All categories

1 year ago

Which represents the solution(s) of the system of equations, y = x2 – x + 1 and y = x? Determine the solution set by graphing.

Mathematics

1 answer:

Reil [10]1 year ago

7 0

Answer:

(1 , 1)

Step-by-step explanation:

Given in the question two equations

Equation 1

y = x² – x + 1

Equation 2

y = x

Equate both equations

x² – x + 1 = x

0 = x² – x + 1 - x

x² – 2x + 1 = 0

x² - x - x + 1 = 0

x(x - 1) -1(x - 1) = 0

(x - 1)(x - 1) = 0

(x-1)² = 0

x - 1 = 0

x = 1

Plug x = 1 in first equation

y = 1² – 1 + 1

y = 1

You might be interested in

Let f(x)=4x-1 and g(x)=2x^2+3. Perform each function operations and then find the domain.

Triss [41]

F(x) = 4x - 1
g(x) = 2x² + 3

1. (f + g)(x) = (4x - 1) + (2x² + 3)
(f + g)(x) = 2x² + 4x + (-1 + 3)
(f + g)(x) = 2x² + 4x + 2
Domain: {x| -∞ < x < ∞}, (-∞, ∞)

2. (f - g)(x) = (4x + 1) - (2x² + 3)
  (f - g)(x) = 4x + 1 - 2x² - 3
(f - g)(x) = -2x² + 4x + 1 - 3
(f - g)(x) = -2x² + 4x - 2
Domain: {x|-∞ < x < ∞}, (-∞, ∞)
3. (g - f)(x) = (2x² + 3) - (4x - 1)
(g - f)(x) = 2x² + 3 - 4x + 1
(g - f)(x) = 2x² - 4x + 3 + 1
(g - f)(x) = 2x² - 4x + 4
Domain: {x| -∞ < x < ∞}, (-∞, ∞)

4. (f · g)(x) = (4x + 1)(2x² + 3)
(f · g)(x) = 4x(2x² + 3) + 1(2x² + 3)
(f · g)(x) = 4x(2x²) + 4x(3) + 1(2x²) + 1(3)
(f · g)(x) = 8x³ + 12x + 2x² + 3
(f · g)(x) = 8x³ + 2x² + 12x + 3
Domain: {x| -∞ < x < ∞}, (-∞, ∞)

5. $(\frac{f}{g})(x) = \frac{4x - 1}{2x^{2} + 3}$
Domain: 2x² + 3 ≠ 0
- 3 - 3
2x² ≠ 0
2 2
  x² ≠ 0
x ≠ 0
(-∞, 0) ∨ (0, ∞)

6. $(\frac{g}{f})(x) = \frac{2x^{2} + 3}{4x - 1}$
Domain: 4x - 1 ≠ 0
+ 1 + 1
4x ≠ 0
4   4
x ≠ 0
  (-∞, 0) ∨ (0, ∞)

6 0

2 years ago

The junior class has 50 students. Twenty-five students take only french, 15 take only Latin, and 10 take both. If a student is c

zavuch27 [327]

There are 15 students who take Latin, and 10 students who take both.
Therefore:
15+10 =25 total students taking Latin
25students / 50 total students = 1/2

The answer is 1/2.

5 0

2 years ago

Read 2 more answers

TWENTY POINTS!!! Baxter is thinking about buying a car for $18,500. The table below shows the projected value of two different c

Anika [276]

Part A: Linear function

explanation:
The table for the value of the two cars with time are given as follows;
Years Car 1 Car 2
1 18,500 18,500
2 17,390 17,500
3 16,500 16,346.6
Plotting the give data, we have;
From the plot of the data, the function that can be used to describe the values of both cars after a fixed number of years is a linear function

Hope this helps a bit

7 0

2 years ago

Read 2 more answers

Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for

sergij07 [2.7K]

Answer:

The number of adults tickets sold = 168.

Step-by-step explanation:

The cost of 1 adult ticket = $10.50

The cost of 1 student ticket = $3.75

The total sales from the ticket = $2071.50

Now, here let us assume

The number of adult tickets sold = a

The number of student tickets sold = b

So, the equation is given as :

10.50 a + 3.75 b = 2071.50

Now, its given the number of students = 82

⇒ <u>b = 82</u>

Putting the value of b in the above equation,w e get:

10.50 a + 3.75 ( 82) = 2071. 50

or, 10.50 a = 2071.50 - 307.5 = 1764

or, a = 1764/10.5 = 168

Hence, the number of adults tickets sold = a = 168.

3 0

2 years ago

Read 2 more answers

Mason used a 30% coupon to buy a new computer. After the discount, the cost of the computer was $728.

shtirl [24]

Answer:

The original price of computer is $ 1040

Solution:

Given that, Mason used a 30% coupon to buy a new computer

After the discount, the cost of the computer was $728

To find: original price of computer

From given question,

price after discount = $ 728

discount = 30 % of original price

Let "x" be the original price of computer

price after discount = original price - discount price

Step-by-step explanation:

5 0

1 year ago