × 4
- Now lets multiply 9 by 40 and 9 by 4
∵ 9(40) = 360
∵ 9(4) = 36
∴ 9 × 40 + 9 × 4 = 360 + 36 = 396
∴ 9 × 44 = 396
2)
- In 4 × 5 1/8 we can write 5 1/8 as (5 + 1/8)
∴ 4 × 5 1/8 = 4(5 + 1/8)
∵ 4(5 + 1/8) = 4 × 5 + 4 × 1/8
- Now lets multiply 4 by 5 and 4 by 1/8
∵ 4(5) = 20
∵ 4(1/8) = 1/2
∴ 4 × 5 + 4 × 1/8 = 20 + 1/2 = 20 1/2
∴ 4 × 5 1/8 = 20 1/2
3)
- In 7 × 3.8 we can write 3.8 as (3 + 0.8)
∴ 7 × 3.8 = 7(3 + 0.8)
∵ 7(3 + 0.8) = 7 × 3 + 7 × 0.8
- Now lets multiply 7 by 3 and 7 by 0.8
∵ 7(3) = 21
∵ 7(0.8) = 5.6
∴ 7 × 3 + 7 × 0.8 = 21 + 5.6 = 26.6
∴ 7 × 3.8 = 26.6
- The distributive property ⇒ a(b + c) = ab + ac
4)
- In 8(x + 7) we will multiply 8 by x and 8 by 7 and add them
∵ 8 × x = 8x
∵ 8 × 7 = 56
∴ 8(x + 7) = 8x + 56
5)
- In 6(11 + x) we will multiply 6 by 11 and 6 by x and add them
∵ 6 × 11 = 66
∵ 6 × x = 6x
∴ 6(11 + x) = 66 + 6x
6)
- In 8(x + 1) we will multiply 8 by x and 8 by 1 and add them
∵ 8 × x = 8x
∵ 8 × 1 = 8
∴ 8(x + 1) = 8x + 8
Solve (X-3)^2/3=9 (the ^ is an exponent)
Step-by-step explanation:
Step-by-step explanation:
To answer the question you have t the square of the differences.
So this means that (x-3)^2= x^2-9x+9
Next youmultiply 3 on both sides which says…
x^2-9x+9=27
x^2-9x=18
So, x equals
9/2+3/2 square root 17
OR
9/2-3/2 square root 17
Please help me do question 21, 22 and 23. I am in 6th grade.
Question 21: 24 minutes
[tex]\frac{3}{\frac{3}{2} } = \frac{x}{12}[/tex]
x = [tex](\frac{3}{\frac{3}{2} })(12)[/tex]
x = 24
Question 22: 20 centimeters
x = one side of the square
x² = 25
x = 5
4x = perimeter
4(5) = perimeter
20 = perimeter
Question 23: 17 sides
Hexagon = 6 sides
Octagon = 8 sides
Triangle = 3 sides
Total amount of sides = 6 + 8 + 3
Total amount of sides = 17
The following box plot shows the class scores on a particular math test:
box plot with number line titled percent with 50 as the minimum, 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum
Which of the following data sets is represented in the box plot?
{40, 50, 50, 77, 77, 100}
{0, 50, 60, 75, 85, 100}
{50, 60, 60, 75, 75, 85, 85, 100}
{60, 65, 70, 75, 85, 85, 85}
Answer:
Choice C
Step-by-step explanation:
Because,
50 is min
75 is middle
100 is max
The correct data set is {50, 60, 60, 75, 75, 85, 85, 100}
Given,
The box plot with number line titled percent with 50 as the minimum, 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum.
We need to determine the following data sets are represented in the box plot.
Let us segregate the following data set by taking the help of a minimum value.
Now, we require a data set that has a minimum value of 50.
There is only one data set given in the option that is a minimum value of 50.
Thus, data set is {50, 60, 60, 75, 75, 85, 85, 100}.
Cross-checked the above data set with more information that is already given in the question.
We required 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum.
Thus, all the above requirements are fulfilled by the data set {50, 60, 60, 75, 75, 85, 85, 100}.
Hence, the correct data set is {50, 60, 60, 75, 75, 85, 85, 100}
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Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour . What is Nina’s rate miles per hour if there are 5,280 feet in a mile?
Which girl bikes faster?
Answer:
Nina's rate in miles per hour is 2.7 miles/hour
Nina bikes faster
Step-by-step explanation:
we know that
1 hour=3,600 seconds
1 mile=5,280 feet
Convert feet to miles
63,360 feet=63,360/5,280=12 miles
Convert seconds to hours
3,400 sec=3,400/3,600=0.94 hours
Find Nina's rate in miles per hour
12/0.94=12.7 miles/hour
Sophia's rate in miles per hour is 10 miles/hour
Compare the rates
12.7 miles/hour > 10 miles/hour
therefore
Nina bikes faster
Answer:
12.7 mph
Nina
Step-by-step explanation:
What is the perimeter of a rectangle with a 7-inch width and a 16-inch length?
Answer:
7+16= 23
23*2=46. ..........
If point C is inside AvB, then __+m CvB= m AvB
Answer: OPTION A
Step-by-step explanation:
It is important to remember the "Angle Addition Postulate" in order to solve this exercise.
You have this larger angle:
[tex]\angle AVB[/tex]
According to the "Angle Addition Postulate", if the point "C" is in the interior of [tex]\angle AVB[/tex], then the measure of this angle can be obtained by adding the angle [tex]\angle AVC[/tex] and the angle [tex]\angle CVB[/tex].
You can observe in the figure that:
[tex]m\angle AVC=39\°\\\\\mangle CVB=23\°[/tex]
Then you get that:
[tex]m\angle AVC+m\angle CVB=m\angle AVB\\\\39\°+23\°=62\°[/tex]
Therefore, the correct answer is Option A.
Answer:answer is actually C
Does anyone know what (-2)^-3 equals? By the way it has to be simpified.
Answer:
-1/8
Step-by-step explanation:
(-2)^-3
The negative exponent means it's the inverse.
1 / ((-2)^3)
-2 cubed is -8.
1 / (-8)
So the simplified answer is -1/8.
Answer:
-8
Step-by-step explanation:
=(-2)^-3
= -2 ×-2 ×-2
= -8
Question 14(Multiple Choice Worth 1 points) (07.06 MC) An unknown number x is at most 30. Which graph best represents all the values of x? Number line graph with closed circle on 30 and shading to the right. Number line graph with closed circle on 30 and shading to the left. Number line graph with open circle on 30 and shading to the left. Number line graph with open circle on 30 and shading to the right
Answer:
Number line graph with closed circle on 30 and shading to the left
Step-by-step explanation:
we know that
The algebraic expression of the phrase " An unknown number x is at most 30" is equal to
[tex]x\leq 30[/tex]
The solution is the interval ------> (-∞,30]
All real numbers less than or equal to 30
Number line graph with closed circle on 30 and shading to the left
see the attached figure
Need help on the stretch problem.
Step-by-step explanation:
ΔACX is an isosceles triangle, so ∠AXC = ∠XAC. We'll call the measure of this angle x°.
∠AXC and ∠BXC are supplementary, so ∠AXC + ∠BXC = 180. That means ∠BXC = 180 − x.
ΔBXC is an isosceles triangle, so ∠XBC = ∠XCB. We'll call the measure of this angle y°.
Angles of a triangle add up to 180, so:
y + y + (180 − x) = 180
2y = x
y = x/2
∠ACX and ∠XCB are complementary, so ∠ACX + ∠XCB = 90.
x + y = 90
x + x/2 = 90
3/2 x = 90
x = 60
Therefore, ∠AXC = ∠XAC = 60°.
kt over k+t for k=13 and t=8
Answer:4.95
Step-by-step explanation:
so you multiply (13*8) because its k*t and then the bottom of the formula is 13+8 because its k+t so 13*8 equals 104 and 13+8 is 21 then you divide 104/21=4.95
Write parametric equations of the line with the equation 3x + 2y = 5.
Answer:
a. x = t, y = -[tex]\frac{3}{2}t[/tex] + [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
The answer is a. x = t, y = -3/2t + 5/2
The parametric equations of the line with the equation 3x + 2y = 5 is mathematically given as
x=t
y = (5-3t)/2
What is the parametric equations of the line with the equation 3x + 2y = 5.?Question Parameter(s):
the line with the equation 3x + 2y = 5.
Generally, the equation for the equation in slope-intercept is mathematically given as
y = 3x -5/ 2
Therefore
y = (5-3t)/2
While
x=t
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Write as percents
1) 3/5
2)7/8
3)4/25
4)27/50
Write as fractions
1)50%
2)34%
3)56%
4)33 1/3%
Answer:
1)3/5=60%
2)7/8=87.5%
3)4/25=16%
4)27/50=54%
fractions
1)50%=0.5
2)34%=0.34
3)56%=0.56
4)331/3%=1.1033
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The area of a rectangle is (x^3 - 5x^2 + 3x - 15), and the width of the rectangle is (x^2 + 3). If area = length c width, what is the length of the rectangle?
Answer:
Length = x-5
Step-by-step explanation:
Length= Area/width
Length = x³-5x²+3x-15/ x²+3
Re-arrange the numerator:
Length=x³+3x-5x²-15/x²+3
Take common from the numerator:
Length=x(x²+3) -5(x²+3)/x²+3
Length=(x²+3)(x-5)/x²+3
Length = x-5
Thus the answer is x-5 ....
What’s the vertex form of F(x)=x^2+2x-3
Answer:
[tex]\large\boxed{f(x)=(x+1)^2-4}[/tex]
Step-by-step explanation:
[tex]\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================[/tex]
[tex]\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================[/tex]
[tex]\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4[/tex]
Find the value of angle E Need help Asap 10 minutes left
Answer:
D
Step-by-step explanation:
the question not give enough explanation and clue
For this case we have that the sum of the internal angles of a quadrilateral is 360 degrees.
In the figure they only give us the measure of an angle. We can not say that the angles C and D or E and F are the same because they do not say it.
Thus, we do not have enough information to solve the problem.
Answer:
Option D
4. A company found that its monthly profit, P, is
given by P = -10x2 + 120x - 150 where x is the
selling price for each unit of the product.
Which of the following is the best estimate of
the maximum price per unit that the company
can charge without losing money?
A $300
C$11
B $210
D $6
Answer:
11
Step-by-step explanation:
Ok so we aren't looking to maximize profits which is equivalent to finding the vertex of the parabola.
But we want to know what is the highest number of x so that our we aren't losing money. We aren't losing money when our profit is 0.
So we are asked to solve P(x)=0 for x and take the highest x of that equation.
[tex]P(x)=0[/tex]
[tex]-10x^2+120x-150=0[/tex]
I'm going to divide both sides by -10 to make the numbers easier to work with later.
[tex]x^2-12x+15=0[/tex]
I'm going to use the quadratic formula.
[tex]x^2-12x+15=0[/tex] when compared to [tex]ax^2+bx+c=0[/tex] gives us [tex]a=1,b=-12,c=15[/tex].
We are going to plug this into our quadratic formula:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].
[tex]x=\frac{12\pm \sqrt{(-12)^2-4(1)(15)}}{2(1)}[/tex]
[tex]x=\frac{12\pm \sqrt{144-60}}{2}[/tex]
[tex]x=\frac{12\pm \sqrt{84}}{2}[/tex]
[tex]x=\frac{12}{2} \pm \frac{\sqrt{84}}{2}[/tex]
[tex]x=6 \pm \frac{\sqrt{84}}{2}[/tex]
I'm ready to put this into my calculator.
The one with the plus gives me 10.5826 approximately.
The one with the minus gives me 1.4174 approximately.
The 10.5826 is the higher number.
So about 11 dollars.
Answer:
C $11
Step-by-step explanation:
If a company found that its monthly profit, P, is given by P = -10x2 + 120x - 150 where x is the selling price for each unit of the product, the best estimate of the maximum price per unit that the company can charge without losing money is $11.
what fraction of the positive integer factors of 1000^3, are perfect squares?
Answer:
25/81
Step-by-step explanation:
1000³ = (10³)³ = 10⁹ = 2⁹ × 5⁹
For a factor to be a perfect square, the exponents must be even. For example:
2⁰ × 5⁰, 2⁰ × 5², 2² × 5⁰, etc.
There are 5 even exponents between 0 and 9 for each 2 and 5. So the number of perfect square factors is 5×5 or 25.
The total number of factors is 9×9 or 81.
So the fraction of positive integer factors that are perfect squares is 25/81.
25/81 is the fraction of the positive integer factors of 1000^3,
What is perfect square ?When you multiply an integer (a "whole" number, positive, negative, or zero) by itself, the resulting product is known as a square number, perfect square, or simply "a square." For example, 0 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.A perfect square is a number that can be written as the product of two integers or as an integer's second exponent. 25 is a perfect square because it is the product of the integer 5 and itself, 5 5 = 25.Perfect squares are significant because they demonstrate how to calculate the square root of a completely exact natural number. A perfect square's square root1000^3 = (10^3)^3 = 10^9 = 2^9 x 5^9
Perfect square factors have even exponents.
There are 5 even exponents between 0 and 9 for each 2 and 5.
Number of perfect square factors: 5x5 =25
Total number of factors: 9x9 =81
Fraction: 25/81
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Which pairs of triangles appear to be congruent? Check all that apply.
Answer:
Step-by-step explanation: just did it on apex
The pairs of triangles appear to be congruent are Triangles 1 and 4, Triangles 1 and 3 and Triangles 3 and 4, that is option B, option C and option E. This can be obtained by understanding the concept of congruence.
Which are the required pairs?Congruent triangles have same size and shape.Corresponding sides and angles are equal. Two congruent triangles can overlap perfectly.In the question, Triangle 2 is larger than the other triangles.
Triangle 1, Triangle 3 and Triangle 4 appears to have the same size and shape.
Thus Triangle 1, Triangle 3 and Triangle 4 appears to be congruent to each other.
Hence the pairs of triangles appear to be congruent are Triangles 1 and 4, Triangles 1 and 3 and Triangles 3 and 4, that is option B, option C and option E.
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90 divided by20 plus 5 multiply by 5
Which of the following is a linear function?
Explanation
The first option indicates that equation could be put in y = mx + b form.A linear equation is in y = mx + b format.Answer
First option: 1/3x = y - 3
Can someone please help me out with this question??
Answer:
Hi there!
The answer to this question is: C
Farah would packs 10 outfits for a 9 day vacation.
Step-by-step explanation:
It follows the pattern having one more outfit than the number of vacation days
A sphere has a diameter of 10 inch. What is the volume of the sphere?
Answer:
≈ 523.6 in³
Step-by-step explanation:
The volume (V) of a sphere is
V = [tex]\frac{4}{3}[/tex] π r³ ← r is the radius
here diameter = 10, hence r = 5, so
V = [tex]\frac{4}{3}[/tex] π × 5³
= [tex]\frac{4}{3}[/tex] π × 125
= [tex]\frac{4\pi (125)}{3}[/tex] ≈ 523.6 ( to 1 dec. place )
If the value of “y” varies directly with “x” and y = -51 when x = 3, find “y” if x = 2
Y =
Answer:
y = - 34
Step-by-step explanation:
Given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = - 51 when x = 3
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-51}{3}[/tex] = - 17
y = - 17x ← equation of variation
When x = 2, then
y = - 17 × 2 = - 34
Final answer:
To find the value of y when x = 2 in a direct variation relationship, determine the constant of variation first and then substitute the given values to find the unknown.
Explanation:
The relationship given is that y varies directly with x. To find y when x = 2, you can use the direct variation formula.
First, find the constant of variation by using the values given: y = kx. Plug in y = -51 and x = 3 to find k.
Once you have k, solve for y when x = 2 using y = kx.
Therefore, when x = 2, y = -34.
The point (0,0) is a solution to which of these inequalities?
O
O
O
O
A. y - 4<3x - 5
B. y - 5< 3x - 4
C. y +5< 3x + 4
D. y + 5 < 3x - 4
Answer:
B.
Step-by-step explanation:
Let's plug in and find out.
A. y-4<3x-5 with (x,y)=(0,0)
0-4<3(0)-5
-4<-5
This is false because -5 is not bigger than -4.
B. y-5<3x-4 with (x,y)=(0,0)
0-5<3(0)-4
-5<-4
This is true because -4 is bigger than -5.
C. y+5<3x+4 with (x,y)=(0,0)
0+5<3(0)+4
5<4
This is false because 4 is not bigger than 5.
D. y+5<3x-4 with (x,y)=(0,0)
0+5<3(0)-4
5<-4
This is false because -4 is not bigger than 5.
The only true inequality I got from plugging in (0,0) for (x,y) was B so that your answer.
Tom bought a pizza. He ate 1/3 of the pizza and gave some of it to his brother. He was then left with 1/5 of the pizza. What fraction of the pizza did Tom give his brother?
Answer:
7/15
Step-by-step explanation:
first recognise that 3/3 is a whole pizza and so is 5/5.
Secondly make all the numbers to have the same denominator
So times both denominators of the fractions together; 5x3=15
Now find 1/3 of 15. Do this by dividing 15 by 3. This equals 5.
So 1/3 is equal to 5/15
Now do the same for 1/5. 15 divided by 5, this equals 3.
So 1/5 is equal to 3/15
Now that we know that the whole pizza is 15/15
We minus 1/3 from 15.
15-5=10. So we now have 10/15 left.
now we know that 'x' is representative of the amount of pizza Tom gave to his bother.
10/15 - 3/15 = x
x = 7/15
So out of the whole pizza (15/15), tom ate 5/15 and was left with 3/15 meaning he gave 7/15 to his brother.
Final answer:
Tom ate 1/3 of the pizza and was left with 1/5 of it, so he gave away 2/15 of the pizza to his brother.
Explanation:
The question is asking which fraction of a pizza Tom gave to his brother. To find out, we know Tom ate 1/3 of the pizza and ended up with 1/5 of it. The fraction that Tom gave his brother is the difference between what he had after eating and what he was left with, thus:
1/3 - 1/5 = (5 - 3) / 15
So, 2/15 of the pizza was given to Tom's brother.
add (4x^2-2x)+(5x-7)
Answer:
4x²+ 3x - 7
Step-by-step explanation:
(4x²-2x)+(5x-7)
= 4x²- 2x + 5x - 7
= 4x²+ 3x - 7
The sum of Expressions is 4x² +3x -7.
What is an Expression?An expression is a mathematical statement consisting of variables, constants and mathematical operators.
The sum of the expression (4x²-2x) and (5x-7) has to be determined
(4x²-2x)+(5x-7)
4x² -2x+5x -7
4x² +3x -7
Therefore, the sum of Expressions is 4x² +3x -7.
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Nico has conducted an observational study to learn about how different personal experiences affect car purchases. Nico surveyed 300 new car buyers at the auto mall and found that 75% of the buyers were shopping for the same model of a car they have owned before. What conclusion can Nico make from his study?
A.Owning the same model of a car previously causes a buyer to purchase that car again, but he cannot draw a cause-and-effect conclusion from an observational study.
B. There may be a link between owning a model of a car and buying that model again, but he cannot draw a cause-and-effect conclusion from an observational study.
C.There may be a link between owning a model of a car and buying that model again, and he can draw a cause-and-effect conclusion from an observational study.
D.Owning the same model of a car previously causes a buyer to purchase that car again, but he can draw a cause-and-effect conclusion from an observational study.
Answer:
Option B is correct.
Step-by-step explanation:
Nico surveyed 300 new car buyers at the auto mall and found that 75% of the buyers were shopping for the same model of a car they have owned before.
This is 225 customers out of 300.
When people are satisfied with their car's current company and brand and model, they can prefer the same thing again for the same better experience. But this is not 100% proven. We can only say that there may be a link between the two things.
Hence, the conclusion that can be drawn here is :
B. There may be a link between owning a model of a car and buying that model again, but he cannot draw a cause-and-effect conclusion from an observational study.
The conclusion of the given study is that; Option B
What is the conclusion of the study?We are told that;
Number of new cars Nico surveyed = 300
Percentage of buyers that surveyed the new cars = 75% .
Thus, number of customers surveying this cars = 75% * 300 = 225 customers
If people are satisfied with their car's current company and brand and model,it means that they can also prefer the same thing again for the same better experience. Thus, the conclusion is that;
B. There may be a link between owning a model of a car and buying that model again, but he cannot draw a cause-and-effect conclusion from an observational study.
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I’m trying to find the missing fraction for this 1/3 + blank =7/12
[tex]\dfrac{1}{3}+x=\dfrac{1}{12}\\\\\dfrac{4}{12}+x=\dfrac{1}{12}\\\\x=-\dfrac{3}{12}=-\dfrac{1}{4}[/tex]
Answer:
1/4
Step-by-step explanation:
The LCD here is 12. Subtract 1/3, or 4/12, from 7/12, to obtain the missing fraction. 7/12 - 4/12 = 3/12, or 1/4. The missing fraction is 1/4.
Wilhich expression is equivalent to 3x/x+1 divided by x+1
Answer:
3x over x+1 MULTIPLIED by 1 over x+1 Letter choice will be A On ingenuity
Step-by-step explanation:
For this case we must find an expression equivalent to:
[tex]\frac {\frac {3x} {x + 1}} {x + 1}[/tex]
Applying double C we have:
[tex]\frac {3x} {(x + 1) (x + 1)} =\\\frac {3x} {(x + 1) ^ 2}[/tex]
Finally, an equivalent expression is:
[tex]\frac {3x} {(x + 1) ^ 2}[/tex]
Answer:
[tex]\frac {3x} {(x + 1) ^ 2}[/tex]
Ralph is 3 times as old as Sara in 4 years Ralph will be twice as old as Sara will be then. Find Ralph’s age now.
If x represents Sarah’s age now, which of the following expressions represents Ralph’s age in four years.
3x
6x
2x+4
3x+4
Answer:
3x+4 Ralph is currently 12 years old.
Step-by-step explanation:
You can find the equation by reading the scenario given. When you read it, it says that Ralph is 3 times as old as Sara and since her current age is going to be used to represent x you will first get 3x. That automatically eliminates the second and third choice given. It then says the equation is for Ralph's age in four years which means to add four to the equation. This gives you 3x+4 as your equation.
When something is tripled and then in a few years it is doubled, it is easiest to first try the number that is being added. So in this case the number is four. When you multiply 4 by 3 you get 12. If Sara is 4 she'll turn eight in four years and if Ralph is 12 he'll turn 16 in four years. 16 divided by 2 is 8 which shows you that Ralph is currently 12