Answer:
We have the measures:
1023 cm
2.3 m
8.72m
6430 mm
1200 mm
6.4 cm
2.5m
0.06km
Now let's write all those measures in the same unit, let's use meters.
We know that:
1cm = 0.01m
1mm = 0.001m
1 km = 1000m
Then, we can rewrie the measures as:
1023 cm = 1023*0.01 m = 10.23 m
2.3 m
8.72m
6430 mm = 6430*0.001 m = 6.430 m
1200mm = 1200*0.001 m = 1.2 m
6.4 cm = 6.4*0.01m = 0.064 m
2.5m
0.06km = 0.06*1000km = 60m
Then the order, from smallest to largest is:
6.4 cm
1200mm
2.3 m
2.5m
6430 mm
8.72m
1023 cm
0.06km
Answer:
A, B, D and F.
Step-by-step explanation:
Rin spends $20 every week on drum lessons.
If:
d = total amount of dollars Rin spends
w = number of weeks
Then: d=20w
w is the independent variable while d is the dependent variable. A change in w will lead to a change in d. Therefore:
(A)The independent variable causes a change in the dependent variable.
(B)The equation is d = 20w.
From the equation: d=20w
When w=1, d=$20
When w=2, d=$40
When w=3, d=$60
When w=4, d=$80
This tallys with the values in Option F.
Therefore:
(D)As the number of weeks increases, the total dollars Rin spends increases.
The correct options are: A, B, D and F.
Answer:
AH = 
Step-by-step explanation:
The opposite sides of a rectangle are congruent , so
GH = RA = 7
Using Pythagoras' identity in right Δ GHA
AH² + GH² = GA²
AH² + 7² = 10²
AH² + 49 = 100 ( subtract 49 from both sides )
AH² = 51 ( take the square root of both sides )
AH = ≈ 7.14 ( to 2 dec. places )
x
=
−
8
,
−
2
Explanation:
Given:
x
2
+
10
x
+
16
=
0
To complete the square put the two
x
terms on the left and the constant on the right of the equation:
x
2
+
10
x
=
−
16
Complete the square by multiplying the
x
-term by
1
2
:
1
2
⋅
10
=
5
and adding the square of this number to the right side of the equation:
5
2
=
25
(
x
+
5
)
2
=
−
16
+
25
UNDERSTANDING CHECK:
(
x
+
5
)
2
=
x
2
+
10
x
+
25
.
The
+
25
was not in the original equation. If we add
+
25
to one side of the equation, we must add the same amount to the other side of the equation to keep it balanced.
(
x
+
5
)
2
=
9
To solve, square root both sides of the equation:
√
(
x
+
5
)
2
=
±
√
9
x
+
5
=
±
3
x
=
−
5
±
3
x
=
−
5
+
3
=
−
2
,
x
=
−
5
−
3
=
−
8
x
=
−
8
,
−
2
Find the greatest common factor (GCF) of 9 and 12 using factor trees. The GCF is 3
Divide each term (9 and 12) over 3
9/3 = 3
12/3 = 4
So 9/12 reduces to 3/4
In other words, 9/12 = 3/4
--------------------------------------
Now focusing on 3/4, we can multiply top and bottom by the same value. Let's say we multiply top and bottom by 5
3*5 = 15
4*5 = 20
So 3/4 = 15/20
--------------------------------------
So two ratios equivalent to 9/12 are 3/4 and 15/20. There are infinitely other ratios that are equivalent.
In short, the answers are 3/4 and 15/20.
