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trasher [3.6K]
4 years ago
13

Please solve the screenshot down below.

Mathematics
1 answer:
Pachacha [2.7K]4 years ago
5 0

The solution is (4,10)

Option C is correct.

Step-by-step explanation:

We need to graph the system of equations.

The equations given are: y=5x-10\\y=x+6

We need to solve the equations to find value of x and y

We can solve these using substitution

Let:

y=5x-10\,\,\,eq(1)\\y=x+6\,\,\,eq(2)

Putting value of y from eq(2) into eq(1)

x+6=5x-10\\Simplifying:\\x-5x=-10-6\\-4x=-16\\x=-16/-4\\x=4

So, value of x = 4

Now, Put value of x in eq(2)

y=x+6\\y=4+6\\y=10

So, Value of y = 10

The graph is shown in figure attached.

The solution is (4,10)

Option C is correct.

Keywords: System of equations

Learn more about system of equations at:

  • brainly.com/question/9045597
  • brainly.com/question/3739260
  • brainly.com/question/13168205

#learnwithBrainly

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Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o
Kruka [31]

For \fbox{\begin \\\math{x}=6\\\end{minispace}} the function f(x)=-x^{2} +4x+12 and g(x)=-x+6 has same value.

Step by step explanation:  

The given functions are,

f(x)=-x^{2}+4x+12

g(x)=-x+6

Step 1:  

Substitute x=1 in f(x)=-x^{2} +4x+12 to obtain the value of f(1).

f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15

Substitute x=1 in g(x)=-x+6 to obtain the value of g(1) .

g(1)=-1+6\\g(1)=5

Step 2:

Substitute x=2 in f(x)=-x^{2} +4x+12 to obtain the value of f(2).

f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16

Substitute x=2 in g(x)=-x+6 to obtain the value of g(2) .

g(2)=-2+6\\g(2)=4

Step 3:

Substitute x=3 in f(x)=-x^{2} +4x+12 to obtain the value of f(3).

f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15

Substitute x=3 in g(x)=-x+6 to obtain the value of g(3) .

g(3)=-3+6\\g(3)=3

Step 4:

Substitute x=4 in f(x)=-x^{2} +4x+12 to obtain the value of f(4).

f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12

Substitute x=4 in g(x)=-x+6 to obtain the value of g(4) .

g(4)=-4+6\\g(4)=2

Step 5:

Substitute x=5 in f(x)=-x^{2} +4x+12 to obtain the value of f(5).

f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7

Substitute x=5 in g(x)=-x+6 to obtain the value of g(5) .

g(5)=-5+6\\g(5)=1

Step 6:

Substitute x=6 in f(x)=-x^{2} +4x+12 to obtain the value of f(6).

f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0

Substitute x=6 in g(x)=-x+6 to obtain the value of g(6) .

g(6)=-6+6\\g(6)=0

Step 7:

As per the given condition f(x)=g(x).

(a). Substitute f(x)=-x^{2} +4x+12 and g(x)=-x+6 in above equation.

-x^{2} +4x+12=-x+6

(b). Multiply with -1 on both sides.

x^{2} -4x-12=x-6

(c). Shift the term x-6 to left hand side.

x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0

(d). Split the middle term in such a way that its sum is 5 and multiplication is 6.

x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1 ,6

It is observed from the above solution that for x=6 both the functions f(x) and g(x) has same value.

Direct method:

f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1

The table for the function f(x)=-x^{2} +4x+12 and g(x)=-x+6 is attached below.

Learn more:  

1. what is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0) brainly.com/question/1332667

2. which is the graph of f(x) = (x – 1)(x + 4)?  brainly.com/question/2334270  

Answer details:  

Grade: Middle school.  

Subjects: Mathematics.  

Chapter: Function.

Keywords: Function, Middle term split method, Binomial,Quadratic, Polynomial, Factorized, Perfect square, Zeros, Zeros of a function, Expression, Equation, x, x^2, x^3, -x^2+4x+12, -x+6, roots of equation.

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