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The area of a square is 169 cm^{2}. What is the length of one side of the square?
Since a square has sides with the same length, the formula for Area is A = s^{2}
Let’s substitute 169 for the Area.
s^{2} = A
s^{2} = 169
s = √169
s = 13
In this situation, 13 doesn’t apply since the side of a square can’t be a negative number.
A right triangle has a side with length 12 in and a hypotenuse with length 20 in. Find the length of the second leg. (Round to the nearest hundredth if needed)
Since we are working with a right triangle, and we are missing a leg, we can use the Pythagorean Theorem to solve for that missing leg
Pythagorean Theorem: A^{2} + B^{2} = C^{2}
A = 12, B = ?, C = 20
12^{2} + B^{2} = 20^{2} Substitute
144 + B^{2} = 400 Simplify
144  144 + B^{2} = 400  144
Subtract 144 from both sides
B^{2} = 256 Simplify
Take the square root of both sides
B = 16
Find the xintercepts for the following equation.
Y = 6x^{2}  7x  3
In order to find the xintercepts, we can let y = 0 and solve for x. We can solve by possible factoring or by using the quadratic formula. Let’s use the discriminant to decide which method would be best.
0 = 6x^{2}  7x  3
where a = 6
b = 7
c = 3
Discriminate: b^{2}  4ac
(7)^{2}  4(6)(3) = 121.
This is positive and a perfect square, so let’s factor!
Use the quadratic formula to find the values of x for the equation:
x^{2}  4x  10 = 0
Given a quadratic equation of the form
ax^{2} + bx + c = 0
the quadratic roots can be evaluated using the formula
For x^{2} − 4x + 10 = 0
∴ x = 5.74 and x = 1.74
Which statement best describes the solutions to the equation below?
3x^{2}  5x + 20 = 0
In order to determine which statement best represents this equation, I would need to find the discriminate. Discriminate: b^{2}  4ac
where: a = 3 b = 5 c = 20
(5)^{2}  4(3) (20) = 215
Since the discriminate is negative, this means that there are no real solutions.
The graph of a quadratic function is called a parabola.
If 5, is a root of the quadratic equation 2x^{2} + Px  15 = 0 and the quadratic equation P (x^{2} +x) + K = 0 has equal roots. What is the value of K?
The given equation is
2x^{2} + Px  15 = 0
2(5)^{2} + P(5)  15 = 0
⇒ 50  5P  15 = 0
⇒ 5P =  35
⇒ P = 7
P(x^{2} + x) + K = 0
⇒ 7(x^{2 }+ x) + K = 0 ⇒ 7x^{2} + 7x + K = 0
⇒ a = 7, b = 7, c = K
∴ D = b^{2}  4ac = (7)^{2}  4(7)K = 49  28K
The equation has equal roots
D = 0 ⇒ 49  28K = 0 ⇒ K = 49/28 = 7/4
If one root of 3x^{2} + 11x +K = 0 is reciprocal of the other then what is the value of K?
The given equation is
3x^{2} + 11x + K = 0
Let one root be α then other root is 1/α
If α, β are the roots of the equation 3x^{2} + 8x + 2 = 0 then the value of (1/α + 1/β) is
We have 3x^{2} + 8x + 2 = 0
and α + β = 8/3, αβ = 2/3
Now
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