Answer:
Step-by-step explanation:
The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.
The correct option is D.
<h3>What is a quadratic equation ?</h3>
A quadratic equation is an algebraic equation of the second degree in x.. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
<h3>
According to the given information:</h3>
Total area = 7 square feet
and,
Total area = Length x Width
So,
7 = (2x + 3)(2x + 2)
7 = 4x2 + 4x + 6x + 6
7 = 4x2 + 10x + 6
4x2 + 10x + 6 - 7 = 0
4x2 + 10x - 1 = 0
Hence,
The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.
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I understand that the question you are looking for is:
Mary wants to hang a mirror in her room. the mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x. Which quadratic equation can be used to determine the thickness of the frame, x?
A. x² + 14x - 2 = 0
B. 2x² + 10x - 7 = 0
C. 3x² + 12x - 7 = 0
D. 4x² + 10x - 1 = 0
Answer:
7
Step-by-step explanation:
form a proportion
12/2=42/x
cross multiply
12x=84
x=7
Find the possible rational roots and use synthetic division to find the first zero.
I chose x=1 (which represents the factor "x-1")
1║2 -7 -13 63 -45
║ 2 -5 -18 45
2 -5 -18 45 0
(x-1) is a factor, (2x³ - 5x² - 18x + 45) is the other factor.
Use synthetic division on the decomposed polynomial to find the next zero.
I chose x = 3 (which represents the factor "x-3")
3║2 -5 -18 45
║ 6 3 -45
2 1 -15 0
Using synthetic division, we discovered that (x-1), (x-3), & (2x² + x -15) are factors. Take the new decomposed polynomial (2x² + x -15) and find the last two factors using any method.
Final Answer: (x-1)(x-3)(x+3)(2x-5)
Answer:
Step-by-step explanation:
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