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Lemur [1.5K]
3 years ago
8

Enter an equation to find three numbers with the following properties. Let x be the first number. The second number is 6 more th

an the first number. The third number is 7 times the second number. The sum of the third number and the product of the first and second numbers is 0. Solve the equation and give the three numbers.
Mathematics
2 answers:
jarptica [38.1K]3 years ago
7 0

First number: x

Second number: (x + 6)

Third number: (x + 6) * 7

Equation: 0 = (x)(x + 6) + 7(x + 6)

Steps to solve:

0 = x^2 + 6x + 7x + 42

0 = x^2 + 13x + 42

Using the quadratic equation, x could equal -7 or -6. In our equation above, both are applicable.

The three numbers could be -6, 0, and 0. Or they could be -7, -1, and -7.

Hope this helps!! :)

krok68 [10]3 years ago
4 0

Answer:

-7, -1, -7

-6, 0, 0

Step-by-step explanation:

x

x+6

7(x+6)

7(x+6)+ x(x+6) = 0

(x+6)(7+x) = 0

x = -6, -7

-6, 0, 0

-7, -1, -7

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PLEASE HELP!!!!<br> I need to solve for a, b, and c
nirvana33 [79]

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

_____

<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 ...

\left[\begin{array}{cccc}1&1&1&50000\\1&-1&-1&0\\25&20&15&1070500\end{array}\right]

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.

___

<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

8 0
3 years ago
Please help
shtirl [24]

Answer:

Step-by-step explanation:

The slope of the line in question is the same as the slope of the line parallel to it. Using y = mx + b, where m is the slope, we find the slope of our line is -3.

Using the pt-slope form, y - y1 = m( x - x1), we get y - (-1) = -3( x - 2) or y + 1 = -3x + 6. Which leads us to y = -3x + 5. QED

4 0
2 years ago
A company manufactures 295 toy car each day. How many toy cars dose the company manufacture in 34 days?
exis [7]

295 X 34 = 10030 <== Cars in 34 days

3 0
3 years ago
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Ipatiy [6.2K]

Answer:

(-4,1) because if the x value repeats the relation is no longer a function

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2 years ago
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Help i dont know what to do i give brainlist
Y_Kistochka [10]

Answer:

473 yd^3

Step-by-step explanation:

The surface area of the square base is (11 yd)^2, or 121 yd^2.

The surface area of one of the slanting sides of the pyramid is

A = (1/2)(b)(h), which comes to A = (1/2)(11 yd)(16 yd) = 88 yd^2.

Thus, four such sides have a combined surface area of 352 yd^2.

Combining the surface areas of the slanting sides with the base area yields 473 yd^3

4 0
3 years ago
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