The Answer to your problem is X=0
x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.
Step-by-step explanation:
Given,
Earning for song played in commercial one time= $30
Earning for song played in movie one time = $80
Let,
x represent the number of commercials Anna's song played.
y represent the number of movies Anna's song played.
According to given statement;
Anna's songs were played on 3 more commercials than movies
x=y+3
her total earnings on the royalties from all commercials and movies was $640.
30x+80y=640
x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.
Keywords: linear equation, substitution method
Learn more about linear equations at:
#LearnwithBrainly
Answer:
angle of intersection: 5.2°
Step-by-step explanation:
The direction vector normal to the plane is ...
n = (1, 1, 3)
The direction vector of the line is ...
m = (1, -3, 1)
Then the angle θ between them can be found from the dot product:
n•m = |n|·|m|·cos(θ)
(1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)
1 = 11·cos(θ)
θ = arccos(1/11) ≈ 84.8°
This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, <em>the line and plane must intersect</em>.
acute angle = 90° -84.8° = 5.2°
_____
The attached graph shows the line and plane meet at a shallow angle, consistent with the above answer.
The answer would be -17/15 or -1 2/15
Answer:
1) 33 cm squared
2) 212.5 cm squared.
Step-by-step explanation:
1) Split the figure into a rectangle and a square. The rectangle is 8 (4 times 2) and the square is 25 (5 times 5). 25+8 =33.
2) Find the area of the shaded and unshaded. 14 times 25 equals 350. Then find the area of the unshaded triangle. 11 times 25 divided by 2 is 137.5. Now subtract. 350-137.5 = 212.5.
*please mark brainliest*
