Answer:
54 degrees
Step-by-step explanation:
Measure of arc DCB is 125*2 = 250.
So, measure of arc BAD is 360-250 = 110.
So, measure of arc AD is 110 - 56 = 54 degrees
*PLEASE ANSWER TY* What is the volume of this prism?
Answer:
80 cube units
Step-by-step explanation:
the king needs a 10th graders help DX
Answer:
12) 1/8 inch = 0.125 inch
= 0.003175 m
= 3.175 x 10-3 m
= 0.3175 cm
13) 2 is rational and π is irrattional. π is approximately 3.14 and is the bigger of two
14) C= 40,005,306.33 m
= 4.0005 x 107 m
15) 12,615,800,000
= 1.26158 x 1010
=126158 x 105
16) Let's take speed of ant as 1Km/h=1000m/h. Then time 1666.875 days
Step-by-step explanation:
solution for x- 4 is equal to 10
Answer:
the answer is 14
Step-by-step explanation:
you first add both side to 4 and get x=14
Answer: x = 14
Explanation: Our only step in solving the equation is to add 4 to both sides and the reason that we can add the same quantity to both sides of an equation is based on the addition property of equality.
So the solution to this equation is x = 14.
(x-yi)(3+5i) is the conjugate of 6+24i
Answer:
x=-3
y=3
(-3-3i)(3+5i)
Step-by-step explanation:
[tex](x-yi)(3+5i)\\=3x+5xi-3yi+5y\\=(3x+5y)+(5x-3y)i\\[/tex]
and we have that must equal
6-24i
3x+5y=6
5x-3y=-24 and if we work it we found out that the solutions are
x=-3 and
y=3
Evaluate -3.28 - (-4.4) + (-p) where p = 9.7
Answer:
-8.58
Step-by-step explanation:
p = 9.7
=> -3.28 - (-4.4) + (-p)
=> -3.28 - (-4.4) + (- (9.7))
=> -3.28 - (-4.4) + (-9.7)
=> -3.28 - (-4.4) -9.7
=> -3.28 +4.4 -9.7
=> -12.98 +4.4
=> -8.58
Answer:
The evaluated answer for this equation is -8.58
Step-by-step explanation:
We are given a value of p so we will use this value for the equation.
-3.28 - (-4.4) + (-p)
Replace p with 9.7
-3.28 - (-4.4) + (-9.7)
Since there is a double negative in front of 4.4, then that means that we are going to be adding -3.28 to 4.4
1.12 + (-9.7)
Subtract 1.42 from 9.7 because there is negative sign in front of 9.7
-8.58
Nate is creating a PSA about building a "green” roof. Which source is most reliable for his research? a blog post written by a community gardener a .com website that advertises fertilizer a .gov or .org website about ecological roofs a book featuring photos of different styles of roof
Answer:
Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of room because
1. It specifically talks about green roof's
2. Unlike the blog post, the .org/.gov is not attempting to sell a product that may change how the article is written.
Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of rooms because It talks explicitly about green roofs.
What is a survey?A survey is research done by any company or an organisation on the group of people or their activity or on any other data like their sells etc to find out the valuable information from that data.
Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of rooms.
1. It specifically talks about green roofs
2. Unlike the blog post, the .org/.gov is not attempting to sell a product that may change how the article is written.
Therefore Nate wants to use a .org (or .gov) site about ecological roofs, a book featuring photos of different styles of rooms because It talks explicitly about green roofs.
To know more about surveys follow
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surface area of sphare
Surface area of sphere is what referred to as Total surface area or lateral surface area because here the surface is curved everywhere.
[tex] \large{ \boxed{ \rm{ \orange{Surface \: area \: of \: sphere = 4\pi {r}^{2} }}}}[/tex]
Total surface area of other 3-D shapes:
Cuboid = 2(lb + bh + hl)Cube = 4s²Cylinder = 2πr(r + h)Cone = πr(l + r)Hemisphere = 3πr²Lateral surface area of these shapes:
Cuboid = 2h(l + b)Cube = 6s²Cylinder = 2πrhCone = πrlHemisphere = 2πr²━━━━━━━━━━━━━━━━━━━━
Which of the following is a solution of y > |x| - 6? A(-1, -5) B(-5, 1) C(5, -1)
Answer:
B(-5, 1)
Step-by-step explanation:
We can test each value in the equation and see if the equation works out.
[tex]y > |x| - 6[/tex]
Let’s try A - (-1, -5).
[tex]-5 > |-1|-6\\\\-5 > 1-6\\-5>-5[/tex]
-5 is NOT greater than -5, it is equal so A doesn’t work.
Let’s try B, (-5, 1).
[tex]1 > |-5| -6\\1 > 5-6\\1 > -1[/tex]
1 IS greater than -1, so B works.
Let’s try C for fun.
[tex]-1 > |5| -6\\-1 > 5-6\\-1 > -1[/tex]
-1 is NOT greater than -1, it is equal, so it doesn’t work.
Hope this helped!
Answer:
B(-5,1)
Let us simply just write this in all scenarios.
A(-1,-5)
-5>|-1|-6
-5>-5
(False)
B(-5,1)
1>|-5|-6
1>-1
(True)
C(5, -1)
-1>|5|-6
-1>-1
False
Determine if the following table represents a quadratic function.
x 1 2
3 4 5
y 13 22 37 58 85
(1 point)
Answer:
The options are not visible enough (See Explanation)
Step-by-step explanation:
Given
x:- 1 || 2 || 3 || 4 || 5
y:- 13 || 22 || 37 || 58 || 85
Required
Determine if the function is quadratic
Calculate the difference between the values of y
[tex]Difference = 22 - 13 = 9[/tex]
[tex]Difference = 37 - 22 = 15[/tex]
[tex]Difference = 58 - 37 = 21[/tex]
[tex]Difference = 85 - 58 = 27[/tex]
The resulting difference are: 9 || 15 || 21 || 27
Next; Calculate the difference between the difference of values of y
[tex]Difference = 15 - 9 = 6[/tex]
[tex]Difference = 21 - 15 = 6[/tex]
[tex]Difference = 27 - 21 = 6[/tex]
The resulting difference are: 6 || 6 || 6
For the function to be quadratic, the above difference must be the same and since they are the same (6), then the function represents a quadratic function.
(I) Factorice completely
x³- 6x² + 11x-6
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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Factor [tex]x^3 - 6x^2 + 11x - 6[/tex]
[tex]x^3 - 6x^2 + 11x - 6[/tex]
= [tex]( x - 1) ( x - 2) ( x - 3)[/tex]
So you would be : [tex]( x - 1) ( x - 2) ( x - 3)[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
The graph below shows Roy's distance from his office (y), in miles, after a certain amount of time (x), in minutes: Graph titled Roys Distance Vs Time shows 0 to 10 on x and y axes at increments of 1.The label on x axis is time in minutes and that on y axis is Distance from Office in miles. Lines are joined at the ordered pairs 0, 0 and 1, 1 and 2, 2 and 3, 3 and 4, 4 and 5, 4 and 6, 4 and 7, 4.5 and 7.5, 5 and 8, 6. Four students described Roy's motion, as shown in the table below: Student Description Peter He drives a car at a constant speed for 4 minutes, then stops at a crossing for 6 minutes, and finally drives at a variable speed for the next 2 minutes. Shane He drives a car at a constant speed for 4 minutes, then stops at a crossing for 2 minutes, and finally drives at a variable speed for the next 8 minutes. Jamie He drives a car at a constant speed for 4 minutes, then stops at a crossing for 6 minutes, and finally drives at a variable speed for the next 8 minutes. Felix He drives a car at a constant speed for 4 minutes, then stops at a crossing for 2 minutes, and finally drives at a variable speed for the next 2 minutes. Which student most accurately described Roy's motion? Peter Shane Jamie Felix
Answer:
Felix
Step-by-step explanation:
The graph contains 3 segments,
first one is for the first 4minutes,
second one is for the next 2 minutes (standing still)
third one is for the last 2 minutes.
Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end. (e.g., from 4 to 6 is 2 minutes).
The student that most accurately described Roy's motion is Felix.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
We need to find the student that most accurately described Roy's motion.
Here we can see that the graph contains 3 segments, first one is for the first 4 minutes, Second one is for the next 2 minutes (standing still) and the third one is for the last 2 minutes.
Now, Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end.
Therefore, the student that most accurately described Roy's motion is Felix.
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A baseball is thrown into the air from the top of a 224-foot tall building. The baseball's approximate height over time can be represented by the quadratic equation h(t) = -16t2 + 80t + 224, where t represents the time in seconds that the baseball has been in the air and h(t) represents the baseball's height in feet. When factored, this equation is h(t) = -16(t - 7)(t + 2). What is a reasonable time for it to take the baseball to land on the ground?
Answer:
7 seconds
Step-by-step explanation:
We assume h(t) represents the height above ground, so that h(t) = 0 will be the point where the ball hits the ground.
The factored form of the equation tells us ...
h(7) = -16(7 -7)(7 +2) = 0
So, the baseball will land on the ground when t=7, seven seconds after first being thrown into the air.
_____
The other value of t that makes h(t) = 0 is -2. Since we only count time after the ball is thrown, t=-2 is an extraneous solution.
when the point ( k, 3 ) lies on each of these lines, find the value of k y= 3x+1 , y= 4x-2 , y=1/2x - 1 and 2x+3y=4
Answer:
see explanation
Step-by-step explanation:
Since (k, 3) lies on each of the lines, the point satisfies the equations.
Substitute x = k, y = 3 into each and solve for k
y = 3x + 1
3 = 3k + 1 ( subtract 1 from both sides )
2 = 3k ( divide both sides by 3 )
k = [tex]\frac{2}{3}[/tex]
-------------------------------------------------------
y = 4x - 2
3 = 4k - 2 ( add 2 to both sides )
5 = 4k ( divide both sides by 4 )
k = [tex]\frac{5}{4}[/tex]
--------------------------------------------------------
y = [tex]\frac{1}{2}[/tex] x
3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )
k = 6
---------------------------------------------------------
2x + 3y = 4
2k + 3(3) = 4
2k + 9 = 4 ( subtract 9 from both sides )
2k = - 5 ( divide both sides by 2 )
k = - [tex]\frac{5}{2}[/tex]
Victoria is scuba diving off the coast of Hawaii. When she is ready to come back to the surface, she rises 40 yards at a safe speed. She climbs 1 foot every 2 seconds. How many minutes will it take her to reach the surface?
Answer:
it will take her 79.76 minutes to rise to the surface
Step-by-step explanation:
Total distance to the surface = 40 yards
speed of rising = 1 foot per seconds
1 foot = 1 second
since the total distance is in yards, let's convert from foot to yards:
1 yard = 3 feet
1 foot = 1/3 yards = 0.333 yards
0.33 yards = 1 second
Next, let's convert from seconds to minutes
60 seconds = 1 minute
∴ 1 second = 1/60 minute
1 second = 0.0167 minute
Therefore the speed at which she rose:
speed
0.333 yards = 0.0167 minutes
Now for a distance of 40 yards:
[tex]1\ yard = \frac{0.0333}{0.0167} minutes\\\therefore\ 40\ yards = \frac{0.0333}{0.0167} \ \times\ \frac{40}{1} \\= \frac{1.332}{0.0167} \\= 79.76\ minutes[/tex]
Answer:
4 minutes
Step-by-step explanation:
A car travels 120m along a straight road that is inclined at 8° to the horizontal. Calculate the vertical distance through which the car rises. (Sin8°=0.1392)
The vertical distance through which the car rises is 16.7 m
What is right triangle?"It is a triangle whose one of the angle is 90°."
What is sine of angle?In right triangle, for angle 'x',
sin(x) = (opposite side of angle x)/hypotenuse
For given example,
Consider the following figure for given situation.
A car travels 120 m along AC.
ΔABC is right triangle with hypotenuse AC.
∠C = 8°
Consider sine of angle C,
[tex]\Rightarrow sin(C)=\frac{AB}{AC}\\\\\Rightarrow sin(8^{\circ})=\frac{AB}{120}\\\\ \Rightarrow 0.1392=\frac{AB}{120}\\\\ \Rightarrow AB = 0.1392\times 120\\\\\Rightarrow AB = 16.70~ m[/tex]
Therefore, the vertical distance through which the car rises is 16.7 m
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which of the following statements must be true about this diagram ? check ALL that apply
Answer:
Check A, B and DStep-by-step explanation:
A. m∠4 = 180° - m∠3
m∠1 = 180° - (m∠3 + m∠2)
m∠3 < m∠3 + m∠2 ⇒ m∠4 >m∠1
B. m∠4 = 180° - m∠3
m∠2 = 180° - (m∠3 + m∠1)
m∠3 < m∠3 + m∠1 ⇒ m∠4 >m∠2
C. Not necessarily {could be but not always}
D. m∠4 = 180° - m∠3
m∠1 + m∠2 + m∠3 = 180° ⇒ m∠1 + m∠2 = 180° - m∠3 = m∠4
E. m∠3 = m∠1 + m∠2 only if m∠3 = 90°
F. Not necessarily. {Could be but also could not be. In the picture is, but we don't know if the diagram is accurate or just approximate.}
If a 15% discount is applied to a 15,000,000 car, what will its price be.
Answer:
$12,750,000
Step-by-step explanation:
15,000,000 x 0.15 = 2,250,000
15,000,000 - 2,250,000 = 12,750,000
Answer:
12750000Step-by-step explanation:
[tex]15\% \: discount \:on \: 15,000,000\\\\= \frac{15}{100} \times 15,000,000\\\\\\= \frac{225000000}{100}\\ \\= 2250000\\\\15 000 000 - 225 0000= 12750000[/tex]
Please help.. Offering 25 points and 5 stars with a thanks
Answer:
2/5
Step-by-step explanation:
There are 2 white and 4 yellow = 6
P(yellow) = yellow /total = 4/6 = 2/3
We keep the ball
Now there are 2 white and 3 yellow = 5
P(yellow) = yellow /total = 3/5
P ( yellow, keep, yellow) = 2/3 * 3/5 = 2/5
We are given 4 yellow balls and 2 white balls. In total, this adds up to 6.
Divide the number of yellow balls to the total number of balls:
4/6 -> 2/3
We are also given 3 yellow and 2 white.
Divide the number of yellow balls to the total number of balls:
3/5
Divide both fractions together:
3/5 * 2/3 = 6/15 = 2/5
Best of Luck!
33. Simplify:
[tex]a ^{2} \times a ^{4} [/tex]
HELP! answer if you can!!!
Answer:
a^2 × a^4
= a^2+4
= a^6
Remember:
a^n × a^m= a^n+m
Hope it helps
if u have any question let me know in comments ^_^
Answer:
[tex]a^2 * a^4 = \\a^{(2 + 4)} = \\a^6[/tex]
Step-by-step explanation:
Hope it helps!
The graph below shows the solution to which system of inequalities ?
Answer:
A
Step-by-step explanation:
A dotted line means its either greater than or less than. A undotted line means its also equal to the number aswell.
To find the right answer all you need is the first part because y has to be greater than or equal to 2 as shown from the graph. So the answer has to be A. As it is the only one that shows this.
I need help comrades, I will give you 5 stars and A big thank you comrades
Answer:
dicontinuity at (-4.-2)zero at (-2.0)
Step-by-step explanation:
answer c
this shoud be correct
Describe how to solve an absolute value equation
*will give brainliest*
Answer:
Step 1: Isolate the absolute value expression.
Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.
Step 3: Solve for the unknown in both equations.
Step 4: Check your answer analytically or graphically.
Step-by-step explanation:
Answer:
Rewrite the absolute value equation as two separate equations, one positive and the other negative
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid
Write out the final solution or graph it as needed
Step-by-step explanation:
what is the value of x ?
Answer:
35
Step-by-step explanation:
it's the same value each side
Find the missing probability. P(A)=720,P(B)=35,P(A∩B)=21100 ,P(A∪B)=?
P( A U B) = 37/50
Step-by-step explanation:
7/20+3/5+21/100
IF YOU NEED MORE HELP LMK
If you can please mark this as the brainliest
Help please! <3 Simplify the expression to find the correct answer. Show your work and explain how you got that answer. [tex]\frac{1}{3}\sqrt{21}-\frac{2}{3}\sqrt{3} x \sqrt{7}[/tex] A. [tex]-\frac{1}{3}\sqrt{21}[/tex] B. [tex]\frac{2}{3}\sqrt{21}[/tex] C. [tex]\frac{2}{3}\sqrt{18×7}[/tex] D. [tex]-\frac{1}{3}\sqrt{63}x\sqrt{7}[/tex]
Answer:
-1/3 sqrt(21)
Step-by-step explanation:
1/3 sqrt(21) - 2/3 sqrt(3) * sqrt(7)
We know sqrt(a) * sqrt(b) = sqrt(ab)
1/3 sqrt(21) - 2/3 sqrt(21)
Factor out sqrt(21)
sqrt(21) (1/3-2/3)
sqrt(21) (-1/3)
-1/3 sqrt(21)
Answer: Choice A) [tex]-\frac{1}{3}\sqrt{21}[/tex]
=====================================================
Work Shown:
I'm guessing that the x you wrote is to signify multiplication. If so, then one way to do the steps is shown in the attached image below.
In step 2, I used the rule that sqrt(x)*sqrt(y) = sqrt(x*y).
Tara has softball practice Tuesday,Wednesday Thursday and Sunday Each practice Is 1 /1 3 hours. Tara says she will have practice for 3 hours this week.
Answer and Step-by-step explanation:
For the first part
Tara is incorrect as she practices the softball in 4 days in a week and she do each practice of minimum one hour
So we can conclude that she practices minimum hours in a week
For the second part
Also in 4 days, she does practice [tex]1 \frac{1}{3}[/tex] hours per day i.e [tex]5 \frac{1}{3}[/tex]
Now convert [tex]1 \frac{1}{3}[/tex] this into a fraction which comes [tex]\frac{4}{3}[/tex]
For four days, it is
= [tex]4 \times \frac{4}{3} \\\\ \frac{16}{3} \\\\ 5 \frac{1}{3}[/tex]
Step-by-step explanation:
Without multiplying, explain how you know Tara is incorrect.
How long will Tara have softball practice this week? Write your answer as a mixed number.
Each practice is [tex]1\frac{1}{3}[/tex] hours
Each practice is more than 1 hour. so 4 days of practice is more than 4 hours.
So Tara is incorrect
Practice for 4 days
[tex]1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}=4\frac{4}{3}=5\frac{1}{3}[/tex]
More than 5 hours .
Tara will have [tex]5\frac{1}{3}[/tex] softball practice this week
Answer:
Tara will have [tex]5\frac{1}{3}[/tex] hours softball practice this week
solve for x 16x - 5 = 18x -2
Answer:
x = -1.5
Step-by-step explanation:
16x - 5 = 18x -2
Subtract 16x from each side
16x-16x - 5 = 18x-16x -2
-5 = 2x-2
Add 2 to each side
-5+2 = 2x-2+2
-3 = 2x
Divide by 2
-3/2 = 2x/2
-3/2 =x
Answer:
-3/2
Step-by-step explanation:
To solve this problem, start by moving all of your x's on to one side, and all of your constants on to the other as such:
16x-5=18x-2
+2 +2
16x-3=18x
-16x -16x
-3=2x
-3/2 = x
P.S. please give me brainliest. Thank you! :)
A book contains 27 pages with print, 8 pages with print and pictures, and 3 blank
pages. What is the theoretical probability of NOT opening the book to a printed
page only?
P(NOT printed page) =
Answer:
P(NOT printed page) = 3/38
Step-by-step explanation:
Total pages = 27+8+3=38
Types of pages that satisfy requirement(s)= 3
Therfore, P(NOT printed page) = 3/38
What is the slope of line p?
HURRY PLEASE
Answer:
2/3
Step-by-step explanation:
(3,2) and (0,0)
The slope of the line is given by
m = (y2-y1)/(x2-x1)
= (2-0)/(3-0)
2/3
PLEASE HELP ME Answer the following two questions in your own words: 1. Why can I divide instead of distribute? Why is that allowed? Ex. why can I divide by 6 in 6(3x + 4) = 12 instead of distribute the 6? 2. When creating common denominators, why do I have to multiply the numerator AND the denominator? Ex. why do I have to multiply 1 by 5 AND 2 by 5 when adding 1/2 + 3/10?
Answer:
1. You can divide both sides of an equation by any number except zero. If dividing both sides simplifies the equation, then it's better to do than than to distribute.
2. A fraction can be thought of as a ratio. To keep the value of the fraction the same, you must multiply or divide the numerator and denominator by the same number. If you multiply only the denominator by a number, the value of the fraction changes.
Step-by-step explanation:
1.
6(3x + 4) = 12
Since the goal in solving this equation is to isolate x, meaning you want x alone on the left side, you need to do whatever legal operations that will accomplish that. Since 6 is a factor and (3x + 4) is a factor in a multiplication, you can divide both sides by 6 simplifying the left side. It is also correct to distribute on the left side, but it will make the solution longer.
Method 1: start by dividing both sides by 6
6(3x + 4) = 12
Step 1: Divide both sides by 6
3x + 4 = 2
Step 2: Subtract 4 from both sides
3x = -2
Step 3: Divide both sides by 3
x = -2/3
Method 2: start by distributing on the left side
6(3x + 4) = 12
Step 1: distribute the 6 on the left side
18x + 24 = 12
Step 2: subtract 24 from both sides
18x = -12
Step 3: divide both sides by 18
x = -12/18
Step 4: reduce the fraction
x = -2/3
As you can see, the solution is the same. The only difference is one extra step with the reduction of the fraction in the case of distributing the 6.
2.
This has to do with the meaning of fractions.
For example, take the fraction 1/2.
This fraction means that you divided the unit into 2 equal parts, shown by the denominator of 2. Then you are taking 1 of those parts, shown by the numerator of 1. 1/2 means 1 out of 2. You can also think of 1/2 as the ratio of 1 to 2.
To add and subtract two factions, we need a common denominator. That means we must rewrite one or both fractions being added or subtracted in a way that they both have the same denominator. We need the fractions to represent the same amounts they did originally. If you changed only the denominator, you'd be changing the actual value of the fraction.
You need to add 1/2 and 3/10.
The least common denominator of 2 and 10 is 10, so we need to have both fractions with a denominator of 10. 3/10 already has a denominator of 10, so we just need to change 1/2 to a fraction with 10 in the denominator. By multiplying 2 by 5 we get 10, so we need to multiply the denominator of 1/2 by 5 to end up with a denominator of 10.
1/2 + 3/10
If you only changed the denominator of 1/2 to 10 by multiplying 2 * 5 = 10, you'd end up with
1/10 + 3/10,
but now think of the fraction 1/10 and compare it to 1/2.
1/2 means divide the unit into 2 equal parts and take 1 part.
1/10 means divide the unit into 10 equal arts and take 1 part.
1/2 is not the same as 1/10, so rewriting the addition
1/2 + 3/10 as 1/10 + 3/10 is actually changing the problem.
Now see what happens when we multiply both the numerator and denominator by the same number, in this case 5.
We change 1/2 to (1 * 5)/(2 * 5) = 5/10. 1/2 equals 5/10. If you divide a unit into 10 equal parts and you take 5 parts, you have taken the same number of parts as if you had divided the unit into 2 parts and taken 1 part.
In other words, 1/2 is exactly the same amount as 5/10. The only difference between 1/2 and 5/10 is the way they are written.
Now we can correctly continue with the addition:
1/2 + 3/10 = 5/10 + 3/10 = 8/10
Finally we reduce 8/10 to 4/5 by dividing both the numerator and denominator by 4.