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BaLLatris [955]
2 years ago
9

How many solutions does the system of equations have? y=-2x+3 y = x² - 6x +3

Mathematics
1 answer:
Mashutka [201]2 years ago
6 0

Answer:

2 solutions

Step-by-step explanation:

y = - 2x + 3 → (1)

y = x² - 6x + 3 → (2)

substitute y = x² - 6x + 3 into (1)

x² - 6x + 3 = - 2x + 3 ( subtract - 2x + 3 from both sides )

x² - 4x = 0 ← factor out x from each term on the left side

x(x - 4) = 0

equate each factor to zero and solve for x

x = 0

x - 4 = 0 ⇒ x = 4

substitute these values into (1)

x = 0 : y = - 2(0) + 3 = 0 + 3 = 3 ⇒ (0, 3 )

x = 4 : y = - 2(4) + 3 = - 8 + 3 = - 5 ⇒ (4, - 5 )

the 2 solutions are (0, 3 ) and (4, - 5 )

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3(x^2+6x+8)
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Which equation is the inverse of y = x2 + 16?<br> 0 y=x²-16<br> y=i -16<br> y=+-16<br> y = x2 - 4
denpristay [2]

Answer:

y = ±√(x-16)

Step-by-step explanation:

To find the inverse of an equation, swap the x- and y-variables:

y = x² + 16

x = y² + 16

Then, solve for the y-variable:

x = y² + 16

y² = x - 16

y = ±√(x-16)

8 0
3 years ago
Adam’s car traveled 465.3 miles on 16.5 gallons of gas. Which equation can be used to determine the average number of miles that
grandymaker [24]

Answer:

465.3 = 16.5x

Step-by-step explanation:

We can determine the miles per gallon  by taking the number of miles driven and dividing by the gallons

465.3 /16.5 =x

Rewriting by multiplying each side by 16.5

465.3 = 16.5x

7 0
3 years ago
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The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fo
PolarNik [594]

Answer:

a)

- the probability she will win the dinner for two is 0.016

- the probability she will not win the dinner for two is 0.984

b)

- Lisa's expected earnings is $0.57

- Money she effectively contributed to the hiking club is $11.43

Step-by-step explanation:

Given the data in the question;

fortune cookies; $1 per cookies

club sold 743

a) Lisa bought 12 cookies. What is the probability she will win the dinner for two?

P( she will win ) = Number of cookies bought / Total number of cookies

P( she will win ) = 12 / 743

P( she will win ) = 0.01615 ≈ 0.016

Therefore,  the probability she will win the dinner for two is 0.016

P( she will not win ) = 1 - P( she will win )

P( she will not win ) = 1 - 0.016

P( she will not win ) = 0.984

Therefore,  the probability she will not win the dinner for two is 0.984

b)  Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? (Round your answer to two decimal places.)$

given that value of dinner = $35

P( she will win ) = 0.01615

so

Lisa's earning = $35 × 0.01615

Lisa's earning = $0.57

Therefore, Lisa's expected earnings is $0.57

- How much did she effectively contribute to the hiking club? (Round your answer to two decimal places.)$

Lisa's contribution = Money she paid for cookies - money from expected earnings

Lisa's contribution = ( 12 × $1 ) -  $ 0.57

Lisa's contribution = $12 -  $0.57

Lisa's contribution = $11.43

Therefore, Money she effectively contributed to the hiking club is $11.43

4 0
3 years ago
Use the graph to complete the statement. O is the origin.<br><br> T&lt;2,1&gt; ο r(90°,O) : (4,-1)
faltersainse [42]

Answer:

(3,5)

Step-by-step explanation:

5 0
2 years ago
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