The equation 5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0 is a quadratic equation
The value of x is 8 or 1
<h3>How to determine the value of x?</h3>
The equation is given as:
5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0
Rewrite as:
-5/x - 2 + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0
Take the LCM
[-5(x + 2) + (x -5)(x- 2)]\[x^2 - 4 + [3x + 8]/[x^2 - 4] = 0
Expand
[-5x - 10 + x^2 - 7x + 10]/[x^2 - 4] + [3x + 8]/[x^2 - 4] = 0
Evaluate the like terms
[x^2 - 12x]/[x^2 - 4] + [3x + 8]/[x^2 - 4 = 0
Multiply through by x^2 - 4
x^2 - 12x+ 3x + 8 = 0
Evaluate the like terms
x^2 -9x + 8 = 0
Expand
x^2 -x - 8x + 8 = 0
Factorize
x(x -1) - 8(x - 1) = 0
Factor out x - 1
(x -8)(x - 1) = 0
Solve for x
x = 8 or x = 1
Hence, the value of x is 8 or 1
Read more about equations at:
brainly.com/question/2972832
Answer:
Look at explanation.
Step-by-step explanation:
<em><u>Dilation of scale factor of 5, because it would become more wide and open by a factor of 5. Reflection over y-axis, because it makes the shape double the size. Dilation of scale factor of 1/2, because it makes the shape half it's size.</u></em> The rotating 90 degrees would only change the shapes position, not the size. The translation would only move the shape to a different area, and not change the size.
Answer:
Because the line is the shortest path between 2 points
Answer:
1.8 cm
6.3 cm²
Step-by-step explanation:
AC⊥BC
BD=BC=x
- (x+5)²+x²=7²
- x²+10x+25+x²=49
- 2x²+10x- 24=0
- x²+5x-12=0
- x=1.8
BC= 1.8 cm
Area of ABC= 1/2*1.8*7= 6.3 cm²
Answer:
2.38 miles
Step-by-step explanation:
From Given diagram:
In ΔABC,
AC=2.5 miles
BC= 3.7 miles
∠BCA= 39.4°
Now as we have two sides and an angle, using law of cosines to find the third side:
c= √(a^2+b^2-2abcosα
AB=√(AC)^2 + (BC)^2 - 2(AC)(BC)cosα
=√(2.5)^2 + (3.7)^2 - 2(2.5)(3.7)cos(39.4°)
=√(2.5)^2 + (3.7)^2 - 2(2.5)(3.7)(0.77)
=√(5.695)
= 2.38 !
