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erik
7 days ago
10

A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening

down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. (1 point)
Mathematics
1 answer:
lawyer [4K]7 days ago
3 0
Since this parabola intersects the center, its formula is:

y = ax². Given that it opens downward, the coefficient a must be negative.

Thus, the equation can be expressed as:

y = - ax², with the axis of symmetry located at x = 0.

The height measures 84 ft when the parabola's opening is 42 ft wide.
This indicates that for the height y, the corresponding x-values are +21 and -21 (due to symmetry).
To find a, let's substitute y and x with their respective values:

y = - ax²

84 = - a(21)²

84 = - a(441), leading to a = - 84/441 ↔ a = - 4/21.

Therefore, the final equation is: y = -4/21 x².
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Jada plans to serve milk and healthy cookies for a book club meeting. She is preparing 12 ounces of milk and 4 cookies per perso
Zina [3917]

Jada intends to provide milk and nutritious cookies at a gathering for her book club. She has planned to offer 12 ounces of milk and 4 cookies for each participant. With her included, the total number of club members is 15. Each package of cookies has 24 cookies and is priced at $4.50. A gallon of milk has 128 ounces and costs $3. Let n denote the club members, m for the ounces of milk, c for the cookies, and b for Jada's budget in dollars. Identify all equations that could represent the relevant quantities and constraints in this scenario.

â m = 12(15)

n refers to the club members

b. 3m + 4.5c = 6

c. 4n =

m stands for ounces of milk

& 44.50) = C

c indicates the cookies

e b=2(3) + 3(4.50)

b denotes Jada's budget in

currency

The equations applicable for representing the quantities and constraints in this scenario are:

a) m = 12(15)

c)4n = c

e) b = 2(3) + 3(4.50)

Detailed explanation:

Jada is set to provide milk and nutritious cookies for her book club meeting

She plans to prepare 12 ounces of milk and 4 cookies for each individual

She has 15 members in total

A pack of cookies contains 24 cookies and costs $4.50

A gallon of milk has 128 ounces and costs $3

Designate the total members by n

Ounces of milk = m

The number of cookies = c

Jada's budget in dollars = d

y = 12(15)

Each individual will receive 4 cookies

4n = c

As one pack contains 24 cookies

She requires = 15 × 4 = 60 cookies

60 ÷ 24 = 2.5

Thus, she would need to purchase 3 packs of cookies

She needs = 15 × 12 = 180 ounces of milk

A gallon of milk contains 128 ounces

180 ÷ 128 = 1.406

She will need to acquire 2 gallons of milk

It's noted: from the prompt

Each gallon of milk costs $3

Each package of cookies costs $4.50

b serves as Jada's dollar budget

b = 2(3) + 3(4.50)

<pThe relevant equations that could signify the quantities and constraints in this scenario are:

Options a, c and e are valid

3 0
3 days ago
The length if Marshall's rectangular poster is 2 times its width.If the perimeter is 24 inches, what is the area of the poster.
Inessa [3926]
Dimensions of the rectangle are defined as Length=2x
Width=x
The formula for perimeter is given by 2(Length) + 2(Width).

First, we need to determine the dimensions of the rectangle, specifically its length and width.

We can derive this equation:
24=2(2x)+2(x)
4x+2x=24
6x=24
x=24/6
x=4

Consequently, Length becomes 2x, leading to 2(4)=8.

Therefore, the length is 8 inches and the width is 4 inches.

Next, we will calculate the area of the rectangle.
The area can be computed as Length multiplied by Width.

Area=(8 in)(4 in)=32 in²

Conclusion: The area of Marshall's rectangular poster is 32 in².

4 0
10 days ago
Scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. what i
AnnZ [3900]
The highest 5% of scores corresponds to the 95th percentile, meaning the cutoff score k is defined as

\mathbb P(X

When transformed into the standard normal distribution,

\mathbb P(X

A cumulative probability of 95% corresponds to a z-score of approximately k^*=1.6449, indicating that the cutoff score is likely around

1.6449=\dfrac{k-76.4}{6.1}\implies k\approx86.4
5 0
10 days ago
Ten liters of pure water are added to a 50-liter pot of soup that is 50% broth. Fill in the missing parts of the table.
Zina [3917]

Answer:

c= 25

d= 60

Step-by-step explanation:

C: This is because 25+0 is simply 25. Essentially, you are not adding anything, so it remains unchanged!:)

D: 50 + 10 = 60. That’s straightforward addition!

Hope this helps!

3 0
5 days ago
Read 2 more answers
555 grams of wool were needed to knit a sweater, a hat, and a scarf. The hat required 5 times less wool than the sweater and 5 g
Zina [3917]

Answer:

The amount of wool required for a sweater was 400 grams.

A hat needed 80 grams of wool.

A scarf required 75 grams of wool.

Step-by-step explanation:

Let

x ------> grams of wool necessary for a sweater

y -----> grams of wool necessary for a hat

z -----> grams of wool necessary for a scarf

From the information given

x+y+z=555 -----> equation A

y=x/5 ----> x=5y -----> equation B

y=z+5 ---> z=y-5 ----> equation C

By substituting equations B and C into equation A, we can solve for y:

(5y)+y+(y-5)=555

7y=560

y=80 grams

Now, find x

x=5(80)=400 grams

Next, determine z

z=80-5=75 grams

In conclusion,

400 grams of wool was required for the sweater,

the hat needed 80 grams of wool, and

the scarf required 75 grams of wool.

4 0
10 days ago
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