Answer:
Solution : ( - 8, - 5π/3 )
Step-by-step explanation:
There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. For r < 0 we have the coordinates ( - 8, 60° ) and ( - 8, - 300° )
. - 300° in radians is - 5π/3, and hence our solution is option d. But let me expand on how to receive the coordinates. Again r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
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So when r is either negative or positive, we can tell that this point is 8 units from the pole. Therefore - r = - 8 in both our second cases ( we are skipping the first two cases for simplicity ). For r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
Our first coordinate is ( - 8, 60° ). Theta will be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Our second point for - r will thus be ( - 8, - 300° )
. - 300° = - 5π/3 radians, and our coordinate will be ( - 8, - 5π/3 ).
Answer:
A, n = (8 - 7p)/m.
Step-by-step explanation:
mn + 7p = 8
mn = 8 - 7p
n = (8 - 7p)/m.
Answer:
The equations which describe this situation are:
C. f + (2f) + (2f + 2.50) = 11.25
E. 5 f = 8.75
Step-by-step explanation:
Here, the number of loaves of bread purchased = 3
The price of a loaf of French bread = f
The price of whole grain bread = 2 x ( Price of the french bread)
= 2 x (f) = 2 f
The price of cinnamon raisin bread
= ( Price of the whole grain bread) + $2.50
= 2 f + $2.50
Also, the total price paid for the 3 loaves of bread = $11.25
⇒ The cost of ( French + whole grain + Cinnamon raisin) bread = $11.25
or, f + (2f) + (2f + 2.50) = 11.25
or, 5 f = 11. 25 - 2.50 = 8.75
or, 5 f = 8 . 75
Hence the equations which describe this situation are:
C. f + (2f) + (2f + 2.50) = 11.25
E. 5 f = 8.75
Let x = number of 5 cent coins.
Then there are (x+2) 10 cent coins.
Let y = 20 cent coins.
Total coins: x+(x+2)+y = 30
2x+y=28
y = 28-2x (1)
Total value: 0.05x + 0.1(x+2) + 0.2y = 3.80
0.15x + 0.2y + 0.2 = 3.80
0.15x + 0.2y = 3.60 (2)
Substitute (1) into (2).
0.15x + 0.2(28-2x) = 3.60
-0.25x + 5.60 = 3.60
2.00 = 0.25x
8 = x
From (1), obtain y = 28 - 2(8) = 12
Answer: (x+2) = 8+2 = 10
Louise has 10 10-cent coins
L=1.5w. And the perimeter of a rectangle is 2w+2l=25 substitute the 1st equation into the second.2w+2(1.5w)=252w+3w=255w=25W=5
