F(x) = x²-4x-5, quadratic function,
Domain (the values if x) is all real numbers.
To find range we should draw a graph or to write an equation in vertex form.
f(x) = x²-4x+4-4-5
f(x) = (x-2)²-9
Point (-2,-9) is the vertex of the parabola, and it is a minimum because a parabola has positive sign in front of x², so it is looking up. Minimum value of y =-9
Range(the values of y) is [-9, ∞)
The equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)
<h3>Circle theorem</h3>
The given diagram shows two intersecting lines tangential to a circle at points A and C.
Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.
Mathematically;
<B = 1/2(arcADC - arcAC)
58 = 1/2(238 -x)
Hence the equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)
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↪Cartesian Coordinates of the system....!!
↪X = rcos⊙ and Y = rsin⊙
↪since here Radius (r) = 10 units and Theta (⊙) = 225°
↪there fore substituting we get as ..
↪X = 10 ( cos 225° ) = 10 * -1/ root 2 = -7.071
↪Y = 10 ( sin 225° ) = 10 * -1/root2 = = -7.071
↪the cordinates are as follows
↪(x,y) = (-7.071, -7.071 )
Answer:
x = ±i(√6 / 2)
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
<u>Algebra II</u>
Imaginary root i
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
2x² + 3 = 0
<u>Step 2: Solve for </u><em><u>x</u></em>
- [Subtraction Property of Equality] Subtract 3 on both sides: 2x² = -3
- [Division Property of Equality] Divide 2 on both sides: x² = -3/2
- [Equality Property] Square root both sides: x = ±√(-3/2)
- Simplify: x = ±i(√6 / 2)
The value of the variable x in the equation –x + 8 + 3x = x – 6 is - 14.
<h3>How to find variable in an equation?</h3>
The variables of an equation can be found as follows:
–x + 8 + 3x = x – 6
The variable in the equation is x.
Therefore,
–x + 8 + 3x = x – 6
combine like terms on the left side
-x + 3x + 8 = x - 6
2x + 8 = x - 6
subtract x form both sides of the equation
2x - x + 8 = - 6
x + 8 = -6
subtract 8 from both sides
x = -6 - 8
x = - 14
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