Answer:
x = -9/22 or -0.409 to the nearest thousandth.
Step-by-step explanation:
Cross multiplying we get:
(3x + 1)(x - 5) = (3x + 2)(x + 2)
3x^2 - 14x - 5 = 3x^2 +8x + 4
3x^2 - 3x^2 - 14x - 8x = 4 + 5
-22x = 9
x = -9/22
So a general harmonic equation is Asin(2πt/T). Little t is just a variable. 6 inches is the height of one maximum and one minimum from equilibrium, so that is the amplitude A. T is the period, or the time of one cycle (or wavelength), which is 2 seconds.
The equation is therefore (in terms of seconds and inches), 6*sin(2πt/2), or 6*sin(πt).
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7. Okay. So the computer was originally $1,080, and the discount is 20%, but David would still have to pay 80% of the original price. To find the sale price, let's multiply. 1,080 * 80% (0.8) is 864. The sale price of the compuet is $864, but now we must add the sales tax to find the total price. We will multiply by 108%, because 100% (representing the price + 8% is 108%, and doing this will get us stright to the total price. 864 * 108% (1.08) is 933.12. There. David paid a total price of $933.12 for the computer.
8. Okay. So we are looking for the amount of discount for the sweater Suzanne bought. First off, let's subtract the prices to find the difference. 40 - 25 is 15. Now, let's divide that by 40 (the original price) to find the discount. 15/40 is 0.375. Or 37.5% when converted into a percentage. There. Suzanne received a 37.5% discount on the sweater when she bought it.
9. So the car was bought for x dollars. 0.88 represents 88%, so the value of the car is 88% of the previous year. An expression that is a way to describe the change in car value is x * (100 - 0.12)^t, because you car loses 12% of the remaining value each year, which leaves 88% of it remaining, and having the t as the exponent represents the number of years. That expression helps find the value of the car currently and can help you compare the values.
9514 1404 393
Answer:
x = -9
Step-by-step explanation:
Segment NL is twice the length of midsegment WV.
2WV = NL
2(x+15) = x+21
2x +30 = x +21 . . . . simplify
x = -9 . . . . . . . . . . . . add -30-x
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<em>Additional comment</em>
This value of x means the other segments are ...
MN = 12
WV = 6
NL = 12
Half a century is 50 years. a century is 100 years
