Answer: 4) 157
Step-by-step explanation:
We know that there is no association between the grade level and the andedness, then we should find that the ratio between left handeds and right handed is the same for both grades.
In 7-th grade we have:
Left handed : 11
Right handed: 72
The ratio is 11/72 = 0.14
Then, the ratio for the 8-th graders must be about the same:
Left handed: 24
Right handed: X
Ratio: 24/X
Let's start with the bigger option, X = 157.
24/157 = 0.15
Ok, we now see that with the bigger option we obtained almost the same ratio (if we use the smaller values for X, we will get a ratio bigger than 0.15, so 0.15 is the better aproximation that we can find to the 0.14 of the 7-th graders)
Then the correct option is 4) 157
The square of the diagonal (d1) of the end face is
.. (d1)^2 = (3 in)^2 +(5 in)^2 = (9 +25) in^2 = 34 in^2
The square of the longest diagonal (d2) will be given by
.. (d2)^2 = (3x in)^2 +(d1)^2
.. = (9x^2 +34) in^2
So, the longest diagonal is
.. d2 = √(9x^2 +34) in
Answer:
With 
So then the x intercept would be (0,-5). And finally we can graph the function as we can see in the figure attached.
Step-by-step explanation:
For this case we know the following function:
We can begin the zeros or the values where the function is 0 like this:
And solving for x we got:
Now we can rewrite the expression like this:
And we can find the position for the vertex at x with this formula:
With
And replacing we got:
And then with the coordinate of x for the vertex we can find the coordinate of y replacing the value of x obtained for the vertex.
Then we can find the intercept using the value of x=0 and replacing into the function we got:
So then the x intercept would be (0,-5). And finally we can graph the function as we can see in the figure attached.
Answer:
Simplifying
2x(3x + -8) = 0
Reorder the terms:
2x(-8 + 3x) = 0
(-8 * 2x + 3x * 2x) = 0
(-16x + 6x2) = 0
Solving
-16x + 6x2 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8 + 3x) = 0
Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:
Simplifying
x = 0
Solving
x = 0
Move all terms containing x to the left, all other terms to the right.
Simplifying
x = 0
Subproblem 2
Set the factor '(-8 + 3x)' equal to zero and attempt to solve:
Simplifying
-8 + 3x = 0
Solving
-8 + 3x = 0
Move all terms containing x to the left, all other terms to the right.
Add '8' to each side of the equation.
-8 + 8 + 3x = 0 + 8
Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8
Combine like terms: 0 + 8 = 8
3x = 8
Divide each side by '3'.
x = 2.666666667
Simplifying
x = 2.666666667
Solution
x = {0, 2.666666667}
Step-by-step explanation:
2x³ +x +3 = (2x² -2x +3)(x +1)
Then (2x³ +x +3)/(x +1) =
2x² -2x +3_____
The picture shows the synthetic division.
