Inequality to find the age of siblings is x²+ 11x + 24 ≤ 150.
Let the age of Holly is x years. Now from the statements of the question we will form the equations.
Sue was born three years before Holly.
Sue = Holly + 3 = x + 3------(1)
Jeremy = Sue + 5
From equation (1)
Jeremy = (x + 3) + 5 = x + 8------(2)
Now statement says the product of Sue's age and Jeremy's age is at most 150.
Sue × Jeremy ≤ 150
(x + 3)(x + 8) ≤ 150
x² + 11x + 24 ≤ 150
Therefore inequality x² + 11x + 24 ≤ 150 can be used to find the age of each sibling.
Answer: x^2+11x+24 </= 150
Given : Regression equation:
y = amount of water lilies the pond hold
3.915 = represents the initial population.
1.106 = represents the increase in population at time x.
x = is a variable of time.
The pond can hold 400 water lilies ⇒ y=400
Putting values in equation we get,
Taking log both side
By logarithm property -
Therefore, 46th day the pond be full.
The improper fraction will be - 34/3
Mixed fractions are expressed as , expressing as an improper fraction will give:
Given the mixed fraction , applying the formula above to express as an improper fraction will give:
Hence the improper fraction will be - 34/3
Learn more here: brainly.com/question/24901550
-11 1/3 = -34/3 put the
From here you should be able to calculate the answer. One of them is -0.52 which is not the one you use. Minus heights do not matter in these problems yet. The other root is your answer.
Problem two is the usual way to express what happens to a projectile in the air. It again is going to be solved by the quadratic equation.
There are two ways to do this problem. If you know physics, you can solve it using the projectile formulas. If you don't , then you can use the trick in the previous problem. You can calculate how long it takes to hit the ground (h will then be zero).
This problem is rather nasty for someone who has not taken physics. There is another trick. You have to divide the time you get from the previous step by 2. When you solve the quadratic for h = 0, you get 11.6 seconds. But that is the time it takes to hit the ground. Half time is when the boulder will be at it's highest point. t = 11.6 / 2 = 5.8 (which your answers record as 5.75).
h = 0
b = 184
c = 20
The answer from this equation is t = 11.6
The time you want is t = 5.75. You can calculate the maximum height by putting 5.75 in for t.
Problem 3 is done exactly the same way as problem two. You just have different numbers. When h = 0 the time taken to reach zero = 2.17 seconds. Therefore the time you want to put into the original equation for the maximum height is 1/2 of 2.17 seconds. From there you can find the maximum height.
Note: there is a lot of math in here. I have gotten you past the physics. I have also alluded to the answers. I think you should be able to carry out the rest.
Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere.
Notice that our sphere has a radius of 9 units so we can plug 9 into our formula.
Now, let's simplify the exponent. 9 units³ is equal to 9 units × 9 units × 9 units or 729 units³.
Notice that we can cross cancel in and to and