Answer:
<em>Similarity doesn't changes angle measures</em>
- ∠U = 56°, ∠U' = 3x - 16
- ∠U = ∠U'
a) 3x - 16 = 56 ⇒ 3x = 72 ⇒ x = 24°
b) ∠T = x + 46 = 24 + 46 = 70°
c) <u>Scale factor:</u>
- k = S'T'/ST = 19/57 = 1/3
<u>Find y using known sides and scale factor:</u>
- U'V'/UV = 1/3
- (y + 4)/63 = 1/3
- y + 4 = 21
- y = 21 - 4
- y = 17
Mistake found
3x-2(2x-4)=2
3x - 4x - 8 = 2 instead of 3x - 4x + 8 = 2
Correct answer
x= -13 y= -30
Answer:
The answer is 76500 : 153000
Step-by-step explanation:
You need to times 2
cscx = sinx tan x + cos x
Using xsx x = 1/sin x and tan x = sin x/cos x
Multiplying both sides by cos x
cot x =1
Correct option is d .
Answer:
They buy 6 hotdogs and 5 popcorn
Step-by-step explanation:
Assume that they buy x hotdogs and y popcorn
∵ They buy a total of 11 hotdogs and popcorn
∵ The number of hotdogs is x and the number of popcorn is y
∴ x + y = 11 ⇒ (1)
∵ Hot dogs cost $2.50 each
∵ Popcorn costs $1.00 each
∵ They spend $20 on hot dogs and popcorn
→ Multiply x by 2.5 and y by 1, add the products and equate the sum by 20
∴ 2.5(x) + 1(y) = 20
∴ 2.5x + y = 20 ⇒ (2)
Now we have a system of equations to solve it
→ Subtract equation (1) from equation (2)
∵ (2.5x - x) + (y - y) = (20 - 11)
∴ 1.5x + 0 = 9
∴ 1.5x = 9
→ Divide both sides by 1.5 to find x
∴ x = 6
→ Substitute the value of x in equation (1) to find y
∵ 6 + y = 11
→ Subtract 6 from both sides
∴ 6 - 6 + y = 11 - 6
∴ y = 5
∴ They buy 6 hotdogs and 5 popcorn
