Answer:
See below.
Step-by-step explanation:
a.
The first figure has 1 square. The second figure has a column of 2 squares added to the left. The third figure has a column of 3 squares added to the left. Each new figure has a column of squares added to the left containing the same number of squares as the number of the figure.
b.
Figure 10 has 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 squares.
c.
The formula for adding n positive integers starting at 1 is:
1 + 2 + 3 + ... + n = n(n + 1)/2
For figure 55, n = 55.
n(n + 1)/2 = 55(56)/2 = 1540
d.
Let's use the formula set equal to 190 and solve for n. If n is an integer, then we can.
n(n + 1)/2 = 190
n(n + 1) = 380
We know that 380 = 19 * 20, so n = 19.
Answer: yes
e.
Use the formula above,
S = n(n + 1)/2, where S is the sum.
f.
n(n + 1) = 1478
38 * 39 = 1482
37 * 38 = 1406
Answer:
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Step-by-step explanation:
Answer:
B) Rational, not an integer.
Step-by-step explanation:
The number is a decimal continuing forever; it is predictable. This means that it is Rational. If the number was not repeating then it would be irrational.
The number is not an integer because it is not a whole number; it is a decimal.
A triangle always adds up to 180 degrees:
Therefore, 48 + 6x + 9x-3 = 180
Solve for x:
180 - 45 = 15x
135 = 15x
x = 9 degrees
They are all multiples of 12. 12x1, 12x2, 12x6, 12x24.
