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Delicious77 [7]

3 years ago

5

The perimeter of a triangle is 28 feet. One side of the triangle is 5 feet longer than the second side. The third side is 8 feet

longer than the second side. Find the length of each side.

1 answer:

Hitman42 [59]3 years ago

7 0

side one is 5 side two is 10 and the third side is 13. 28 is not divisible by three so if one side i 5 ft longer and another side is 8 ft longer then you add them 5+8=13 then subtract 13 from the perimeter 28-13=15 then divide 15 by 3 and get 5 5 5. add 5 (5+5) (5+8).

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On average, the merchandise shop sells 80 CDs for every 1 vinyl record. Estimate how many vinyl records they are likely to sell

sp2606 [1]

The merchandise shop sells 80 CDs for every 1 vinyl record. We have to find how many vinyl records they are likely to sell if the merchandise shop sells 760 CDs:
         80 CDs -------------------- 1 vinyl record
        760 CDs --------------------- x vinyl records
     ---------------------------------------------------------
        80 : 760 = 1 : x
        80 x = 760
        x = 760 : 80
        x = 9.5 or 9 ( we need a whole number )
       Answer: They are likely to sell 9 vinyl records.

7 0

3 years ago

Read 2 more answers

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- an

slega [8]

Answer:

1) There were 33 $4,000 investors and 27 $8,000 investors.

2) The solution in x = 4, y = 9.

3) There were 24 nickels and 56 dimes.

Step-by-step explanation:

1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. If the partnership raised $348,000, then how many investors contributed $4,000 and how many contributed $8,000?

I am going to say that:

x is the number of investors that contributed 4,000.

y is the number of investors that contributed 8,000.

Building the system:

There are 60 investors. So:

$x + y = 60$

In all, the partnership raised $348,000. So:

$4000x + 8000y = 348000$

I am going to simplify by 4000. So:

$x + 2y = 87$

Solving the system:

The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:

$1)x + y = 60$

$2)x + 2y = 87$

I am going to multiply 1) by -1. So we have

$1)-x - y = -60$

$2)x + 2y = 87$

By addition, the x are going to cancel each other

$-x + x - y + 2y = -60 + 87$

$y = 27$

For x:

$x + y = 60$

$x = 60-y = 60-27 = 33$

There were 33 $4,000 investors and 27 $8,000 investors.

2) Solve the system by row-reducing the corresponding augmented matrix.

$2x + y = 17$

$x + y = 13$

This system has the following augmented matrix:

$\left[\begin{array}{ccc}2&1&17\\1&1&13\end{array}\right]$

To help the row reducing, i am going to swap the first with the second line:

$L1 L2$

So we have:

$\left[\begin{array}{ccc}1&1&13\\2&1&17\end{array}\right]$

Now, reducing the first column.

$L2 = L2 - 2L1$

So we have:

$\left[\begin{array}{ccc}1&1&13\\0&-1&-9\end{array}\right]$

Now we do:

$L2 = -L2$

And the matrix is:

$\left[\begin{array}{ccc}1&1&13\\0&1&9\end{array}\right]$

Now to reduce the second column, we do:

$L1 = L1 - L2$

$\left[\begin{array}{ccc}1&0&4\\0&1&9\end{array}\right]$ .

So the solution is:

x = 4, y = 9.

3) A jar contains 80 nickels and dimes worth $6.80. How many of each kind of coin are in the jar?

I am going to say that x is the number of nickels and y is the number of dimes.

Each nickel is worth 5 cents and each dime is worth 10 cents.

Building the system:

There are 80 coins in all:

$x + y = 80$

They are worth $6.80. So:

$0.05x + 0.10y = 6.80$

Solving the system:

$1)x + y = 80$

$2)0.05x + 0.10y = 6.80$

I am going to divide 1) by -10, so we can cancel y. So:

$1)-0.10x - 0.10y = -8$

$2)0.05x + 0.10y = 6.80$

Adding:

$-0.10x + 0.05x - 0.10y + 0.10y = -8 + 6.80$

$-0.05x = -1.2$ *(-100)

$5x = 120$

$x = \frac{120}{5}$

$x = 24$

Also

$x + y = 80$

$y = 80-x = 80-24 = 56$

There were 24 nickels and 56 dimes.

8 0

3 years ago

A bowl of fruit is on the table. It contains 5 apples, 2 oranges, and 2 bananas. Christian and Aaron come home from school and r

Sholpan [36]

The probability that both grab oranges would be = $\frac{1}{36}$

Step-by-step explanation:

Given,

A bowl contains,

Apples = a = 5

Oranges = o = 2

bananas = b = 2

Total fruits in bowl = x = a + o + b = 5 + 2 + 2 = 9

Now, Christian and Aaron come home from school and randomly grab one fruit each.

The probability of first selecting orange would be = $\frac{o}{b} = \frac{2}{9}$

Now, the oranges left would be 2 - 1 = 1

and total fruits would be = 9 - 1 = 8

Hence, the probability of selecting second orange would be = $\frac{1}{8}$

Therefore, the probability that both grab oranges would be = $\frac{1}{8} * \frac{2}{9} = \frac{1}{36}$

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3 years ago

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adell [148]

Answer:

What

Step-by-step explanation:

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3 years ago

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Anika [276]

Answer:

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Step-by-step explanation:

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3 years ago