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4 years ago

What is two thirds of eight

1 answer:

8 0

5 + 0.33333...

<span>If you don't immediately recognize 0.33333.... as 1/3 (a very common fraction you should memorize), you can do the following. </span>

<span>x = 0.33333... </span>

<span>Multiply that by 10 to shift everything 1 place to the left: </span>
<span>10x = 3.33333... </span>

<span>Now subtract: </span>
<span>10x - x = 3.33333... - 0.33333... </span>
<span>9x = 3 </span>
<span>x = 3/9 </span>
<span>x = 1/3 </span>

<span>Answer: </span>
<span>5 1/3 </span>

<span>P.S. Here's a shortcut way to turn a repeating decimal into a fraction. </span>

<span>1) Take the repeated part and put it over an equivalent number of nines. </span>

<span>Example: </span>
<span>0.57575757... = 57/99 </span>

<span>At that point, see if you can reduce the fraction: </span>
<span>= 19/33 </span>

<span>Another example: </span>
<span>0.123123123... = 123/999 </span>
<span>= 41/333 </span>

<span>So in your example: </span>
<span>5.33333... = 5 + 0.33333... </span>
<span>= 5 + 3/9 </span>
<span>= 5 1/3</span>

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For circle H, JN = x, NK = 2, LN = 3, and NM = 6. Solve for x.

Advocard [28]

Answer:

The value of x is 9 ⇒ C

Step-by-step explanation:

In a circle, if two chords intersected at a point inside it there are four segments created, two in each cord, the products of the lengths of the line segments on each chord are equal.

<em>Let us use this rule to solve the question</em>

In circle H

∵ Jk and LM are chords intersected at point N inside the circle

∴ The created segments are JN, Nk, and LN, NM

→ By using the rule above

∴ JN × NK = LN × NM

∵ JN = x and NK = 2

∵ LN = 3 and NM = 6

→ Substitute these values in the equation above

∴ x × 2 = 3 × 6

∴ 2x = 18

→ Divide both sides by 2 to find x

∴ $\frac{2x}{2}=\frac{18}{2}$

∴ x = 9

∴ The value of x is 9

8 0

3 years ago

What is the measure of each angle

kolbaska11 [484]

Your answer is X=22
Step-by-step
5X - 31= 79
5x= 79+31
X=110/5
So x=22 same as on

5 0

3 years ago

The population of wolves in a sanctuary has been growing by about 20 wolves a year. In 2012, there were 415 wolves in the sanctu

Masteriza [31]

Answer:

A: P = 20n +415

B: P = 20t + 375

C: Both equations agree, and in 2018 there will be about 535 wolves

D: The advantage of defining the input variable is that it helps simplify the calculation and makes it more intuitive.

Step-by-step explanation:

P = <u>Number of wolves</u>

n = <u>number of years since 2012</u>

<em>we know </em><em>in 2012</em><em> there were </em><u><em>415 wolves in the sanctuary</em></u><em>, and that the </em><em>sanctuary </em><em>has been </em><em>growing about </em><u><em>20</em></u><u><em> wolves </em></u><u><em>a year.</em></u>

we know this is correct because we are trying to create an equation that represents the number of wolves(p) throughout the years(n), so we are trying to figure out what P equals. We know that the sanctuary grows about <u>20</u> wolves a year, and n is the number of years since 2012. As well as obviously,<u> we add 415 to our equation because there is </u><u>already 415 wolves in the sanctuary.</u>

P = <u>Number of wolves</u>

t = <u>number of years since 2010</u>

x = <u>unknown variable(number of wolves in 2010)</u>

Here we are trying to identify what x is,<u> in 2012 there was 415, each year the number of wolves grew by 20.</u>

P = 40 - 415 = 375

<u>We now know there were 375 wolves in 2010</u>

<h3>Hence our equation is P = 20t + 375</h3>

<h3>C:</h3><h3>First let's plug in our first equation</h3>

P = 20n + 415

(To find n all we do is subtract 2018 and 2012, which equals 6.)

P = 20(6) + 415

(Solve)

P = 120 + 415

<em>Our first equation tells us that in 2018 there will be 535 wolves.</em>

<h3>Plug in our second equation</h3>

P = 20t + 375

(To find t all we do the same thing we did last time except now we subtract 2018 from 2010, which equals 8)

P = 20(8) + 375

P = 160 + 375

<h2>Both our equations agree, and in 2018 there will be 535 wolves.</h2>

The advantage of defining the input variable is that it helps simplify the calculation and makes it more intuitive.

7 0

2 years ago

This diagram is a straightedge and compass construction. A is the center of one circle, and B

Serhud [2]

Answer:

Correct choices are a, b, e

Step-by-step explanation:

As per diagram, the circles are equal.

<u>Since the distance AB is the radius of both circles:</u>

AB = AC = BC = BD = AD = r

<u>So the answer choices:</u>

a. AC = BC

Correct, both equal to r

b. AC = BD

Correct, both equal to r

C. CD = AB

Incorrect. Half of CD is the leg of 30-60-90 triangle and is equal to r√3/2, so CD = AB√3

d. ABCD is a square

Incorrect. ACBD is rhombus

e. ABD is an equilateral triangle

Correct, all three sides are equal to r

f. CD = AB + AB

Incorrect as CD = AB√3

3 0

3 years ago

Using the definitions of even integer and odd integer, give a proof by contraposition that this statement is true for all intege

kvasek [131]

Suppose $n$ is even, i.e. there is some integer $k$ such that $n=2k$ . Then

$3n-5=3(2k)-5=6k-5=6k-6+1=2(3k-3)+1=2K+1$

where $K$ is just some other integer. Therefore $3n-5$ is odd, proving the contrapositive, and so the original statement is also true.

4 0

4 years ago