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Slav-nsk [51]
3 years ago
15

Alicia purchased h half gallons of ice cream for 3.50 each p packages of ice cream cones for 2.50 each she purchased 14 items an

d spent 43$ which system of equations could be used to determine how many of each item Alicia purchased
Mathematics
1 answer:
eimsori [14]3 years ago
4 0

Answer:

H + P = 14

3.50H + 2.50P = 43

Step-by-step explanation:

Given that

H denotes half gallons of ice cream

P denotes packages of ice cream cones

Now  

H + P = 14

And,  

3.50H + 2.50P = 43

So, the systems of equations would be

H + P = 14

3.50H + 2.50P = 43

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From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th
wel

Answer:

\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}

Step-by-step explanation:

The <u>width</u> of a square is its <u>side length</u>.

The <u>width</u> of a circle is its <u>diameter</u>.

Therefore, the largest possible circle that can be cut out from a square is a circle whose <u>diameter</u> is <u>equal in length</u> to the <u>side length</u> of the square.

<u>Formulas</u>

\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}

\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}

\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}

If the diameter is equal to the side length of the square, then:
\implies \sf r=\dfrac{1}{2}s

Therefore:

\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}

So the ratio of the area of the circle to the original square is:

\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}

Given:

  • side length (s) = 6 in
  • radius (r) = 6 ÷ 2 = 3 in

\implies \sf \textsf{Area of square}=6^2=36\:in^2

\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)

Ratio of circle to square:

\implies \dfrac{28}{36}=\dfrac{7}{9}

5 0
2 years ago
A summer camp had
trapecia [35]

The equation that relates the number of campers this year to the number of campers last year is c = 440 / 1.10

The number of campers last year is 400.

<h3>What are percentages?</h3>

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are used to measure frequency.

<h3>How many campers attended last year?</h3>

The number of campers last year = number of campers this year / (1 + percentage increase)

440 / 1.1 = 400

To learn more about percentages, please check: brainly.com/question/25764815

3 0
2 years ago
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