Let q and n represent the number of quarters and nickels respectively.
q=3n and .05n+.25q=1.6 These are the conditions in mathematical terms.
To solve, use the value of q from the first equation in the second equation to get:
.05n+.25(3n)=1.6 carry out indicated multiplication on left side
.05n+.75n=1.6 combine like terms on left side
.8n=1.6 divide both sides by .8
n=2, since q=3n
q=6
So Peggy had 2 nickels and 6 quarters.
Answer:
life changes over time?
Step-by-step explanation:
sorry if it is wrong. I havent done this yet
Answer:
The correct answer is: 3x² (4x - 1) / (x - 4) (x - 3) ∧ restriction x ≠ 3, x ≠ 4, x ≠ 0 and x ≠ 1/4
Step-by-step explanation:
Given:
((16x² - 8x + 1) / (x² - 7x + 12)) : ((20x² - 5x) / 15x³) =
dividing with one fraction is the same as multiplying with its reciprocal value
((16x² - 8x + 1) / (x² - 7x + 12)) · (15x³ / (20x² - 5x))
First we need to factorize both numerators and denominators
16x² - 8x + 1 = (4x - 1)² This is square binomial
x² - 7x + 12 = x² - 4x - 3x + 12 = x (x - 4) - 3 (x - 4) = (x - 4) ( x - 3)
20x² - 5x = 5x (4x - 1)
(4x - 1)² / (x - 4) (x - 3) · 15x³ / 5x (4x - 1)
The existence of this rational algebraic expression is possible only if it is:
x - 4 ≠ 0 and x - 3 ≠ 0 and x ≠ 0 and 4x - 1 ≠ 0 =>
x ≠ 4 and x ≠ 3 and x ≠ 0 and x ≠ 1/4 This is restriction
Finally we have:
3 x² (4x - 1) / (x - 4) (x - 3)
God with you!!!
Answer:
y = 5cos(πx/4) +11
Step-by-step explanation:
The radius is 5 ft, so that will be the multiplier of the trig function.
The car starts at the top of the wheel, so the appropriate trig function is cosine, which is 1 (its maximum value) when its argument is zero.
The period is 8 seconds, so the argument of the cosine function will be 2π(x/8) = πx/4. This changes by 2π when x changes by 8.
The centerline of the wheel is the sum of the minimum and the radius, so is 6+5 = 11 ft. This is the offset of the scaled cosine function.
Putting that all together, you get
... y = 5cos(π/4x) + 11
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The answer selections don't seem to consistently identify the argument of the trig function properly. We assume that π/4(x) means (πx/4), where this product is the argument of the trig function.
Answer:
15.2 m
Step-by-step explanation:
You need to draw a figure. Start by drawing a horizontal segment approximately 10 cm long; that is the ground. Label the left end point A and the right endpoint B. On the right endpoint, B, go up a short 1 cm vertically. That is 1.5 m, the height of Zaheer. Label that point C. Now from that point draw a horizontal line that ends up above point A. Label that point D. Now go back to point C. Draw a segment up to the left at a 30 deg angle with CD. End the segment vertically above point D. Label that point E. That is the top of the flagpole. Draw a vertical segment down from point E through point D ending at point A. Segment AE is the flagpole. Go back to point C. Move 3 cm to the left on segment CD, and draw a point there and label it F. That is where Zaheer moved to. Now connect point F to point E. That is a 45-deg elevation to point E, the top of the flagpole.
m<EFD = 45 deg
m<EFC = 135 deg
m<FEC = 15 deg
m<ECD = 30 deg
We now use the law of sines to find EC
(sin 15)/10 = (sin 135)/EC
EC = 27.32
Because of the 30-60-90 triangle, ED = EC/2
ED = 13.66
Now we add the height of Zaheer to find AE.
13.66 + 1.5 = 15.16
Answer: 15.2 m
