Select the correct responses in the table. The relationship between two numbers is described below, where x represents the first
number and y represents the second number. The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to the first number multiplied by 7. Select the equations that form the system that models this situation. Then, select the solution(s) of the system.
1 answer:
9514 1404 393
Answer:
- x² = y + 16
- 4y - 1 = 7x
- (5, 9)
Step-by-step explanation:
Writing equations from words is mostly a matter of understanding what the English words mean.
If the first number is x, then the square of the first number is x². That is said to be equal to the sum of the second number (y) and 16:
x² = y + 16 . . . . the first equation
The wording "the difference of A and B" is usually intended to be interpreted to mean A-B. Here, we have the difference of 4 times the second number (4y) and 1, so ...
4y -1
This is equal to the first number (x) multiplied by 7, so ...
4y -1 = 7x . . . . the second equation
__
These can be solved a variety of ways. When no method is specified, I like to use a graphing calculator. It shows the only integer solution for this pair of equations is ...
(x, y) = (5, 9)
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Answer:
(Missing part of the question is attached)
Estimates are too large.
Step-by-step explanation:
Suppose the only information we know about the function is:
where the graph of its derivative is shown in the attachment
<h3>(a)</h3>If the function is differentiable at point
, the tangent line to the graph of
at 1 is given by the equation:
So we call the linear function:
We know the as it is given in the question, and
from the graph attached. Substitute in the equation of
.
At x=1, is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve
. Thus, The estimates are too large.
