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2 years ago

Please help??? Thank you!!!

Mathematics

1 answer:

Anna11 [10]2 years ago

5 0

Answer:

Step-by-step explanation:

The graph that would give the result of an integration and hence f would be the top one. f = x^4/4 - x^3 + a constant (perhaps zero) would look like the top graph. Just to show you that is true, I've enclosed a graph. The graph is of f which is given 2 lines up.

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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

10 months ago

What is the equation in slope-intercept form of the line that has a slope of -2/3, and passes through the point (6, 2)?

Jet001 [13]

Answer:

Y=-2/3x+6

Step-by-step explanation:

Y=-2/3x+b

2=-2/3•6+b

2=-4+b

6=b

3 0

3 years ago

A door to a playhouse is 50 inches tall. Which of the following is another measure equal to the height?

Effectus [21]

Answer:

4 ft 2 in.

Step-by-step explanation:

A door to a playhouse is 50 inches tall

we know that

1 in---------------> is 0.0833333 ft

50 in-------------> 50*0.0833333---------> 4.167 ft

4.167 ft----------> [4 ft+0.167 ft]

remember that

1 in---------------> is 0.0833333 ft

X in----------------> 0.167 ft

X=0.167/0.0833333----------> X=2 in

4.167 ft----------> [4 ft+0.167 ft]--------> [4 ft+2 in]

5 0

2 years ago

Square root of 180 in radical form

slega [8]

6 √ 5

Simplify down and come to 6 √ 5

6 0

2 years ago

.write the number in .000101 in scientific notation

schepotkina [342]

Answer:

1.01*10^-4

Step-by-step explanation:

first nonzero digit is 4 places to the right of the decimal point

.000101

move decimal point 4 places to the right

1.01

multiply by 10^-4 since it was 4 places to the right

1.01*10^-4

6 0

2 years ago