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3 years ago

Evaluate: -8 over 9 + 4 over 9 - 2 over 9

Mathematics

2 answers:

stepan [7]3 years ago

4 0

The answer is -2/3 from the solution above

sergiy2304 [10]3 years ago

4 0

-8/9 + 4/9 = -4/9

-4/9 - 2/9 = -6/9 reduces to -2/3

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1 hour = 3,600 seconds and 1 mile = 5,280 feet. Make a conjecture about how you could convert a speed of 15 miles per hour to fe

MrRissso [65]

Answer:

multiply by feet per mile and divide by seconds per hour

Step-by-step explanation:

To get the desired units, multiply by a factor that is equal to 1, but has the desired units in the numerator and the units you're converting from in the denominator.

For units in the denominator that you want to change, use the inverse of the above multiplier.

We have miles/hour, which has miles in the numerator. We want feet/second, which has feet in the numerator, so we need to multiply by the ratio of feet per mile: 5280 ft/mi.

We also have hours in the denominator, where we want seconds. So, we divide by the factor 3600 s/h.

$\dfrac{15\,\text{mi}}{\text{h}}\cdot\dfrac{5280\,\text{ft}}{\text{mi}}\cdot\dfrac{\text{h}}{3600\,\text{s}}=22\,\text{ft/s}$

6 0

3 years ago

There are 50 deer in a particular forest. The population is increasing at a rate of 15% per year. Which exponential growth funct

NemiM [27]

Answer:

The expression that represents the number of deer in the forest is

y(x) = 50*(1.013)^x

Step-by-step explanation:

Assuming that the number of deer is "y" and the number of months is "x", then after the first month the number of deer is:

y(1) = 50*(1+ 0.15/12) = 50*(1.0125) = 50.625

y(2) = y(1)*(1.0125) = y(0)*(1.0125)² =51.258

y(3) = y(2)*(1.0125) = y(0)*(1.0125)³ = 51.898

This keeps going as the time goes on, so we can model this growth with the equation:

y(x) = 50*(1 - 0.15/12)^(x)

y(x) = 50*(1.013)^x

8 0

4 years ago

A pool measuring 16 meters by 22 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the po

lesantik [10]

Let X be the width of the path.

The width of the path would be the width of the pool plus 2x, so 2x +16

The length of the path would be the length of the pool plus 2x, so 2x+22

The total area is 832 square feet.

Area is found by multiplying the length by the width.

So you have:

(2x+16) (2x+22) = 832

Use the Foil Method:

(2x+16) (2x+22) = 4x^2 +76x+352

Now you have:

4x^2 +76x+352 = 832

Subtract 832 from both sides:

4x^2 +76x+352-832 = 0

Simplify:

4x^2 +76x -480

Factor the left side:

4(x-5)(x+24) = 0

Divide both sides by 4:

(x-5)(x+24) = 0

Set both parenthesis to equal 0 and solve for x:

x=5 and x = -24

The width of the path cannot be a negative number, so the width is 5 meters.

8 0

3 years ago

Solve the following equation; domain 0< x < 360; 3 cot x + sqrt 3 = 0

kondaur [170]

ANSWER

$x =120 \degree \: or \: 300 \degree$

EXPLANATION

We want to solve the trigonometric equation

$3 \cot(x) + \sqrt{3} = 0$

We group like terms to obtain,

$3\cot(x) = - \sqrt{3}$

Divide both sides of the equation by 3 to get,

$\cot(x) = - \frac{ \sqrt{3} }{3}$

We can reciprocate both sides to get,

$\tan(x) = - \frac{3}{ \sqrt{3} }$

We simplify the right hand side to get,

$\tan(x) = - \sqrt{3}$

Since the tangent ratio is negative, it implies that it is either in the second quadrant or fourth quadrant.

In the second quadrant,

$x = 180 \degree - arctan( \sqrt{3})$

$x = 180 \degree - 60 \degree = 120 \degree$

In the fourth quadrant,

$x = 360 \degree - arctan( \sqrt{3})$

$x = 360 \degree - 60 \degree$

$x = 300 \degree$

6 0

4 years ago

Describe something true about any pair of interior and exterior angles?

BaLLatris [955]

The interior angles of a shape are the angles inside the shape. The exterior angles are the angles formed between a side-length and an extension. Rule: Interior and exterior angles add up to 180 ° 180\degree 180°.

6 0

3 years ago