For this case suppose that we have a linear system of equations of the form:
ax + by = c
dx + ey = f
The solution of the system is an ordered pair of the form:
(x, y)
That is, both lines intersect at a point.
The point of intersection in this case is:
(3, 4)
Therefore, the system has one solution.
Answer
the system will have:
one solution
Nick is incorrect because he subtracted 3-1 and 3-2. The answer is 1 3/4 It is that distance because 3 2/4-1 3/4=1 3/4.
Since segments ST and PQ are parallel, triangles SRT and PRQ are similar due to the AAA postulate. In general, the ratio between the corresponding sides of two similar triangles is constant; therefore,

Furthermore,

Finding PR and RS,

Then,


Solving for PS,

Solve the quadratic equation in terms of PS, as shown below
![\begin{gathered} \Rightarrow PS^2+16PS-132=0 \\ \Rightarrow PS=\frac{-16\pm\sqrt[]{16^2-4(-132)}}{2}=\frac{-16\pm28}{2} \\ \Rightarrow PS=-22,6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5CRightarrow%20PS%5E2%2B16PS-132%3D0%20%5C%5C%20%5CRightarrow%20PS%3D%5Cfrac%7B-16%5Cpm%5Csqrt%5B%5D%7B16%5E2-4%28-132%29%7D%7D%7B2%7D%3D%5Cfrac%7B-16%5Cpm28%7D%7B2%7D%20%5C%5C%20%5CRightarrow%20PS%3D-22%2C6%20%5Cend%7Bgathered%7D)
And PS is a segment; therefore, it has to be positive.
Hence, the answer is PS=6
Answer:
B'(-7 , -2)
Step-by-step explanation:
First we must understand the coordinate-axis, when we want to move a point to the left or right we do it on the x-axis. to move up or down is on the y axis.
now if we move to the left we go to the negative and to the right the positive
as we are going to move to the left we have to subtract the value that he gave us (4) only to the part of x
B(-3 , -2)
-3 - 4 = -7
B'( -7 , -2)
We have that the total students there are 500. The 12-graders there are 200. Probability is defined as the ratio of positive outcomes of an event, over all the possible outcomes. Suppose we pick student randomly. Then, there are 200 positive outcomes (positive outcome: we pick a student in 12th grade) and there are totally 500 outcomes (we can pick 500 students in total from Riverside High School). This ratio gives:

. The requested probability is 0.40