[tex]\displaystyle \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
[tex] \displaystyle\large \bf( 2 \sqrt { 5 } + 3 \sqrt { 6 } ) ^ { 2 }[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \large \sf( 2 \sqrt { 5 } + 3 \sqrt { 6 } ) ^ { 2 }[/tex]
Use the algebraic identify [tex]\sf\left(a+b\right)^{2}=a^{2}+2ab+b^{2} [/tex]to expand [tex]\sf\left(2\sqrt{5}+3\sqrt{6}\right)^{2}[/tex].[tex] \large \sf \: 4\left(\sqrt{5}\right)^{2}+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2} [/tex]
The square of [tex]\sf\sqrt{5}[/tex] is 5.[tex] \large \sf4\times 5+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2} [/tex]
Multiply 4 and 5 to get 20.[tex] \large \sf20+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2} [/tex]
To multiply [tex]\sf\sqrt{5}[/tex] and [tex]\sf\sqrt{6}[/tex], multiply the numbers under the square root.[tex] \large \sf20+12\sqrt{30}+9\left(\sqrt{6}\right)^{2} [/tex]
The square of [tex]\sf\sqrt{6}[/tex] is 6.[tex] \large \sf20+12\sqrt{30}+9\times 6 [/tex]
Multiply 9 and 6 to get 54.[tex] \large \sf20+12\sqrt{30}+54 [/tex]
Add 20 and 54 to get 74.[tex] \large \boxed{\bf12 \sqrt{30} + 74 = 139.72..}[/tex]
Rewrite 0.580 80 repeating decimal
Step-by-step explanation:
first off, we'll move the non-repeating part in the decimal to the left-side, by doing a division by a power of 10.
then we'll equate the value to some variable, and move the repeating part over to the left as well.
anyhow, the idea being, we can just use that variable, say "x" for the repeating bit, let's proceed,
\begin{gathered}\bf 0.580\overline{80}\implies \boxed{\cfrac{5.80\overline{80}}{10}}\qquad \textit{now, let's say }x= 5.80\overline{80}\\\\ -------------------------------\end{gathered}
0.580
80
⟹
10
5.80
80
now, let’s say x=5.80
80
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
\begin{gathered}\bf thus\qquad \begin{array}{llll} 100\cdot x&=&580.80\overline{80}\\ &&575+5.80\overline{80}\\ &&575+x \end{array}\qquad \implies 100x=575+x \\\\\\ 99x=575\implies x=\cfrac{575}{99}\qquad therefore\qquad \boxed{\cfrac{5.80\overline{80}}{10}}\implies \cfrac{\quad \frac{575}{99}\quad }{10} \\\\\\ \cfrac{\quad \frac{575}{99}\quad }{\frac{10}{1}}\implies \cfrac{575}{99}\cdot \cfrac{1}{10}\implies \cfrac{575}{990}\implies \stackrel{simplified}{\cfrac{115}{198}}\end{gathered}
thus
100⋅x
=
580.80
80
575+5.80
80
575+x
⟹100x=575+x
99x=575⟹x=
99
575
therefore
10
5.80
80
⟹
10
99
575
1
10
99
575
⟹
99
575
⋅
10
1
⟹
990
575
⟹
198
115
simplified
Because 80 is repeat and simply .80 = .8
So, answer is 0.5(8)
Good luck.
If two functions are inverses of each other, which 2 statements are true?
A The graph of an inverse of a function is a reflection of the function across the line y=x. B f(g(x)) = x and g(f(x)) = x
C The graph of an inverse of a function is a reflection of the function across the line y=0. D f(g(x)) =1 and g(f(x)) = 1
Answer:
A and B
Step-by-step explanation:
To be inverses, the inverse composite functions must equal x, since the input and output must be equal as how much you used as your input, which is x. B proves that. Also, the graph must reflect over y = x, which is the line that runs through the origin
maurice bought a car costing £8248. he paid a deposit of £1975 and 6 monthly instalments of £511. estimate the amount maurice still owes
Hello :D
£8000 - £2000 = £6000
6 x 500 = £3000
£6000 - £3000
-2.5+ what number equals a positive number
Answer:
the answer would be 0.5
Step-by-step explanation:
if you take -2.5 + 0.5 it will give you 3.0
I hope this helps i dont think im that bright when it comes to decimals but i hope this helps :)
Please help if you don't want to do both at least do the first one
thx;)
Answer:
the first one is -1 and the second one is -48
A business uses straight-line depreciation to determine the value y of a piece of machinery over a 10-year period. Suppose the original value (when t=0) is equal to $34,000 and its value is reduced by $3400 each year. Write the linear equation that models the value y of this machinery at the end of year t.
The linear equation that models the value y of this machinery at the end of year t is y = $34,000 - $3,400t
A linear equation is an algebraic equation in the form :
y = mx + b
where y = intercept
m = slope
x and y are variables
Depreciation is used in expensing the cost of the asset
The value of the asset reduces by $3400 every year
The equation is :
y = $34,000 - $3,400t
At the end of one year, y = $34,000 - $3,400(1) = $30,600
At the end of two years, y = $34,000 - $3,400(2) = $27,200
At the end of ten years, y = $34,000 - $3,400(10) = 0
To learn more about linear equations, please check : https://brainly.com/question/19770987?referrer=searchResults
The perimeter of a rectangle is 92 cm. If the length is 22 cm, how wide is the rectangle?
A) First write an equation you can use to answer this question. Use w as your variable in the equation.
Answer:
W = 24cm
Step-by-step explanation:
p of a rectangle = 92
L = 22cm and W = ?
p = 2(L+W)
92 = 2(22+W)
92 = 44 + 2W
2W = 92 - 44
2W = 48
W = 48/2
W = 24cm
Which ratio is equivalent to 12 Over 2?
4 Over 6
24 Over 36
36 Over 6
6 Over 8
Answer:
36 over 6
Step-by-step explanation:
36 ÷ 6=12÷2
Geometry Review Homework
The answer would be 10 I believe.
Ques
Kurt decides to leave a 11 % tip after eating dinner at Sun Bistro. If the bill is $15.28, how much should
he pay? Round to the nearest cent.
Answer:
$1.68
Step-by-step explanation:
15.28 x .11=1.68
Plz help I need help I am very confused
Answer:
[tex] - \frac{5}{7} [/tex]
Step-by-step explanation:
[tex] - \frac{2}{7} - \frac{3}{7} [/tex]
[tex] \frac{ - 2 - 3}{7} [/tex]
[tex] = \frac{ - 5}{7} [/tex]
pls help me- will provide brainliest
Answer:
[tex]f(x) = 5 \tan(x + \frac{\pi}{2} )[/tex] (third option)
Step-by-step explanation:
attached
Can someone please help, will mark brainliest!! Ty!!
Answer:
E.) WX
F.) S and T
G.) ZV and VY
H.) VW
I hope this is right!!!
You got this
Math test scores:
93, 86, 93, 85, 73
mean =
median =
mode(s)
range =
Answer fast
Answer:
Mean: 87.5
Mode: NO mode
Median: 88
Hope this helps!!!!! :)
mean is 86 , median is 85 and mode is 93 , range is 10
Which of the following statements are true? Select all that apply.
Answer:
A,B,C
Step-by-step explanation:
the last number is the degree
plz help picture added
Find the value of ab when a =
9/11
and b =
7/10
The answer is
(Simplify your answer.)
a= 9/11 and b=7/10
now,
ab = (9/11)×(7/10)
=63/110.......
the value of ab is 63/110 when a = 9/11 and b = 7/10
What is Simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given, the values of a and b are 9/11 and 7/10 respectively
thus,
ab = 9/11 * 7/10
simplifying it
ab = 63/110
Therefore, the value of ab is 63/110 when a = 9/11 and b = 7/10
Learn more about Simplification here:
https://brainly.com/question/28996879
#SPJ
In one state lottery game, you must select four digits. hOW MANY NUMBERS MAY BE CHOSEN
Help me pleaseeeeeee
Which Native American group built cities and had widespread trade throughout the Midwestern region of North America?
giving brainlest
Explanation/answer
Explanation: Because the mound builders built cities and traded far and wide throughout the midwestern region. Which Native American groups built cities? Answer Expert Verified The varying cultures collectively called Mound Builders were inhabitants of North America who, during a 5,000-year period, constructed various styles of earthen mounds for religious and ceremonial, burial, and elite residential purposes. DONT FORGET TO GIVE BRAINILEST
Answer:
mound builders
Step-by-step explanation:
Because the mound builders built cities and traded far and wide throughout the Midwestern region
What an equation that represents the line.
Answer: The answer is y = 2x + 2
How much time has passed 8:15 to 2:30
Answer:
The time passed between 8:15 to 2:30 is 6 hours 15 minutes.
Multiply
-0.5•(-0.4)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. -0.5•(-0.4) =
B. The expression is undefined
(Answer quickly)
To multiply numbers or expressions means that we calculate the product of the numbers or expressions. The value of [tex]-0.5 \times (-0.4)[/tex] is [tex]0.2[/tex]
Given that:
[tex]-0.5 \times (-0.4)[/tex]
Cancel out the negative signs
[tex]-0.5 \times (-0.4) = 0.5 \times (0.4)[/tex]
Using a calculator, we have:
[tex]-0.5 \times (-0.4) = 0.2[/tex]
Hence, the value of [tex]-0.5 \times (-0.4)[/tex] is [tex]0.2[/tex]
Read more about multiplication at:
https://brainly.com/question/620034
Find the median weight of 7 students from the following data: 32 kg , 40 kg , 35 kg , 42 kg , 30 kg, 45 kg , 37 kg
Class : 7
Subject: optional mathematics
okok I know its easy
Answer:
37 kg
Step-by-step explanation:
Put the numbers in order from least to greatest
30, 32, 35, 37, 40, 42, 45
cross numbers out until you get to the middle number
30, 32, 35, 37, 40, 42, 45
32, 35, 37, 40, 42
35, 37, 40
37 kg
Explanation :
We know that, the median of an ungrouped data is the number in the middle of sequence when it is arranged ascending or depending and the number of terms is odd.
therfore , the sequence will be :
30kg , 32kg , 35kg , 37kg , 40kg , 42kg , 45kg
Here, 37 kg is the middle value i.e median of the given data .
hope it helps !!
Mr. and Mrs. Simpson went to the movies. They bought some popcorn for $25.50, two boxes of candy for $18 and two drinks for $14.25. They gave the cashier some money and received $2.25 back. How much did they give the cashier?
Gymnast Clothing manufactures expensive hockey jerseys for sale to college bookstores in runs of up to 150. Its cost (in dollars) for a run of x hockey jerseys is
C(x) = 1500 + 10x + 0.2x2 (0 ≤ x ≤ 150)
1. Gymnast Clothing sells the jerseys at $90 each. Find the revenue function.
2. Find the profit function.
3. How many should Gymnast Clothing manufacture to make a profit?
The Revenue function for the number of jerseys x sold is ; R(x) = 90x
The profit function from the sale of x jerseys is ; P(x) = - 0.2x² + 80x - 1500
The number of Jerseys to manufacture in other to make profit = 20
The revenue made is the total amount made from the sale of the hickey jerseys :
Sales price per jersey = $90
Hence, the revenue made, R(x) = 90x
The Cost function, C(x) = C(x) = 1500 + 10x + 0.2x²
Recall :
Profit = Revenue - Cost
Hence,
P(x) = R(x) - C(x)
P(x) = 90 - (0.2x² + 10x + 1500)
P(x) = 90 - 0.2x² - 10x - 1500
P(x) = - 0.2x² + 80x - 1500
To make profit, equate P(x) to 0 ;
0.2x² - 80x + 1500 = 0
Using a quadratic calculator :
x = 380.22 or x = 19.72
Hence, to make a profit, the number of jerseys that must be sold is 20.
Learn more : https://brainly.com/question/4966056
The cost of parking in a parking garage in Chicago is represented by the equation
y x = + 15 20 where y is the total cost (in dollars) and x is the time (in hours). The table
shows the total cost to park in a parking garage in Denver. Which city’s parking garage
charges more per hour and by how much more? After how many hours would parking in
Both cities cost the same?
Hours, x 2 3 4 5
Cost, y 43 51 59 67
Answer:
ok
Step-by-step explanation:
What are the coefficients of the terms?
5 9
t+8t -t
Step-by-step explanation:
t coefficient = 1
+ 8t coefficient = 8
-t coefficient =( -1)
Find the approximate side length of a square game board with an area of 120in^2
Answer:
11
Step-by-step explanation:
area of square is side length squared so [tex]\sqrt{120}[/tex] =10.95 or approximatly 11
I need help look at the attached image
