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3 years ago

Find the product. (2a^2+b) (3a-3b) Enter the correct answer.

Mathematics

1 answer:

Leona [35]3 years ago

3 0

<h3>Answer: 6a^3-6a^2b+3ab-3b^2</h3>

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Work Shown:

(2a^2+b)(3a-3b)

c(3a-3b) ..... let c = 2a^2+b

3ac-3bc .... distribute

3a(c)-3b(c)

3a(2a^2+b)-3b(2a^2+b) .... plug in c = 2a^2+b

3a(2a^2)+3a(b)-3b(2a^2)-3b(b) ... distribute

6a^3+3ab-6a^2b-3b^2

6a^3-6a^2b+3ab-3b^2

You could also use the FOIL rule to get the same result. The box method is a visual way to keep track of the terms.

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you had 21$ to spend on 7 raffle tickets. After buying them you had 0$. How much did each raffle ticket cost?

VLD [36.1K]

They cost $3.00. Divide 21÷7=3

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3 years ago

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Given the graph below, what is the y-intercept(s)? Give your answer(s) as an ordered pair.

Irina18 [472]

Answer:

(0, 4)

General Formulas and Concepts:

<u>Algebra I</u>

The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis.

Step-by-step explanation:

According to the graph, the line passes the y-axis at y = 4. Therefore, our y-intercept is (0, 4).

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3 years ago

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the d

Sloan [31]

Answer:

D) Quadratic

Step-by-step explanation:

A function is graphed on a coordinate grid.

As the domain values approach infinity, the range values approach infinity.

Domain: If $x\rightarrow \infty$ then

Range: $y\rightarrow \infty$

As the domain values negative infinity, the range values approach infinity.

Domain: If $x\rightarrow -\infty$ then

Range: $y\rightarrow \infty$

We need to choose correct option which follows given domain and range.

Only quadratic function will follow the rule because it has even degree polynomial.

Quadratic function: $f(x)=ax^2+bx+c$

Degree = 2 and leading coefficient is positive.

Domain: $x\belong (-\infty,\infty)$

Range: $y\belong (b,\infty)$

Hence, D is correct option.

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4 years ago

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convert the repeating decimal to an improper fraction or mixed number. Include your work in your final anwser 152

Nezavi [6.7K]

If you mean .152 bar as in .152152152.....then let x=.152 then:

1000x-x=152.152-.152

999x=152

x=152/999 (this cannot be reduced any further as they have no common primes)

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3 years ago

How to find extreme values of a function.

baherus [9]

Answer:

See below

Step-by-step explanation:

Extreme values of a function are found by taking the first derivative of the function and setting it equal to 0. To determine if it's a minimum or maximum, we set the second derivative equal to 0 and determine if its positive or negative respectively.

Let's do $f(x)=3x^4+2x^3-5x^2+7$ as an example

By using the power rule where $\frac{d}{dx}(x^n)=nx^{n-1}$ , then $f'(x)=12x^3+6x^2-10x$

Now set $f'(x)=0$ and solve for $x$ :

$0=12x^3+6x^2-10x$

$0=2x(6x^2+3x-5)$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-3\pm\sqrt{3^2-4(6)(-5)}}{2(6)}$

$x=\frac{-3\pm\sqrt{9+120}}{12}$

$x=\frac{-3\pm\sqrt{129}}{12}$

$x=-\frac{3}{12}\pm\frac{\sqrt{129}}{12}$

$x=-\frac{1}{4}\pm\frac{\sqrt{129}}{12}$

$x_1=0,x_2\approx0.6965,x_3=-1.1965$

By plugging our critical points into $f(x)$ , we can see that our extreme values are located at $(0,7)$ , $(0.6965,5.956)$ , and $(-1.1965,2.565)$ .

The second derivative would be $f''(x)=36x^2+12x-10$ and plugging in our critical points will tell us if they are minimums or maximums.

If $f''(x)>0$ , it's a minimum, but if $f''(x)$ , it's a maximum.

Since $f''(0)=-10$ then $(0,7)$ is a local maximum

Since $f''(0.6965)=15.822>0$ , then $(0.6965,5.956)$ is a local minimum

Since $f''(-1.1965)=27.18>0$ , then $(-1.1965,2.565)$ is a global minimum

Therefore, the extreme values of $f(x)=3x^4+2x^3-5x^2+7$ are a global minimum of $(-1.1965,2.565)$ , a local minimum of $(0.6965,5.956)$ , and a local maximum of $(0,7)$ .

Hope this example helped you understand! I've attached a graph to help you visualize the extreme values and where they're located.

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3 years ago