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goldfiish [28.3K]

3 years ago

14

What is the equation, in standard form, of a parabola that models the values in the table?

1 answer:

kirza4 [7]3 years ago

5 0

<span> f(x) = ax^2 + bx + c

f(0) = ax^2 + bx + c = 5, c = 5
f(-2) = 4a + -2b + 5 = 1 ----------(1)
f(4) =16a + 4b + 5 = -59 ----------(2)
4a -2b = -4
</span><span>16a + 4b = -64
16a + 4(-2-2a)= -64
16a - 8 - 8a = -64
8a = -56
<span>a = 7
</span>4a - 2b = -4
28 - 2b = -4
b = 16

</span><span>f(x) = 7x^2 + 16x + 5</span>

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A car braked with a constant deceleration of 64 ft/s2, producing skid marks measuring 50 ft before coming to a stop. How fast wa

vitfil [10]

Answer:

The initial speed of the car was 80 ft/s.

Step-by-step explanation:

The deceleration is the rate at which the car speed decreases. In this case the speed of the car goes all the way down to 0 ft/s and in order to do that it travelled 50 ft. So we will call the initial speed at which the car started to brake "v_0" and use Torricelli's equation to find it. The equation is given by:

v^2 = (v_0)^2 + 2*a*S

Where v is the final speed, v_0 is the initial speed, a is the rate of acceleration and S is the space travelled. Using the values that the problem gave to us we have:

0^2 = (v_0)^2 - 2*64*50

0 = (v_0)^2 - 6400

(v_0)^2 = 6400

v_0 = sqrt(6400) = 80 ft/s

Notice that in this case "a" was negative, since the car was decelerating instead of accelerating.

The initial speed of the car was 80 ft/s.

4 0

3 years ago

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EastWind [94]

Answer:

4π, √150, 11 4/9 hope it helps

Step-by-step explanation:

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3 years ago

5. For Which value of x is line L parallel to line m?

laiz [17]

Answer:

$x=22$

Step-by-step explanation:

we know that

If line l is parallel to line m

then

$130\°+(2x+6)\°=180\°$ -----> by supplementary angles (consecutive interior angles)

solve for x

$136+2x=180$

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3 years ago

A cone and its dimensions are shown in the diagram. What is the volume of the cone in cubic inches?

Vinvika [58]

Answer:

The exact value of the volume is equal to

$V=19\frac{397}{512}\pi\ in^{3}$

Step-by-step explanation:

we know that

The volume of a cone is equal to

$V=\frac{1}{3}\pi r^{2} h$

we have

$D=5\frac{5}{8}\ in$

convert to an improper fraction

$D=5\frac{5}{8}\ in=\frac{5*8+5}{8}=\frac{45}{8}\ in$

$r=(45/8)/2=\frac{45}{16}\ in$

$h=7\frac{1}{2}\ in=\frac{7*2+1}{2}=\frac{15}{2}\ in$

substitute in the formula of volume

$V=\frac{1}{3}\pi (\frac{45}{16}^{2})(\frac{15}{2})=\frac{30,375}{1,536}\pi\ in^{3}$

Simplify

$\frac{30,375}{1,536}=\frac{29,184}{1,536}+\frac{1,191}{1,536}=19\frac{397}{512}$

substitute

$V=19\frac{397}{512}\pi\ in^{3}$

4 0

3 years ago

A number cube with faces labeled 1 to 8 is rolled once. The number rolled will be recorded as the outcome. Consider the followin

andrew11 [14]

Answer to A:

50%

Explanation for A:

We're looking for how many numbers are odd, so theres 1, 3, 5 ,7, four numbers.

We have a total of 8 numbers.

$\frac{4}{8} = 0.5$

To make any number a percent we move the point over to the right by two, which makes our final answer 50%

Answer to B:

37.5%

Explanation for B:

If the number is less than four, that means we need to find if it will roll the first three numbers. We, once again, have eight total possibilities

$\frac{3}{8} = 0.375$

0.375 can be turned into our final answer, 37.5%

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