The vertex form of a quadratic function is:
f(x) = a(x - h)² + k
The coordinate (h, k) represents a parabola's vertex.
In order to convert a quadratic function in standard form to the vertex form, we can complete the square.
y = 2x² - 5x + 13
Move the constant, 13, to the other side of the equation by subtracting it from both sides of the equation.
y - 13 = 2x² - 5x
Factor out 2 on the right side of the equation.
y - 13 = 2(x² - 2.5x)
Add (b/2)² to both sides of the equation, but remember that since we factored 2 out on the right side of the equation we have to multiply (b/2)² by 2 again on the left side.
y - 13 + 2(2.5/2)² = 2(x² - 2.5x + (2.5/2)²)
y - 13 + 3.125 = 2(x² - 2.5x + 1.5625)
Add the constants on the left and factor the expression on the right to a perfect square.
y - 9.875 = 2(x - 1.25)²
Now, we need y to be by itself again so add 9.875 back to both sides of the equation to move it back to the right side.
y = 2(x - 1.25)² + 9.875
Vertex: (1.25, 9.875)
Solution: y = 2(x - 1.25)² + 9.875
Or if you prefer fractions
y = 2(x - 5/4)² + 79/8
Answer:
Step-by-step explanation:
+6x-5=0
we divide the coefficient of the X by half :
in this case: 6/2 = 3 , then we do the following
The result obtained is raised to square power: 3^2=9
we sum and subtract by 9 to maintain the balance of the equation:
+6x+9-9-5=0
we have:
-9-5=0
= 14
lets apply square root on both sides of the equation:
we know:
so we have:
abs(x+3)=
from where two solutions are obtained
finally we have:
28. Surface Area
This is some sort of house-like model so for every face we see there's a congruent one that's hidden. We'll just double the area we can see.
Area = 2 × ( [14×9 rectangle] + 2[15×9 rectangle]+[triangle base 14, height 6] )
Let's separate the area into the area of the front and the sides; the front will help us for problem 29.
Front = [14×9 rectangle] + [triangle base 14, height 6]
= 14×9 + (1/2)(14)(6) = 14(9 + 3) = 14×12 = 168 sq ft
OneSide = 2[15×9 rectangle] = 30×9 = 270 sq ft
Surface Area = 2(168 + 270) = 876 sq ft
Answer: D) 876 sq ft
29. Volume of an extruded shape is area of the base, here the front, times the height, here 15 feet.
Volume = 168 * 15 = 2520 cubic ft
Answer: D) 2520 cubic ft
Answer:
68 %
Step-by-step explanation:
The Empirical rule formula states that:
• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
Mean of 96 and a Standard deviation of 17
Applying , the first empirical rule for 1 standard deviation from the mean, we have:
μ - σ
96 - 17
= 79
μ + σ
96 + 17
= 113
Therefore, the percentage of IQ scores that are between 79 and 113 is 68%
Answer:
B- 1 inch= 2 feet
Step-by-step explanation:
For this make a fraction, and then simplify. This will show the scale factor.
So, the answer will be 1 inch=2 feet.
