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2 years ago

Select the function that matches the graph. y = 3x y = 3x2 + 1 y = 3x - 1 y = 3x + 1

Mathematics

2 answers:

Brut [27]2 years ago

7 0

Answer:

the first one goes through (0,0) ||||||| the second is an exponential function so it goes through (0,1) and in a u shape going up ||||||| The third goes through (0,-1) ||||||||| The fourth goes through (0,1)

Step-by-step explanation:

these are identifiein traits so you can find wich one the graph corresponds to since u never gave us a graph.

-BARSIC- [3]2 years ago

5 0

Answer:

The graph is missing, but we can draw and describe each option.

<h3>Choice 1</h3>

$y=3x$

This is a linear function which passes throuhg the origin of the coordinate system because it doesn't have the constant $b$ which is the y-intercept of the line.

The first image attached shows this function.

<h3>Choice 2</h3>

$y=3x^{2} +1$

This is a quadratic function. Its graph belongs to a parabola, all quadratic functions are represented by a parabola. In this case, the parabola has a vertex at (0,1). The second image attached shows this function.

<h3>Choice 3</h3>

$y=3x-1$

This is also a linear function, which is parallel to the first function, because they have the same slope of 3. But this one has y-intercept at (0,-1). The third image attached shows this function.

<h3>Choice 4</h3>

$y=3x+1$

This is also a linear function parallel to function 1 and function 3. The fourth image attached shows its graph. In this case, the line has y-intercept at (0,1).

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Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.

Mice21 [21]

Answer:

<em>LCM</em> = $8y^{4}(y+ 10)^{2}(y + 8)$

Step-by-step explanation:

Making factors of $8y^{6}+ 144y^{5}+ 640y^{4}$

Taking $8y^{4}$ common:

$\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)$

Using <em>factorization</em> method:

$\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times 4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)$

Now, Making factors of $2y^{4} + 40y^{3} + 200y^{2}$

Taking $2y^{2}$ common:

$\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)$

Using <em>factorization</em> method:

$\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10) ............ (2)$

The underlined parts show the Highest Common Factor(HCF).

i.e. <em>HCF</em> is $2y^{2} (y+ 10)$ .

We know the relation between <em>LCM, HCF</em> of the two numbers <em>'p' , 'q'</em> and the <em>numbers</em> themselves as:

$HCF \times LCM = p \times q$

Using equations <em>(1)</em> and <em>(2)</em>: $\Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)$

Hence, <em>LCM</em> = $8y^{4}(y+ 10)^{2}(y + 8)$

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