If you compare table values to answer choices, you can see right away that several don't work. The number of centimeters is greater than the number of inches, so adding to or multiplying the number of centimeters by some number more than 1 will not give you the smalller number that is inches.
While it may work for the first number (5 inches) to add 7.7 to get the first number of centimeters (12.7), you have to know that you can only add like to like. You can only add inches to inches (getting a result of inches), or centimeters to centimeters (getting a result of centimeters). From the point of view of the units involved, it is <em>nonsensical</em> to add a pure number to a number of inches and expect to get a number of centimeters.
So, we're down to the second choice:
- The number of inches is multiplied by 2.54 to find the number of centimeters.
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To find the pattern in the table, you can ...
- observe that the inch values differ by 1
- observe that the centimeter values differ by 2.54
- realize that the constant differences mean the relation between inches and centimeters is linear, and that a change in an inch value of 1 inch is multiplied by 2.54 to find the corresponding change in centimeter value.
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I don't know what the first step in your problem solving process is supposed to be. In my problem solving process, the first step is always to <em>look at what you are given</em>. The next step is <em>look at what you are being asked for</em>.
Will do first question of each concept only because the rest of the questions are the same concept (the same few repeat but whatever).
1. <em>Total angle = (n - 2) * 180 --> 4 * 180 = 360°</em>
<em>70 + 130 + 120 + θ = 360</em> --> 320 + θ = 360 --> θ = 40
4. Total angle =<em> (10 - 2) * 180</em> --> 8 * 180 = <em>1440</em>
<em>1440/10</em> = 144°
6. Interior: (n - 2) * 180 --> 10 * 180 = 1800
Exterior: 12 * 180 = 2160 --> 2160 - 1800 = 360
9. (n - 2) * 180 --> 3 * 180 = 540
90 + 90 + 150 + 160 + θ = 540 --> 490 + θ = 540 --> θ = 50
13. Interior: (n - 2) * 180 --> 2 * 180 = 360
Exterior: n * 180 - (n - 2) * 180 --> 180n - 180n + 360 --> 360 (always the same)
16. 7r + 4r + 8r + 5r = 360 --> 24r = 360 --> r = 15
The tangent ratio is used for right triangles
One way in which to do this problem would involve subtracting 5 from 7 (result: 2) and then subtracting 3/5 from 8/9.
To subtract 3/5 from 8/9, you'd need to find the lowest common denominator (LCD) of 3/5 and 8/9, convert both fractions to have this LCD, and then subtract.
The LCD is (5)(9)=45. Then 8/9 and 3/5 become 40/45 and 27/45.
Subtracting 27/45 from 40/45 results in the fraction 13/45.
Then the full solution is 2 13/45.
You could also do this problem by converting 7 8/9 and 5 3/5 into improper fractions:
71/9 - 28/5. Again, the LCD is 45. Can you rewrite both fractions with 45 as the common denominator and then perform the subtraction?
Answer:
(fg)(x) = 6x³ - 2x² + 12x - 4
Step-by-step explanation:
( f g ) ( x ) = f ( x ) * g ( x )
f(x) = 2x² + 4
g(x) = 3x – 1
( f g ) ( x ) = (2x² + 4) (3x – 1)
= 6x³ - 2x² + 12x - 4
