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3 years ago

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A used book store is selling 3 records and 5 CDs for $60. You can also buy 6 records and 4 CDs for $80. Find the cost of one CD.

Write the linear system that describes this situation.

1 answer:

krek1111 [17]3 years ago

5 0

9514 1404 393

Answer:

3r +5c = 60

6r +4c = 80

Step-by-step explanation:

There are many aspects of "this situation" that could be described by equations. We are guessing that you want equations that will help you determine the costs of a record and a CD, assuming the costs are the same for each instance of the media.

Let r and c represent the costs of a record and a CD, respectively.

3r +5c = 60 . . . . . . . the value of the first purchase

6r +4c = 80 . . . . . . . the value of the second purchase

These equations comprise a linear system describing an aspect of the situation.

_____

<em>Comment on the question</em>

The numbers make no sense, as the cost of a CD is $(6 2/3), the cost of a record is $(8 8/9).

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If each quadrilateral below is a parallelogram, find the missing measures.

prisoha [69]

Step-by-step explanation:

We will use parallelogram properties to answer our given problems.

(1) Since we know that opposite sides of parallelogram are congruent, therefore measure of side MN and side KN will be equal to the measure of their opposite sides.

LM=KN and KL=MN

Upon substituting our given values we will get,

45=KN and 31=MN

Property: The opposite angles of parallelogram are congruent and consecutive angles are supplementary.

We have been given $m\angle N=119^{o}$ , therefore $m\angle L=119^{o}$ .

We will find measure of angle K by using supplementary angles.

$m\angle N+m\angle M=180^{o}$

$119^{o}+m\angle M=180^{o}$

$m\angle M=(180-119)^{o}$

$m\angle M=61^{o}$

By opposite angles of parallelogram $m\angle K=61^{o}$ .

(2) Opposite sides of parallelogram are equal. Therefore, CF=DE and FE=CD.

Upon substituting our given values we will get,

CF=10 and FE=15.

Property: Diagonals of parallelogram bisect each other.

So CE will be 2 times CG and GD will be half the length of FD.

$CE=2\times 7=14$

$GD=\frac{1}{2}\times 22=11$

(3) Property: Opposite sides of parallelogram are congruent.

$SR=PQ$ and $QR=PS$

Upon substituting our given values we will get,

$SR=24$ and $QR=19$

Property: Diagonals of parallelogram bisect each other.

So SQ will be 2 times TQ and PT will be half the length of PR.

$SQ=2\times 10=20$

$PT=\frac{1}{2}\times 42=21$

Property: The opposite angles of parallelogram are congruent and consecutive angles are supplementary.

$m\angle PQR=106^{o}$

$m\angle PQS=m\angle QSR$ Alternate interior angles.

$m\angle PQS=49^{o}$

$m\angle QRS=m\angle QPS$ Opposite angles of parallelogram.

$m\angle PQR+m\angle QPS=180^{o}$

$106^{o}+m\angle QPS=180^{o}$

$m\angle QPS=180^{o}-106^{o}$

$m\angle QPS=74^{o}$

Therefore, measure of angle QRS will 74 degrees.

$m\angle PRS=m\angle QPR$ Alternate interior angles.

$35^{o}=m\angle QPR$

$m\angle RPS=74^{o}-m\angle QPR$

$m\angle RPS=74^{o}-35^{o}$

$m\angle RPS=39^{o}$

Now let us find measure of angle PSQ.

$m\angle PSQ=m\angle PQR-m\angle QSR$

$m\angle PSQ=106^{o}-49^{o}$

$m\angle PSQ=57^{o}$

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blagie [28]

$(x_1;\ y_1);\ (x_2;\ y_2)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\(3;\ 2);\ (-2;\ 3)\\\\\boxed{m=\dfrac{3-2}{-2-3}=\dfrac{1}{-5}=-\dfrac{1}{5}}$

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3 years ago

If there are 1,200 calories in 8 oz of hot fudge, how many calories are in 3 oz of hot fudge?

guapka [62]

1200/8 = x/3
150 = x/3
150 * 3 = x
450 = x

450 calories

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The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for larger vehicles. T

Flauer [41]

Answer:

40

Step-by-step explanation:

Do 60 × 10.00 to get 600. Then do 800-600 to get 200. Then do 200÷5.00 to get 40.

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A card is selected randomly from a jar that contains 15 cards, numbered from 25 to 39. What is the probability that the card sel

VikaD [51]

Answer:

The probability that the card selected bears a number less than 34 is 0.3333.

Step-by-step explanation:

Let random variable <em>X</em> be defined as the number on the selected card.

There are <em>N</em> = 15 total cards.

The number on the cards are as follows:

S = {25, 26, 27,..., 38, 39}

The probability of an event, <em>E</em> is the ratio of the number of favorable outcomes to the total number of outcomes.

$P(E)=\frac{n(E)}{N}$

In this case we need to compute the probability that the card selected bears a number less than 34.

The favorable outcomes are:

<em>s</em> = {25, 36, 37, 38, 39}

<em>n</em> (X < 34) = 5

Compute the probability that the card selected bears a number less than 34 as follows:

$P(X$

$=\frac{5}{15}\\\\=\frac{1}{3}\\\\=0.3333$

Thus, the probability that the card selected bears a number less than 34 is 0.3333.

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