so.. the left-hand-side does indeed simplify to x+7, so the equation does check out.
however, notice something, for the equation of x+7, when x = 6, we get (6) + 7 which is 13.
BUT for the rational, we get
so, even though the siimplification is correct, the rational or original expression is constrained in its domain.
Answer:
One cup of coffee is $3.25
Step-by-step explanation:
Create a system of equations where c is the cost of a cup of coffee and d is the cost of a donut
2c + 4d = 10.5
c + 5d = 8.25
Solve by elimination by multiplying the top equation by -5 and the bottom equation by 4
-10c - 20d = -52.5
4c + 20d = 33
Add them together and solve for c
-6c = -19.5
c = 3.25
So, a cup of coffee is $3.25
Times -7 by everything in the parentheses. so
-7 times 5y=-35y
-7 times -2u=14u
-7 times -5 = 35
therefore 35y+14u+35
A) cos a = (√22)/5; tan a = (√66)/22
B) sin a = (2√2)/3; tan a = 2√2
C) sin a = (√30)/6; cos a = (√6)/6
D) sin a = 3/5; tan a = 3/4
E) sin a = (5√26)/26; cos a = (√26)/26
F) sin a = 3/5; tan a = 3/4
Explanation
The ratio for sine is opposite/hypotenuse. This means the side opposite the angle is √3 and the hypotenuse is 5. Using the Pythagorean theorem to find the adjacent side,
(√3)² + A² = 5²
3+A² = 25
A² = 22
A=√22
This means that cos a = adjacent/hypotenuse = (√22)/5 and tan a = opposite/adjacent = (√3)/(√22) = (√66)/22.
B) The ratio for cosine is adjacent/hypotenuse; this means the side adjacent to the angle is 1 and the hypotenuse is 3. Using the Pythagorean theorem to find the side opposite the angle (p),
1² + p² = 3²
1+p² = 9
p² = 8
p=√8 = 2√2
This means that sin a = opposite/hypotenuse = (2√2)/3 and tan a = opposite/adjacent = (2√2)/1 = 2√2.
C) The ratio for tangent is opposite/adjacent; this means that the side opposite the angle is √5 and the side adjacent the angle is 1. Using the Pythagorean theorem to find the hypotenuse,
(√5)²+1² = H²
5+1=H²
6=H²
√6 = H
This means that sin a = opposite/hypotenuse = (√5)/(√6) = (√30)/6 and cos a = adjacent/hypotenuse = 1/(√6) = (√6)/6.
D) The ratio for cosine is adjacent/hypotenuse; this means that the side adjacent the angle is 4 and the hypotenuse is 5. Using the Pythagorean theorem to find the side opposite the angle, p:
4²+p²=5²
16+p²=25
p²=9
p=3
This means that sin a = opposite/hypotenuse = 3/5 and tan a = opposite/adjacent = 3/4.
E) The ratio for tangent is opposite/adjacent;; this means that the side opposite the angle is 5 and the side adjacent the angle is 1. Using the Pythagorean theorem to find the hypotenuse,
5²+1²=H²
25+1=H²
26=H²
√26 = H
This means that sin a = opposite/hypotenuse = 5/(√26) = (5√26)/26 and cos a = adjacent/hypotenuse = 1/(√26) = √26/26.
F) 0.8 = 8/10; The ratio for cosine is adjacent/hypotenuse. This means that the side adjacent the angle is 8 and the hypotenuse is 10. Using the Pythagorean theorem to find the side opposite the angle, p:
8²+p² = 10²
64+p² = 100
p² = 36
p=6
This means that sin a = opposite/hypotenuse = 6/10 = 3/5 and tan a = opposite/adjacent = 6/8 = 3/4.
Answer:
(p + q)² - ∛(h·3k) or (p + q)² - ∛(h·3k)
Step-by-step explanation:
Cube root of x: ∛x
Product of h and 3k: h·3k
Sum of p and q: p + q
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From (p + q)² subtract ∛(h·3k) This becomes, symbolically:
=> (p + q)² - ∛(h·3k)
