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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

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Mrs. Olga’s $250 investment earns 19% interest compounded annually. What will her balance be after 3 years?
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Answer:

The answer is A. $421.29

Step-by-step explanation:

Just keep finding 19% of the numbers next, and you add that all up and you get the answer.

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Answer:

N(AUC∩B') = 121

The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is 121

Step-by-step explanation:

Let A represent snickers, B represent Twix and C represent Reese's Peanut Butter Cups.

Given;

N(A) = 150

N(B) = 204

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N(A∩B) = 75

N(A∩C) = 100

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How many students like Reese's Peanut Butter Cups or Snickers, but not Twix;

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This can be derived by first finding;

N(AUC) = N(A) + N(C) - N(A∩C)

N(AUC) = 150+206-100 = 256

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N(A∩B U B∩C) = N(A∩B) + N(B∩C) - N(A∩B∩C) = 75 + 98 - 38 = 135

N(AUC∩B') = N(AUC) - N(A∩B U B∩C) = 256-135 = 121

N(AUC∩B') = 121

The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is 121

See attached venn diagram for clarity.

The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is the shaded part

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