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2 years ago

Jeremy wants to determine the number of solutions for the equation below without actually solving the equation.

Mathematics

2 answers:

Degger [83]2 years ago

8 0

Answer:

1 solution

Step-by-step explanation:

Jeremy can simplify the equation enough to determine if the x-coefficient on one side of the equation is the same or different from the x-coefficient on the other side. Here, that simplification is ...

-3x -3 +3x = -3x +3 +3

We see that the x-coefficient on the left is 0; on the right, it is -3. These values are different, so there is one solution.

In the attached, the left-side expression is called y1; the right-side expression is called y2. The two expressions are equal where the lines they represent intersect. That point of intersection is x=3. (For that value of x, both sides of the equation have a value of -3.)

<em>Additional comment</em>

If the equation's x-coefficients were the same, we'd have to look at the constants. If they're the same, there are an infinite number of solutions. If they are different, there are no solutions.

AysviL [449]2 years ago

6 0

Answer:

there is only one solution

Step-by-step explanation:

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Solve:<br><br> a.x3+x2-8x - 12x+2<br> b. x3-4x2-3x + 18x-3<br> c. x2 + 4x + 4<br> d. x2 - 6x + 9

NeTakaya

<h2>Steps:</h2>

So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\div \frac{x-3}{x+2}$

Next, remember that <u>dividing by a number is the same as multiplying by its reciprocal.</u> To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\times \frac{x+2}{x-3}$

Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:

$(\frac{f}{g})(x)=\frac{x^2+2x-3x-6}{1}\times \frac{x+2}{x-3}$

Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

$(\frac{f}{g})(x)=\frac{x(x+2)-3(x+2)}{1}\times \frac{x+2}{x-3}$

Now you can rewrite it as:

$(\frac{f}{g})(x)=\frac{(x-3)(x+2)}{1}\times \frac{x+2}{x-3}$

Next, multiply:

$(\frac{f}{g})(x)=\frac{(x-3)(x+2)^2}{x-3}$

Next, divide:

$(\frac{f}{g})(x)=(x+2)^2$

And lastly, simplify:

A good tip: $(x+y)^2=x^2+2xy+y^2$

$(\frac{f}{g})(x)=x^2+4x+4$

<h2>Answer:</h2>

<u>The correct option is C. x² + 4x + 4.</u>

7 0

3 years ago

At the bank, Sheila made 5 deposits, each in the same amount. Her sister Sherri made 4 deposits, each in the same amount. Each o

irinina [24]

The equation would be 4y=5x 4(x+15)=5x x+15=y

let x be the amount that Shelia deposits each time

let y represent the amount that Sherri deposits each time

4(x+15)=5x

4x+60=5x

-4x -4x

60=x

Check:

x+15=y 60+15=y y=75

4(75)=5(60)

300=300

Shelia deposits $60 each time.

5 0

2 years ago

Read 2 more answers

How do i solve x/8=3/4

dusya [7]

Answer:

Quite simply. The answer is X=6

Since you have a full fraction, you can find a common denominator in both fractions and multiply. (The common denominator would be 8, so you would multiply 4 by 2 to get 8. Do the same thing to the top, do multiply 3 by 2 to get 6). Now the fraction is 6/8, and since it's equal to incomplete fraction, you know X is 6.

5 0

2 years ago

Find the total surface area of the figure below:

kow [346]

Answer:

Step-by-step explanation:

Formula -

Triangle Area - 1/2bh

Square - l x w

Triangle - 5 x 7 = 35/2 = 17.5

Since there are four triangle, we will multiply 17.5 x 4 which is equal to 70

Square - 5 x 5 = 25

Now we add both 70 and 25 which is 95

So the total surface area is 95

8 0

2 years ago

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The rental rate for a cement mixer has a flat rate of $40 plus $20 for each day of the rental. The graph shows points representi

Fiesta28 [93]

Answer:

Step-by-step explanation:

y= 20x+40

y- is the cost of rental

x-number of days

20 is the slope

40-flat rate and the y-intercept is at (0,40)

4 0

2 years ago