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2 years ago

Find the value of x for which the graph of y = 3x^2 - 8x + 7 achieves its minimum y-value.

Mathematics

1 answer:

gulaghasi [49]2 years ago

7 0

Answer:

<h3>The y value achieves its minimum at x = 4/3</h3>

Step-by-step explanation:

Given the graph of y to be 3x² - 8x + 7, to get the value of x for which the graph function achieves its minimum y value, we need to find its turning point first.

At the turning point, dy/dx = 0

Given y = 3x² - 8x + 7

$\frac{dy}{dx} = 6x-8\\ at\ turning\ point\ 6x-8 = 0$

$6x = 8\\x = \frac{8}{6}\\ x =\frac{4}{3}$

The y value achieves its minimum at x = 4/3

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Which of the following number sentences is an example of the Distributive Property?

leonid [27]

Answer:

d. 7 × (10 + 9) = (7 × 10) + (7 × 9)

Step-by-step explanation:

The format of writing numbers in distributive property is a(b+c) = (a×b)+(a×c)

We can see that in choice d. 7 × (10 + 9) = (7 × 10) + (7 × 9) it is in correct format of writing numbers in distributive property. Thus, choice d. is correct.

Verification:-

a(b+c) = (a×b)+(a×c)

7 × (10 + 9) = (7 × 10) + (7 × 9)

7 0

3 years ago

Match the following rational expressions to their rewritten forms.

Nookie1986 [14]

Answer:

Answer image is attached.

Step-by-step explanation:

Given rational expressions:

$1.\ \dfrac{x^2+x+4}{x-2}\\2.\ \dfrac{x^2-x+4}{x-2}\\3.\ \dfrac{x^2-4x+10}{x-2}\\4.\ \dfrac{x^2-5x+16}{x-2}$

And the rewritten forms:

$(x-2)+\dfrac{6}{x-2}\\(x+3)+\dfrac{10}{x-2}\\(x+1)+\dfrac{6}{x-2}\\(x-3)+\dfrac{10}{x-2}$

We have to match the rewritten terms with the given expressions.

Let us consider the rewritten terms and let us solve them one by one by taking LCM.

$(x-2)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x-2)^{2}+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+4+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+10}{x-2}$

So, correct option is 3.

$(x+3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x+3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{(x^2+3x-2x-6)+10}{x-2}\\\Rightarrow \dfrac{x^2+x+4}{x-2}$

So, correct option is 1.

$(x+1)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x+1)(x-2)+6}{x-2}\\\Rightarrow \dfrac{x^{2} +x-2x-2+6}{x-2}\\\Rightarrow \dfrac{x^{2} -x+4}{x-2}$

So, correct option is 2.

$(x-3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x-3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{x^2-3x-2x+6+10}{x-2}\\\Rightarrow \dfrac{x^2-5x+16}{x-2}$

So, correct option is 4.

The answer is also attached in the answer area.

7 0

2 years ago

Find the volume of the cylinder. Round your answer to the nearest tenth

valentinak56 [21]

I think it's 85 but Is this like a multiple choice question?

8 0

3 years ago

Read 2 more answers

Which expression is equivalent to 6 (a-3)?

maksim [4K]

Answer:

Step-by-step explanation:

It's very easy

4 0

3 years ago

Read 2 more answers

40 points and I will choose brainlyist <br><br> below is the question.

ipn [44]

Using proportions, the expected number of adults in Palm City whose main source of news is the internet or newspaper is of 19,413.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of adults in Palm City whose main source of news is the internet or newspaper is found as follows:

p = (62 + 88)/(62 + 88 + 128 +24 + 38) = 0.4412.

Hence, out of 44,000 adults, the expected number is found as follows:

0.4412 x 44000 = 19,413.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

7 0

2 years ago

Find the value of x for which the graph of y = 3x^2 - 8x + 7 achieves its minimum y-value.​

Find the value of x for which the graph of y = 3x^2 - 8x + 7 achieves its minimum y-value.