1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
spayn [35]
3 years ago
9

What are the solutions to the system of equations? Y=x^2-7x+12 and y=-x+7

Mathematics
2 answers:
matrenka [14]3 years ago
6 0

\bf \begin{cases} y=x^2-7x+12\\ y=-x+7 \end{cases}\implies \stackrel{y}{x^2-7x+12}=\stackrel{y}{-x+7} \\\\\\ x^2-6x+12=7\implies x^2-6x+5=0 \\\\\\ (x-5)(x-1)=0 \implies \blacktriangleright x= \begin{cases} 5\\ 1 \end{cases} \blacktriangleleft \\\\[-0.35em] ~\dotfill

\bf y=-x+7\implies \stackrel{x=5}{y=-(5)+7}\implies \blacktriangleright y=2\blacktriangleleft \\\\\\ y=-x+7\implies \stackrel{x=1}{y=-(1)+7}\implies \blacktriangleright y=6 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (5,2)\qquad (1,6)~\hfill

siniylev [52]3 years ago
5 0

Answer:

(5, 2), (1, 6)

Step-by-step explanation:

We have a system composed of two equations

The first is a quadratic equation and the second is a linear equation.

y=x^2-7x+12

y=-x+7

To solve the system, equate both equations and solve for x

x^2-7x+12 = -x+7\\\\x^2 -6x +5=0

To solve the quadratic equation we must factor it.

You should look for two numbers a and c that when multiplying them obtain as result 5 and when adding both numbers obtain as result -6.

This is:

a * c = 5\\a + c = -6

The numbers searched are -5 and -1

So

x^2 -6x +5 = (x-5)(x-1) = 0

Finally the solutions to the system of equations are:

x= 5, x=1

You might be interested in
Can someone please help ?!
artcher [175]
The answer is the second option y=-3x-2
3 0
3 years ago
4. A kitten weighs 4 pounds. What is the approximate mass of the kitten in kilograms?​
Margarita [4]

Answer:

1.81 kilograms

Step-by-step explanation:

5 0
2 years ago
What is the meaning of this WW1 quote?
Ghella [55]
The Great War (WW1) killed many empires who had been around for hundreds of years. It introduced some very inhumane weapons such as gas, and was the 1st war when old tactics met new ones. Back then, a war on this scale has never been seen. 

It also gave birth to many new nations 
3 0
3 years ago
josh got 20% discount at a sale. He got a new shirt for $12. what was the original price of the shirt
jenyasd209 [6]

Answer:

$15.00

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Determine the mode(s) of the data 2, 2, 2,3,5,5, 6, 7, 8, 8, 8, 9, 10.
Genrish500 [490]

To find the mode, put all the numbers in order from least to greatest, then count how many times you see a number. The number you see the most is the mode. In this problem, we have more than one mode, we have two. The number two appears three times and so does number eight. Having two modes is called bimodal, and having more than two modes is called multimodal. So we have a bimodal of two and eight from this data.

6 0
3 years ago
Other questions:
  • Given the function f(x)=6|x-2|+3, for what values of x is f(x)=39?
    13·1 answer
  • If amy earns 237.60 after working 33 hours what is the hourly rate
    8·1 answer
  • A wheelchair ramp rises 1.5 feet for every 18 feet of horizontal distance it covers. Find the rate of chance of the ramp.
    11·1 answer
  • Need geometry help asap!<br><br> image above✨
    13·1 answer
  • Which are perfect squares?
    11·2 answers
  • PLEASE HELP!!!! URGENT !!!!! (40 points!!!)
    14·1 answer
  • Gabe paid $ 120 for 3 shirts and 2 pairs of pants.
    12·1 answer
  • HEY PEOPLE I NEED HELP ASAP I NEED TO SHOW WORK PLS HELP
    14·2 answers
  • Q+a-r=7.098.888<br> q=?<br> a=1.000.000<br> r=? <br> can someone help me please
    6·1 answer
  • Question 1
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!