Given:
side lengths of right triangles = 12 cm ; 16 cm ; 20 cm
lateral area = 192 cm²
lateral area of a triangular prism = perimeter * height
192 cm² = (12 cm + 16 cm + 20 cm) * height
192 cm² = 48 cm * height
192 cm² / 48 cm = height
4 cm = height
The height of the pedestal in the shape of a triangular prism is 4 cm.
Answer:
Line d : y = -3x - 3
Line e : y = -3x - 2
Line f : y= -3x + 2
Step-by-step explanation:
Given that,
The slope of each line is -3.
Now,
We know that,
Equation of line is represented by y = mx + c
where m is the slope and c is the y-intercept.
Now,
Given that,
Line d goes through (0, - 3) and (- 1, 0).
So,
y-intercept of Line d is -3
∴ we get
Equation of Line d is : y = -3x -3
Now,
Given that,
Line e goes through (-1, 2) and (0, -2).
So,
y-intercept of Line e is -2
∴ we get
Equation of Line e is : y = -3x - 2
Now,
Given that,
Line f goes through (0, 2) and (1, -1).
So,
y-intercept of Line e is 2
∴ we get
Equation of Line f is : y = -3x + 2
Ok so you would plug in 18 for the x so it would be 6(18)-12 and then 6x18 is 108 and 108-12=96 so your answer is 96
Answer:
a. closed under addition and multiplication
b. not closed under addition but closed under multiplication.
c. not closed under addition and multiplication
d. closed under addition and multiplication
e. not closed under addition but closed under multiplication
Step-by-step explanation:
a.
Let A be a set of all integers divisible by 5.
Let
∈A such that 
Find 

So,
is divisible by 5.

So,
is divisible by 5.
Therefore, A is closed under addition and multiplication.
b.
Let A = { 2n +1 | n ∈ Z}
Let
∈A such that
where m, n ∈ Z.
Find 

So,
∉ A

So,
∈ A
Therefore, A is not closed under addition but A is closed under multiplication.
c.

Let
but
∉A
Also,
∉A
Therefore, A is not closed under addition and multiplication.
d.
Let A = { 17n: n∈Z}
Let
∈ A such that 
Find x + y and xy


So,
∈ A
Therefore, A is closed under addition and multiplication.
e.
Let A be the set of nonzero real numbers.
Let
∈ A such that 
Find x + y

So,
∈ A
Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.
Therefore, A is not closed under addition but A is closed under multiplication.
Answer:
6x + 35
Step-by-step explanation:
First Distribute
8x + 3x + 15 -5x +20
Then collect like terms
6x + 35
to solve you would need the value of x to plug it!