Answer:
k = 1
Step-by-step explanation:
English Translation
Find k if the point P (-1, 2k + 1) belongs to the graph of the function f (x) = - 4x^2 + 7.
The function is given as
y = f(x) = -4x² + 7
and point (-1, 2k+1) lies on the graph.
This point means that, at x = -1, y = 2k+1
y = -4x² + 7
Substituting the values in
2k + 1 = -4(-1)² + 7
2k + 1 = -4 + 7 = 3
2k = 3 - 1
2k = 2
k = 1
Hence, the point (-1, 2k+1) is (-1, 3)
To check,
y = -4x² + 7
3 = -4(-1)² + 7
3 = -4 + 7
3 = 3
So, this is truly correct.
Hope this Helps!!!
Answer:
D
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant
Using the distance formula
= | y + 1 |
Squaring both sides
(x + 5)² + (y - 5)² = (y + 1)^2 , that is
(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides
(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify
y² + 2y + 1 - y² + 10y - 25 = (x + 5)²
12y - 24 = (x + 5)² ← factor left side
12(y - 2) = (x + 5)² ← divide both sides by 12
y - 2 = 
(x + 5)² ← add 2 to both sides
y = (x + 5)² + 2
or
f(x) = (x + 5)² + 2 → D
Answer:
Step-by-step explanation:
In retail grocery stores in the US, you can find ice cream packaged in sizes of 1 cup (half pint), 1 pint, 1 quart, 1/2 gallon, 1 gallon, and perhaps some odd sizes in between. For commercial purposes, ice cream may be packaged in tubs of 3- or 5-gallons or more.
1 teaspoon would be an unusually small size, and 1 mL is about 1/5 of a teaspoon. These quantities are somewhat smaller than would be considered a "serving" of ice cream, so would generally be of little practical use.
Answer:
$9400
Step-by-step explanation:
1.5x4=6%
100-6=94
0.94x10000=9400
-1.9 = x/.5 given equation
multiply both sides by .5
.5(-1.9) = x/(.5) *(.5)
-.95 = x
check: -1.9 = -.95/ .5
