Answer:
x = 18 , y = 45
Step-by-step explanation:
The angle vertically opposite 4x - 7 is congruent to it and forms a same- side interior angle with 6x + 7.
Same- side interior angles sum to 180° , then
6x + 7 + 4x - 7 = 180 , that is
10x = 180 ( divide both sides by 10 )
x = 18
Then
6x + 7 = 6(18) + 7 = 108 + 7 = 115
6x + 7 and 3y - 20 are vertically opposite angles and are congruent , so
3y - 20 = 115 ( add 20 to both sides )
3y = 135 ( divide both sides by 3 )
y = 45
Answer:
-17
Step-by-step explanation:
Answer:
x ≈ 16.52
Step-by-step explanation:
Use the tangent ratio in the right triangle to find x
tan36° = 
= 
Multiply both sides by x
x × tan36° = 12 ( divide both sides by tan36° )
x = 12 / tan36° ≈ 16.52 ( to 2 dec. places )
First, we calculate the area of one paver. This is:
12 x 12 = 144 square feet
Now, the number of pavers required may be determined by dividing the total surface area to be covered by the surface area of one paver, as:
number of pavers = 600 / 144
Number of pavers = 4.2
Because 0.2 pavers can not be obtained, 5 pavers are needed to completely cover 600 square feet.
Answer:
19404
Step-by-step explanation:
sum of arithmetic series is
Sn = n/2 (2a + (n-1)d)
or
Sn = n/2 (a + an)
a = 1st unit
an = last unit
d = difference
8-3 or 13-8 so d = 5
then first step is to find the value of n
an = a + (n-1)d
438 = 3 + (n-1)5
438 - 3 = 5n - 5
435 = 5n - 5
435 + 5 = 5n
440 = 5n
n = 440/5
n = 88
then we can find the sum
Sn = 88/2 (3 + 438)
S88 = 19404
