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
Rudik [331]
2 years ago
8

Natalie won 45 pieces of gum playing the

Mathematics
1 answer:
SIZIF [17.4K]2 years ago
4 0
Natalie gave away 27
You might be interested in
Solve the system of equations.<br><br><br><br> −2x+5y =−35<br> 7x+2y =25
Otrada [13]

Answer:

The equations have one solution at (5, -5).

Step-by-step explanation:

We are given a system of equations:

\displaystyle{\left \{ {{-2x+5y=-35} \atop {7x+2y=25}} \right.}

This system of equations can be solved in three different ways:

  1. Graphing the equations (method used)
  2. Substituting values into the equations
  3. Eliminating variables from the equations

<u>Graphing the Equations</u>

We need to solve each equation and place it in slope-intercept form first. Slope-intercept form is \text{y = mx + b}.

Equation 1 is -2x+5y = -35. We need to isolate y.

\displaystyle{-2x + 5y = -35}\\\\5y = 2x - 35\\\\\frac{5y}{5} = \frac{2x - 35}{5}\\\\y = \frac{2}{5}x - 7

Equation 1 is now y=\frac{2}{5}x-7.

Equation 2 also needs y to be isolated.

\displaystyle{7x+2y=25}\\\\2y=-7x+25\\\\\frac{2y}{2}=\frac{-7x+25}{2}\\\\y = -\frac{7}{2}x + \frac{25}{2}

Equation 2 is now y=-\frac{7}{2}x+\frac{25}{2}.

Now, we can graph both of these using a data table and plotting points on the graph. If the two lines intersect at a point, this is a solution for the system of equations.

The table below has unsolved y-values - we need to insert the value of x and solve for y and input these values in the table.

\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & a \\ \cline{1-2} 1 & b \\ \cline{1-2} 2 & c \\ \cline{1-2} 3 & d \\ \cline{1-2} 4 & e \\ \cline{1-2} 5 & f \\ \cline{1-2} \end{array}

\bullet \ \text{For x = 0,}

\displaystyle{y = \frac{2}{5}(0) - 7}\\\\y = 0 - 7\\\\y = -7

\bullet \ \text{For x = 1,}

\displaystyle{y=\frac{2}{5}(1)-7}\\\\y=\frac{2}{5}-7\\\\y = -\frac{33}{5}

\bullet \ \text{For x = 2,}

\displaystyle{y=\frac{2}{5}(2)-7}\\\\y = \frac{4}{5}-7\\\\y = -\frac{31}{5}

\bullet \ \text{For x = 3,}

\displaystyle{y=\frac{2}{5}(3)-7}\\\\y= \frac{6}{5}-7\\\\y=-\frac{29}{5}

\bullet \ \text{For x = 4,}

\displaystyle{y=\frac{2}{5}(4)-7}\\\\y = \frac{8}{5}-7\\\\y=-\frac{27}{5}

\bullet \ \text{For x = 5,}

\displaystyle{y=\frac{2}{5}(5)-7}\\\\y=2-7\\\\y=-5

Now, we can place these values in our table.

\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}

As we can see in our table, the rate of decrease is -\frac{2}{5}. In case we need to determine more values, we can easily either replace x with a new value in the equation or just subtract -\frac{2}{5} from the previous value.

For Equation 2, we need to use the same process. Equation 2 has been resolved to be y=-\frac{7}{2}x+\frac{25}{2}. Therefore, we just use the same process as before to solve for the values.

\bullet \ \text{For x = 0,}

\displaystyle{y=-\frac{7}{2}(0)+\frac{25}{2}}\\\\y = 0 + \frac{25}{2}\\\\y = \frac{25}{2}

\bullet \ \text{For x = 1,}

\displaystyle{y=-\frac{7}{2}(1)+\frac{25}{2}}\\\\y = -\frac{7}{2} + \frac{25}{2}\\\\y = 9

\bullet \ \text{For x = 2,}

\displaystyle{y=-\frac{7}{2}(2)+\frac{25}{2}}\\\\y = -7+\frac{25}{2}\\\\y = \frac{11}{2}

\bullet \ \text{For x = 3,}

\displaystyle{y=-\frac{7}{2}(3)+\frac{25}{2}}\\\\y = -\frac{21}{2}+\frac{25}{2}\\\\y = 2

\bullet \ \text{For x = 4,}

\displaystyle{y=-\frac{7}{2}(4)+\frac{25}{2}}\\\\y=-14+\frac{25}{2}\\\\y = -\frac{3}{2}

\bullet \ \text{For x = 5,}

\displaystyle{y=-\frac{7}{2}(5)+\frac{25}{2}}\\\\y = -\frac{35}{2}+\frac{25}{2}\\\\y = -5

And now, we place these values into the table.

\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}

When we compare our two tables, we can see that we have one similarity - the points are the same at x = 5.

Equation 1                  Equation 2

\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}                 \begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}

Therefore, using this data, we have one solution at (5, -5).

4 0
3 years ago
Simplify expression (5xy^-6/x^4 y^-2)^2
ipn [44]
Here it is...........................

4 0
3 years ago
. Simplify an expression for the area of the rectangle shown above
mel-nik [20]
8x+3x5=66 there you go
3 0
2 years ago
emily has saved 75.25 so far for a new phone. the cell phone that she want costs 102.19 How much more money does she need to pur
Alenkinab [10]

Answer:

emily has saved 75.25 so far for a new phone. the cell phone that she want costs 102.19

How much more money does she need to purchase a phone?

The Correct Answer Is $ 26.94

xXxAnimexXx

Have a great day!

6 0
2 years ago
A company purchased $10,000 of merchandise on January 5 with terms 2/10, n/30. On January 7, it returned $1,200 worth of merchan
s2008m [1.1K]

Answer:

C. Debit Accounts Payable $8,800; credit Merchandise Inventory, $176; credit Cash $8,624.

Step-by-step explanation:

Data given in the question is inconsistent with the options given.

Terms 2/10, n/30 means there is a discount of 2% is available on payment of due amount within discount period of 10 days after sale with net credit period of 30 days.

Purchases = $10,000

Returns = $1,200

Amount Due = $10,000 - $1,200 = $8,800

As the payment is made after discount period, so no discount will be availed. Full amount of $8,800 will be paid.

A similar and correct question is given below and answer is made accordingly.

A company purchased $10,000 of merchandise on January 5 with terms 2/10, n/30. On January 7, it returned $1,200 worth of merchandise. On January 12, it paid the full amount due. Assuming the company uses a perpetual inventory system, and records purchases using the gross method, the correct journal entry to record the payment on January 12 is:

Debit Accounts Payable $10,000; credit Merchandise Inventory $200; credit Cash $9,800.

Debit Merchandise Inventory $8,800; credit Cash $8,800.

Debit Accounts Payable $8,800; credit Merchandise Inventory, $176; credit Cash $8,624.

Debit Cash $1,600; credit Accounts Payable $1,600.

Debit Accounts Payable $8,624; credit Cash $8,624.

Solution

Terms 2/10, n/30 means there is a discount of 2% is available on payment of due amount within discount period of 10 days after sale with net credit period of 30 days.

Purchases = $10,000

Returns = $1,200

Amount Due = $10,000 - $1,200 = $8,800

As the payment is made within discount period, so discount will be availed

Discount = $8,800 x 2% = $176

Cash Paid = $8,800 - $176 = $8,624

5 0
3 years ago
Other questions:
  • The area of the photo will be half the area of the entire ad. What is the value of x
    14·1 answer
  • A rectangle is 5 times as long as it is wide. The perimeter is 70 cm. Find the dimensions of the rectangle. round to the nearest
    13·2 answers
  • Solve for F. C= 5/9 (F-32)
    6·1 answer
  • Please help me someone
    15·1 answer
  • Solve 3x−5 = 9 help solve for x
    5·2 answers
  • Tyler's age is three less than his brother's age. The sum of their ages is 11.
    5·2 answers
  • The first term in a geometric series is 64 and the common ratio is 0.75. Find the sum of the first 4 terms in the series.
    10·1 answer
  • "tis greater than zero and less than or equal to 5" Complete the following steps to receive full credit for this question: . The
    11·1 answer
  • The cost of one pound of bananas is greater than $0.41 and less than $0.50. Sarah pays $3.40 for x pounds of bananas. Which ineq
    14·2 answers
  • The sum of two numbers is 36. Four times the smaller is one less than the larger. Find the numbers
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!