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:
Congruent angles have the same angle.
Answer:
The equation of the line would be y = -1/3x - 4
Step-by-step explanation:
In order to find this, we first need to find the slope of the original line. We do this by solving for y.
2x + 6y = 10
6y = -2x + 10
y = -1/3x + 5/3
Now that we see the slope as -1/3, we know the new line will have the same slope thanks to the definition of parallel lines. So, we can use this slope and the point in point-slope form to find the equation.
y - y1 = m(x - x1)
y - -5 = -1/3(x - 3)
y + 5 = -1/3x + 1
y = -1/3x - 4
5x + 18y = 23
x + 3y = 2 .....multiply by -5
----------------
5x + 18y = 23
-5x - 15y = -10 (result of multiplying by -5)
----------------add
3y = 13 <=== the resulting equation
Answer:
48 cubes
Step-by-step explanation:
You could fit these cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm x 2 2/3 cm x 2/3 cm.
