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3 years ago

7

Slope and the y-intercept for y=9x-9

1 answer:

bija089 [108]3 years ago

6 0

Slope is 9 or 9/1 and the y-intercept is -9 or (0,-9)

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if there’s 12 girls selling cookies that are 2.75 and they need to reach $360 how many boxes would each girl have to sell

Sindrei [870]

Answer:

11 each

Step-by-step explanation:

360/2.75=130.9

rounding up, 131x2.75=360.25

131/12=10.9 boxes each

therefore each girl will have to sell 11 boxes

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Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length

Dennis_Churaev [7]

Answer:

k = 9

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Step-by-step explanation:

Equation of parabola: $y=k (x-\frac13)^2$

<u />

<u>Part 1</u>

If the curve passes through point $(\frac23 ,1)$ , this means that when $x=\dfrac23$ , $y = 1$

Substitute these values into the equation and solve for $k$ :

$\implies 1=k \left(\dfrac23-\dfrac13\right)^2$

$\implies 1=k \left(\dfrac13 \right)^2$

Apply the exponent rule $\left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c}$ :

$\implies 1=k \left(\dfrac{1^2}{3^2} \right)$

$\implies 1=\dfrac{1}{9}k$

$\implies k=9$

<u>Part 2</u>

The chord of a parabola is a line segment whose endpoints are points on the parabola.

We are told that one end of the chord is at $(\frac23 ,1)$ and that the chord is horizontal. Therefore, the y-coordinate of the other end of the chord will also be 1. Substitute y = 1 into the equation for the parabola and solve for x:

$\implies 1=9 \left(x-\dfrac13 \right)^2$

$\implies \dfrac19 = \left(x-\dfrac13 \right)^2$

$\implies \sqrt{\dfrac19} = x-\dfrac13$

$\implies \pm \dfrac13 = x-\dfrac13$

$\implies x=\dfrac23, x=0$

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:

$\implies \dfrac23-0=\dfrac23$

**Please see attached diagram for drawn graph. Chord is in red**

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Korolek [52]

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UNO [17]

<u>Question 1</u>

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