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2 years ago

Writ the recurring decimal as 0.15 as a fraction in it's simplest form

Mathematics

1 answer:

Tema [17]2 years ago

6 0

Answer:

3/20

Step-by-step explanation:

0.15 = 15*100/1*100

= 15/100

= 3/20

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Find the

Mazyrski [523]

Answer:

54 cm

Step-by-step explanation:

The area (A) of an equilateral triangle is

A = $\frac{s^2\sqrt{3} }{4}$ ( s is the side length ) then

$\frac{s^2\sqrt{3} }{4}$ = 81 $\sqrt{3}$ ( multiply both sides by 4 to clear the fraction )

s² $\sqrt{3}$ = 324 $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

s² = 324 ( take the square root of both sides )

s = $\sqrt{324}$ = 18

Thus

perimeter = 3 × 18 = 54 cm

3 0

2 years ago

-. A 6-foot-tall man is standing 50 feet from a flagpole. When he looks at the top of the flagpole,

taurus [48]

Answer:

The height of the flagpole is 46 feet

Step-by-step explanation:

First we find the ratio to connect the variables

Tan(∅) = opposite/adjacent

Plug in the Variables

Tan(39) = x/50

Solve for x

50*tan(39) = x

x = 40.48

Don't forget to include the man's height

40.48 + 6 = 46.48

7 0

2 years ago

Terry needs to carry a pole that

Natasha2012 [34]

Answer:

Yes, The pole will fit through the door because the diagonal width of the door is 10.8 feet, which is longer than the length of the pole.

Step-by-step explanation:

Using the Pythagorean Theorem, ( $a^2+b^2=c^2$ ) we can measure the hypotenuse of a right triangle. Since the doorway is a rectangle, and a rectangle cut diagonally is a right triangle, we can use Pythagorean Theorem to measure the diagonal width of the doorway.

Plug in the values of the length and width of the door for a and b. The c value will represent the diagonal width of the doorway:

$6^2+9^2=c^2$

$36+81=c^2$

$117=c^2$

Since 117 is equal to the value of c multiplied by c, we must find the square root of 117 to find the value of c.

$\sqrt{117} =10.8$

$10.8=c$

Yes, The pole will fit through the door because the diagonal width of the door is 10.8 feet, which is longer than the length of the pole, measuring 10 feet.

7 0

2 years ago

Prove that if a and b are positive integers whose sum is a prime p, their greatest common divisor is 1.

Tasya [4]

Proof by contadiction.

Let assume there exist such positive integers $a$ and $b$ whose sum is a prime number $p$ , that their greatest common divisor is greater than 1.

$a,b\in\mathbb{Z^+}\\d=\text{gcd}(a,b)>1\\\\a=de\\b=df\\e,f\in\mathbb{Z^+}\\\\a+b=p\\de+df=p\\d(e+f)=p\\$

Since $p$ is a prime number and $d>1$ , then $d=p \wedge e+f=1$ , but we assumed earlier that $e,f\in\mathbb{Z^+}$ , and there are no two positive integers that sum up to 1.