Answer:
=14x² −3x −1
Step-by-step explanation:
simplifying step-by-step.
9x2+5x2+5x−3−(8x−2)
Distribute the Negative Sign:
=9x2+5x2+5x−3+−1(8x−2)
=9x2+5x2+5x+−3+−1(8x)+(−1)(−2)
=9x2+5x2+5x+−3+−8x+2
Combine Like Terms:
=9x2+5x2+5x+−3+−8x+2
=(9x2+5x2)+(5x+−8x)+(−3+2)
=14x2+−3x+−1
Answer:
=14x2−3x−1
I guess the parent function to be: y = |8x|.
To translate a function m units to the right, you must substitute x by x-m. You had y = |8x|. You substitute x by x-1/4, to get:
y = |8(x-1/4)| = |8x-2|
So, the function was translated to the right 1/4 unit.
To translate a function vertically n units, you add (translate up) or subtract (translate down) m to the function. You had y = |8x-2|. You subtract 7 to get:
y = |8x-2|-7
Hence, the parent function was translated 7 units down.
The vertex is the point where the content of the absolute value changes its sign, that is, the where it equals zero:
8x-2 = 0 <=> x=1/4
The x coordinate of the vertex is therefore x=1/4. To calculate the y coordinate of the vertex, you must substitute the x coordinate in the equation of the function, to get:
x=1/4 => y = |8(1/4)-2| - 7 = -7
The vertex is, therefore, (1/4,-7).
Finally, the axis of symmetry is a vertical line through the vertex: x=1/4 (the equation of a vertical line is of the form x=a).
The correct answer is D).
Answer:
Step-by-step explanation:
Let's define our variables. Let a represent the number of adult tickets sold, s represent the number of senior tickets sold, and r represent the number of senior tickets sold.
We know that a total of 350 tickets were sold. So, the number of adult, student, and senior tickets sold must total 350. Therefore, we can write the following equation:
We know that each adult ticket costs $4, each student ticket costs $2.50, and each senior ticket costs $2. We are given that a total of $1095 was collected. Therefore, the number of tickets multiplied by their respective price must equal $1095. So, we can write the following equation:
Finally, we know that 40 fewer senior tickets were sold than student tickets. So, however many students tickets were sold, we can subtract 40 to get the number of senior tickets sold. Therefore:
So, our system of equations is:
And we're done!
Answer:
A. always
Step-by-step explanation:
we know that
Parallel lines are those lines which never intersect to each other and always have same distance between them
Two lines always have same distance will only be possible when they lie on same plane
and we know that
same plane means co-planar
so, two lines will be parallel only if they are co-planar
It means that
Parallel lines are always co-planar
So,
Answer is
A. always
