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1 year ago

Solve the equation x^2+6x= -11/4

Mathematics

1 answer:

xxTIMURxx [149]1 year ago

8 0

Answer:

Step-by-step explanation:

First, move the -11/4 to the other side, so the expression can equal 0.

$x^2+6x+11/4=0$

To make the equation easier to work with, multiply both sides by 4, cancelling out the fraction.

$4x^2+24x+11=0$

There are many ways to solve a quadratic equation (factoring, quadratic formula, completing the square).

Solving this equation by factoring is the easiest. Factoring with a leading coefficient greater than one can be difficult and there are many ways to accomplish it. The way I'm going to do it is to first find the factors of $4x^2$ and then the factors of 11. And then multiply across, add the middle terms (derived from multiplying) and try to make it equal 24x.

$4x^2$ : 24x 11:

2x 22x 11

2x 2x 1

24x (works)

I'll then take the factors diagonal. (2x+1)(2x+11)=0

So $x=-\frac{1}{2}, -\frac{11}{2}$

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Explain why the exponents cannot be added in the product 12^3 x<br> 11^3.

sergij07 [2.7K]

Answer:

see explanation

Step-by-step explanation:

The exponents can only be added if the bases are the same

Here one base is 12 and the other is 11

So the rule of addition is not applicable.

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2 years ago

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1. What is the actual distance around the garden? Explain your reasoning.

Mrrafil [7]

First find the number of ft around the garden and if it took Clare 30 min to walk the entire distance divide your previous answer by 30 so you can see how many ft per minute she was walking

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2 years ago

All of the functions shown below are either exponential growth or decay functions.

AlekseyPX

Answer:

Step-by-step explanation:

If an exponential function is in the form of y = a(b)ˣ,

a = Initial quantity

b = Growth factor

x = Duration

Condition for exponential growth → b > 1

Condition for exponential decay → 0 < b < 1

Now we ca apply this condition in the given functions,

1). $y=3.2(1+0.45)^{2x}$

Here, (1 + 0.45) = 1.45 > 1

Therefore, It's an exponential growth.

2). $y=(0.85)^{3x}$

Here, (0.85) is between 0 and 1,

Therefore, it's an exponential decay.

3). y = (1 - 0.03)ˣ + 4

Here, (1 - 0.03) = 0.97

And 0 < 0.97 < 1

Therefore, It's an exponential decay.

4). y = 0.5(1.2)ˣ + 2

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2 years ago

For the following system, if you isolated x in the first equation to use the substitution method, what expression would you subs

alekssr [168]

Answer:

$x=2y+6$

Step-by-step explanation:

So we have the system:

$-x+2y=-6\\3x+y=8$

If we isolate the x-variable in the first equation:

$-x+2y=-6$

Subtract 2y from both sides:

$-x=-6-2y$

Divide both sides by -1:

$x=2y+6$

Therefore, we would substitute the above into the second equation:

$3x+y=8\\3(2y+6)+y=8$

The answer is 2y+6

Further notes:

To solve for the system, distribute:

$6y+18+y=8$

Simplify:

$7y+18=8$

Subtract:

$7y=-10$

Divide:

$y=-10/7\approx-1.4286$

Now, substitute this value back into the isolated equation:

$x=2(-10/7)+6\\x=-20/7+42/7\\x=22/7\approx3.1429$

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2 years ago

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PtichkaEL [24]

Answer:

$y = 8x + 16$

$x = 12$

Step-by-step explanation:

Given two points on the line (0, 16) and (3, 40), an equation for the line can be written using the slope-intercept line equation which takes the format $y = mx + b$ .