9514 1404 393
Answer:
b, c, d -- (all but the first)
Step-by-step explanation:
The key take-away regarding what relation is or is not a function is the following: a function has no repeated x-values.
The x-values in the table are -3, -1, 0, 2, so any suggested ordered pair with one of those as an x-value cannot be added to the table. The only such pair in the list is the first one (-3, 4). It cannot be added. All of the remaining three pairs can be added and the relation will remain a function.
Answer:
Step-by-step explanation:
First Question
The top question has 2 solutions because eventually you will have to take the square root of (x - 4)^2. One square root will be plus, and the other minus
(x - 4)^2 - 28 = 8 Add 28 to both sides
(x - 4)^2 -28+28 = 8+28 Collect like terms
(x - 4)^2 = 36 Take the square root.
sqrt( (x - 4)^2 ) = sqrt(36)
x - 4 = +/- 6
=============
x - 4 = + 6
x = 6 + 4
x = 10
============
x - 4 = - 6
x = - 6 + 4
x = - 2
The two solutions are (10,0) and (-2,0)
Second Question
The question is solved correctly up to the point where the square root needs to be taken. It is incorrect at that point.
x^2 - 6x - 7 = 0 Add 7 to both sides.
x^2 - 6x = 7 Add 1/2 the linear term and square it to both sides.
x^2 - 6x + (6/2)^2 = 7 + (6/2)^2 Expand the right
x^2 - 6x + 3^2 = 7 + 9
x^2 - 6x + 9 = 16 express the square on the left
(x - 3)^2 = 16 Take the sqrt of both sides.
x - 3 = sqrt(16)
x - 3 = +/-4
============
x - 3 = 4
x = 4 + 3
x = 7
===========
x -3 = - 4
x = - 4 + 3
x = - 1
==========
Solutions
(7,0) and (-1,0)
<h3>Answer:</h3>
The attached shows a graph
<h3>Explanation:</h3>
A graphing calculator can graph this for you when you give it the equation.
For graphing by hand, it is helpful to recognize that the equation is in "slope-intercept" form. This means the constant term (-9) is the y-intercept, the point on the y-axis where the line crosses. Mark the point -9 on the y-axis. (The coordinates are (0, -9).
The slope is 5/3, the coefficient of x. This means the line goes up 5 units for every 3 units it goes to the right. The point that is 3 over and 5 up from (0, -9) is (0+3, -9+5) = (3, -4). Mark that point.
Draw a line through the marked points.
<em>-</em><em>1</em><em>1</em><em> </em><em>and</em><em> </em><em>-</em><em>1</em><em>1</em><em> </em><em>are</em><em> </em><em>the</em><em> </em><em>two</em><em> </em><em>numbers</em><em> </em><em>that</em><em> </em><em>adds</em><em> </em><em>to</em><em> </em><em>-</em><em>2</em><em>2</em><em> </em><em>and</em><em> </em><em>multiply </em><em>to</em><em> </em><em>1</em><em>2</em><em>1</em>
<em>If</em><em> </em><em>we</em><em> </em><em>add</em><em> </em><em>1</em><em>1</em><em> </em><em>and</em><em> </em><em>1</em><em>1</em><em> </em><em>then</em><em> </em><em>it</em><em> </em><em>equals</em><em> </em><em>to</em><em> </em><em>-</em><em>2</em><em>2</em><em>.</em>
<em>if</em><em> </em><em>we</em><em> </em><em>multiply</em><em> </em><em>1</em><em>1</em><em> </em><em>and</em><em> </em><em>1</em><em>1</em><em> </em><em>then</em><em>,</em><em>it</em><em> </em><em>equals</em><em> </em><em>to</em><em> </em><em>1</em><em>2</em><em>1</em>
<em>hope</em><em> </em><em>it</em><em> </em><em>helps</em><em>.</em><em>.</em><em>.</em>
<em>Good</em><em> </em><em>luck</em><em> </em><em>on</em><em> </em><em>your</em><em> </em><em>assignment</em>
False. One half of a number y is more than 22