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3 years ago

3 1/10- 2 5/6 in simplest form

Mathematics

1 answer:

Allushta [10]3 years ago

8 0

Answer:

$\frac{4}{15}$

Step-by-step explanation:

$3 \frac{1}{10} - 2 \ \frac{5}{6}$

Convert the above mixed numbers to improper fractions through this simple approach: 3 × 10 + 1 /10 = 31/10. Similarly, 2 × 6 + 5 /6 = 17/6

$\frac{31}{10} - \frac{17}{6}$

Take the LCM of the denominators and simplify. LCM = 60. Thus, 60/10 = 6; 6 × 31 = 186. Also, 60/6 =10; 10×17 =170 all divide by 60:

$= \frac{186 - 170}{60}$

Common factors between the numerator and denominator is 4, therefore 16/4 = 4 and 60/4 = 15.

$= \frac{16}{60} = \frac{4}{15}$

Therefore the answer is 4/15 in simplest form.

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Is anyone able to figure this out, I can't do this

katrin [286]

Answer:

C. √2 - 1

Step-by-step explanation:

If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)

Let r = the radius of the small circle

Using Pythagoras' Theorem $a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

to find the diagonal of the square:

$\implies r^2 + r^2 = c^2$

$\implies 2r^2 = c^2$

$\implies c=\sqrt{2r^2}$

So the diagonal of the square = $\sqrt{2r^2}$

We are told that the radius of the large circle is 1:

⇒ Diagonal of square + r = 1

$\implies \sqrt{2r^2}+r=1$

$\implies \sqrt{2r^2}=1-r$

$\implies 2r^2=(1-r)^2$

$\implies 2r^2=1-2r+r^2$

$\implies r^2+2r-1=0$

Using the quadratic formula to calculate r:

$\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}$

$\implies r=\dfrac{-2\pm\sqrt{8}}{2}$

$\implies r=-1\pm\sqrt{2}$

As distance is positive, $r=-1+\sqrt{2}=\sqrt{2}-1$ only

5 0

2 years ago

Read 2 more answers

A nurse sees 25 patients in 5 hours. At this rate, approximately how many patients will the nurse be able to see in an 8-hour pe

AleksandrR [38]

Answer:

40 patients

Step-by-step explanation:

Divide 25 by 5 to get 5 patients per hour (the rate).

Since there are 8 hours, multiply 8 by 5 to get 40 patients in 8 hours.

3 0

2 years ago

What is the average rate of change of the function over the interval x = 0 to x = 8? f(x)=2x−1/3x+5 Enter your answer, as a frac

max2010maxim [7]

Answer:

15 2/3, or 47/3

Step-by-step explanation:

I'm going to assume, correctly or not, that you actually meant f(x) = 2x^2 - (1/3)x + 5. Double check on this right now, please.

If I'm right, then evaluate f(x) at x = 0 and x = 8:

f(0) = 5

and

f(8) = 2(8)^2 - (1/3)(8) + 5 = 128 - 8/3 + 5 = 133 - (2 2/3), or: 130 1/3

Then the average rate of change of f(x) = 2x^2 - (1/3)x + 5 over the interval [0,8] is:

130 1/3 - 5 125 1/3

a. r. c. = ------------------- = ---------------- = 15 2/3, or 47/3

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3 0

3 years ago

2 Points

masya89 [10]

The answer is 120. Because inscribed angle is Half of the arc measure. Double 60 and we get 120.

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3 years ago

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the slope of a line passing through h (-2, 5) is -3/4. Which ordered pair represents a point on this line?

rosijanka [135]

Answer:

Step-by-step explanation:

Calculate the slope of the given points with the point (- 2, 5 )

If the slope is - $\frac{3}{4}$ then the point is on the line

Calculate slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 1)

m = $\frac{-1-5}{6+2}$ = $\frac{-6}{8}$ = - $\frac{3}{4}$ ← point (6, - 1) is on the line

Repeat with (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (2, 8)

m = $\frac{8-5}{2+2}$ = $\frac{3}{4}$ ← point (2, 8) is not on the line

Repeat with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (- 5, 1)

m = $\frac{1-5}{-5+2}$ = $\frac{-4}{-3}$ = $\frac{4}{3}$ ← point (- 5, 1) is not on the line

Repeat with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (1, 1)

m = $\frac{1-5}{1+2}$ = - $\frac{4}{3}$ ← point (1, 1) is not on the line

Thus the point on the line is (6, - 1 ) → A

4 0

2 years ago

3 1/10- 2 5/6 in simplest form​

3 1/10- 2 5/6 in simplest form