Use traditional algorithm to find the quotient 3 ) 137

What is the next number in the sequence below.<br> 216, 72, 24,

tiny-mole [99]

The next number in the sequence is 8

4 0

3 years ago

The amount of chlorine in a swimming pool varies directly with the volume of water. the pool has 2.5 milligrams of chlorine per

djverab [1.8K]

Answer:

Find out the how much chlorine is in the pool .

To prove

As given

The amount of chlorine in a swimming pool varies directly with the volume of water.

The pool has 2.5 milligrams of chlorine per liter of water.

i.e

2.5 milligrams of chorine = 1 litre of water

There are 8000 gallons of water in the swimming pool.

As 1 gallons = 3.78541 litre (Approx)

Now convert 8000 gallons of water in litres.

8000 gallons = 8000 × 3.78541 litre

= 30283.28 litres

Now calculate chlorine in the pool for 30283.28 litres of waters.

As

2.5 milligrams of chlorine = 1 litre of water

2.5 × 30283.28 milligrams of chlorine = 30283.28 litre of water

75708.2 milligrams of chlorine for 30283.28 litre of water .

3 0

3 years ago

Read 2 more answers

O is the centre of the circle, EF is a tangent, angle BCE = 28°, angle ACD = 31°

andriy [413]

Answer

a. 28˚

b. 76˚

c. 104˚

d. 56˚

Step-by-step explanation

Given,

∠BCE=28° ∠ACD=31° & line AB=AC .

According To the Question,

a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°

b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚

thus , ∠ABC=76° .

c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,

Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°

Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)

∠DAB = 180° - 107° ⇔ 73°

& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°

Now, In Triangle ADC Sum of angles in a triangle is 180°

∠ADC = 180° - (31° + 45°) ⇔ 104˚

d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre

For Diagram, Please Find in Attachment

4 0

3 years ago

HEEELP

Drupady [299]

Answer: (c)

Step-by-step explanation:

Given

$f(x)=\dfrac{1}{x-3}\\\\g(x)=\sqrt{x+5}$

Here, $\sqrt{x+5}\ \text{is always greater than equal to 0}\\\Rightarrow x+5\geq 0\\\Rightarrow x\geq -5\quad \ldots(i)$

To get $f\left(g(x)\right)$ , replace $x$ in $f(x)$ by $g(x)\ \text{i.e. by}\ \sqrt{x+5}$

$\Rightarrow f\left(g(x)\right)=\dfrac{1}{\sqrt{x+5}-3}\\\\\text{Denominator must not be equal to 0}\\\\\therefore \sqrt{x+5}-3\neq0\\\Rightarrow \sqrt{x+5}\neq 3\\\Rightarrow x+5\neq 9\\\Rightarrow x\neq 4\quad \ldots(ii)$

Using $(i)$ and $(ii)$ it can be concluded that the domain of $f\left(g(x)\right)$ is all real numbers except 0.

Therefore, its domain is given by

$x\in [-5,4)\cup (4,\infty)$

Option (c) is correct.

5 0

3 years ago

Choose the best answer that represents the property used to rewrite the expression.

Andre45 [30]

Answer:

The Quotient Property.

Step-by-step explanation:

Since all three logarithms have the same base (base-5), and you are subtracting 6 and 3, to solve this all you need to do is 6 / 3 because of the Quotient Property.

You aren't multiplying anything, so you wouldn't use the Product Property.

You are not messing around with powers, so you wouldn't use the Power Property.

And you aren't using addition or multiplication, so you wouldn't use the Commutative Property.

Hope this helps!

5 0

3 years ago