Answer:
528 cm²
Step-by-step explanation:
The surface area of this prism comprises:
- 2 congruent triangles (the bases of the prism)
- 2 congruent rectangles (rectangle 1 and 2) - since the triangle has 2 sides of equal length
- 1 rectangle (rectangle 3)
Area of a triangle = 1/2 × base × height
= 1/2 × 16 × 6
= 48 cm²
Area of rectangle 1 / 2 = width × length
= 10 × 12
= 120 cm²
Area of rectangle 3 = width × length
= 16 × 12
= 192 cm²
Total Surface Area = 2 triangles + 2 rectangles + rectangle 3
= (2 × 48) + (2 × 120) + 192
= 96 + 240 + 192
= 528 cm²
Answer:
w=-5
Step-by-step explanation:
3w=-18+3
3w=-15
w=-5
Answer:
Part 1: m = -7
Part 2: y = -7x -11
Part 3: 7x + y = -11
Step-by-step explanation:
Part 1
Select 2 points, in this case (-2, 3) and (-1, -4) and then use the slope formula
m = (y2 - y1) / (x2 - x1)
m = (-4 -3) / (-1 - -2) =
m = -7/1
m = -7
Part 2
Use the point-slope form equation to find the slope-intercept form
y - y1 = m(x - x1)
y - 3 = -7(x - -2)
y = -7(x +2) +3
y = -7x -14 +3
y = -7x -11
Part 3
Move the x and y to the same side of the equation
y = -7x -11
7x + y = -11
Answer:
7/36
Step-by-step explanation:
1 die has 6 faces
When two dice are rolled, the total number of outcomes
= 6 × 6 = 36
The Probability of having(5) =
(1 & 4), (2 & 3) , ( 3 & 2), (4 & 1)
= 4
The probability of having (10) =
(5 & 5), (4 & 6) , ( 6 & 4)
= 3
The probability that the score on the dice is either 5 or 10.
P(5) + P(10)
= 4/36 + 3/36
= 7/36
"The sum of two numbers is 20" can be translated mathematically into the equation:
x + y = 20.
"... and their difference is 10" can be translated mathematically as:
x - y = 10
We can now find the two unknown numbers, x and y, because we now have a system of two equations in two unknowns, x and y. We'll use the Addition-Subtraction Method, also know as the Elimination Method, to solve this system of equations for x and y by first eliminating one of the variables, y, by adding the second equation to the first equation to get a third equation in just one unknown, x, as follows:
Adding the two equations will eliminate the variable y:
x + y = 20
x - y = 10
-----------
2x + 0 = 30
2x = 30
(2x)/2 = 30/2
(2/2)x = 15
(1)x = 15
x = 15
Now, substitute x = 15 back into one of the two original equations. Let's use the equation showing the sum of x and y as follows (Note: We could have used the other equation instead):
x + y = 20
15 + y = 20
15 - 15 + y = 20 - 15
0 + y = 5
y = 5
CHECK:
In order for x = 15 and y = 5 to be the solution to our original system of two linear equations in two unknowns, x and y, this pair of numbers must satisfy BOTH equations as follows:
x + y = 20 x - y = 10
15 + 5 = 20 15 - 5 = 10
20 = 20 10 = 10
Therefore, x = 15 and y = 5 is indeed the solution to our original system of two linear equations in two unknowns, x and y, and the product of the two numbers x = 15 and y = 5 is:
xy = 15(5)
xy = 75
