Answer:
Plant A produced 15,000 panels.
Step-by-step explanation:
Let plant B produce x panels
Plant A then produced x - 2000 panels
2% of panels from plant A were defective
3% of panels from plant B were defective
The two plants together produced 810 defective panels so;
2/100(x - 2000) + 3/100(x) = 810
0.02x - 40 + 0.03x = 810
0.05x = 850
x = 17,000 panels
So plant B produced 17,000 panels
Plant A produced 17,000 - 2,000 panels = 15,000 panels.
Answer:
(3) y = 4x
Step-by-step explanation:
In order for the equation not to change, the point (0, 0) must be on the original line and so on the line after dilation. The only equation with (0, 0) as a point on the line is y=4x.
Dilation about the origin moves all points away from the origin some multiple of their distance from the origin. If a point is on the origin, it doesn't move. We call that point the "invariant" point of the transformation. For the equation of the line not to change, the invariant point must be on the line to start with.
G( - 3 ) = 8 * ( - 3 ) + 2 = -24 + 3 = - 21 ;
( fog )(-3) = f( g(-3) ) = f( - 21 ) = 6 * ( -21 ) + 7 = - 126 + 7 = - 119
One way to solve this is to use Pythagorean theorem: the square of one leg of triangle plus square of other leg of the triangle equals c the hypotenuse (longest side of triangle). You might see this as the formula a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.
In this case, the legs are 3√2 and the hypotenuse is h.
Using the formula:
(3√2)² + (3√2)² = h²
18 + 18 = h²
h = 6
The other way to do this is with trigonometric angles.
Remember cosine is adjacent over hypotenuse.
cos(45°) = (3√2) / h
h = (3√2) / cos(45°)
h = 6
Answer:
Step-by-step explanation:
Birth Rate in 1994 = 14.6 births per thousand population.
Birth Rate in 2004 = 14.32 births per thousand population.
A linear equation is of the form: y=mx+c
Where:
- x=years after 1994
- y=the birth rate
- m=Yearly Birth Rate
First, we determine the birth rate per year
Therefore, a linear equation that relates y in terms of x is of the form:
When x=0, y=14.6
14.6=-0.028(0)+c
c=14.6
Therefore, the linear equation that relates y in terms of x is:
