What is the y intercept of the graph y= -2x^2 -4x-3

If ∠4 = 98°, then ∠3 = ?<br> look at image

Ksju [112]

Step-by-step explanation:

∠4 = ∠1 & ∠2 = ∠3

360 - 2(98) = ∠2 + ∠3

∠3 = 164/2

∠3 = 82°

6 0

3 years ago

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Which statement best reflects the solution(s) of the equation?

Inessa [10]

x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Step-by-step explanation:

We need to solve the equation $\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$ and find values of x.

Solving:

Find the LCM of denominators x-1,x and x-1. The LCM is x(x-1)

Multiply the entire equation with x(x-1)

$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}\\\frac{1}{x-1}*x(x-1)+\frac{2}{x}*x(x-1)=\frac{x}{x-1}*x(x-1)\\Cancelling\,\,out\,\,the\,\,same\,\,terms:\\x+2(x-1)=x^2\\x+2x-2=x^2\\3x-2=x^2\\x^2-3x+2=0$

Now, factoring the term:

$x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0\\x-1=0\,\,and\,\, x-2=0\\x=1\,\,and\,\, x=2$

The values of x are x=1 and x=2

Checking for extraneous roots:

Extraneous roots: The root that is the solution of the equation but when we put it in the equation the answer turns out not to be right.

If we put x=1 in the equation, $\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$ the denominator becomes zero i.e

$\frac{1}{1-1}+\frac{2}{1}=\frac{1}{1-1}\\\frac{1}{0}+2=\frac{1}{0}$

which is not correct as in fraction anything divided by zero is undefined. So, x=1 is an extraneous solution.

If we put x=2 in the equation,

$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$

$\frac{1}{2-1}+\frac{2}{2}=\frac{2}{2-1}\\\frac{1}{1}+1=\frac{2}{1}\\1+1=2\\2=2$

So, x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Keywords: Solving Equations and checking extraneous solution

Learn more about Solving Equations and checking extraneous solution at:

#learnwithBrainly

5 0

4 years ago

Find the exact value of each expression, if it defined. ( if answer is undefined, enter undefined) tan (-1)

Triss [41]

Answer:

$tan(-1) \approx -0.02$

Step-by-step explanation:

The given expression is

$tan(-1)$

The tangent of -1 is defined, it's around -0.02.

The tangent is a trigonometric function with a period of $\pi$ , where each period is separated by a vertical asymptote which indicates that the function is not determined through all its domain, that's what the question refers to when it says "if is undefined, enter undefined".

However, at $x=-1$ , the tangent is determined, that means, there's no asymptote on that coordinate, that's why it has a "determined value", which is -0.02 approximately.

$tan(-1) \approx -0.02$

6 0

3 years ago

Triangle X Y Z is shown. Angle X Y Z is 75 degrees and angle Y Z X is 50 degrees. The length of X Y is 2 and the length of X Z i

Kay [80]

Answer:

2.5

Step-by-step explanation:

7 0

4 years ago

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Consumer Math The sales tax in the town where Amanda lives is 7%. Amanda paid $35 in sales tax on a new stereo. What was the pri

Natasha2012 [34]

Answer

Find out the what was the price of the stereo .

To prove

Let us assume that the price of the stereo be x .

As given

Consumer Math The sales tax in the town where Amanda lives is 7%.

7% is written in the decimal form

$= \frac{7}{100}$

= 0.07

As given

Amanda paid $35 in sales tax on a new stereo .

Than the equation becomes

x × 0.07 = 35

$x = \frac{35}{0.07}$

solving the above

x = $ 500

Therefore the price of the stereo is $ 500 .

Hence proved

5 0

4 years ago