Answer:
Step-by-step explanation:
To get rid of the decimal point in the numerator, we count the numbers after the decimal in 6.584, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.
Therefore, in this case we multiply the numerator and denominator by 1000 to get the following fraction: 6584 / 1000
Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.
The GCD of 6584 and 1000 is 8. When we divide the numerator and denominator by 8, we get the following: 823 / 125
Therefore, 6.584 as a fraction is as follows: 823 / 125
Answer:
A: geometric; 4 times
B: arithmetic: 4 more
Step-by-step explanation:
An arithmetic model is a linear model, where the rate of change is constant. Growth or decay is by a constant amount from one interval to the next.
A geometric model is an exponential model, in which the rate of change is proportional to the amount. Growth or decay is by a constant factor from one interval to the next.
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<h3>A)</h3>
The equation for the sequence is given in "explicit" form:
The exponent can be split so this can be rewritten as ...
If this were written in recursive form, it would look like ...
The fact that terms are related by a constant factor tells you the model is geometric. The factor tells you each hour the population is 4 times what it was in the previous hour.
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<h3>B)</h3>
The given equation is in "recursive" form. It tells you each term is 4 more than the previous one. This constant difference between terms means the model is arithmetic.
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<em>Additional comment</em>
In general, words like "more" or "increase" refer to addition, and the words "times" or "factor" refer to multiplication.
Solve for x:5 x + 3 (x + 4) = -20
3 (x + 4) = 3 x + 12:3 x + 12 + 5 x = -20
Grouping like terms, 5 x + 3 x + 12 = (5 x + 3 x) + 12:(5 x + 3 x) + 12 = -20
5 x + 3 x = 8 x:8 x + 12 = -20
Subtract 12 from both sides:8 x + (12 - 12) = -12 - 20
12 - 12 = 0:8 x = -20 - 12
-20 - 12 = -32:8 x = -32
Divide both sides of 8 x = -32 by 8:(8 x)/8 = (-32)/8
8/8 = 1:x = (-32)/8
The gcd of -32 and 8 is 8, so (-32)/8 = (8 (-4))/(8×1) = 8/8×-4 = -4:Answer: x = -4
First use distributive property on -3(t+5), which would be -3t minus -15.
Then, add all like terms: -3t-15+4t+2 ---> -3t+4t+2-15 --> t-13.
t-13=8, add 13 to both sides. This cancels the -13 and makes 8 to 21.
Therefore, t=21
