Answer:
For a trapezium of height H, parallel side 1 X, and parallel side 2 Y, the area is:
A = (1/2)*H*(X + Y)
with this we can complete the table.
a)
Here we know:
X = 7cm
Y = 11cm
H = 6cm
Then: A = (1/2)*6cm*(7cm + 11cm) = 54 cm^2
b)
Here we know:
X = 8 m
Y = 10 m
A = 126 m^2
Then:
126 m^2 = 0.5*H*(8m + 10m)
126 m^2 = H*9m
126 m^2/9m = H = 14m
Then the height of this trapezoid is 14m
c)
Here we know:
X = 5mm
H = 8mm
A = 72 mm^2
Then:
72 mm^2 = 0.5*8mm*(5mm + Y)
72 mm^2 = 4mm*(5mm + Y)
72mm^2/4mm = 5mm + Y
18 mm = 5mm + Y
18mm - 5mm = Y
13 mm = Y
Then the parallel side 2 is 13 mm long.
Answer:
Divisible by 3 is the answer
Step-by-step explanation:
First get everything to have the same base of 5
25^11 - 5^19
(5^2)^11 - 5^19
5^(2*11) - 5^19
5^22 - 5^19
Now factor out the GCF 5^19 to get
5^22 - 5^19
5^(19+3) - 5^(19+0)
5^19*5^3 - 5^19*5^0
5^19(5^3 - 5^0)
5^19(125 - 1)
5^19*(124)
At this point, we factor the 124 into 31*4 to end up with this full factorization: 5^19*31*4
Therefore, 25^11 - 5^19 is equivalent to 5^19*31*4
Since 31 is a factor of the original expression, this means the original expression is divisible by 31.
Answer:
The actual dimensions of the kitchen are 
by 
Step-by-step explanation:
step 1
Find the scale of the drawing
To find the scale , remember that is equal to the ratio of the corresponding dimension in the drawing divided by the corresponding actual dimension
so
step 2
To find the actual dimensions of the kitchen, divide the dimension in the drawing by the scale
so
Answer:
2/5
Step-by-step explanation:
Given Marcellus drank 1/4 gallon of the limeade and Marcy drank 1/8 gallon of the limeade
Given that only 5/8 portion of the pitcher contains limeade
Total amount drunk = amount drunk by Marcellus + amount drunk by Marcy
Total amount drunk = 
= 
The amount of Limeade remained = The amount initially - the amount drunk
The amount remained = 
= 
Fractional part = amount remained / amount initially = 
= 
Answer:
see below
Step-by-step explanation:
Let's solve your equation step-by-step.
3(
77
2
−
5
2
y)+7y=111
Step 1: Simplify both sides of the equation.
3(
77
2
−
5
2
y)+7y=111
(3)(
77
2
)+(3)(
−5
2
y)+7y=111(Distribute)
231
2
+
−15
2
y+7y=111
(
−15
2
y+7y)+(
231
2
)=111(Combine Like Terms)
−1
2
y+
231
2
=111
−1
2
y+
231
2
=111
Step 2: Subtract 231/2 from both sides.
−1
2
y+
231
2
−
231
2
=111−
231
2
−1
2
y=
−9
2
Step 3: Multiply both sides by 2/(-1).
(
2
−1
)*(
−1
2
y)=(
2
−1
)*(
−9
2
)
y=9
Answer:
y=9
