Answer:segment YZ ≈ 19.4 inangle X ≈ 85.3°angle Z ≈ 26.7°Explanation:1) Given two side lenghts and one angle you can use sine law:

2) Using the sides with length 43 in and 40in, and the corresponding opposite angles, Z and 68°, that leads to:

From which you can clear sinZ and get:
sinZ = 43 × sin(68) / 40 = 0.9967
⇒ Z = arcsine(0.9967) ≈ 85.36°
3) The third angle can be determined using 85.36° + 68° + X = 180°
⇒ X = 180° - 85.36° - 68° = 26.64°.
4) Finally, you can apply the law of sine to obtain the last missing length:

From which: x = 40 × sin(26.64°) / sin(68°) = 19.34 in
The answer, then is:
segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°
Answer:
25
Step-by-step explanation:
We require to solve for n, hence
n(n + 1) = 325
multiply both sides by 2 to eliminate the fraction
n(n + 1) = 650
n² + n = 650
subtract 650 from both sides to have equation in standard form
n² + n - 650 = 0 ← in standard form
(n + 26)(n - 25) = 0 ← in factored form
equate each factor to zero and solve for n
n + 26 = 0 ⇒ n = - 26
n - 25 = 0 ⇒ n = 25
however, n > 0 ⇒ n = 25
Wake up to reality! Nothing ever goes as planned in this world. The longer you live, the more you realize that in this reality only pain, suffering and futility exist.- Madara Uchiha
Answer:
542.50
Step-by-step explanation:
Given:
Least square regression equation :
y = 102.50 + 0.65x + residual
y = predicted fare
x = distance in miles
Intercept = 102.50
Slope = 0.65
Distance in miles, x = 500 miles
y = 102.50 + 0.65(500) + 115
y = 102.50 + 325 + 115
y = 427.5 + 115
y = 542.50
Answer:
The answer is E.
Step-by-step explanation:
If the game costs $10 originally then the following would be true:
B = $10
$10.00 x .18 = $1.80 so the discount is $1.80
10.00 - 1.80 = $8.20