Identify the function in which y varies directly with x.
2 answers:
Answer: The correct option is (C) y = 4x.
Step-by-step explanation: We are given to identify the function in which y varies directly with x.
We know that
if y varies directly as x, then we write as follows :
Out of the given options, equation (i) matches with the third option y = 4x, for k = 4.
Therefore, the correct option is (C) y = 4x.
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Answer:
or
Step-by-step explanation:
This is factorable.
The leading coefficient is 1.
Since this is a quadratic all we have to do is find two numbers that multiply to be c and add up to be b to factor the expression that is to the left of the equal sign.
By the way a quadratic expression looks like .
So we want to find two numbers that multiply to be -6 and add up to be -1.
Those numbers are -3 and 2 since (-3)(2)=-6 and -3+2=-1.
So the factored form is:
.
Since we have a product is zero then at least one of the factors need to be zero in order for the equation to hold.
So this means we have the following two equations to solve:
or
First equation we will add 3 on both sides.
Second equation we will subtract 2 on both sides.
or
<h2>a) Select all that apply</h2>
<em> are each perpendicular to the line of reflection</em>
<em></em>
This option is the only one that is correct. The line of reflection is . When we talk about reflection, we are talking about reflecting across a line, or axis. Reflecting a shape means looking at the mirror image on the other side of the axis. So in this case, this mirror is the line of reflection. As you can see, these three segments
<em> </em>form a right angle at the point each segment intersects the line
.
Since the line is an axis that allows to get a mirror image, therefore it is true that:
To find those values , count the number of units you get from the point S to L, which is 3 units. Do the same to find
but from the point T to M, which is 6 units and finally, for
but from the point U to N, which is 4 units. Therefore:
<em>The line of reflection is the perpendicular bisector of each segment joining a point and its image. </em>
<em />
A bisector is the line dividing something into two equal parts. In this case, the line of reflection divides each segment into two equal parts and is perpendicular because this line form a right angle with each segment. As we demonstrated in a) each segment is perpendicular to the line of reflection, so the first statement is false. On the other hand, each side of the original triangle is not perpendicular to its image and this is obvious when taking a look at the figure. Finally, as we said the line of reflection is perpendicular to each of the mentioned segments, so they can't be parallel as established in the last statement.