Answer:
The common difference is same = d = -9
Therefore, the data represent a linear function.
Step-by-step explanation:
Given the table
x y
1 4
2 -5
3 -14
4 -23
5 -32
Finding the common difference between all the adjacent terms of y-values
d = -5 - 4 = -6,
d = -14 - (-5) = -14+5 = -9
d = -23 - (-14) = -23 + 14 = -9
d = -32 - (-23) = -32 + 23 = -9
It is clear that the common difference between all the adjacent terms is same.
Thus,
d = -9
We know that when y varies directly with x, the function is a linear function.
Here, it is clear that each x value varies 1 unit, and each y value varies -9 units.
i.e. The common difference is same = d = -9
Therefore, the data represent a linear function.
Answer:
C
Step-by-step explanation:
For the given intervals
( - ∞, - 5) ← use any value < - 5 but not - 5, the parenthesis ) indicates that x is less than - 5 but not equal to - 5
(- 5, - 1) ← - 4, - 3, - 2 can be used but not - 5 or - 1
(- 1, 4) ← 0, 1, 2, 3 can be used but not - 1 or 4
(4, ∞ ) ← use any value > 4 but not 4
Hence
3 can be used in (- 1, 4)
- 6 can be used in (- ∞, - 5)
zero can be used in (- 1, 4)
- 5 cannot be used in any of the given intervals
In a full rotation, 360°, a point on the edge of a gear would travel a distance equal to its circumference. The circumference of a circle is:
C=2πr, and since we are only traveling 150°, we need to set up an appropriate ratio for circumference to the distance the point travels:
d/C=150/360
d=5C/12 and since C=2πr
d=10πr/12
d=5πr/12, and since r=4in
d=5*4π/12 in
d=20π/12 in
d=5π/3 in
d≈5.24 in (to nearest hundredth of an inch)
The correct answer is A. Think of this as a graph in the y=Mx+b form. When graphing these equations, you should be able to see that the lines for A and B match up with the picture. However, since everything below the line is shaded, this must mean that the graph includes everything under the line. Y must be less than everything that is input. The correct answer is A.
-R
Answer:
<u><em>The Father is currently 47 and the Son is 7</em></u>
Step-by-step explanation:
Let F and S be the present ages of Father and Son, respectively.
We are told that <u>(F-2) = 9(S-2)</u> [2 years ago, father age was nine times the son age]
We also learn that <u>(F+3) = 5(S+3)</u> [3 years later it will be 5 times only]
Take the first expression and isolate one of the variables (S or F). I'll isolate F:
(F-2) = 9(S-2)
F = 9S - 16
Now use this in the second expression:
(F+3) = 5(S+3)
((9S-16)+3) = 5(S+3)
9S-13 = 5S+15
4S = 28
S = 7
Since F = 9S-16,
F = 9*(7)-16
F = 47
<u><em>Father is 47 and Son is 7</em></u>
CHECK:
Was the father 9 times the age of his son 2 years ago?
Father would have been 45 and son 5. Yes, 9*5 = 45
In 3 years will he be 5 times older than his son? Yes, Father would be 50 and son would be 10. 5*(10) = 50
