Answer:
x = 11/7 y = -1/7
Step-by-step explanation:
2x + y = 3
2x + y - 2y = 3 - 2y
y = 3 - 2x
x - 3(3 - 2x) = 2
x - 9 + 6x = 2
x - 9 + 6x + 9 = 2 + 9
x + 6x = 11
7x = 11
7x / 7 = 11/7
x = 11/7
2(11/7) + y = 3
22/7 + y = 3
22/7 + y - 22/7 = 3 - 22/7
y = -1/7
The calculation is:
I see you have doubts, so I will explain each step.
Step 1: simpliy 576 / 64. In this case when you divide 576 by 64 you get 9 that is a whole number, so that is its simplest form.
Step 2: Calculate the square root of 9, which is 3.
If you use a simple calculator you will obtain that, but the square root of 9 is a calculation that you should know by yourself.
Remember that the square root a number N is the number that multiplied by itself results in the number N. For example the squere root of 4 is 2, because 2 times 2 is 4. So, the square root of 9 is 3 because 3 times 3 is 9.
It will be very helpful for you to learn the 12 first squares because with that you will be able to tell the square roots of the most elemental numbers:
1^2 = 1 => √1 = 1
2^2 = 4 => √4 = 2
3^2 = 9 => √9 = 3
4^2 = 16 => √16 = 4
5^2 = 25 => 25 = 5
6^2 = 36 => √36 = 6
7^2 = 49 => √49 = 7
8^2 = 64 => √64 = 8
9^2 = 81 => √81 = 9
10^2 = 100 => √100 = 10
11^2 = 121 => √121 = 11
12^2 = 144 => √144 = 12
Answer:
the ratio of the distance in inches travelled by the tip of the hour hand to the distance in inches travelled by the tip of the minute hand is <em>0.125</em>.
Step-by-step explanation:
The given information is:
- length of the hour hand, l = 6 inches
- length of the minute hand, b = 8 inches
Therefore, since the tip of the minute moves from 12 to 3, it moved a distance of:
s₁ = r θ
s₁ = (8)(π/2)
s₁ = 4π inches
The hour hand moves 30 degrees / 60 = 1/2 degree in a minute.
Therefore, in 30 minutes the hour hand moves a distance of:
s₂ = r θ
s₂ = 6(30×1/2×π/180)
s₂ = π/2 inches
Therefore, the ratio of the distance in inches travelled by the tip of the hour hand to the distance in inches travelled by the tip of the minute hand is:
s₂ / s₁ = (π/2) / 4π
<em>s₂ / s₁ = 0.125</em>
<h3>
Answer: B. Yes, d = 3</h3>
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Explanation:
d = common difference, which is what we add on each time to get the next term
In this case, d = 3 means we add 3 each time to generate each new term
- -11+3 = -8
- -8+3 = -5
- -5+3 = -2
- -2+3 = 1
This pattern continues on forever.
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Another way to see that d = 3 is to notice this is the difference between any two adjacent terms.
- d = term2 - term1 = -8 - (-11) = -8 + 11 = 3
- d = term3 - term2 = -5 - (-8) = -5 + 8 = 3
- d = term4 - term3 = -2 - (-5) = -2+5 = 3
- d = term5 - term4 = 1 - (-2) = 1 + 2 = 3
Each gap is 3 units wide, which helps us see we have an arithmetic sequence.
A sequence like {-11,-8,-5,-2,2} is not arithmetic because the gap between the terms of -11,-8,-5,-2 is 3, but the gap from -2 to 2 is not 3. So the gap must stay the same the entire time to get an arithmetic sequence.