Michelle is making a scale model of her favorite car. The actual car is 8 feet long and 4 feet wide. Michelle wants her model to be 12 inches in length. Which could be used to find the width of her model if she used the same ratio?

Given:

Focus of a parabola = [tex]\left(1,\dfrac{1}{2}\right)[/tex]

Directrix: [tex]y=3[/tex]

To find:

The equation of the parabola.

Solution:

The equation of a vertical parabola is:

[tex]y-k=\dfrac{1}{4a}(x-h)^2[/tex]            ...(A)

Where, [tex](h,k)[/tex] is center, [tex](h,k+a)[/tex] is focus and [tex]y=k-a[/tex] is the directrix.

On comparing the focus, we get

[tex](h,k+a)=\left(1,\dfrac{1}{2}\right)[/tex]

[tex]h=1[/tex]

[tex]k+a=\dfrac{1}{2}[/tex]           ...(i)

On comparing the directrix, we get

[tex]k-a=3[/tex]              ...(ii)

Adding (i) and (ii), we get

[tex]2k=\dfrac{7}{2}[/tex]

[tex]k=\dfrac{7}{4}[/tex]

Putting [tex]k=\dfrac{7}{4}[/tex] is (i), we get

[tex]\dfrac{7}{4}+a=\dfrac{1}{2}[/tex]

[tex]a=\dfrac{1}{2}-\dfrac{7}{4}[/tex]

[tex]a=\dfrac{-5}{4}[/tex]

Putting [tex]a=\dfrac{-5}{4},h=1,k=\dfrac{7}{4}[/tex] in (A), we get

[tex]y-\dfrac{7}{4}=\dfrac{1}{4\times \dfrac{-5}{4}}(x-1)^2[/tex]

[tex]y-\dfrac{7}{4}=\dfrac{-1}{5}(x^2-2x+1)[/tex]

[tex]y-\dfrac{7}{4}=-\dfrac{1}{5}(x^2)-\dfrac{1}{5}(-2x)-\dfrac{1}{5}(1)[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x-\dfrac{1}{5}+\dfrac{7}{4}[/tex]

On further simplification, we get

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{35-4}{20}[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex]

Therefore, the equation of the parabola is [tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex].

Note: Option C is correct but the leading coefficient should be negative.

Answer:

8. 12 in

9. 30 ft

10. 87.92 in

Step-by-step explanation:

Answer:

12in, 30ft, 87.92in

Step-by-step explanation:

question 8: 24/2 = 12in

question 9: 15(2) = 30ft

question 10:

C = 2πr

C =2(3.14)(14)

C= 87.92in

Answer:

9.6315

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

You will get $279,841.74 in that 50 years.

Answer:

117.3

Step-by-step explanation:

7*4=117.29=117.3

Answer and Step-by-step explanation:

Theoretically, we should expect the coin to flip 250, or very close to 250 times, and land on heads.

This is because the probability of getting heads is [tex]\frac{1}{2}[/tex], or 50%.

There is a 50% chance of landing heads or tails, so that means it would land 250 times on heads out of 500 flips of the coin.

#teamtrees #PAW (Plant And Water)

Answer:

250 times

Step-by-step explanation:

The coins has the heads or tails, with two options there is a 50% probability of landing on heads or tails.

500 x 50% = 250 times

Answer:

x=146 degrees

Step-by-step explanation:

A supplementary angle is the conrisponding angle that adds to the other angle so it is 180. So 180-34= 146

Answer: 14.5 feet

Step-by-step explanation: that’s he correct answer delta math gave me AFTER I got it wrong

Answer:

14.5

Step-by-step explanation:

Answer:

the answer would be 3.4 + 4 = 7.4 .

Answer:

the answer would be 3.4 + 4 = 7.4 .

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

b.POT↔️NUS

Step-by-step explanation:

hope it helps

Answer:

Use M a t h W a y

Step-by-step explanation:

it all together

Answer:

d=2m

area(A)=196m

l=60m

now,

A=d(l+b-d)

196=2(60+b-2)

196=2(58+b)

196=116+2b

2b=196-116

2b=80

b=40m

Answer:

The equation of the line is;

y = 0.8x + 1

Step-by-step explanation:

Here, we want to get the equation of the line

The general equation of a straight line is;

y = mx + b

m

is the slope and b is the y-intercept

The y-intercept is simply the point on the y-axis where the line crosses the y-axis

we have this point at (0,1)

so we have;

y = mx + 1

to get m, we get any other point on the line and substitute its coordinates before we solve for m

we can identify the point (-2.5, -1)

substituting the coordinates

-1 = -2.5(m) + 1

-2.5m = -1-1

-2.5m = -2

m= 2/2.5

m= 0.8

so we have the equation of the line as;

y = 0.8x + 1

Answer: 4.25 miles

Step-by-step explanation:

The distance he biked on Thursday and Friday combined is:

= 3.5 + 4.25

= 7.75 miles

On Saturday he biked 12 miles. The number of miles he biked over Thursday and Friday is:

= 12 - 7.75

= 4.25 miles

Answer:

y=16x

Step-by-step explanation:

y=(8)(2)x

--HEART IF THIS HELPED OR BRAIN ME!!--

The ordered pairs (-3, 1), (-2, 2), (-1, 4), (0, 8), (1, 16), (2, 32) and (3, 64) on the graph are plotted below.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

The given equation is y=8×2ˣ.

Here, in table

x        -3      -2     -1      0     1      2      3

y         1        2      4     8     16   32    64

So, the ordered pairs are (-3, 1), (-2, 2), (-1, 4), (0, 8), (1, 16), (2, 32) and (3, 64)

Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y=0.

Horizontal Asymptote: y=0

Therefore, the ordered pairs on the graph are plotted below.

Learn more about the exponential function here:

brainly.com/question/11487261.

#SPJ5

Answer:

It’s b

Step-by-step explanation:

Just think

Answer:

1. The probability that she throws a multiple of 3 and flips tails is 1/6

2. The probability that Cymra draws a red marble put it back and draws a red marble again is 25/196

3.  The probability that Cole flips three tails in a row, P(3T) is 1/8

4. The number of shots Linda is expected to make if she takes 175 shots is 56

Step-by-step explanation:

1. The number of sides on the special die Li rolls = 12 sides

The numbers on the die are 1 through 12

The number of faces on the penny = 2 (heads and tails)

The number of multiples of 3 on the die = 3, 6, 9, and 12 = 4

The probability that she throws a multiple of 3, P(3) = 4/12 = 1/3

The probability that she flips tails rather than heads = 1/2

∴ The probability that she throws a multiple of 3 and flips tails = 1/3 × 1/2 = 1/6

2. The number red marbles in the bag = 5

The number green marbles in the bag = 6

The number blue marbles in the bag = 3

The total number of marbles in the bag = 5 + 6 + 3 = 14

The probability that Cymra draws a red marble put it back and draws a red marble again is given as follows;

The probability with replacement of picking two red marbles = 5/14 × 5/14 = 25/196

3. The probability that Cole flips three tails in a row P(3T) = (1/2)×(1/2)×(1/2) = 1/8

The probability that Cole flips three tails in a row, P(3T) = 1/8

4. The percentage of times Linda makes her free throws in the past 5 basketball practices = 32%

The number of shots she is expected to make if she takes 175 shots = 175 × 32/100 = 56.

Answer:

13260 square inches

Step-by-step explanation:

In DEF e = 100 inches f = 740 inches and angle D = 159°. Find the area of DEF to the nearest square inch

The formula to solve the above question is

1/2absinθ

a = 100 inches

b = 740 inches

θ = 159°

The area of the triangle =

1/2 × 100 × 740 × sin 159°

= 13259.61 square inches

Approximately = 13260 square inches

Therefore, the area of DEF = 13260 square inches

Step-by-step explanation:

A=s2

100=5×5

100/25=25x/25

x=4

Answer:

D. 16

Step-by-step explanation:

You first need to find the total percentage who liked vanilla, then subtract it from the total percentage of chocolate.

To find the total of those who liked vanilla you would have to add the given percentages and then subtract that from 100.

Chocolate: 42%

Strawberry: 18%

Coffee: 14%

Vanilla: x

42 + 18 = 60 + 14 = 74%

100 - 74 = x

Vanilla = x = 26%

To find how many more like chocolate than vanilla, you would subtract the two percentages.

Chocolate: 42%

Vanilla: 26%

42 - 26 = 16

Answer:

16.33628179866692

Step-by-step explanation:

I dont know how far you wanted me to round so you will have to do that part

Answer:

75.4

Step-by-step explanation:

Answer:

S.A = 65.94

Step-by-step explanation:

S.A = [tex]\pi r^{2} + \pi rl[/tex]

3.14 x 3 x 3 = 28.26

3.14 x 3 x 4 = 37.68

37.68 + 28.26 = 65.94

Let me know if this helps!

Answer:

Step-by-step explanation: