Evaluate the expression below when y = -3. 2y + 7 -4y − 10
1 answer:
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Answer:
- 25000 seats in section A
- 14100 seats in sectin B
- 10900 seats in section C
Step-by-step explanation:
The problem statement tells you half the total number of seats are in section A, so you already know that there are 25000 A seats. The revenue from those seats is
... 25000×$25 = $625,000
so the revenue from B and C seats must total
... $1,070,500 - 625,000 = $445,500
If all 25000 of the B/C seats were C seats, the revenue would be
... 25000×$15 = $375,000
The actual revenue from those seats is $445,500 -375,000 = $70,500 more than that. We know each B seat generates $5 more revenue, so there must be ...
... $70,500/$5 = 14,100 . . . . B seats
Then the balance of the 25000 B and C seats are C seats:
... 25,000 - 14,100 = 10,900 . . . . C seats
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<em>Alternate Solution Method</em>
The new Brainly answer format requires the answer be supplied before the working. In order to find the answer quickly so that I can fill in that section, I used a matrix method for solving the problem. The problem equations can be written ...
- a + b + c = 50000
- a - b - c = 0
- 25a + 20b + 15c = 1070500
so the augmented matrix is ...
A graphing calculator can be used to find the solution to this, generally using a function that produces the reduced row-echelon form. The attachment shows the solution using a TI-84 calculator.
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<em>Comment on the Working</em>
Since the number of A seats is equal to the total of B and C seats, the number of A seats must be half the total number of stadium seats. Having figured that out, the problem is reduced to one of finding the mix of B and C seats that will produce the remaining revenue.
As with many mixture problems, it is convenient to look at differences. Start with the assumption that all of the desired revenue comes from the least contributor. Here, that is C seats. Then figure the difference that using a B seat makes ($20 -15 = $5) and the difference of the actual revenue and the amount that you got by assuming all C seats: 445,500 -375,000 = 70,500. Since replacing a C seat by a B seat adds $5 to the revenue, it is easy to figure the number of such replacements required in order to raise the revenue by $70,500.
If you write the equation for B seats, you find the solution to the equation mirrors this verbal description:
... 20b + 15(25000-b) = 445,500
... 5b = 445,500 - 375000 . . . . simplify, subtract 375000
... b = 70500/5 = 14100
Answer:
Step-by-step explanation:
From the figure attached,
Point B has been dilated to form point B'.
B(3, 1) → B'(6, 2)
→ B'[(2 × 3), (2 × 1)]
Since rule for the dilation of a point (x, y) by a factor of k is,
B(x, y) → B'(kx, ky)
By comparing the coordinates k = 2 is the scale factor by which the point B has been dilated about the origin.
Therefore, other vertices of the quadrilateral will be,
A(-2, 3) → A'(-4, 6)
C(1, -1) → C'(2, -2)
D(-3, -2) → D'(-6, -4)
Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
<h3>What is a matrix?</h3>- A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.
- For instance, consider a matrix with two rows and three columns.
To find the order of matrix:
- We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.
- Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.
- Dimension is assigned to the provided matrix: 6 × 5
- This means the given matrix contains six rows and five columns.
- As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.
- The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.
To prove:
- In other words, the inner products of the dimensions should be equal.
- That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.
- The dimensions of the matrix are given by, row × column.
Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
Know more about matrix here:
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