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3 years ago

What is the answer expand and simplify 3x-2^2

Mathematics

1 answer:

tensa zangetsu [6.8K]3 years ago

3 0

Answer:

3x^2 - 4

Step-by-step explanation:

3x^2 - 2^2

3x^2 - 4

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Identify the interval on which the quadratic function is positive.

Alenkasestr [34]

Answer:

$\textsf{1. \quad Solution: $1 < x < 4$,\quad Interval notation: $(1, 4)$}$

$\textsf{2. \quad Solution: $-2 < x < 4$,\quad Interval notation: $(-2, 4)$}$

Step-by-step explanation:

<h3>Question 1</h3>

The intervals on which a quadratic function is positive are those intervals where the function is above the x-axis, i.e. where y > 0.

The zeros of the quadratic function are the points at which the parabola crosses the x-axis.

As the given quadratic function has a negative leading coefficient, the parabola opens downwards. Therefore, the interval on which y > 0 is between the zeros.

To find the zeros of the given quadratic function, substitute y = 0 and factor:

$\begin{aligned}y&= 0\\\implies -7x^2+35x-28& = 0\\-7(x^2-5x+4)& = 0\\x^2-5x+4& = 0\\x^2-x-4x+4& = 0\\x(x-1)-4(x-1)&= 0\\(x-1)(x-4)& = 0\end{aligned}$

Apply the zero-product property:

$\implies x-1=0 \implies x=1$

$\implies x-4=0 \implies x=4$

Therefore, the interval on which the function is positive is:

Solution: 1 < x < 4
Interval notation: (1, 4)

<h3>Question 2</h3>

The intervals on which a quadratic function is negative are those intervals where the function is below the x-axis, i.e. where y < 0.

The zeros of the quadratic function are the points at which the parabola crosses the x-axis.

As the given quadratic function has a positive leading coefficient, the parabola opens upwards. Therefore, the interval on which y < 0 is between the zeros.

To find the zeros of the given quadratic function, substitute y = 0 and factor:

$\begin{aligned}y&= 0\\\implies 2x^2-4x-16& = 0\\2(x^2-2x-8)& = 0\\x^2-2x-8& = 0\\x^2-4x+2-8& = 0\\x(x-4)+2(x-4)&= 0\\(x+2)(x-4)& = 0\end{aligned}$

Apply the zero-product property:

$\implies x+2=0 \implies x=-2$

$\implies x-4=0 \implies x=4$

Therefore, the interval on which the function is negative is:

Solution: -2 < x < 4
Interval notation: (-2, 4)

3 0

1 year ago

The record low temperature in Kansas is -40°F. The record low temperature in Florida is -2°F. What is the difference between the

MatroZZZ [7]

The answer is 38 degrees. It WOULD be -38, but difference can not be negative.

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3 years ago

If there was 200 kids= 100% and 43 of them left what is the percent

STALIN [3.7K]

Answer:

It would be 86 as 43% of 200 is 86

Step-by-step explanation:

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3 years ago

A spinner is divided into four equal sections. Which situation can be represented using this simulation?

snow_lady [41]

Answer:

A. picking a red rose from a vase with two red, two pink, two yellow, and two white roses

Step-by-step explanation:

please mark this answer as brainlest

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3 years ago

Work out 1 over 8 of 760

ASHA 777 [7]

Answer:

The answer is 95

Step-by-step explanation:

1 over 8 of 760

(1/8) × 760

760/8 = 95

Thus, The answer is 95

-TheUnknownScientist 72

4 0

3 years ago

Read 2 more answers