Answer:
624
Step-by-step explanation:
The sequence is 49, 47, 45,...., 7, 5, 3. This is an arithmetic sequence, because the difference between terms is the same.
The sum of the first n terms of an arithmetic sequence is:
S = n/2 (a₁ + an)
where a₁ is the first term and an is the nth term.
Here, we know that a₁ = 49 and an = 3. But we need to find what n is. To do that, we use definition of an arithmetic sequence:
an = a₁ + (n-1) d
where d is the common difference (in this case, -2)
3 = 49 + (n-1) (-2)
2(n-1) = 46
n - 1 = 23
n = 24
So there are 24 terms in the sequence.
The sum is:
S = 24/2 (49 + 3)
S = 12 (52)
S = 624
There are 624 bricks in the wall.
To calculate the size of super small or super large objects, like microscopic bacteria or the distance from Earth to the Sun
Answer:
Option (D)
Step-by-step explanation:
Zero of any function is defined by the x-value of the function when y = 0.
Let the equation of the line given in the graph is,
y = mx + b
where m = slope of the line
b = y-intercept of the line
Slope of a line passing through
and
is defined by the formula,
m = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
If the passes through (0, -3) and (-2, 0)
m = ![\frac{-3-0}{0+2}](https://tex.z-dn.net/?f=%5Cfrac%7B-3-0%7D%7B0%2B2%7D)
m = ![-\frac{3}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7D)
Fro the graph,
y-intercept 'b' = -3
Therefore, equation of the line is,
![y=-\frac{3}{2}x-3](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B2%7Dx-3)
For y = 0,
![0=-\frac{3}{2}x-3](https://tex.z-dn.net/?f=0%3D-%5Cfrac%7B3%7D%7B2%7Dx-3)
![\frac{3}{2}x=-3](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7Dx%3D-3)
x = -2
Therefore, option (D) will be the answer.
Answer:
Distance B = 1275 kilometers.
Step-by-step explanation:
Let the two distances and time be A and B respectively.
Given the following data;
Distance A = 17 kilometers.
Time A = 8 minutes.
Distance B =?
Time B = 60 minutes.
First of all, we would find the constant speed;
Speed = distance/time
Substituting into the equation, we have;
Speed = 17/8
Speed = 2.125 km/m
Now, to find the distance B;
Distance B = speed * time
Distance B = 2.125 * 60
<em>Distance B = 1275 km</em>
Answer: 7.48611111111111111........
Step-by-step explanation: