1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zhenek [66]
3 years ago
5

Two friends are going to the mall to buy pizza. One of the friends buys 1cheese slice and 2 pepperoni slices for $8.75. Her frie

nd purchases 2 chese slices and 3 pepperoni slices for $15.00. Find the cost of each.
Mathematics
1 answer:
GarryVolchara [31]3 years ago
6 0

Answer:

The cost of each:

1 cheese slice = c = $3.75

1 pepperoni slice = p = $2.5

Step-by-step explanation:

Let the cost:

1 cheese slice = c

1 pepperoni slice = p

Two friends are going to the mall to buy pizza.

One of the friends buys 1cheese slice and 2 pepperoni slices for $8.75.

c + 2p = $8.75.....Equation 1

c = $8.75 - 2p

Her friend purchases 2 chese slices and 3 pepperoni slices for $15.00.

2c + 3p = $15.00.....Equation 2

We substitute 8.75 - 2p for c in Equation 2

2(8.75 - 2p) + 3p = $15.00

17.5 - 4p + 3p = 15

Collect like terms

- 4p + 3p = 15 - 17.5

-p = -2.5

p = $2.5

c = $8.75 - 2p

c = $8.75 - 2(2.5)

c = $8.75 - 5.0

c = $3.75

The cost of each:

1 cheese slice = c = $3.75

1 pepperoni slice = p = $2.5

You might be interested in
How to know if a function is periodic without graphing it ?
zhenek [66]
A function f(t) is periodic if there is some constant k such that f(t+k)=f(k) for all t in the domain of f(t). Then k is the "period" of f(t).

Example:

If f(x)=\sin x, then we have \sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x, and so \sin x is periodic with period 2\pi.

It gets a bit more complicated for a function like yours. We're looking for k such that

\pi\sin\left(\dfrac\pi2(t+k)\right)+1.8\cos\left(\dfrac{7\pi}5(t+k)\right)=\pi\sin\dfrac{\pi t}2+1.8\cos\dfrac{7\pi t}5

Expanding on the left, you have

\pi\sin\dfrac{\pi t}2\cos\dfrac{k\pi}2+\pi\cos\dfrac{\pi t}2\sin\dfrac{k\pi}2

and

1.8\cos\dfrac{7\pi t}5\cos\dfrac{7k\pi}5-1.8\sin\dfrac{7\pi t}5\sin\dfrac{7k\pi}5

It follows that the following must be satisfied:

\begin{cases}\cos\dfrac{k\pi}2=1\\\\\sin\dfrac{k\pi}2=0\\\\\cos\dfrac{7k\pi}5=1\\\\\sin\dfrac{7k\pi}5=0\end{cases}

The first two equations are satisfied whenever k\in\{0,\pm4,\pm8,\ldots\}, or more generally, when k=4n and n\in\mathbb Z (i.e. any multiple of 4).

The second two are satisfied whenever k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}, and more generally when k=\dfrac{10n}7 with n\in\mathbb Z (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when k is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

Let's verify:

\sin\left(\dfrac\pi2(t+20)\right)=\sin\dfrac{\pi t}2\underbrace{\cos10\pi}_1+\cos\dfrac{\pi t}2\underbrace{\sin10\pi}_0=\sin\dfrac{\pi t}2

\cos\left(\dfrac{7\pi}5(t+20)\right)=\cos\dfrac{7\pi t}5\underbrace{\cos28\pi}_1-\sin\dfrac{7\pi t}5\underbrace{\sin28\pi}_0=\cos\dfrac{7\pi t}5

More generally, it can be shown that

f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))

is periodic with period \mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n).
4 0
3 years ago
How do you solve -4x - 10 < 2
viva [34]
There is a way and you will find it but not from me
5 0
2 years ago
Evaluate the expression when f = 4.16/f
astraxan [27]

9514 1404 393

Answer:

  4

Step-by-step explanation:

Maybe you want the value of 16/f when f=4. Put the value of f where f is and do the arithmetic.

  \dfrac{16}{f}=\dfrac{16}{4}=\boxed{4}

5 0
2 years ago
What is the answer to x+y=2
Ahat [919]

Answer:

u need 2 equation to solve

Step-by-step explanation:

7 0
3 years ago
The observations of 124.53, 124.55, 142.51, and 124.52 are obtained when taping the length of a line. What should the observer c
mylen [45]

Answer: the observer should consider to eliminate or to retake the third measure.

Explanation:

The four measures taken are 124.53, 124.55, 142.51 and 124.52.

As it can be easily seen, the third measure is much different from the other three. This means that something went wrong during the observation: it can be either the measure taken wrong or that the number was written wrong (if you switch the 2 and the 4 you get a number similar to the other ones).

If the third measure is not considered, an estimate of the mean would place it around 124.5, while if the outlier (the detatched number) is considered an estimate of the mean would increase to about 129.

Therefore, in order to obtain a more reliable mean, the observer should consider to eliminate or to retake the third measure.

6 0
3 years ago
Other questions:
  • An industrial center produces refrigerator motors, but it has a 0.03 defective rate. What is the probability that the machine pr
    7·1 answer
  • I hate this part I need help for 4 and 5 is it a b c or d
    12·1 answer
  • Geometry math question
    12·2 answers
  • If the volume of a sphere is 972(3.14) cubic inches what is the radius- a. 7 icnches b. 9 inches c. 108 inch d. 324 inch
    6·2 answers
  • Tell me the answer please. Give me a short answer and a step-by-step explanation.
    10·1 answer
  • Evaluate the expression pleasse :)!!! I hate my anxiety:)<br><br><br> (0.4)(−3.5)(−9)
    9·1 answer
  • The perimeter of the triangle is 30 cm.<br>The perimeter of the rectangle is also 30 cm.​
    10·1 answer
  • Need help on this problem can you help me pls?
    13·1 answer
  • 3x+2y=5 and 7x+2y=9<br> plz help me with this<br> it will be very helpfull
    9·1 answer
  • From the height of 30 meters above sea level of a cliff, a ship is sighted due west. The angle of depression is 20How far from t
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!