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yuradex [85]
2 years ago
8

Can someone help me find the functions zeros

Mathematics
2 answers:
Amiraneli [1.4K]2 years ago
8 0

\bf g(x) = 2(x-3)^2-8\implies \stackrel{g(x)}{0}=2(x-3)^2-8\implies 8=2(x-3)^2 \\\\\\ \cfrac{8}{2}=(x-3)^2\implies 4=(x-3)^2\implies \pm\sqrt{4}=x-3\implies \pm 2 = x-3 \\\\\\ \pm 2 +3 = x\implies x = \begin{cases} 5\\ 1 \end{cases}

Amiraneli [1.4K]2 years ago
8 0

Answer:

(5,0) or (1,0)

Step-by-step explanation:

1.) First you distribute the parenthesis (as it goes first in the PEMDAS series)

2(x-3)^{2} -8=2(x-3)(x-3)-8= 2(x^{2} -6x+9)-8

2.) Distribute the 2 into the expression in the parenthesis and simplify

2(x^{2} -6x+9)-8=2x^{2} -12x+18-8=\\2x^{2} -6x+10=g(x)

3.) Factor the quadratic

(there is many ways for different equations, so it is hard to explain how to, maybe go online if you are struggling, that's how I do mine)

2x^{2} -12x+10=2(x-5)(x-1)=0

<u><em>(</em></u><em>Editors note: reason why we must put zero to solve for the functions zero is because we must find the "X" when "Y=0", or in this case "g(x)=0")</em>

<u><em></em></u>

4.) Separate each of the parenthesis that you factored from the equation into two equations and solve for x when g(x)=0

2(x-5)=0\\2x-10=0\\2x=10\\\frac{2x}{(2)} =\frac{10}{(2)} \\x=5

(x-1)=0\\x=1

<u><em>So when y=0, x=5 or 1</em></u>

<u><em></em></u>

5.) Turn the x and y values given into point form

<u><em>(x=5,1) (y=0) so... (5,0) and (1,0)</em></u>

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3 years ago
A biology test is worth 100 points and has 36 questions.
Ad libitum [116K]

Answer:

(a) 7 essays and 29 multiple questions

(b) Your friend is incorrect

Step-by-step explanation:

Represent multiple choice with M and essay with E.

So:

M + E= 36 --- Number of questions

2M + 6E = 100 --- Points

Solving (a): Number of question of each type.

Make E the subject of formula in M + E= 36

E = 36 - M

Substitute 36 - M for E in 2M + 6E = 100

2M + 6(36 - M) = 100

2M + 216 - 6M = 100

Collect Like Terms

2M - 6M = 100 - 216

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Divide both sides by -4

M = \frac{-116}{-4}

M = 29

Substitute 29 for M in E = 36 - M

E = 36 - 29

E = 7

Solving (b): Can the multiple questions worth 4 points each?

It is not possible.

See explanation.

If multiple question worth 4 points each, then

2M + 6E = 100 would be:

4M + xE = 100

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

4 * 29 + x * 7 = 100

116 + 7x = 100

Subtract 116 from both sides

116-116 + 7x = 100 -116

7x = 100-116

7x = -16

Make x the subject

x = -\frac{16}{7}

Since the essay question can not have worth negative points.

Then, it is impossible to have the multiple questions worth 4 points

<em>Your friend is incorrect.</em>

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2 years ago
Please help asap !!!!!
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Two shapes are similar if all their corresponding side measures are in the same proportion.

The triangles UVW and YVX are similar because their side lengths are in the proportion 1:2, given the tick marks provided in the drawing.

This means that the measure of VX is twice the measure of VW,

The measure of YV is twice the measure of UV

The measure of XY is twice the measure of UW

This last proportion gives the equation:

z + 46 = 2z

Solving for z:

z = 46

Thus, XY = z+46 = 92

XY = 92 units

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