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3 years ago

Which of the following is the slope-intercept form of 6x + 2y = 28

Mathematics

2 answers:

PolarNik [594]3 years ago

4 0

The answer is Y=-3x+14

olasank [31]3 years ago

4 0

None of these answers are correct.

The answer is y= -3x+14

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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

length of chord = 2/3

Step-by-step explanation:

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

Part 1

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 $\left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c}$ :

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

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

$\implies k=9$

Part 2

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**

6 0

2 years ago

What is the solution of the system of equations? 4x-3y=-1 3x-9y=33

ehidna [41]

Step-by-step explanation:

4x+13y=-9y+3y=33

17x=-6y=33

5 0

3 years ago

Emaan charges a fixed amount for a bracelet, with an additional charge for each charm a customer adds to the bracelet. Write a l

DIA [1.3K]

Answer:

f(x) = y + (x*p)

Step-by-step explanation:

Since we are not given actual values we will need to make the function with only variables. Each variable will represent the following...

Fixed Cost: y

Cost per charm: p

Number of charms: x

Therefore, using the variables mentioned above we can combine them into the following linear function using the number of charms as our main input for our function...

f(x) = y + (x*p)

6 0

3 years ago

Tamisha ordered 4 pepperoni pizzas and 2 sausage pizzas for $60.50. Megan ordered 2 pepperoni pizzas and 3 sausage pizzas for $4

Ahat [919]

Answer: Look at picture

8 0

3 years ago

Someone Explain to me how 5. Is valid ???

vichka [17]

This is valid through the law of syllogism. If you swap lines 1 and 2, then you'll have this argument:

If I step on a beehive, then I will get stung.

If I get stung by a bee, then it will hurt.

Therefore, if I step on a beehive, then it will hurt

------------------

So it's like connecting a chain together. Point A (stepping on the hive), leads to point B (getting stung), which leads to point C (getting hurt). We can take a shortcut to bypass point B to jump from A to C in one step. Check out the attached image for a visual of what I'm referring to.

6 0

3 years ago