Answer:
C
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
6x + 10y = 8 ( subtract 6x from both sides )
10y = - 6x + 8 ( divide each term by 10 )
y = -
x +
= -
x 6 +
← in slope- intercept form
with slope m = -
→ C
If the parabola has y = -4 at both x = 2 and x = 3, then since a parabola is symmetric, its axis of symmetry must be between x = 2 and x = 3, or at x = 5/2. Our general equation can then be:
y = a(x - 5/2)^2 + k
Substitute (1, -2): -2 = a(-3/2)^2 + k
-2 = 9a/4 + k
Substitute (2, -4): -4 = a(-1/2)^2 + k
-4 = a/4 + k
Subtracting: 2 = 2a, so a = 1. Substituting back gives k = -17/4.
So the equation is y = (x - 5/2)^2 - 17/4
Expanding: y = x^2 - 5x + 25/4 - 17/4
y = x^2 - 5x + 2 (This is the standard form.)
Answer:
x = -5
y = 6
Step-by-step explanation:
3x + 7y = 27 --------------(I)
-3x + y = 21 -----------(II)
Add equation (I) & (II) and so x will be eliminated and we can find the value of y.
(I) 3x + 7y = 27
(II) <u> -3x + y = 21 </u> {add}
8y = 48
y = 48/8
y = 6
Plugin y = 6 in equation (I)
3x +7*6 = 27
3x + 42 = 27
3x = 27 - 42
3x = -15
x = -15/3
x = -5
The r% of a quantity x is computed by dividing x in 100 parts, and considering r of such parts. So, the r% of the male is

and similarly, the r% of female is

The number of males decreased by this quantity, so now it is

and the number of female increased by this quantity, so now it is

we know that these two new counts are the same number, so we can build and solve the equality

Subtract 20 and add 0.3r from both sides:

Divide both sides by 0.5 to solve for r:

Let's check the answer
The 20% of 30 is
, while the 20% of 20 is 4. So, we are stating that
which is true because both expressions evaluate to 24.