Jerry thinks that x < 4 is a solution to the following inequality: 2x + 10 < 4x - 20
1 answer:
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One form of the equation of a parabola is
y = ax² + bx + c
The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6 (1)
a - b + c = -12 (2)
9a + 3b + c = 0 (3)
Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6 (4)
9a + 3b - 6 = 0
9a + 3b = 6 (5)
Substitute a = b - 6 from (4) into (5).
9(b - 6) + 3b = 6
12b - 54 = 6
12b = 60
b = 5
a = b - 6 = -1
The equation is
y = -x² + 5x - 6
Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
= -[ (x - 2.5)² - 2.5²] - 6
= -(x - 2.5)² + 6.25 - 6
y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
The axis of symmetry is x = 2.5
Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.
Answer: y = -(x - 2.5)² + 0.25
y = ax² + bx + c
The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6 (1)
a - b + c = -12 (2)
9a + 3b + c = 0 (3)
Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6 (4)
9a + 3b - 6 = 0
9a + 3b = 6 (5)
Substitute a = b - 6 from (4) into (5).
9(b - 6) + 3b = 6
12b - 54 = 6
12b = 60
b = 5
a = b - 6 = -1
The equation is
y = -x² + 5x - 6
Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
= -[ (x - 2.5)² - 2.5²] - 6
= -(x - 2.5)² + 6.25 - 6
y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
The axis of symmetry is x = 2.5
Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.
Answer: y = -(x - 2.5)² + 0.25
The image is missing so i have attached it.
Answer:
Volume = 1.5 litres
Step-by-step explanation:
Using pythagoras theorem, we can get the height (h) of the cylinder
14² + h² = 17²
h² = 289 - 196
h = √93
Now, volume of a cylinder is;
V = πr²h
In the image, r = diameter/2 = 14/2 = 7cm
Thus,
V = π × 7² × √93
V = 1485 cm³
Now, 1 litre = 1000 cm³
Thus, volume = 1485/1000 = 1.485 litres ≈ 1.5 litres
Answer:
1) Repaid for the loan = $239,511.60
2) Percentage = 58.2%
3) Average amount = $387.53
Step-by-step explanation:
Given :
Amount $100,000
Rate 7%
Payments 360 - $665.31
Total interest $139,511.60
To find :
1) How much will be repaid for this loan?
Repaid for the loan = Amount - Total interest
Repaid for the loan = 100,000 + 139,511.60
Repaid for the loan = $239,511.60
2) What percentage will be repaid for this loan?
3) What will be the average amount per payment for interest?