Answer:
Measure of angle 1 is 60° and angle 2 is 30°.
Step-by-step explanation:
Let us assume Conrad drew two angles ∠1 = x and ∠2 = y.
Now we go through the question.
Three times the measure of angle 1 is 30 more than 5 times the measure of angle 2.
Now we form the equation 3x = 30+5y
⇒ 3x-5y = 30---------(1)
Again the question says,the sum of twice the measure of angle 1 and twice the measure of angle two is 180.
We form the equation again.
⇒ 2x+2y = 180
2(x+y) = 180
Now we divide the equation by 2 on both the sides
⇒ x+y = 90-------(2)
we multiply equation (2) by 5.
⇒ 5(x+y) = 5×90 = 450
⇒ 5x+5y =450---------(3)
Now we add equation (1) and equation (3)
(3x-5y)+(5x+5y)=30+450
3x-5y+5x+5y =480
8x =480
x = 480÷8 = 60
Now we put the value of x in equation (2)
⇒ 60+y =90
⇒ y = 90-60 = 30
So the angle 1 is 60 and angle 2 is 30.
Answer:
The profit of the bakery for this batch of rolls is C. $ 132
Step-by-step explanation:
You know the following this about the problem:
- xy=300 is the total cost of the production of the rolls, where x is the cost of the rolls and y is the number of rolls.
- Day 1 the bakery sold 4/5 of the rolls at 1.50 its value.
- Day 2 the bakery sold 1/5 of the rolls ar 0.8 of the price of Day 1.
The total gain of the sales is:
Day 1 + Day 2
and you know that xy =300, then the total gain is:
And the profit is the total gain less the total cost:
Profit = 432-300=132
Answer:
Step-by-step explanation:
L=2W
P=2(L+W), given L=2W and P=126
2(2W+W)=126
6W=126
W=21 and L=42
Answer:
336 ways ;
56 ways
Step-by-step explanation:
Number of ways to have the officers :
Number of qualified candidates, n = 8
Number of officer positions to be filled = 3
A.)
Using permutation (since the ordering matters):
nPr = n! ÷(n-r)!
8P3 = 8! ÷ (8-3)!
8P3 = 8! ÷ 5!
8P3 = (8*7*6)
8P3 = 336 ways
B.) Different ways of appointing committee: (ordering doesn't count as officers can also be appointed)
Using the combination relation :
nPr = n! ÷(n-r)!r!
8C3 = 8! ÷ (8-3)! 3!
8C3 = 8! ÷ 5!3!
8C3 = (8*7*6) ÷ (3*2*1)
8C3 = 336 / 6
8C3 = 56 ways
