Find the sum of 2√5 and 3√16 in simplest form. Also, determine whether the result is rational or irrational and explain your answer
Answers
Answer:
2√5 +12 or 16.47213595....
Step-by-step explanation:
Part A - The sum of 2√5 and 3√16 in its simplest form is 2(√5 + 6).
The given numbers are surds.
To find the sum of 2√5 and 3√16, we perform the arithmetic operation of addition on the surds.
So, 2√5 + 3√16 = 2√5 + 3 × 4 (√16 = 4)
2√5 + 3√16 = 2√5 + 12
Factorizing out the factor 2 from both expressions, we have
2√5 + 3√16 = 2√5 + 6 × 2
2√5 + 3√16 = 2(√5 + 6)
So, the sum of 2√5 and 3√16 in its simplest form is 2(√5 + 6).
Part B - The result is irrational.
The result is irrational because 2(√5 + 6) cannot be expressed as a ratio of two integers since √5 is irrational and √5 + 6 is irrational and thus 2(√5 + 6) is also irrational since it cannot be expressed as a ratio of two integers. Also, its decimal representation is non-terminating or repeating.
Thus, the result is irrational.
Learn more about surds here:
https://brainly.com/question/20459639
Related Questions
Combining Like Terms
-4x - 2 + 5x = -4
I know the answer is -2 but I don’t know how to get -2
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x-2=-4
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can anyone help please :)
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Answer:
148°
Step-by-step explanation:
the angles are equal
Please help giving brainiest
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Answer:
(0, -1); maximum
The system of equations id graphed on the coordinate plane.
y=4x +3
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;~; ...................IMA FAILL ;;;;;;;;;;----;;;;;;;;;;;;
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How many solutions does this system have?
12x-4y--8
y-3x+ 2
O one
O two
O
an infinite number
no solution
Answers
Step-by-step explanation:
12x-4y=-8y=3x+212x-4(3x+2)=-812x-12x-8=-8
0=0
I think,no solution
janelle came to the bat 262 times in 91 games. at this rate, how many times should she expect to have at bat in full season of 162 games?
Answers
Answer:
465 times
Step-by-step explanation:
[tex]r=\frac{262}{91} = 2.87[/tex]
In full season of 162 games
[tex]162r=162(2.87)[/tex] = 465
A graph of f(x) = 10x2 – 11x – 6 is shown on the coordinate grid. What are the zeros of f(x)?
Answers
Answer:
-2/5 and 3/2
this is the answer for your question i probably send it to late for your answer but i hope it helps
What are the coordinates of vertex B' if the figure is rotated
90° counterclockwise about the origin?
Answers
Answer:
Answer: B'(-5,2)
Step-by-step explanation:
Rotations
When rotating a point B(x,y) 90 degrees counterclockwise about the origin it maps to an image point B'(-y,x).
The image shows a figure formed by points ABCD. The coordinates of B are B(2,5).
This point will be rotated 90 degrees counterclockwise about the origin, thus the coordinates of the image point B' are B'(-5,2).
Answer: B'(-5,2)
Solve each question using elimination
-4x-2y=-12
4x+8y=-24
Answers
Answer:
(3,6) or x= 3 and y= 6
(-6,-3) or x= -6 and y= -3
Select the correct solution for 8x = 56.
O A. X= 1/7
O B. X = 48
O c. x = 64
O D. x = 7
Answers
whats the quotient of -72 divided by -9?
Answers
Answer:
8
Step-by-step explanation:
9 |08|
72
- 0
72
-
72
00
Select all functions from the tables given below that show Y as a function of X.
A.
B.
C.
D.
E.
Answers
Answer: I dunnowhy are you asking me
Step-by-step explanation: the line of the perpendicular angle is non existent
6. In a class 85% of the students were present on a
certain day. If there were only 34 students present
on that day, how many students were absent on that
day?
Answers
Answer:
I think it's 6 kids absent
Step-by-step explanation:
Hope this helps
please answer my question I will mark brainliest
Answers
Answer:
Wouldn't it be A because the spinner has a 1/8th of a chance to land on a number
Step-by-step explanation:
Find the missing angle:
100° 29°
?
A. 60 degrees
B. 55 degrees
C. 51 degrees
D. 90 degrees
Answers
Answer:
c. 51 degrees is the missing angle.
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Answers
Answer:
the slope or gradient is 8/2=4
Mr. gracia is at Dunkin' Donuts .he has $17.50 in his pocket ,and he buys a sandwich for $2.50 and 5 coffees using cash . Write an inequality to determine the possible cost of each coffee
Answers
Answer:
The coffee is $3 or less
Step-by-step explanation:
Set up an inequality where c is the cost of one coffee:
17.50 [tex]\geq[/tex] 5c + 2.50
Solve for c:
17.50 [tex]\geq[/tex] 5c + 2.50
15 [tex]\geq[/tex] 5c
3 [tex]\geq[/tex] c
So, the coffee is $3 or less
What is the value of 100?
Answers
Answer:
10
Step-by-step explanation:
Means back the numbers into multiples of several small numbers
Like:; 1. We take LCM of 40
Just break into multiples of small number
40= 2×2×2×5
2. We take LCM of 50
50= 5×5×2
So LCM for 100 is 2×2×5×5
after that see the pairs in the LCM like 2×2 or 3×3 or 4×4(same numbers)
Then write the the single number in place of two multipled numbers
Like:; 2×2 is written as 2 // 3×3 is written as 3
So we can write 100 into 2×2×5×5 and then after selecting pairs (2×2)×(5×5)
write pairs in single number 2×5
And so we get 2×5=10
So we find root of 100 that is 10
16 divided by (x + 4) in WORD FORM
Answers
Answer:
sixteen divded by the sum of x and 4
Step-by-step explanation:
Hey there!
In order to do 16 divided by (x+4), you can first do 16/x + 16/4. Then, simplify 16/4, and then the answer to the question is 16/x + 4.
Hope this is what you were looking for! Let me know if you need more help! Good luck and have a great day!
work out the surface area of this triangular prism
Answers
Nancy and bill collect coins. Nancy has x coins. Bill has 9 coins fewer than 5 times the number of coins Nancy has. Write and simplify an expression for the total number of coins Nancy and Bill have.
Answers
Answer:
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Step-by-step explanation:
Help and what is function
Answers
^70 POINTS
can someone help me with this i rlly need it
The length of a rectangle is 1 inch less than twice its width, and its perimeter is 40 inches. Find the width of the rectangle.
7 in.
13 in.
14 in.
If the second equation is multiplied by 5 and then the equations are added, the result is _____.
x + 5y = 3
2x - y = -2
9x = 13
11x = -7
9x = -7
For the following system, use the second equation to make a substitution for x in the first equation.
x + 3y = 5
x + 7 = 2y
What is the resulting equation?
2y + 2x + 3y = 5
2y + 7 + 3y = 5
2y - 7 + 3y = 5
Graph the following system of equations. Click on the graph until the correct one appears.
y > -x + 1
y ≤ 2x - 3
Find A B if A = {3, 6, 9, 12} and B = {2, 4, 6, 8, 10}.
{6}
{2, 3, 4, 6, 8, 9, 10, 12}
Choose the correct mathematical translation for the given statement.
She is at most twenty years old.
x 20
x ≥ 20
Answers
Answer:
1) 7 in
2) 11x=-7
3)2y - 7 + 3y = 5
4) i DONT'KNOWN
Step-by-step explanation:
1)
step 1
the length of the rectangle is 1 inch less than twice its width ( in other words , you have to subtract 1 to twice the width to get the length)
Let
L represents the length
W represent the width
Hence
Twice width= 2w
Now , replace
L=2w-1 equation (1)
Also
The perimeter =40 inches
[tex]perimeter= 2(L+W) 40=2(L+W) equation (2)[/tex]
Step 2
Solve for w
Replace equation (1) in equation (2)
[tex]40=2(L+W) equation (2)\\40=2((2W-1)+W)\\40=2(3W-1)\\40=6W-2\\Add 2 in both sides\\40+2=6W-2+2\\42=6W\\Divide both sides by 6\\\frac{42}{6}=\frac{6W}{6} \\7=W[/tex]
so ,the width is 7 in.
2) Given the equations
[tex]x+5y=3\\2x-y=-2[/tex]
The first step is to multiply the second equation by 5 (both sides of the equation)
[tex]5(2x-y=-2)\\5(2x-y)=5.(-2)\\5.2x-5.y=-10\\10x-5y=-10\\[/tex]
Next is to add both equations
x+5=3 +10x-5y=-10 = 11x+0y=-7
The result is 11x=-7
3)[tex]x+3y=5\\x+7=2y[/tex]
To make a substitution for x using the second equation in the first equation you :
1. solve for x the second equation
Subtract 7 in both sides of the equation:
[tex]x+7-7=2y-7\\x=2y-7\\[/tex]
2.Substitute the x in the first equation for the value of x you get in step 1 :
[tex]2y-7+3y=5[/tex]
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can sum1 do number 3 for me plz i will mark brainliest
Answers
Answer:
Addition-
(9x+27)
Subraction-
(x-63)
Multiplication-
(20x-810)
Division-
(1.25x-0.4)
Step-by-step explanation:
The expression 8 + 2x can be written as _____.
4(2 + x)
2(4 + x)
2(4 + 2x)
Answers
Answer: 2(4 + x)
Step-by-step explanation:
i just multiplied across the parentheses. we can rule out the first option, because it would multiply out to be 8 + 4x.
the second option is the one that i calculated second, so i knew that i could rule out the last one my default.
just for kicks, if we multiplied the third option, it would come out to 8 + 4x.
help............please
Answers
Answer:
k=5
Step-by-step explanation:
subtract 14 from both sides
Answer:
19=4+k is easy that means 10-x=100+11 so the answer is 70
Step-by-step explanation:
Im new too this math and i could use a little help !:)
Answers
Answer:
25 degrees
Step-by-step explanation:
A right triangle is considered 90 degrees, so subtract 90 degrees by 65 degrees.
90 - 65 = 25
Hence, angle A equals 25 degrees.
Which line has a slope of 0.625, and which line has a slope of 1.6?
Explain why the slopes of these lines are 0.625 and 1.6.
Answers
Answer:
The answer is below
Step-by-step explanation:
The equation of a straight line is given by:
y = mx + b; where y and x are variables, b is the y intercept (i.e. value of y when x is zero), m is the slope of the line.
The slope of a line passing through the points [tex](x_1,y_1)\ and\ (x_2,y_2)\ is:[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let the point where the two lines intersect be the origin (0, 0).
Line 1 passes through (0, 0) and (8, 5). Hence:
slope of line 1 = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{5-0}{8-0} =0.625[/tex]
Line 2 passes through (0, 0) and (5, 8). Hence:
slope of line 2 = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{8-0}{5-0} =1.6[/tex]
Kayla thinks that the slope of a vertical line is undefined, while Joshua argues that the slope of a vertical line is zero. Who is correct?
Answers
Answer:
Kayla
Step-by-step explanation:
Vertical lines are always undefined because if your answer has to be divided by zero, the answer is an undefined operation.
Horizontal lines always have the slope of zero!
Check ALL of the ratios that are equivalent to 5:8 (Select al that apply) 10:16 8:5 2.5:4 40:25 15 to 24
Answers
Answer:
10 ,16 AND 8
Step-by-step explanation:
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