Given:
Prove:
Solution:
Putting the value of equation (ii) into the equation (i):
putting the value x into the equation (i):
Therefore, the value of x= 4
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If f(2) = 22 – 5, then what is the value of f(2) + f(5)?
2 answers:
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Let's find the perimeter first by adding all the side lengths together. There are two missing side lengths, which we can find by taking the side opposite them and subtract the side behind the missing side from them.
I've attached a diagram showing how to find the side lengths.
Now let's add all the side lengths together: 4 cm + 8 cm + 8 cm + 2 cm + 4 cm + 6 cm = 32 cm
The perimeter of this figure is 32 cm.
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To find the area we can divide this figure into 2 rectangles. On the second attached diagram, I've split the figure into two and labeled the length and width of each rectangle.
Area of a rectangle = length * width
Area of red labeled rectangle = 4 cm * 2 cm = 8 cm²
Area of yellow labeled rectangle = 8 cm * 4 cm = 32 cm²
Add the two areas together: 8 + 32 = 40
The area of the figure is 40 cm².
Answer:
Compare the given equation of the circle (x - 1)² + (y -2)² = 2²
with standard form of circle: (x - h)² + (y - k)² = r²
Here, (h, k) is the center of the circle
and r is the radius of the circle.
Thus, The center of the circle is: (1, 2)
Also, for finding the point of intersections of (x - 1)² + (y -2)² = 2² and y = 2x + 2,
Substitute the value of y from equation of line in the equation of circle.
(x - 1)² + (2x + 2 - 2)² = 2²
⇒ (x - 1)² + (2x)² = 2²
⇒ x² + 1 - 2x + 4x² = 4
⇒ 5x² - 2x - 3 = 0
Applying Middle term splitting method
5x² - 5x + 3x - 3 = 0
⇒ 5x(x - 1) + 3(x - 1) = 0
⇒ (5x + 3)(x - 1) = 0
⇒ x = and x = 1
Thus, we get coordinates: and (1, 4)