Answer:
a) TO = OP = 13
b) Height = 12
Step-by-step explanation:
a) Isosceles triangle TOP with base TP = 10 cm, side TO = OP = x cm.
Perimeter of triangle TOP = 36 cm
=> TO + OP + TP = 36
=> x + x + 10 = 36
=> 2x = 26
=> x = 13
=> TO = OP = 13 cm.
b) Apply Pythagorean theorem:
height^2 + (base/2)^2 = side^2 (height^2 + (TP/2)^2 = TO^2)
or
height^2 + (10/2)^2 = 13^2
or
height^2 + 25 = 169
or
height^2 = 144
or
height = 12
Hope this helps!
Answer:
the first one
Step-by-step explanation:
Answer:
14,850
Step-by-step explanation:
You need the sum of
3 + 6 + 9 + 12 + ... + 294 + 297
Factor out a 3 from the sum
3 + 6 + 9 + 12 + ... + 294 + 297 = 3(1 + 2 + 3 + 4 + ... + 98 + 99)
You need to add all integers from 1 to 99 and multiply by 3.
The sum of all consecutive integers from 1 to n is:
[n(n + 1)]/2
The sum of all consecutive integers from 1 to 99 is
[99(99 + 1)]/2
The sum you need is 3 * [99(99 + 1)]/2
3 + 6 + 9 + 12 + ... + 294 + 297 =
= 3 * [99(99 + 1)]/2
= 3 * [99(100)]/2
= 3 * 9900/2
= 14,850
Answer:
41/45
Step by Step Explanation:
Add: 8/
10
+ 1/
9
= 8 · 9/
10 · 9
+ 1 · 10/
9 · 10
= 72/
90
+ 10/
90
= 72 + 10/
90
= 82/
90
= 2 · 41/
2 · 45
= 41/
45
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 9) = 90. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 9 = 90. In the following intermediate step, cancel by a common factor of 2 gives 41/
45
.
In other words - eight tenths plus one ninth = forty-one forty-fifths.
X intercept: y = 0
y= -3/4x -4
0 = -3/4 x - 4
4= -3/4 x
4 • -4/3 = x
-5.3 = x
y intercept: x = 0
y = -3/4 x -4
y = -3/4 (0) -4
y = -4
the points are (-5.3, 0) and (0, -4)
