Is m+b rational or irrational
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Answer:
I believe it is rational
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Solve. 3(4x + 2x) = 8
The system of equations below has exactly one (x, y) pair for its solution.4x+6y=244x+6y=242x+y=82x+y=8If we double each side of the second equation, 2x+y=82x+y=8, we have 4x+2y=164x+2y=16. Explain why the same pair that is the solution to the system is also a solution to this new equation.If needed, you can support your explanation with hanger diagrams (upload a picture), or by inventing a situation that the equations represent.If we add the two equations in the original system, we have 6x+7y=326x+7y=32. Explain why the same (x, y) pair is also a solution to this equation.Again, you can support your explanation with diagrams or a situation, if needed.
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Answers
Answer:
3 inches
Step-by-step explanation:
Lenght = 18 inches
Width =15 inches
Perimeter of the rectangular painting and frame = 90 inches
Let X be the width of the frame
The width of the framed picture = 15 + 2x
The length of the framed picture = 18 + 2x
Perimeter = 2 (L + W)
90 = 2(15 + 2x + 18+ 2x)
90 = 2(33 + 4x)
90 = 66 + 8x
8x = 90 - 66
8x = 24
x = 24/8
x = 3 inches
the width of the frame is 3 inches
Final answer:
To determine the width of the frame, subtract twice the frame width from the length and width of the outer rectangle and set up an equation based on the perimeter.
Explanation:
To determine the width of the frame, we need to first find the dimensions of the inner rectangle formed by the painting. If we subtract twice the frame width from the length and width of the outer rectangle, we get the length and width of the inner rectangle. Let's call the width of the frame 'x'.
The length of the inner rectangle is 15 inches - 2 inches, and the width of the inner rectangle is 18 inches - 2 inches. The perimeter of the inner rectangle is the sum of its four sides, which can be calculated using the
formula P = 2l + 2w. We know that the perimeter of the inner rectangle is 90 inches, so we can set up the equation:
90 = 2(15 - 2x) + 2(18 - 2x)
Solving this equation will give us the value of 'x', which represents the width of the frame.
Learn more about the Dimensions of a rectangular frame here:
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15 hundreds is equal to 1500.
15 tens is equal to 150.
18 ones is equal to 18.
So just add them up.
8000 + 1500 = 9500.
9500 + 150 = 9650.
9650 + 18 = 9668.
The number is 9668
Answers
The discriminant is equal to −16, which means the equation has two real number solutions.
The discriminant is equal to 24, which means the equation has no real number solutions.
The discriminant is equal to 24, which means the equation has two real number solutions.
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-1=5 x^2 - 2 x
5 x^2 - 2 x + 1 = 0, then we substitute: a=5, b=-2, c =1
to discriminant formula: D= b^2 - 4 a c = (-2)^2 - 4 * 5 * 1 = 4 - 20 = - 16
Answer:
The discriminant is equal to -16 which means the equation has no real number solutions.
The correct option regarding the discriminant of the quadratic equation is given by:
The discriminant is equal to −16, which means the equation has no real number solutions.
What is the discriminant of a quadratic equation and how does it influence the solutions?
A quadratic equation is modeled by:
The discriminant is:
The solutions are as follows:
- If
, and it is a perfect square, it has 2 rational solutions.
- If
- If
, it has 1 rational solutions.
- If
, it has 2 complex solutions.
In this problem, we have that:
5x² - 2x = -1
5x² - 2x + 1 = 0
Hence the coefficients are a = 5, b = -2 and c = 1, while the discriminant is given by:
No real solutions, hence the first option is correct.
More can be learned about the discriminant of quadratic equations at brainly.com/question/19776811
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Answer:
x² + x + 5
Step-by-step explanation:
Using Synthetic division
- 5 | 1 6 10 25
↓ - 5 - 5 - 25
-----------------------
1 1 5 0 ← remainder
Since the remainder is zero then (x + 5) is a factor of the polynomial
The Quotient = x² + x + 5
Thus
x³ + 6x² + 10x + 25 = (x + 5)(x² + x + 5)