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3 years ago

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To reach her summer reading goal, Elisa has to read at least 30 books. The inequality b ≥ 30 represents the number of books she

needs to read. Which of the following is the solution to this inequality?

1 answer:

rewona [7]3 years ago

4 0

Answer:

hii

have a good day for you!

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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

Joe Summers buys a gas grill and accessories. The cost, including tax, amounts to $850.00. Joe finances the grill over 12 months

Anettt [7]

Answer:

$66.5

Step-by-step explanation:

The cost, including tax, amounts to $850.00.

Down payment =$150

Amount after paying down payment = $850-$150=$700

Interest rate = 14 %

So, interest on $700 = $\frac{14}{100} \times 700 =98$

So, c = $98

Total payment = amount financed + c = 700+98=$798

Now Joe finances the grill over 12 months

So, no. of payments = 12

Now Monthly payment = Total of payments ÷ number of payments

=798 ÷ 12

=$66.5

Hence Joe's monthly payments (principal plus interest) is $ 66.5

7 0

2 years ago

Celine ate brunch at a restaurant. The bill came to $72.80. If she left a 15% tip, what was the total cost of her brunch?

DedPeter [7]

Answer:

<em>$83.69</em>

Step-by-step explanation:

Given the following

Initial Cost of the brunch = $72.80

Percentage tip = 15%

Tip paid = 15% of $72.60

Tip paid = 0.15 * 72.60

Tip paid = $10.89

Total cost of brunch = $72.80 + $10.89

Total cost of brunch = $83.69

<em>Hence the total cost of her brunch is $83.69</em>

7 0

2 years ago

Charlotte used a calculator to subtract.

Sati [7]

Answer:

Step-by-step explanation:

1. She omitted the 0 from the minuend, entering 24.59 instead of 204.59

2. She misplaced the decimal point of the minuend, entering 93.64 instead of 936.4

3. She typed 4 instead of 5 in the minuend, entering 46.3 instead of 56.3

4 0

2 years ago

Yesterdays summer read 75 pages of her book if she reads at a pace of two pages per minute today which table shows only viable s

rjkz [21]

Answer:

D

Step-by-step explanation:

Nobody read backwards for 16 minutes

4 0

2 years ago

Read 2 more answers