All categories

3 years ago

What number produces a rational number when add to 1/2

Mathematics

1 answer:

ANTONII [103]3 years ago

3 0

Step-by-step explanation:

1/4(0.25)

1/2 + 1/4 = 3/4 (0.75)

You might be interested in

Write an inequality to represent the graph.

Goshia [24]

Answer:

$y \leq -\frac{3}{4}x+2$

y is less than or equal to negative three fourths times x plus 2

Step-by-step explanation:

step 1

Find the equation of the solid line

we have the coordinates (0,2) and (4,-1)

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{-1-2}{4-0}$

$m=\frac{-3}{4}$

$m=-\frac{3}{4}$

<em>Find the equation of the line in slope intercept form</em>

$y=mx=b$

where

m is the slope

b is the y-intercept (value of y when the value of x is equal to zero)

we have

$m=-\frac{3}{4}$

$b=2$ ---> is given

substitute

$y=-\frac{3}{4}x+2$

Remember that

The shading area is below the line

therefore

The inequality is

$y \leq -\frac{3}{4}x+2$

y is less than or equal to negative three fourths times x plus 2

7 0

3 years ago

Please help easy stuff.....

Karo-lina-s [1.5K]

The answer is 27
Remember that the number inside the lines are always positive so in this case it will be
|-8|+19 which will equal to
8+19=27

7 0

3 years ago

Read 2 more answers

Below for question 10.

Monica [59]

Answer:

3/56

Step-by-step explanation:

There are 8 letters in the word DECEMBER. The probability of picking a C first is 1/8, since there's only one C. Since the letter is not replaced, there are now 7 letters to choose from, out which 3 of those are the letter E. Therefore, the probability of picking an E second is 3/7. The total probability then is equal to $\frac{1}{8}$ times $\frac{3}{7}$ , which is equal to $\frac{3}{56}$ .

Hope this helps! :D

3 0

3 years ago

Find the exact value of the expression.

Tresset [83]

$\sin(a-b)=\sin a \cos b-\cos a \sin b$ . If we let $a=\cos^{-1} \left(\frac{5}{6} \right)$ and $b=\tan^{-1} \left(\frac{1}{2} \right)$ , then the given expression is equal to:

$\sin \left(\cos^{-1} \left(\frac{5}{6}} \right) \right) \cos \left(\tan^{-1} \left(\frac{1}{2} \right) \right)-\cos\left(\cos^{-1} \left(\frac{5}{6} \right) \right) \sin \left( \tan^{-1} \left(\frac{1}{2} \right) \right)$

Using the Pythagorean identities $\sin^{2} x+\cos^{2} x=1$ and $\tan^{2} x+1=\sec^{2} x$ ,

$1) \sin^{2} \left(\cos^{-1} \left(\frac{5}{6} \right) \right)+\cos^{2} \left(\cos^{-1} \left(\frac{5}{6} \right) \right)=1\\\sin^{2} \left(\cos^{-1} \left(\frac{5}{6} \right) \right)+\frac{25}{36}=1\\\sin^{2} \left(\cos^{-1} \left(\frac{5}{6} \right) \right)=\frac{11}{36}\sin \left(\cos^{-1} \left(\frac{5}{6} \right) \right)=\frac{\sqrt{11}}{6}$

$2) \tan^{2} \left(\tan^{-1} \left(\frac{1}{2} \right) \right)+1=\sec^{2} \left(\tan^{-1} \left(\frac{1}{2} \right) \right)\\\frac{1}{4}+1=\sec^{2} \left(\tan^{-1} \left(\frac{1}{2} \right) \right)\\\frac{5}{4}=\sec^{2} \left(\tan^{-1} \left(\frac{1}{2} \right) \right)\\\sec \left(\tan^{-1} \left(\frac{1}{2} \right) \right)=\frac{\sqrt{5}}{2}\\\implies \cos \left(\tan^{-1} \left(\frac{1}{2} \right) \right)=\frac{2}{\sqrt{5}}=\frac{2\sqrt{5}}{5}$

$\cos^{2} \left(\tan^{-1} \left(\frac{1}{2} \right) \right)+\sin^{2} \left(\tan^{-1} \left(\frac{1}{2} \right) \right)=1\\\frac{4}{5}+\sin^{2} \left(\tan^{-1} \left(\frac{1}{2} \right) \right)=1\\\sin^{2} \left(\tan^{-1} \left(\frac{1}{2} \right) \right)=\frac{1}{5}\\\left(\tan^{-1} \left(\frac{1}{2} \right) \right)=\frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5}$

This means we can write the original expression as:

$\left(\frac{\sqrt{11}}{6} \right) \left(\frac{2\sqrt{5}}{5} \right)-\left(\frac{5}{6} \right) \left(\frac{\sqrt{5}}{5} \right)\\=\frac{2\sqrt{11}\sqrt{5}}{30}-\frac{5\sqrt{5}}{30}\\=\boxed{\frac{\sqrt{5}(2\sqrt{11}-5)}{30}}$