All categories

3 years ago

X-1 / x-1 = 1 What is x?

Mathematics

1 answer:

lions [1.4K]3 years ago

4 0

Answer:

$\large\boxed{x\in\mathbb{R}-\{1\}}\to\text{any real number except 1}$

Step-by-step explanation:

$\dfrac{x-1}{x-1}=1\\\\\text{Domain:}\ x-1\neq0\qquad\text{add 1 to both sides}\\\\x\neq1\\\\\text{We know:}\ \dfrac{a}{a}=1\ \text{for any real number except 0}.\\\\\text{Therefore}\ x\ \text{is any real number except 1}.$

You might be interested in

A business has two loans totaling $50,000. One loan has a rate of 8% and the other has a rate of 12%. This year, the business ex

Debora [2.8K]

Answer:

the 8% loan has a principal of $37500

the 12% loan has a principal of $12500

Step-by-step explanation:

Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).

$I=P*r*t$

Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":

$I=P*r*t\\I1=x * 0.12*1\\I2=y*0.08*1$

Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:

$I1=x * 0.12*1\\I2=y*0.08*1\\I1+I2 = 0.12x+0.08y\\4500=0.12x+0.08y$

This is our first equation in the variables x and y which are our unknowns.

Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:

$x+y=50000$

We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:

$y=50000-x\\4500 = 0.12x +0.08 y\\4500=0.12x+0.08(50000-x)\\4500=0.12x+4000-0.08x\\4500=0.12x-0.08x+4000\\4500=0.04x+4000\\4500-4000=0.04x\\500=0.04x\\x=\frac{500}{0.04} =12500$

Therefore the amount of the loan at 12% is $12500

Now to find the amount of the second loan "y" we use the equation for the totals of the loans:

$x+y=50000\\12500+y=50000\\y=50000-12500=37500$

Therefore, the loan at 8% is $37500

5 0

3 years ago

A given line has the equation 10x+2y=-2.

Iteru [2.4K]

The equation of a line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

If two lines are parallel then their slopes are equal.

We have the following line:

$10x + 2y = -2\\2y = -10x-2\\y = -5x-1$

Thus, the slope of the line is -5.

Therefore a parallel line is of the form:

$y = -5x + b$

We replace the point $(0,12)$

$12 = -5 (0) + b\\12 = b$

Finally, the equation is of the form:

$y = -5x + 12$

Answer:

$5x + y = 12$

8 0

3 years ago

Suppose the a mountain bike that sells for $419 is on sale for 20.5% off.

nata0808 [166]

Regular price: $419
Sale price: (1-0.205)($419) = $333.11

The bike will cost $333.11 before tax. You haven't shared the tax rate, but I can at least tell you that the cost of the bike after tax will be

(1.00 + rate as a decimal fraction)*$333.11.

Example: If the tax rate is 7.5%, then the bike will cost (1.00+0.075)*($333.11).

8 0

3 years ago

1. 112 2. 136 3. 68 4. 158 5. 129

RideAnS [48]

Answer:

4. 158

Step-by-step explanation:

First let's make things a little simpler and put these arcs in terms of x. We know that the degree measure around the outside of a circle, regardless of its size, is 360. So let's say that arc BC is x. That means that arc BDC is 360 - x. This is because arc BC + arc BDC = 360. Substituting in our x's we have:

x + 360 - x = 360 and

360 = 360. (That's just the proof that putting in our x's as we did does in fact work!)

Following the formula then, we have

$22=\frac{1}{2}(360-x-x)$ and

$22=\frac{1}{2}(360-2x)$

Multiply both sides by 2 to get rid of the fraction and get

44 = 360 - 2x

Subtract 360 rom both sides to get

-316 = -2x

Divide both sides by -2 to get that x = 158

Since we are looking for arc BC and we designated arc BC as our x, that means that arc BC = 158.

3 0

3 years ago

Complete the equation. 5x + 5.2 10.0

skad [1K]

I do t think it’s right so far but x=1.04

8 0

3 years ago