f(x) = 10x -5 and g(x) = (x+5)/10 are inverses of each other , Option D is the correct answer.
<h3>What is a Function ?</h3>
A function is a mathematical statement which relates two variables , a dependent and an independent variable.
The inverse of a function is found by replacing every y by x and vice versa , and then solve for y
The equation
f(x) = 4/x - 3
or
y= 4/x -3
Replacing y by x
x = 4/y -3
x +3 = 4/y
y = 4/(x+3)
Which do not correlate with the given inverse
f(x) = 10x -5
y = 10x -5
for finding inverse
10y -5 = x
10y = x+5
y = (x+5)/10
g(x) = (x+5)/10
Therefore , Option D is the correct answer.
To know more about Function
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To determine if 1/3 and 4/12 are equivalent fractions, you can either simplify 4/12 or raise 1/3. I'm going to explain with an example. So we have 1/8 and 3/24. I usually make the denominators (The lower number of the fraction) the same. To do that i multiply 8 by which ever number i think will calculate to 24. So 8 times 3 is 24. So i would change the number 8 to the number 24. But what you do to the bottom you HAVE to do to the top. So i multiplied the number 8 by 3 to get 24. No i am going to multiply the top of 1/8 (which is 1, or the numerator) by 3. And 1 times 3 is 3. And that gives me 3/24. It equals the second fraction, so 1/8 and 3/24 is equivalent.
So taking your fractions, 1/3 and 4/12, we just see how many times 3 goes into 12. Or what times 3 equals 12. That is 4. So what we do to the bottom we MUST do to the top, right? So we multiply 1 by 4. That gives us 4. So 1/3 changed into 4/12. So our first fraction is now 4/12 and our second fraction is also 4/12. So they are equivalent! Hope this helped <span />
Given:
To find:
Draw a graph of a line that is perpendicular to the given line and passing through a given point.
Explanation:
As we know that relation between two slopes of perpendicular slopes of lines:
Slope of given line y = 4x + 1 is:
So, the slope of line perpendicular to given line is:
Also, so line equation that is perpendicular to given line is:
Also, the required line is passing thorugh given point (2, 3), i.e.,
So, line equation that is perpendicular to given line is:
The required graph of line is:
Answer:
True.
Here, radius of the sphere = radius of the cylinder = r
Diameter of the sphere = height of the cylinder = 2r
Surface area of the sphere = 4πr2
Curved surface area of the cylinder = 2πr (2r) = 4πr2
Step-by-step explanation:
Lets split this into two parts; a semi circle and triangle. We can solve fro the area of both individually first.
Area of the Semi Circle:
Formula: A = (πr²)/2
The radius is the diameter divided by two (16 / 2 = 8)
A = (π*8²)/2
A = (π64)/2
A = 200.96/2
A = 100.48 meters
The area of the semi circle is 100.48 meters
Area of the Triangle:
Formula: A = bh/2
A = 16*12/2
A = 192/2
A = 96 meters
The area of the triangle is 96 meters.
To find the total area of the shape, we can add.
100.48 + 96 = 196.48 meters.
Best of Luck!
