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lara31 [8.8K]
3 years ago
6

Mariana averaged 80 on her first three math exams. The first score was 86. The second score was 74. What was the third exam scor

e?​
Mathematics
1 answer:
Anna71 [15]3 years ago
6 0

The three scores are 86, 74, and an unknown score x. The average (i.e. the sum divided by how many there are) is 80, so we have

\dfrac{86+74+x}{3}=80

Multiply both sides by 3 and you get

160+x=240

Subtract 160 from both sides to get

x=240-160=80

Note: you could solve this exercise very quickly if you notice that the two numbers, 86 and 74, are symmetrical with respect to 80, which is the average. So, the third number must be the average.

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schepotkina [342]
Since y = 5x-1, we can fill it into 3x + 3y = -3. First, let's look at relating to a simpler equation. Let's say that x + y = 9 and y = 3 + 5. Now, we can fill it in to get that x + (3 + 5) = 9. Now, we know that 3+5 is 8, so x + 8 = 9. Now, x = 1. Likewise, we can do the same. For 3x + 3y = -3, all we need to do is to switch the y in 3x + 3y = -3 with 5x - 1. So it would become 3x + 3(5x - 1) = -3. Now we distribute to get 3x + 15x - 3 = -3. Now add three to both sides to get 3x + 15x = 0. Now simplify to get 18x = 0. Now we know that x = 0. Now fill x into y = 5x - 1. So y = 5(0) - 1. Now we know that y = -1.

To check fill in the answer to 3x + 3y = -3.
3(0) + 3(-1) = -3
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7 0
3 years ago
3. Complete the square for 3x2 - 6x = 21.<br> Help
PSYCHO15rus [73]

Answer:

x=1+2√2 or x=1−2√2

Step-by-step explanation:

Let's solve your equation step-by-step.

3x2−6x=21

Step 1: Since the coefficient of 3x^2 is 3, divide both sides by 3.

3x2−6x

3

=

21

3

x2−2x=7

Step 2: The coefficient of -2x is -2. Let b=-2.  

Then we need to add (b/2)^2=1 to both sides to complete the square.

Add 1 to both sides.

x2−2x+1=7+1

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Step 3: Factor left side.

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Step 4: Take square root.

x−1=±√8

Step 5: Add 1 to both sides.

x−1+1=1±√8

x=1±√8

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Hi there!

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