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3 years ago

Is the following relation a function?

Mathematics

2 answers:

astra-53 [7]3 years ago

8 0

Answer:

yes!!!

Step-by-step explanation:

Short explanation. The same y value can be true for many "exs". But the same x value can only have ONE y value to define a function. So if you draw y = 0.5 across that graph that you have given us, you get many x values that have 0.5 as a y value.

If on the other hand, you draw a line of x = 1, there is only 1 value that y has and that is zero.

This is a function.

Pavel [41]3 years ago

7 0

Yes, I think so I'm sorry if I'm wrong

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Nookie1986 [14]

Answer:

$\large\boxed{y=\dfrac{1}{4}x^2-x-4}$

Step-by-step explanation:

The equation of a parabola in vertex form:

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

(h, k) - vertex

The focus is

$\left(h,\ k+\dfrac{1}{4a}\right)$

We have the vertex (2, -5) and the focus (2, -4).

Calculate the value of a using $k+\dfrac{1}{4a}$

k = -5

$-5+\dfrac{1}{4a}=-4$ add 5 to both sides

$\dfrac{1}{4a}=1$ multiply both sides by 4

$4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4$

$\dfrac{1}{a}=4\to a=\dfrac{1}{4}$

Substitute

$a=\dfrac{1}{4},\ h=2,\ k=-5$

to the vertex form of an equation of a parabola:

$y=\dfrac{1}{4}(x-2)^2-5$

The standard form:

$y=ax^2+bx+c$

Convert using

$(a-b)^2=a^2-2ab+b^2$

$y=\dfrac{1}{4}(x^2-2(x)(2)+2^2)-5\\\\y=\dfrac{1}{4}(x^2-4x+4)-5$

use the distributive property: a(b+c)=ab+ac

$y=\left(\dfrac{1}{4}\right)(x^2)+\left(\dfrac{1}{4}\right)(-4x)+\left(\dfrac{1}{4}\right)(4)-5\\\\y=\dfrac{1}{4}x^2-x+1-5\\\\y=\dfrac{1}{4}x^2-x-4$

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3 years ago

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8_murik_8 [283]

Answer:

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Step-by-step explanation:

x/2=10

20/2=10

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3 years ago

1/4z-2/7=5/7 what is z

Alenkasestr [34]

Answer:

z=4

Step-by-step explanation:

1/4z-2/7=5/7

1/4z= 5/7+2/7

1/4z=1

z=4

3 0

3 years ago

D₁ vide using x² - 2x² 2× +3× -5 by ×-3 using synthetic division.

Vaselesa [24]

Answer:

Step-by-step explanation:

I think you are trying to use synthetic division for

$x^{4} -2x^{3} -2x^{2} +3x-5$ divided by x-3

First

x -3 = 0 , make it equal to 0 and add 3 to both sides

x = 3

Then we write all the coefficients and continue with

a pattern of multiply by 3 and add to the next coefficient.

See attachment.

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Korolek [52]

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