Answer:
500=2.5x+200
x=the amount of desserts.
500-200=2.5x
300=2.5x
x=120
Step-by-step explanation:
Step-by-step explanation:
h = -490t² + 1470t
When h = 980:
980 = -490t² + 1470t
Simplifying:
0 = -490t² + 1470t - 980
0 = t² - 3t + 2
Factoring:
0 = (t - 1) (t - 2)
t = 1, 2
There are two solutions because the rocket first reaches the height of 980 cm as it's going up at 1 second, then it reaches that height again as it's coming down at 2 seconds.
Answer:
26.0 cm
Step-by-step explanation:
Given quadrilateral ABCD with diagonal BD forming triangles ABD and BCD, and angles A=90°, C=52°, ADB=35°, and CBD=52°, you want the length of CD to 3 significant figures.
<h3>Law of Sines</h3>
The law of sines tells you the relation between sides and opposite angles is ...
a/sin(A) = b/sin(B) = c/sin(C)
This lets us write two proportions that can be solved for the measure of CD.
In triangle ABD:
BD/sin(A) = AB/sin(D)
BD = AB·sin(90°)/sin(35°) = 12 cm/sin(35°) ≈ 20.921 cm
In triangle BCD:
CD/sin(B) = BD/sin(C)
CD = BD·sin(B)/sin(C) = 20.921 cm·sin(102°)/sin(52°) ≈ 25.969 cm
The length of CD is about 26.0 cm.
Answer:
f ∘ g(5) = 47
Step-by-step explanation:
We are given the following functions:
![f(x) = 3x + 2, g(x) = 2x + 5](https://tex.z-dn.net/?f=f%28x%29%20%3D%203x%20%2B%202%2C%20g%28x%29%20%3D%202x%20%2B%205)
Composite function:
The problem asks their composite function at x = 5. So
![f \circ g = f(g(x)) = f(2x + 5) = 3(2x + 5) + 2 = 6x + 15 + 2 = 6x + 17](https://tex.z-dn.net/?f=f%20%5Ccirc%20g%20%3D%20f%28g%28x%29%29%20%3D%20f%282x%20%2B%205%29%20%3D%203%282x%20%2B%205%29%20%2B%202%20%3D%206x%20%2B%2015%20%2B%202%20%3D%206x%20%2B%2017)
![f(g(5)) = 6(5) + 17 = 30 + 17 = 47](https://tex.z-dn.net/?f=f%28g%285%29%29%20%3D%206%285%29%20%2B%2017%20%3D%2030%20%2B%2017%20%3D%2047)
We have that f ∘ g(5) = 47