Answer:
Here c represents the total number of children in choir.
As per the statement:
Total number of boys in choir = 12
It is also given that: Three sevenths of a children's choir are boys.
⇒ Total number of boys = 
or
By cross multiply we have;
84 = 3c
Divide both sides by 3 we have;
c = 28
Therefore, the total number of children in choir is 28 children
Answer:
(x + 2)(4x - 2).
Step-by-step explanation:
(x+2)(2x+1)+(x+2)(2x-3)
Note that (x + 2) is common to 2 parts of the expression. So we have:
(x + 2)(2x + 1 + 2x - 3)
= Ix + 2)(4x - 2)
The answer is: 10 x¹³ y¹⁰ .
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1x^8 * 2y^(10) * 5x^5 =
1* 2* 5 * x^8 * x^5 * y^(10) =
10 * x^(8+5) * y^(10) =
10 * x^(13) * y^(10) = 10 x^(13) y^10 ; write as:
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10 x¹³ y¹<span>⁰ .
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Answer:
12.1 cm
Step-by-step explanation:
Using the law of sines, we can find angle C. Then from the sum of angles, we can find angle B. The law of sines again will tell us the length AC.
sin(C)/c = sin(A)/a
C = arcsin((c/a)sin(A)) = arcsin(8.2/13.5·sin(81°)) ≈ 36.86°
Then angle B is ...
B = 180° -A -C = 180° -81° -36.86° = 62.14°
and side b is ...
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 13.5·sin(62.14°)/sin(81°) ≈ 12.0835
The length of AC is about 12.1 cm.
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<em>Comment on the solution</em>
The problem can also be solved using the law of cosines. The equation is ...
13.5² = 8.2² +b² -2·8.2·b·cos(81°)
This is a quadratic in b. Its solution can be found using the quadratic formula or by completing the square.
b = 8.2·cos(81°) +√(13.5² -8.2² +(8.2·cos(81°))²)
b = 8.2·cos(81°) +√(13.5² -(8.2·sin(81°))²) . . . . . simplified a bit
Answer:
Step-by-step explanation:
-3x - 5 = 16
add 5 to both sides of the equation
-3x = 21
divide both sides by -3
x = -7
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-4(y - 2) = 12
distribute the -4 to everything in the parentheses
-4y + 8 = 12
subtract 8 from both sides of the equation
-4y = 4
divide both sides of the equation by -4
y = -1
