<u>Answer:</u>
f(x) = (2x + 1)(2x − 1)
Explanation:
As we can see from the above function f(x) = 4
− 1, we need to find x-intercept, i.e., the value of x where this function's value is zero.
So let us Equate the function with zero
4 - 1 = 0 => 4 = 1 => = 1/4 => x = 
Hence we get 2 values of x, i.e., +1/2, and -1/2.
So now we need to check out the functions which are zero at this values of x, so let us substitute values of x in each and every option and see the values of functions.
Option A - f(x) = (4x + 1)(4x − 1) = 3, -3
Option B - f(x) = (2x + 1)(2x − 1) = 0
Option C - f(x) = 4(x2 + 1) = 5
Option D - f(x) = 2(x2 − 1) = -3/2
Hence answer is Option B
<h3>Answer:
122 degrees</h3>
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Explanation:
Angle BAC can be shortened to "angle A" since the letter A is in the middle.
Angle BCA can be shortened to "angle C" for similar reasoning.
We're told that angles A and C are base angles. For any isosceles triangle, the base angles are congruent
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Let's use this fact to solve for x.
angle A = angle C
7x+1 = 5x+9
7x-5x = 9-1
2x = 8
x = 8/2
x = 4
Once we know what x is, we can find each base angle
- angle A = 7x+1 = 7*4+1 = 28+1 = 29
- angle C = 5x+9 = 5*4+9 = 20+9 = 29
Both angles A and C are 29 degrees each, so this confirms we have the correct x value.
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The last step is to use the fact that all three angles of a triangle add to 180 degrees. This will help us find angle B, which is the vertex angle.
A+B+C = 180
29+B+29 = 180
B+58 = 180
B = 180-58
B = 122
The vertex angle is 122 degrees.
So we can say either angle B = 122, or we could say angle ABC = 122
"angle ABC" is the same as "angle CBA".
Given that the quadratic equation is 
We need to determine the y - value of the vertex.
<u>The x - value of the vertex:</u>
The x - value of the vertex can be determined using the formula,
where 
Substituting these values, we get;
Simplifying the terms, we get;
Thus, the x - value of the vertex is -5.
<u>The y - value of the vertex:</u>
The y - value of the vertex can be determined by substituting the x - value of the vertex ( x = -5) in the equation
Thus, we get;
Simplifying the values, we have;
Thus, the y - value of the vertex is 49.
The bottom of the ladder is 10.5 feet away from the wall
Step-by-step explanation:
The given scenario forms a right triangle.
Where
The length of ladder will be the hypotenuse
The wall on which the window is situated will ebt he perpendicular and
The distance between the foot of ladder and the wall will be the base
So,
Hypotenuse = H = 20 foot
Perpendicular = P = 17 feet
Base = B = ?
Using the Pythagoras theorem
The bottom of the ladder is 10.5 feet away from the wall
Keywords: Triangle, Pythagoras Theorem
Learn more about Pythagoras theorem at:
#LearnwithBrainly
40º
7) In this problem, we can see that both tangent lines to that circle come from the same point O.
So, we can write out the following considering that there is one secant line DO and one tangent line to the circle AO
