help me

The fire department is setting off fireworks. They notice that the casings of the fireworks hit the ground 78 seconds after the firework was launched. The firework exploded at a maximum height of 760.5 meters.

Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation. (Hint: You may want to rewrite the equation in equivalent forms.)

Answers

Answer 1

The firework is an illustration of the equation of a parabola.

The x-intercepts are 0 and 78, the y-intercept is 0, and the vertex is (39,760.5)

The casings hit the ground after 78 seconds.

This means that, a point on the graph is:

[tex]\mathbf{(x,y) = (78,0)}[/tex]

The firework exploded at a maximum of 760.5.

This means that, the vertex is:

[tex]\mathbf{(h,k) = (39,760.5)}[/tex]

The equation of a parabola is:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

So, we have:

[tex]\mathbf{0 = a(78 - 39)^2 + 760.5}[/tex]

[tex]\mathbf{0 = a(39)^2 + 760.5}[/tex]

Subtract 760.5 from both sides

[tex]\mathbf{a(39)^2 =- 760.5}[/tex]

[tex]\mathbf{1521a =- 760.5}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{760.5}{1521}}[/tex]

[tex]\mathbf{a =- 0.5}[/tex]

Substitute [tex]\mathbf{a =- 0.5}[/tex] and [tex]\mathbf{(h,k) = (39,760.5)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -0.5(x - 39)^2 + 760.5}[/tex]

See attachment for the graph of [tex]\mathbf{y = -0.5(x - 39)^2 + 760.5}[/tex].

From the graph:

The x and y intercepts are the points where the graph crosses the x and y axes. The vertex is the maximum point on the graph

From the equation:

Set x to 0, to calculate the value of y for the y-interceptSet y to 0, to calculate the value of x for the x-intercept.The vertex is represented as: (h,k)

Hence, the x-intercepts are 0 and 78, the y-intercept is 0, and the vertex is (39,760.5)

Read more about parabolas at:

https://brainly.com/question/5430838

Help Me The Fire Department Is Setting Off Fireworks. They Notice That The Casings Of The Fireworks Hit

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2 [tex]\frac{3}{4}[/tex]

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Substitute the given values into the expression

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Answer:

Step-by-step explanation:

Step one- is solving the left side of the equation using PEMDAS, 1.4x10 = 14

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answer: 21.59

I hope this helps! Let me know if you have any questions! Good luck on the rest of your assessment!

Mark this as Brainliest (if i helped of course) if you get a chance:)

Answer:

21.59cm

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Multiply 8.5 by 2.54 to convert in. to cm.

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Answers

Using the hypergeometric distribution, it is found that there is a 0.0455 = 4.55% probability that both light bulbs failed the test.

The bulbs are chosen without replacement, and this is why the hypergeometric distribution is used to find the probability.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

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x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.

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12 bulbs, thus [tex]N = 12[/tex]3 failed the test, thus [tex]k = 3[/tex].2 are selected, thus [tex]n = 2[/tex].

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0.0455 = 4.55% probability that both light bulbs failed the test.

A similar problem is given at https://brainly.com/question/24826394

Marie bought 6 pounds of apples for $0.87 per pound and
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Answer:

5.22

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rjskstks5oslyatkao5sylslgsltsirsotzktzo

Answer:

$4.78

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6 x 0.87 = 5.22

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