Find their gradients using the change in y coords divided by the change in x coords. once you have the gradients (or slopes), multiply them by eachother - if the product is (-1) then theyre perpdendicular, if not, they are either parallel or intersect at a point
Answer: x=3
Step-by-step explanation: 3x+2=11
-2 -2
3x=9
x=3
Here, we are required to find the first term of an arithmetic progression which has a second term of 96 and a fourth term of 54.
- The first term of the progression which has a <em>second term</em> of 96 and a <em>fourth term</em> of 54 is; a = 117.
<em>In Arithmetic progression, the N(th) term of the progression is given by the formular;</em>
T(n) = a + (n-1)d
where;
Therefore, from the question above;
- T(2nd) = a + d = 96..............eqn(1)
- and T(4th) = a + 3d = 54..........eqn(2)
By solving the system of equations simultaneously;
we subtract eqn. 2 from 1, then we have;
<em>-2d = 42</em>
Therefore, d = -21.
However, the question requests that we find the first term of the progression; From eqn. (1);
a + d = 96
Therefore,
Ultimately, the first term of the progression is therefore; a = 117
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Answer:
<h2>2.3 < x < 8.7</h2>
Step-by-step explanation:
Look at the picture.
We have a = 5.5, b = x and c = 3.2.
Substitute:
(1)
5.5 + x > 3.2 <em>subtract 5.5 from both sides</em>
x > - 2.3
(2)
5.5 + 3.2 > x
8.7 > x
(3)
x + 3.2 > 5.5 <em>subtract 3.2 from both sides</em>
x > 2.3
From (1), (2) and (3) we have:
2.3 < x < 8.7
