Answer:
Percentage change from 125cm to 87.5cm is 30% decrease.
Step-by-step explanation:
Percentage change of a to b is given by
Here we have a = 125 and b = 87.5
Substituting
Percentage change from 125cm to 87.5cm is -30%.
That is 30 decrease.
Percentage change from 125cm to 87.5cm is 30% decrease.
Place the figures in order from least surface area to greatest surface area.
Answer:
Figure 1's surface area: 550
Figure 2's surface area: 530
Figure 3's surface area: 790
So, the order of the figures' surface areas is: Figure 2 < Figure 1 < Figure 3.
Step-by-step explanation:
Bearing in mind that the surface area of a 3D object is the total area of its surface (that is the sum of the areas of its faces), we can count the number of distinct shapes in each figure, calculate their areas and add them up. Be careful not to add the faces that are "inside".
Figure 1
Its surface area consists of 13 squares of 5x5and 3 rectangles of 15x5. So, its surface area is (13x25 + 3x75)
Figure 2
Its surface area consists of 6 squares of 5x5, 3 rectangles of 17x5, 1 rectangle of 13x5 and 2 triangles of base 12 feet and height 5 feet. So, its surface area is (17x5x3+6x5x5+13x5+12x5x2:2)
Figure 3
Its surface area consists of 2 rectangles of 12.5x5, 1 rectangle of 11x5, 2 triangles of base 12 feet and height 5 feet, 1 rectangle of 11x13, 2 rectangles of 12.5x11 and 1 rectangle of 12x11.
So, its surface area is (2x12.5x5+11x5+2x12x5:2+11x13+2x12.5x11+12x11)
Answer:
Least surface area to greatest surface area:
Blue - Red - Green
Step-by-step explanation:
All the surfaces of the shapes are rectangles, then their surface is computed as:
Surface = Length*Width
Blue figure
Area of the top:
5*5 + 5*5 + 5*5 + 5*5 + 5*5 = 125 ft^2
Area of the sides:
2*(5*10) = 100 ft^2
Area of the bottom:
10*5 = 50 ft^2
Area of the front and the back
2*(5*5 + 15*5) = 200 ft^2
Total: 125 + 100 + 50 + 200 = 475 ft^2
Red figure
Area of the top:
5*5 + 13*5 = 90 ft^2
Area of the left side:
5*10 = 50 ft^2
Area of the right side:
5*5 = 25 ft^2
Area of the bottom:
17*5 = 85 ft^2
Area of the front and the back:
2*(17*5 + 12*5/2 + 5*5) = 280 ft^2
Total: 90 + 50 + 25 + 85 + 280 = 530 ft^2
Green figure
Area of the top:
12.5*11 + 13*11 = 280.5 ft^2
Area of the left side:
11*5 = 55 ft^2
Area of the bottom:
(12.5+12)*11 = 269.5 ft^2
Area of the front and the back:
2*(12.5*5 + 12*5/2) = 185 ft^2
Total: 280.5 + 55 + 269.5 + 185 = 790 ft^2
A.They are perpendicular because their slopes are equal.
B.They are perpendicular because their slopes are negative reciprocals.
C.They are not perpendicular because their slopes are equal.
D.They are not perpendicular because their slopes are not negative reciprocals.
we know that
If two lines are perpendicular then, the product of their slopes is equal to minus one, that means that their slopes are negative reciprocals
so
Step
Find the slope of the line HJ
we know that
the slope between two points is equal to
substitute the values
Step
Find the slope of the line HJ
we know that
the slope between two points is equal to
substitute the values
Step
Verify if the two lines are perpendicular
Find the product m1 by m2
so
--------> the slopes are not negative reciprocals
therefore
the answer is the option
D.They are not perpendicular because their slopes are not negative reciprocals
Answer:
The sum of the first twenty-seven terms is 1,188
Step-by-step explanation:
we know that
The formula of the sum in arithmetic sequence is equal to
where
n is the number of terms
a1 is the first term
d is the common difference (constant)
step 1
Find the common difference d
we have
n=7
a1=-8
S=28
substitute and solve for d
step 2
Find the sum of the first twenty-seven terms
we have
n=27
a1=-8
d=4
substitute
tower main deck adult $25
tower main deck child $19
top deck all $32