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3 years ago

Which of the following equations produces a linear function?

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

8 0

Answer:

a, b, and c

Step-by-step explanation:

all of them are in the form y=mx+b except for c, which does not have a constant slope throughout the entire line, it will be decreasing or negative until 0, and then increasing or positive after 0, so the slopes would not be the same.

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Match the parabolas represented by the equations with their vertices. y = x2 + 6x + 8 y = 2x2 + 16x + 28 y = -x2 + 5x + 14 y = -

GaryK [48]

Consider all parabolas:

$y = x^2 + 6x + 8,\\y=x^2+6x+9-9+8,\\y=(x^2+6x+9)-1,\\y=(x+3)^2-1.$

When x=-3, y=-1, then the point (-3,-1) is vertex of this first parabola.

$y = 2x^2 + 16x + 28=2(x^2+8x+14),\\y=2(x^2+8x+16-16+14),\\y=2((x^2+8x+16)-16+14),\\y=2((x+4)^2-2)=2(x+4)^2-4.$

When x=-4, y=-4, then the point (-4,-4) is vertex of this second parabola.

$y =-x^2 + 5x + 14=-(x^2-5x-14),\\y=-(x^2-5x+\dfrac{25}{4}-\dfrac{25}{4}-14),\\y=-((x^2-5x+\dfrac{25}{4})-\dfrac{25}{4}-14),\\y=-((x-\dfrac{5}{2})^2-\dfrac{81}{4})=-(x-\dfrac{5}{2})^2+\dfrac{81}{4}.$

When x=2.5, y=20.25, then the point (2.5,20.25) is vertex of this third parabola.

$y =-x^2 + 7x + 7=-(x^2-7x-7),\\y=-(x^2-7x+\dfrac{49}{4}-\dfrac{49}{4}-7),\\y=-((x^2-7x+\dfrac{49}{4})-\dfrac{49}{4}-7),\\y=-((x-\dfrac{7}{2})^2-\dfrac{77}{4})=-(x-\dfrac{7}{2})^2+\dfrac{77}{4}.$

When x=3.5, y=19.25, then the point (3.5,19.25) is vertex of this fourth parabola.

$y =2x^2 + 7x +5=2(x^2+\dfrac{7}{2}x+\dfrac{5}{2}),\\y=2(x^2+\dfrac{7}{2}x+\dfrac{49}{16}-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x^2+\dfrac{7}{2}x+\dfrac{49}{16})-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x+\dfrac{7}{4})^2-\dfrac{9}{16})=2(x+\dfrac{7}{4})^2-\dfrac{9}{8}.$

When x=-1.75, y=-1.125, then the point (-1.75,-1.125) is vertex of this fifth parabola.

$y =-2x^2 + 8x +5=-2(x^2-4x-\dfrac{5}{2}),\\y=-2(x^2-4x+4-4-\dfrac{5}{2}),\\y=-2((x^2-4x+4)-4-\dfrac{5}{2}),\\y=-2((x-2)^2-\dfrac{13}{2})=-2(x-2)^2+13.$

When x=2, y=13, then the point (2,13) is vertex of this sixth parabola.

3 0

3 years ago

Can someone help me on this

fiasKO [112]

I know that i had it on a test its -2.11 Hope you ace it!

7 0

3 years ago

Read 2 more answers

Solve 15x+3y=9,10x+7y=-4

TiliK225 [7]

Answer:

x = 1, y = -2

Step-by-step explanation:

15x + 3y = 9 (1)

10x + 7y = -4 (2)

3 × (2) - 2 × (1)

3 × (2)

30x + 21y = -12 (3)

2 × (1)

30x + 6y = 18 (4)

(3) - (4)

15y = -30

y = -30 / 15

y = -2

sub y = -2 into (1)

15x + 3y = 9

15x + (3 × -2) = 9

15x - 6 = 9

15x = 9 + 6

15x = 15

x = 15 / 15

x = 1

4 0

3 years ago

Identify the pattern then write the next three terms in each sequence 2,8,32,128

Allisa [31]

Step-by-step explanation:

the difference is the previous term multiplied by 4 to get the next term

2,8,32,128,512,2048,8192

Hope that helps :)

3 0

3 years ago

How many times can 7 go 48 with out going over?

Paul [167]

48÷7= 6.85
That would be your answer

8 0

3 years ago