Question 1
cos(C) = adj/hyp
cos(C) = BC/AC
cos(C) = 15/17
Answer: Choice C) 15/17
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Question 2
sin(E) = opp/hyp
sin(E) = FD/DE
sin(E) = 24/25
So angle E is the answer
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Question 3
AC is the adjacent side to the given angle A = 33 degrees
AB = 14 is the hypotenuse
cos(angle) = adjacent/hypotenuse
cos(33) = x/14
14*cos(33) = x
x = 14*cos(33)
x = 11.741
x = 11.7
Answer: 11.7
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Question 4
x = length of board
cos(angle) = adj/hyp
cos(55) = 6/x
x*cos(55) = 6
x = 6/cos(55)
x = 10.46068
x = 10.5
Answer: 10.5
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Question 5
112 is the adjacent side to the given angle 62 degrees
x = height of building, which is the opposite leg
tan(angle) = opp/adj
tan(62) = x/112
112*tan(62) = x
x = 112*tan(62)
x = 210.641364
x = 210.6
Answer: 210.6
Answer: nickels = 14, dimes = 42, quarters = 18
<u>Step-by-step explanation:</u>
Let n represent nickels <em>which has a value of $0.05 </em>
Let d represent dimes <em>which has a value of $0.10</em>
Let q represent quarters <em>which has a value of $0.25</em>
It is given that:
n = n
d = 3n
q = n + 4
and their total value is $9.40 ⇒ n + d + q = $9.40
Use substitution to find the quantity of nickels:
.05(n) + .10(3n) + .25(n + 4) = 9.40
5n + 10(3n) + 25(n+4) = 940 <em>multiplied by 100 </em>
5n + 30n + 25n + 100 = 940 <em>distributed</em>
60n + 100 = 940 <em>added like terms</em>
60n = 840 <em>subtracted 100</em>
n = 14 <em>divided by 60</em>
n = 14
d = 3n
= 3(14)
= 42
q = n + 4
= (14) + 4
= 18
Step-by-step explanation:
−4x+5−13x+39=180
Step 1: Simplify both sides of the equation.
−4x+5−13x+39=180
−4x+5+−13x+39=180
(−4x+−13x)+(5+39)=180(Combine Like Terms)
−17x+44=180
−17x+44=180
Step 2: Subtract 44 from both sides.
−17x+44−44=180−44
−17x=136
Step 3: Divide both sides by -17.−17x
−17
=
136
−17
x=−8
Answer:
x=−8
Answer:
30 different ways
Step-by-step explanation:
Hi
for the first topping she can choose 1 of 6 items
so she has 6 choices
and then the second topping she has 5 choices as each topping can only be chosen once
so it comes 6 * 5 = 30
Answer:
-5 and -5.5;
-12.5 and 2
Step-by-step explanation:
Two negative addends, can be added together to give -10.5.
For example:
(-5) + (-5.5) = -5 - 5.5 = -10.5
Also, it is possible for one of the addends to be negative while the other is positive, and their sum will give us -10.5.
For example:
The sum of -12.5 and 2 will give us -10.5.
We are adding a positive and a negative number here. As usual, we will subtract the smaller number from the bigger number, while the result will carry the sign of the bigger number, which in this case is negative sign.
Thus:
(-12.5) + (2) = -10.5
