Answer:
Slope is positive for all x, so always increasing
Step-by-step explanation:
Increasing/decreasing depends on the slope of the function, which is f'
f'(x) = 9x² + 18x + 25
If f'(x) > 0 for all x, then his claim is correct (increasing for all x)
If there's even 1 x-value for which f'(x) is not positive, his claim is incorrect
f'(x) is a quadratic function.
9x² + 18x + 25
9(x² + 2x) + 25
9(x² + 2(x)(1) + 1² - 1²) + 25
9(x + 1)² - 9 + 25
9(x + 1)² + 16
Since the minimum value of f' is 16, it's always positive.
Hence, the claim is correct
Answer:
The rug will fit. The rug is smaller than the parallelogram.
Step-by-step explanation:
This question is testing to see if you can figure out how the rug may fit in the room.
The rug does fit. Here's how we know.
The only given information from the question is...
- Length and Width of the <em>Rectangular Rug</em>
- Area of the Parallelogram
Notice that you can use the Length and the Width to get the area of the Rectangular Rug. We need to find the area of the rectangle so we can compare it to the parallelogram.
The area of the Parallelogram is listed at : 108 sqft
The area of the rectangular rug is : 60 sqft
- <em>Area of rectangle = Length * Width</em>
- <em>6 * 10 = 60</em>
<em />
The question now asks us if the rug will fit in her room. Well, 60 sqft is less than 108 sqft. So, yes, it will fit.
Let Cameron be x years old now.
-
<u>Now:</u>
Cameron = x
Uncle =3x
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<u>4 years ago:</u>
Cameron = x - 4
Uncle = 3x - 4
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<u>4 years ago, Uncle is 4 times older:</u>
3x - 4 = 4(x - 4)
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<u>Find x:</u>
3x - 4 = 4(x - 4)
3x - 4 = 4x - 16
4x - 3x = 16 - 4
x = 12
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<u>Find the age:</u>
Cameron = x = 12
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Answer: Cameron is 12 years old now.
The answer to 8a. is 17, the answer to 8b. is 3.9, the answer to 8c. is 1 / 2, the answer to 8d. is 7 7 / 8, the answer to 9a. is commutative property, the answer to 9b. is multiplicative identity property, the answer to 9c. is associative property, and the answer to 9d. is additive inverse property.
Regarding the whole "explain using mental math" thing, I pretty much just used the fact that 8a. and 8b. both had the same number of decimal places. For 8c., I just made each number have a denominator of 10. And last, for 8d., all of the denominators were already the same, which made it pretty easy. I apologize for this section of my answer being so informal lol, I haven't had to do these kinds of problems in like 5 years <span />
Step 1:
a) Write the quadratic model
a = -15.64
b = -1.24
c = 5.23
b) t = 0.30
c) t = 0.52 seconds
d) 0.30 is more likely to be relaible.
e)
