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3 years ago

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Mathematics

1 answer:

Sloan [31]3 years ago

7 0

Answer:

a) 2x+2x+x+x+x=42

b) x=6

c) 6 cm, 6cm, 6cm, 12cm, 12cm

Step-by-step explanation:

First think of how you'll get perimeter. Since in the question it says you add all of the sides to get the perimeter, you write the variables being added together and equal it to 42. Next, you add all of the x's together, which you would get 7x=42. Then, you divide 7x and 42 by 7, giving you x=6. Finally, you plug in 6 into the x's, making sure to multiply the ones that are 2(6) into 12. To check if this is true, add the sides together and make sure you get 42.

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Sunny_sXe [5.5K]

Answer:

Part 1) "a" value is $2$

Part 2) The vertex is the point $(1,8)$

Part 3) The equation of the axis of symmetry is $x=1$

Part 4) The vertex is a minimum

Part 5) The quadratic equation in standard form is $y=2x^{2}-4x+10$

Step-by-step explanation:

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

if a > 0 then the parabola open upward (vertex is a minimum)

if a < 0 then the parabola open downward (vertex is a maximum)

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

$x=h$

In this problem we have

$y=2(x-1)^{2}+8$ -----> this is the equation in vertex form of a vertical parabola

The value of $a=2$

a>0 then the parabola open upward (vertex is a minimum)

The vertex is the point $(1,8)$

$(h,k)=(1,8)$

The equation of the axis of symmetry is $x=1$

The equation of a vertical parabola in standard form is equal to

$y=ax^{2}+bx+c$

Convert vertex form in standard form

$y=2(x-1)^{2}+8$

$y=2(x^{2}-2x+1)+8$

$y=2x^{2}-4x+2+8$

$y=2x^{2}-4x+10$

see the attached figure to better understand the problem

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