Using the dimensions of a reduced rectangle and one given measurement of an original rectangle:
- Set up a proportion using the corresponding parts
- Solve the proportion to find the missing measure
<h3>What is Reduction?</h3>
Reduction is a type of dilation that reduces the size of an original figure to form a new figure that is similar to the original. The corresponding lengths of both figures are therefore proportional.
Assuming the dimensions of the reduced rectangle are 10 cm by 4 cm, and the length of the original rectangle is given as 8 cm, to find the missing measure (x), do the following:
Set up a proportion using the corresponding parts
10/8 = 4/x
Solve the proportion using cross products to find x:
10x = (8)(4)
10x = 32
x = 32/10
x = 3.2 cm
The missing length is 3.2 cm.
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Answer:
x²+9x+18
Step-by-step explanation:
- (x+6)(x+3)
- x(x+3)+6(x+3)
- x²+3x+6x+18
- x²+9x+18
#1 5x + 4 = 19
-4 -4
______
5x = 15
________
5 5
X = 3
#2. 6m + 1 = -23
-1 -1
________
6 m = -24
__________
6 6
M = 4
#3. 5 + 4d = 37
-5 -5
____________
4d = 32
_______
4 4
D = 8
#4. -7y + 3 = -25
-3 -3
_______
-7y = -28
________
-7 -7
Y =4
#5. 15 + 1/2y = -3
-15 -15
_____________
1/2y = -18
________
1/2 1/2
Y = -36
#6. 7m + 36 = 85
-36 -36
_______
7m = 49
_________
7 7
M = 7
If the pool's being filled at a constant rate, then this rate is equal to the average rate, which would be
(2352 gal - 1372 gal) / (12 min - 7 min) = 980/5 gal/min = 196 gal/min
Step-by-step explanation:
when 2 shapes are similar, it means that all their angles are the same compared with each other.
and all distances (incl. side lengths) if one shape correlate to the corresponding distances in the other shadow by the same ratio or factor.
we have one side (30 m in A and 50 m in B), where we have both measures.
we see that the ratio to "go" from A to B is 30/50 = 3/5.
that means a distance in A is the same distance in B multiplied by 3/5.
and that factor is the same also for every other side.
therefore,
x = 15 m × 3/5 = 3 m × 3 = 9 m
y × 3/5 = 18 m
3y = 90 m
y = 30 m