All categories

2 years 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]2 years 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

Barbara wants to buy some glittery heart-shaped beads to make friendship bracelets. The beads she wants come in a small pack wit

AleksAgata [21]

Answer:

I feel u

Step-by-step explanation:u need help too

5 0

2 years ago

Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6

lora16 [44]

Answer:

The answer is the option C

graph of $3x$ minus $3$ , with discontinuity at negative $2$ , negative $9$

Step-by-step explanation:

we have

$f(x)=\frac{9x^{2}+9x-18}{3x+6}$

Simplify

$f(x)=9\frac{(x^{2}+x-2)}{3(x+2)}$

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

Step 1

Convert to a factored form the numerator

$x^{2}+x-2=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2}+x=2$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$x^{2}+x+0.25=2+0.25$

$x^{2}+x+0.25=2.25$

Rewrite as perfect squares

$(x+0.5)^{2}=2.25$

Square root both sides

$x+0.5=(+/-)1.5$

$x=-0.5(+/-)1.5$

$x=-0.5+1.5=1$

$x=-0.5-1.5=-2$

$x^{2}+x-2=(x-1)(x+2)$

Step 2

Simplify the function f(x)

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

The domain of the function f(x) is all real numbers except the number $x=-2$

Because the denominator can not be zero

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

$f(x)=3x-3$ ------> with a discontinuity at $x=-2$

$f(-2)=3(-2)-3=-9$

The discontinuity is at point $(-2,-9)$

the answer in the attached figure

8 0

2 years ago

Read 2 more answers

Is 419108 divisible by 4?

ollegr [7]

Answer:

Yes it is

Step-by-step explanation:

It is 104777

7 0

1 year ago

Read 2 more answers

For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 52

Ludmilka [50]

Answer:

the probability that a sample of the 35 exams will have a mean score of 518 or more is 0.934 or 93.4%.

Step-by-step explanation:

This is s z-test because we have been given a sample that is large (greater than 30) and also a standard deviation. The z-test compares sample results and normal distributions. Therefore, the z-statistic is:

(520 - 518) / (180/√35)

= 0.0657

Therefore, the probability is:

P(X ≥ 0.0657) = 1 - P(X < 0.0657)

where

X is the value to be standardised

Thus,

P(X ≥ 0.0657) = 1 - (520 - 518) / (180/√35)

= 1 - 0.0657

= 0.934

Therefore, the probability that a sample of the 35 exams will have a mean score of 518 or more is 0.934 or 93.4%.

3 0

2 years ago

Jala put $600 in an interest bearing account with a annual compound interest rate of 5%. Jala determined that after seven years,

Inessa [10]

Answer:

7.4 years would be the correct answer

4 0

2 years ago

Read 2 more answers