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Zarrin [17]
3 years ago
15

Pls help me with this math problem​

Mathematics
1 answer:
DENIUS [597]3 years ago
4 0

Answer:

The four rational numbers between -\frac{1}{2} and \frac{1}{2} can be:

  • -\frac{1}{3}
  • -\frac{1}{4}
  • \frac{1}{5}
  • \frac{1}{7}

Step-by-step explanation:

The definition of rational numbers is usually a number of the type a/b where b is different from zero, therefore, to choose the numbers that are between -1/2 (= -0.5) and 1/2 (= 0.5) <u><em>it is enough with choose fractional numbers whose dividend is 1 and its divisor is any number greater than 2, either negative or positive,</em></u> in the answer we choose options such as 1/7 or -1/3, but following the guide I give you, you could choose numbers like 1/16, -1/9 or 1/40 if you wish, always respecting the guidelines given for the dividend and the divisor.

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Answer:

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Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3).
Romashka-Z-Leto [24]

The equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3) in slope intercept form is y = \frac{-1}{5}x + \frac{16}{5}

<h3><u>Solution:</u></h3>

Given that a line is parallel to line x + 5y = 10 and passes through the point (1, 3)

We have to find the equation of line

<em><u>The slope intercept form is given as:</u></em>

y = mx + c  -------- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

<em><u>Let us first find the slope of line</u></em>

Given equation of line is x + 5y = 10

5y = -x + 10\\\\y = \frac{-1}{5}x + \frac{10}{5}\\\\y = \frac{-1}{5}x + 2

On comparing the above equation of line with slope intercept form,

m = \frac{-1}{5}

We know that slopes of parallel lines are equal

So the slope of line parallel to given line is also m = \frac{-1}{5}

<em><u>Let us find the equation of line with slope m = -1/5 and passes through the point (1, 3)</u></em>

\text {substitute } m=\frac{-1}{5} \text { and }(x, y)=(1,3) \text { in eqn } 1

3 = \frac{-1}{5} \times 1 + c\\\\15 = -1 + 5c\\\\16 = 5c\\\\c = \frac{16}{5}

<em><u>Thus the required equation is:</u></em>

\text {substitute } m=\frac{-1}{5} \text { and } c=\frac{16}{5} \text { in eqn } 1

y = \frac{-1}{5}x + \frac{16}{5}

Thus the required equation of line is found

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The true statement for f(x) = 2(3)^x is the y-intercept is (0, 2).

<h3>How to determine the true statement?</h3>

The function is given as:

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Set x = 0 to determine the y-intercept

f(0) = 2(3)^0

Evaluate

f(0) = 2

This means that the y-intercept of f(x) = 2(3)^x is (0,2)

Read more about y-intercept at:

brainly.com/question/14180189

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