<h3>The value of x is 4.10</h3>
<em><u>Solution:</u></em>
Given that,
The angle Johnny holds his pen on paper creates a linear pair
Angles in a linear pair are supplementary angles
Two angles are supplementary, when they add up to 180 degrees
The measure of one angle is 13x + 7
The measure of the second angle is one less than twice the first angle
Therefore,
Measure of second angle = twice the first angle - 1
Measure of second angle = 2(13x + 7) - 1
Measure of second angle = 26x + 14 - 1
Measure of second angle = 26x + 13
Therefore,
Measure of first angle + measure of second angle = 180
13x + 7 + 26x + 13 = 180
39x + 20 = 180
39x = 180 - 20
39x = 160
x = 4.1
Thus value of x is 4.10
Answer:
b
Step-by-step explanation:
Using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 1)
d = 
= 
= 
= 
→ b
Answer:
The pair which are inverse of each other are:
Option: C
Step-by-step explanation:
Two functions f(x) and g(x) are said to be inverse of each other if:
fog(x)=gof(x)=x
i.e. the composition of two functions give identity no matter what the order is.
A)
and 
Now we calculate fog(x):
Hence, option: A is incorrect.
B)
Now we calculate fog(x):
Hence, option: B is incorrect.
D)
![f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3](https://tex.z-dn.net/?f=f%28x%29%3D9%2B%5Csqrt%5B3%5D%7Bx%7D%5C%20and%5C%20g%28x%29%3D9-x%5E3)
Now we calculate fog(x):
![fog(x)=9+\sqrt[3]{9-x^3}\neq x](https://tex.z-dn.net/?f=fog%28x%29%3D9%2B%5Csqrt%5B3%5D%7B9-x%5E3%7D%5Cneq%20x)
Hence, option: D is incorrect.
C)
Now we calculate fog(x):
Similarly,
Hence, option: C is the correct option.
Answer:
11. x = -3+√37 ≈ 3.08276
12. x = 11.2
13. x = -6 +6√5 ≈ 7.41641
Step-by-step explanation:
In each case, the relation of interest is ...
(distance to circle near) × (distance to circle far) = (distance to circle near) × (distance to circle far)
When there is only one point of intersection of the secant with the circle—because it is a tangent—then the product is the square of the length of the tangent.
11. 2(2+12) = x(x +6)
x² +6x -28 = 0
(x +3)² -37 = 0
x = -3+√37 ≈ 3.08276
12. 5(5+x) = 9(9)
5x +25 = 81
x = 56/5 = 11.2
13. x(x +12) = 12(12)
x² +12x -144 = 0
(x +6)² -180 = 0
x = -6 +√180 ≈ 7.41641
_____
<em>Comment on this secant rule</em>
This rule turns out to apply whether the point of intersection of the secant lines is outside the circle (as in these problems) or inside the circle (as in problem 9). The product of the two distances from the point of intersection to the circle is a constant for a given pair of intersecting secants/chords.
