35.99 write each decimal as a mixed number in simplest form

URGENT PLEASE HELP! What is the slope of the line <br> y = -2x - 4?

Tju [1.3M]

Answer:

-2 is the slope

Step-by-step explanation:

4 0

3 years ago

Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!

Greeley [361]

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

$\frac{3}{x + 4} - \frac{1}{x + 3} = \frac{x + 9}{(x^2 + 7x + 12)}$

To solve this we need to remove the denominators.

Then we can first multiply both sides by (x + 4) to get:

$\frac{3*(x + 4)}{x + 4} - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

$3 - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x + 3)

$3*(x + 3) - \frac{(x + 4)*(x+3)}{x + 3} = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$3*(x + 3) - (x + 4) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$(2*x + 5) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x^2 + 7*x + 12)

$(2*x + 5)*(x^2 + 7x + 12) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)$

$(2*x + 5)*(x^2 + 7x + 12) = (x + 9)*(x + 4)*(x+3)$

Now we need to solve this:

we will get

$2*x^3 + 19*x^2 + 59*x + 60 = (x^2 + 13*x + 3)*(x + 3)$

$2*x^3 + 19*x^2 + 59*x + 60 = x^3 + 16*x^2 + 42*x + 9$

Then we get:

$2*x^3 + 19*x^2 + 59*x + 60 - ( x^3 + 16*x^2 + 42*x + 9) = 0$

$x^3 + 3x^2 + 17*x + 51 = 0$

So now we only need to solve this.

We can see that the constant is 51.

Then one root will be a factor of 51.

The factors of -51 are:

-3 and -17

Let's try -3

p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0

Then x = -3 is one solution of the equation.

But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.

This means that we can take a factor (x + 3) out, so we can rewrite our equation as:

$x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0$

The other two solutions are when the other term is equal to zero.

Then the other two solutions are given by:

x = ±√17

And neither of these have problems in the denominators, so we can conclude that the solutions are:

x = √17 and x = -√17

6 0

3 years ago

Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.1

NeTakaya

Answer:

22 square feet

Step-by-step explanation:

Area of shaded region = Area of square - Area of circle. The diameter of the circle is also the length of the side of the square as the circumference of the circle is on the circumference of the square.

Area of circle = 3.14 × r × r

r = 10 ÷ 2

= 5

Area of circle = 3.14 × 5 × 5

= 78.5

Area of square = length × length

Area of square = 10 × 10

= 100

Area of shaded region = Square - Circle

= 100 - 78.5

= 21.5

= 22 (to the nearest square foot)

I hope this helps :)

7 0

3 years ago

Convert 25 feet per second to miles per hour, with work show.

bulgar [2K]

we know there are 5280 feet in 1 mile, and there are 3600 seconds in 1 hour.

$\bf \cfrac{25 \underline{ft}}{sec}\cdot \cfrac{mi}{5280 \underline{ft}}\cdot \cfrac{3600 \underline{sec}}{hr}\implies \cfrac{25\cdot 3600}{5280}\cfrac{mi}{hr}\implies \cfrac{375}{22}\cfrac{mi}{hr}\implies 17.0\overline{45}\frac{mi}{hr}$

5 0

3 years ago

6.75 + StartFraction 3 Over 8 EndFraction x = 13 and one-fourth

amid [387]

Easy the answer is B: 17 and one-third

3 0

3 years ago

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