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1 year ago

what number, when added to the numerator and to the denominator of $\frac{5}{8}$, results in a fraction whose value is 0.4?

1 answer:

3 0

The required number is -3 which when added to the numerator and to the denominator of 5/8 results in a fraction whose value is 0.4.

<h3>What is a fraction?</h3>

Fraction is the ratio of a particular part to the whole parts of an object. A fraction has a numerator and a denominator.

<h3>Calculation:</h3>

The given fraction is 5/8

Consider a number as 'x' which is added to both the numerator and the denominator of the given fraction.

So,

(5 + x)/(8 + x)

Since it is given that the result is 0.4 i.e., 4/10, we can write

(5 + x)/(8 + x) = 4/10

⇒ 10(5 + x) = 4(8 + x)

⇒ 50 + 10x = 32 + 4x

⇒ 10x - 4x = 32 - 50

⇒ 6x = -18

⇒ x = -18/6

∴ x = -3

Therefore, the required number is -3.

Check:

(5 + (-3))/(8 + (-3)) = (5 - 3)/(8 - 3) = 2/5 = 0.4

Learn more about fractions here:

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3 years ago

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3 years ago

Evaluate the expression when C=1/2 and D=1/12<br> 3(1/4+C²)+2D<br> Please hurry!

Mkey [24]

Answer is 1 1/12
3(1/4 + 1/2^2)+ (2x1/12)
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3 years ago

Read 2 more answers

Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

slega [8]

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

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Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

$(x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\$

The slope of line A is 7

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Now let's find the slope of line B.

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\$

-------------

Now onto line C.

$(x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\$

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Lastly we have line D.

$(x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\$

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Here's a summary of the slopes we found

$\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}$

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

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1 year ago