Step-by-step explanation:
we have two lines you have to draw.
one is all in the bottom left quadrant (for x<=0) and one in the upper right quadrant (for x>5).
the easiest is for x>5. the line function is only
f(x) = y = 3
so, this is a horizontal line on the grid line for y = 3. it starts above x=5 and then goes all the way to the right ("to infinity and beyond !"). just, if possible, mark the starting point at x=5 as a little empty "circle" instead of a full dot, as x=5 is explicitly excluded (due to x>5).
and for x<=0 the line
f(x) = y = 4x - 3
goes sharp down but goes a little bit to the left the further down it goes. it starts with x=0, which gives y=-3 per the function.
so, the starting point (with a full dot, as x=0 is included) is (0,-3).
from there it goes sharp down and a little bit to the left.
for example the next point is for x=-1, which gives y=-7, so it is the point (-1,-7). x=-2 gives y=-11 and the point (-2,-11).
the line has to go through so these points and further down (again, "to infinity and beyond !"), as to move further left on the negative x-axis.
Answer:
The lengths of all three sides of the triangle are 4.75 units, 9.5 units and 10.75 units.
Step-by-step explanation:
Let the longest side of the triangle is a and the shortest side length is c and the intermediate one is b.
So, a > b > c.
Therefore, the perimeter of the triangle will be, a + b + c = 25 ............. (1) {Given}
Now, given that, a = c + 6 .......... (2)
And, b = 2c ............ (3)
Now, from equations (1), (2) and (3), we get
(c + 6) + 2c + c = 25
⇒ 4c = 25 - 6 = 19
⇒ c = 4.75 units.
So, from equation (2) we get,
a = c + 6 = 10.75 units. and
From equation (3) we get,
b = 2c = 9.5 units.
Therefore, the lengths of all three sides of the triangle are 4.75 units, 9.5 units, and 10.75 units. (Answer)
Given the functions:
1. You need to substitute the function g(x) into the function f(x), in order to find:
Then:
2. You need to substitute this value of "x into the function:
And then evaluate, in order to find:
You get:
Hence, the answer is:
Answer: (0, -4)
Step-by-step explanation:
Answer:
81 times the original size
Step-by-step explanation:
AA0ktA=3A0=?=?=25hours=A0ekt
Substitute the values in the formula.
3A0=A0ek⋅25
Solve for k. Divide each side by A0.
3A0A0=e25k
Take the natural log of each side.
ln3=lne25k
Use the power property.
ln3=25klne
Simplify.
ln3=25k
Divide each side by 25.
ln325=k
Approximate the answer.
k≈0.044
We use this rate of growth to predict the number of bacteria there will be in 100 hours.
AA0ktA=3A0=?=ln325=100hours=A0ekt
Substitute in the values.
A=A0eln325⋅100
Evaluate.
A=81A0
At this rate of growth, we can expect the population to be 81 times as large as the original population.