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3 years ago

Is 2(6 – 3x) + x equivalent to 2(3x) + x + 12?

Mathematics

1 answer:

tia_tia [17]3 years ago

6 0

Answer:

Step-by-step explanation:

Carry out indicated operations to see if they are equal

2(6-3x)+x=2(3x)+x+12

2(6)+2(-3x)+x=6x+x+12

12-6x+x=6x+x+12 combine like terms on both sides

12-5x=12+7x (we can see here they are unequal but we can continue) subtract 12 from both sides

-5x=7x divide both sides by x

-5=7

7 is not equal to -5 so the original expressions aren’t equivalent.

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The axis of symmetry for the graph of the function is f(x) = x2 + bx + 10 is x = 6. What is the value of b?

joja [24]

Answer:

$b=-12$

Step-by-step explanation:

we have

$f(x)=x^{2}+bx+10$

we know that

The equation of a vertical parabola into vertex form is equal to

$y=a(x-h)^{2} +k$

where

(h,k) is the vertex of the parabola

and the axis of symmetry is equal to $x=h$

In this problem we have the axis of symmetry $x=6$

the x-coordinate of the vertex is equal to $6$

therefore

For $x=6+1=7$ -----> one unit to the right of the vertex

Find the value of $f(7)$

$f(7)=7^{2}+b(7)+10$

$f(7)=59+7b$

For $x=6-1=5$ -----> one unit to the left of the vertex

Find the value of $f(5)$

$f(5)=5^{2}+b(5)+10$

$f(5)=35+5b$

Remember that

$f(5)=f(7)$ ------> the x-coordinates are at the same distance from the axis of symmetry

$59+7b=35+5b$ ------> solve for b

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Put the steps of solving the equation in order from first to last.<br> 2x + 1 = -1

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Answer:

x = 1

Step-by-step explanation:

2x + 1 = -1

2x = -1 - 1

2x = -2

x = -2 ÷ -2

x = 1

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3 years ago