Let the lowest score be x.
<u>The 3 consecutive even scores are:</u>
1st score = x
2nd score = x + 2
3rd score = x + 4
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<u>Sum of their score is 270:</u>
x + (x + 2) + (x + 4) = 270
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<u>Solve x:</u>
x + (x + 2) + (x + 4) = 270
x + x + 2 + x + 4 = 270
3x + 6 = 270
3x = 264
x = 88
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<u>Find their scores:</u>
1st score = x = 88
2nd score = x + 2 = 88 + 2 = 90
3rd score = x + 4 = 88 + 4 = 92
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Answer: The scores are 88, 90 and 92
Answer:
∠13 ≅ ∠16 - Vertical Angles Theorem
∠10 ≅ ∠14 - corresponding angles for parallel line p and q cut by the transversal s
∠5 ≅ ∠13 - corresponding angles for
parallel lines r and s cut by
the transversal q
∠1 ≅ ∠5 - corresponding angles for
parallel lines r and s cut by
the transversal q
Step-by-step explanation:
Linear Pair Theorem won't be used. When you look at the lines on the image you see that 13 and 16 are vertical from each other making there answer the vertical angles theorem. When you look at 10 and 14 you see that they lie on p and q with s going in the center of them. When you look at 5 and 13 they lie on s and r with q going down the middle of them. With 1 and 5 they also lie on p and q but r goes down the center of them instead of s.
First, let's write two expressions, letting x= the number of months which have elapsed:
Bill: 120 + 10x
Phil: 150 + 4x
If we set them equal to each other, then solve for x, that will be the number of months where their weights equal each other:
120+10x = 150 + 4x [starting equation]
-120 -4x -120 -4x [ subtract 120 from both sides, and 4x from both sides, to isolate the term with the variable]
<u>6x</u> = <u>30</u> [divide both sides by 5]
5 5
x=6. They will weigh the same in six months.
The minimum value of a function is the place where the graph has a vertex at its lowest point.
There are two methods for determining the minimum value of a quadratic equation. Each of them can be useful in determining the minimum.
(1) By plotting graph
We can find the minimum value visually by graphing the equation and finding the minimum point on the graph. The y-value of the vertex of the graph will be the minimum.
(2) By solving equation
The second way to find the minimum value comes when we have the equation y = ax² + bx + c.
If our equation is in the form y = ax^2 + bx + c, you can find the minimum by using the equation min = c - b²/4a.
The first step is to determine whether your equation gives a maximum or minimum. This can be done by looking at the x² term.
If this term is positive, the vertex point will be a minimum; if it is negative, the vertex will be a maximum.
After determining that we actually will have a minimum point, use the equation to find it.
Answer:
11^3/5
Step-by-step explanation:
The exponent of 3 becomes the numerator while the 5 in the root becomes the denominator which creates the fraction 3/5. So the final answer is 11^3/5
