<h3>
Answer: 21</h3>
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Work Shown:
Vertical angles are always congruent.
This means they are equal in measure.
A = B
3x-30 = 2x-9
3x-2x = -9+30
x = 21
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Side note:
if x = 21, then,
A = 3*x-30 = 3*21-30 = 33 degrees
B = 2*x-9 = 2*21-9 = 33 degrees
Answer:
As we know:
A nickle is worth 5 cents.
A dime is worth 10 cents.
A quarter is worth 25 cents.
Here is what Robert had:
Number of nickles (a)
Number of dimes (b)
Number of quarters (c)
Here is assumption:
5a + 10b + 25c = 850
a = 3b
c = b + 10
=> 5(3b) + 10b + 25(b + 10) = 850
=> 50b + 250 = 850
=> 50b = 600
=> b = 600/50 = 12
=> a = 3b = 3 x 12 = 36
=> c = b + 10 = 12 + 10 = 22
=> Number of nickles: 36
=> Number of dimes: 12
=> Number of quarters: 22
Hope this helps!
:)
Answer:
16
Step-by-step explanation:
ratio is 5:4:1
David: Malachy: Paul
David gets 20 (that is 4 times more than the original ration. so need to multiply everything by 4)
4*4=16
1*4=4
new ration- 20:16:4
So David gets 20
Malachy gets 16
Paul gets 4
Chris is incorrect. To check the answer, replace m with 8 and simplify the left side. So m/6 turns into 8/6 which converts to the decimal value 1.333 (use a calculator)
Therefore the original equation m/6 = 48 becomes 1.333 = 48 after you plug in m = 8 and simplify fully. The two sides of 1.333 = 48 are not the same, so m = 8 is not the solution.
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The solution is actually 288 and we can prove it so like this
m/6 = 48
288/6 = 48 .... replace m with 288
48 = 48 .... use a calculator to compute 288/6
So the solution m = 288 is confirmed
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How did I get this answer? By multiplying both sides by 6
m/6 = 48
6*(m/6) = 6*48 ..... multiply both sides by 6
m = 288
So Chris mistakenly divided both sides by 6, which explains how he got 48/6 = 8 as the solution. Instead he should have multiplied both sides by 6. This is to undo the operation "divide by 6" that is being applied to m in the original equation.
For the equation of the line expressed as Ax + By + C = 0, the value of the slope (m) is calculated by -A / B. For perpendicular lines, the slope of one should be the negative reciprocal of the other. From the choices given, the lines that are perpendicular is Option A.
