Step-by-step explanation:
The vertex form of the equation for a parabola is given by
where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as
Also, since the parabola passes through (4, -7), we can use this to find the value for a:
or
Therefore, the equation of the parabola is
<h3>
Answer: 12 inches</h3>
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Explanation:
Notice the double tickmarks on segments WZ and ZY. This tells us the two segments are the same length. Let's say they are m units long, where m is a placeholder for a positive number.
That would mean m+m = 2m represents the length of segment WY, but that's equal to 10 as the diagram shows. We have 2m = 10 lead to m = 5 after dividing both sides by 2.
We've shown that WZ and ZY are 5 units long each. In short, we just cut that length of 10 in half.
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Let's focus on triangle XYZ. This is a right triangle with legs XZ = unknown and ZY = 5. The hypotenuse is XY = 13.
We'll use the pythagorean theorem to find XZ
a^2 + b^2 = c^2
(XZ)^2 + (ZY)^2 = (XY)^2
(XZ)^2 + (5)^2 = (13)^2
(XZ)^2 + 25 = 169
(XZ)^2 = 169-25
(XZ)^2 = 144
XZ = sqrt(144)
XZ = 12
Segment XZ is 12 inches long.
Answer:
3520.176 feet per minute
Step-by-step explanation:
First, we must convert 40 miles per hour (mph) to miles per minute (mpm):
40 mph = 40 miles/hour / 60 minutes/hour = 0.6667 miles per minute
Next, we convert miles per minute to feet per minute by multiplying 5280 ft per mile:
0.6667 mpm = 0.6667 miles/minute * 5280 ft/mile = 3520.176 feet per minute
Answer:
see explanation
Step-by-step explanation:
(a)
Note the squared value in column 3 which is the square of 1 more than the row number, that is
row 2 → (2 + 1)² →3²
row 3 → (3 + 1)² → 4²
Find the square root of 676 = 26 → (25 + 1)² = 26²
Hence the row number is 25
(b)
The pattern in column 1 is [ row number × (row number + 2 ) + 1 ]
row number is n then n(n + 2) + 1 = n² + 2n + 1
Answer:
Its 3
Step-by-step explanation:
