Three equal squares are superimposed as indicated in the figure. The areas of the overlapping zones are 2 cm², 5 cm², and 8 cm², respectively. The total area of the non-overlapping area of the squares is 117 cm². What is the length of the side of each square?
Answers
Answer: The square side lengths are 1 cm, 5 cm, and 11 cm.
===========================================================
Explanation:
Refer to the diagram below.
Define the following areas
A,B,C = non-overlapped regionsD,E,F = overlapped regionsIt doesn't really matter how you set up the labels, or what letters you pick, as long as you stay consistent.
We're told that "The areas of the overlapping zones are 2 cm², 5 cm², and 8 cm²", so let's make
D = 2E = 5F = 8Furthermore, we are told that "The total area of the non-overlapping area of the squares is 117 cm²" which means A+B+C = 117
---------------------------------------
Refer to the diagram. For now, focus on the upper right square. It has regions A, E, and F. The area of this square is A+E+F
Similarly, the area of the left-most square is D+B+E
The area of the bottom-most square is C+F+D
Add up the expressions we found and we get
(A+E+F)+(D+B+E)+(C+F+D) = A+B+C+2D+2E+2F
This represents the sum of all three square areas even if we peeled the squares apart to not overlap.
----------------------------------------
Let's plug in A+B+C = 117
We get
A+B+C+2D+2E+2F
117+2D+2E+2F
Now plug in D = 2, E = 5, and F = 8
117+2(2)+2(5)+2(8)
117+4+10+16
117+30
147
The sum of the three square areas is 147 square cm.
----------------------------------------
Now we have to do a bit of trial and error. We're looking for ways to break up 147 such that it is a sum of three squares.
In other words, we want to find integers m,n,p such that m^2+n^2+p^2 = 147
Let's try subtracting off 121
147-121 = 26
I picked 121 since it's the largest perfect square just smaller than 147
Repeat this process, but do so for 25 since 25 is smaller than 26
26-25 = 1
We can see that
1 + 25 + 121 = 147
1^2 + 5^2 + 11^2 = 147
One solution is m = 1, n = 5, p = 11. There may be other solutions. Keep in mind that m,n,p are positive whole numbers.
So we got a bit lucky with our trial and error process. If we didn't find such a triple, we'd have to try other possible combos of squares until we get the right match.
Because 1^2 + 5^2 + 11^2 = 147, this means the squares' side lengths are 1, 5, and 11.
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Answer:
=
−
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Step-by-step explanation:
2
−
2
+
1
=
7
Answer:
Ok that other answer is invalid the actual answer is = -4
Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Explanation:
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Answers
Answer:
10.80
Step-by-step explanation:
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What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
You are going to attend night classes for 4 months. You have to earn an additional $987 for tuition within this time.
You decide to take a second job that pays $9 dollars an hour.
Taxes are 12% of your earnings, and you are able to save the rest.
Let x be the minimum number of hours you will need to work in order to save enough money for your tuition alone.
From the data given, we can frame a linear equation in one variable.
987 = 9x - 12% of 9x
987 = 9x - (0.12)(9)x
987 = 9x - 1.08x
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x = 987/7.92
x = 124.62 ≈ 125 hours
Thus, the minimum number of hours you will need to work in order to save enough money for your tuition alone is 125 hours.
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Which two expressions are equivalent?
(F was wrong) H 7(x − 3) and 7x − 7 • 3
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Answers
Answer:
The correct answer is:
Option H: 7(x − 3) and 7x − 7 • 3
Step-by-step explanation:
Equivalent expressions are those expressions that simplify to the same expression i.e. the result of both expressions is the same. There is no change of sign or variable or any quantity.
Option H:
The two expressions are:
7(x − 3) and 7x − 7 • 3
[tex]7(x-3) = 7x - 21\\7x - 7.3 = 7x-21[/tex]
It can clearly be seen that both the expressions result in same expression
Hence,
The correct answer is:
Option H: 7(x − 3) and 7x − 7 • 3
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Answers
Answer:
b
Step-by-step explanation:
Answer:
option B
Step-by-step explanation:
a is located in the left side of 0 . HENCE IT IS A NEGATIVE NUMBER . b & c are on the right side of 0. HENCE BOTH ARE POSITIVE NUMBER
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By comparing -a & -c , we'll get to know that :-
-a > -c
Compare rational numbers
Which of the following inequalities are correct?
Choose all answers that apply:
0 >
3
7
P
Te
Report a problem
Stuck? Watch a video or use a hint.
2 of 7 -OOOOOO
Check
Answers
Answer:
[tex]0 > - \frac{3}{7} \\ - \frac{2}{7} > - \frac{3}{7} [/tex]
Step-by-step explanation:
Only the third option is wrong.
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Answers
Equation: y = 10m + 40
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Answers
all sides are congruent, so it has side-side-side congruence :)
The pair of triangles that is congruent by Side-Side-Side rule of congruency is option 4 .
Required:
The option with a pair of triangles that congruent by Side-Side-Side SSS rule of congruency.
Solution;
The given information in option [1] are;
A pair of congruent alternate interior angles, and a pair of angles in option [1] are congruent by Angle-Side-Angle rule of congruency.Option [2]
The information given in option [2] are two angles and an adjacent side, therefore;The length of the triangles in option [2] are congruent by Angle-Angle-Side rule of congruencyOption [3]
From the given parameters, the rule of congruency for option [3] is Side-Angle-Side congruencyOption [4]
The triangles have a common side that is shared.3 tic marks and 2 tic mark indicating that the corresponding sides are congruent are placed on the other two sides.Therefore, b of one triangle are congruent to the corresponding three sides of the other triangle, indicating that triangles are congruent by Side-Side-Side rule of congruency.
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Suppose that y varies directly with x, and y = 10 when x = 25.
(a) Write a direct variation equation that relates x and y.
Equation:
(b) Find y when x = 6.
y =
Answers
Answer:
Equation: y = 0.4x
y = 2.4
Step-by-step explanation:
Use the direct variation equation, y = kx, where k is a constant
Plug in x and y:
y = kx
10 = k(25)
Solve for k:
0.4 = k
So, the equation is y = 0.4x
Then, use this equation to find y when x = 6:
y = 0.4x
y = 0.4(6)
y = 2.4
A direct proportion is a proportion such that the ratio between both variables remains constant thus the given proportion will be y = 04x and the value of y at x = 6 will be 2.4.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
a)
Let's say the direct proportion as,
y = kx
Given that y = 10 when x = 25.
10 = k(25)
Solve for k,
0.4 = k
Therefore, the equation will be y = 0.4x
y = 0.4x
b)
The value of y when x = 6
y = 0.4(6)
y = 2.4
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Which of the following is a proportional relationship? SELECT ALL THAT APPLY
A)
[tex] \frac{2}{3} = \frac{8}{12} [/tex]
B)
[tex] \frac{6}{7} = \frac{12}{13} [/tex]
C)
[tex] \frac{15}{20} = \frac{9}{12} [/tex]
D) None of the above
Answers
Answer:
a
Step-by-step explanation:
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