Solved on Jan 23, 2024

Determine the value of "a" in the equation $y = a x(x - 6)$ by substituting the vertex point $(25, 3)$ . Round "a" to one decimal place.

STEP 1

Assumptions
1. The equation of Eva's flight is given in factored form as $y = a x(x - 6)$ .
2. The vertex point of the parabola is given as $(25, 3)$ .
3. We need to find the value of the coefficient $a$ .
4. The vertex form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.

STEP 2

Since the vertex point $(25, 3)$ is given, we can substitute $x = 25$ and $y = 3$ into the equation to solve for $a$ .
$y = a x(x - 6)$

STEP 3

Substitute the vertex point into the equation.
$3 = a \cdot 25(25 - 6)$

STEP 4

Simplify the equation by performing the subtraction inside the parentheses.
$3 = a \cdot 25(19)$

STEP 5

Multiply the numbers inside the parentheses by 25.
$3 = a \cdot 475$

STEP 6

Now, solve for $a$ by dividing both sides of the equation by 475.
$a = \frac{3}{475}$

STEP 7

Calculate the value of $a$ .
$a = \frac{3}{475} \approx 0.0063$

STEP 8

Round $a$ to one decimal place.
$a \approx 0.0$
The value of "a" rounded to one decimal place is 0.0.

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Determine the value of "a" in the equation $y = a x(x - 6)$ by substituting the vertex point $(25, 3)$ . Round "a" to one decimal place.

STEP 1

STEP 2

Since the vertex point $(25, 3)$ is given, we can substitute $x = 25$ and $y = 3$ into the equation to solve for $a$ .
$y = a x(x - 6)$

STEP 3

Substitute the vertex point into the equation.
$3 = a \cdot 25(25 - 6)$

STEP 4

Simplify the equation by performing the subtraction inside the parentheses.
$3 = a \cdot 25(19)$

STEP 5

Multiply the numbers inside the parentheses by 25.
$3 = a \cdot 475$

STEP 6

Now, solve for $a$ by dividing both sides of the equation by 475.
$a = \frac{3}{475}$

STEP 7

Calculate the value of $a$ .
$a = \frac{3}{475} \approx 0.0063$

STEP 8

Round $a$ to one decimal place.
$a \approx 0.0$
The value of "a" rounded to one decimal place is 0.0.

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Determine the value of "a" in the equation y=ax(x−6)y = a x(x - 6)y=ax(x−6) by substituting the vertex point (25,3)(25, 3)(25,3). Round "a" to one decimal place.

STEP 1

STEP 2

Since the vertex point (25,3) (25, 3) (25,3) is given, we can substitute x=25 x = 25 x=25 and y=3 y = 3 y=3 into the equation to solve for a a a.y=ax(x−6) y = a x(x - 6) y=ax(x−6)

STEP 3

Substitute the vertex point into the equation.3=a⋅25(25−6) 3 = a \cdot 25(25 - 6) 3=a⋅25(25−6)

STEP 4

Simplify the equation by performing the subtraction inside the parentheses.3=a⋅25(19) 3 = a \cdot 25(19) 3=a⋅25(19)

STEP 5

Multiply the numbers inside the parentheses by 25.3=a⋅475 3 = a \cdot 475 3=a⋅475

STEP 6

Now, solve for a a a by dividing both sides of the equation by 475.a=3475 a = \frac{3}{475} a=4753​

STEP 7

Calculate the value of a a a.a=3475≈0.0063 a = \frac{3}{475} \approx 0.0063 a=4753​≈0.0063

STEP 8

Round a a a to one decimal place.a≈0.0 a \approx 0.0 a≈0.0The value of "a" rounded to one decimal place is 0.0.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine the value of "a" in the equation $y = a x(x - 6)$ by substituting the vertex point $(25, 3)$ . Round "a" to one decimal place.

Since the vertex point $(25, 3)$ is given, we can substitute $x = 25$ and $y = 3$ into the equation to solve for $a$ .
$y = a x(x - 6)$

Substitute the vertex point into the equation.
$3 = a \cdot 25(25 - 6)$

Simplify the equation by performing the subtraction inside the parentheses.
$3 = a \cdot 25(19)$

Multiply the numbers inside the parentheses by 25.
$3 = a \cdot 475$

Now, solve for $a$ by dividing both sides of the equation by 475.
$a = \frac{3}{475}$

Calculate the value of $a$ .
$a = \frac{3}{475} \approx 0.0063$

Round $a$ to one decimal place.
$a \approx 0.0$
The value of "a" rounded to one decimal place is 0.0.