The perpendicular bisector of RT is B. SU.
We have that
case 1)<span>system of equations is
</span><span>y=−12x−1
y=14x−4
using a graph tool
see the attached figure
the solution of the system is the point (0.115,-2.385)case 2)
</span>system of equations is
<span>blue line passing through coordinates A (0, -4) and B (4, -3)
</span><span>red line passing through coordinates C(0, -1) and D (4, -3)
</span>using a graph tool
see the attached figure
the solution of the system is the point (4,-3)<span>
</span>
Answer:
a) OA = 1 unit
b) OB = 3 units
c) AB = √10 units
Step-by-step explanation:
<u>Given function</u>:

<h3><u>Part (a)</u></h3>
Point A is the y-intercept of the exponential curve (so when x = 0).
To find the y-value of Point A, substitute x = 0 into the function:

Therefore, A (0, 1) so OA = 1 unit.
<h3><u>Part (b)</u></h3>
If BC = 8 units then the y-value of Point C is 8.
The find the x-value of Point C, set the function to 8 and solve for x:

Therefore, C (3, 8) so Point B is (3, 0). Therefore, OB = 3 units.
<h3><u>Part (c)</u></h3>
From parts (a) and (b):
To find the length of AB, use the distance between two points formula:


Therefore:





Step-by-step explanation:
1) i will asume x2 and z2 are squares here.
ok, here we only have restrictions to x and z, so y can take all the values in R.
is a circle of radius 6, you can see this if for example we set z = 0, then x goes from -6 to 6, the same if we set x = 0 then z goes from -6 to 6.
and the equation
describes a circle.
So here, the region is the solid cylinder of radius 6, where the Y axis is also the axis of the cylinder.
2) you tipped the same inequality but different numbers in the right side, here i think you are saying that the inequalities describes the set of all points whose distance from the y-axis is equal or less tan 6.
Answer:
1. x = 2
y = 1
2. x = 3 or 6 (Mistake or typo in problem)
3. y = 13
4. x = 7
y = 15
5. x = 4
Step-by-step explanation:
1. 6x - 3 = x + 7, 5x = 10, x = 2
3y + 2 = y + 4, 2y = 2, y = 1
2. There is most likely a typo. Either 8x = 24 and x = 3 or 2x + 10 = 3x + 4 and x = 6
3. 5y -3 = 2y + 36, 3y = 39, y = 13
4. 8y + 11 + 3y + 4 = 180, 11y + 15 = 180, 11y = 165, y = 15
7x = 3y + 4 = 49, x = 7
5. 7x - 10 = 4x + 2, 3x = 12, x = 4