Answer:
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)
Step-by-step explanation:
The standard form of the equation of a parabola is (y - k)² = 4p (x - h), where
- The vertex of the parabola is (h , k)
- The focus is (h + p, k)
∵ The vertex of the parabola is (3 , -2)
∴ h = 3 and k = -2
∵ The focus is (5 , -2)
∴ h + p = 5
- Substitute h by 3 to find p
∵ 3 + p = 5
- Subtract 3 from both sides
∴ p = 2
∵ The standard form of the equation of the parabola is (y - k)² = 4p (x - h)
- Substitute the values of h , k , and p in the equation
∴ (y - -2)² = 4(2) (x - 3)
∴ (y + 2)² = 8 (x - 3)
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)
Answer in fraction form: x = 55/4
Answer in decimal form: x = 13.75
Both forms are equivalent, but they say it in a slightly different way.
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Work Shown:
AC/QY = CD/YW
(x+5)/15 = 5/4
4(x+5) = 15*5
4x+20 = 75
4x = 75-20
4x = 55
x = 55/4
x = 13.75
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Explanations:
- The first step is possible because the polygons are similar. Similar figures have their corresponding sides be in the same proportion or ratio. Note how side AC has the double red angle (at point A) and a single red angle (point C). The side QY has the same idea in the same order. This is why AC corresponds to QY. The ratio AC/QY is the same as CD/YW.
- In the second step, I plugged in the expressions that the diagram shows. This is the substitution property.
- On step 3, I cross multiplied. The general format is A/B = C/D cross multiplies to A*D = B*C.
Answer:
105/4 or 26.25 mi
Step-by-step explanation:
hillsdale to fairfax 8 7/8 = 71/8
fairfax to yardley = 17 3/8 = 139/8
71/8 + 139/8 = 105/4 or 26 2/8
Answer:
it could be -50.35 and 50.35 since the absolute value is just the positive value of the number
