A company builds computers. it cost $6700

Factor the polynomial in quadratic form<br> X^4-36

Leona [35]

Factored
(x^2 +6)(x^2 - 6)
(x^2 + 6)(x + sqrt (6))(x - sqrt (6))

5 0

3 years ago

Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded? -Above the solid line

baherus [9]

The statement which correctly describes the shaded region for the inequality is $\fbox{\begin\\\ Above the dashed line\\\end{minispace}}$

Further explanation:

In the question it is given that the inequality is $6y-3x>9$ .

The equation corresponding to the inequality $6y-3x>9$ is $6y-3x=9$ .

The equation $6y-3x=9$ represents a line and the inequality $6y-3x>9$ represents the region which lies either above or below the line $6y-3x=9$ .

Transform the equation $6y-3x=9$ in its slope intercept form as $y=mx+c$ , where $m$ represents the slope of the line and $c$ represents the $y$ -intercept.

$y$ -intercept is the point at which the line intersects the $y$ -axis.

In order to convert the equation $6y-3x=9$ in its slope intercept form add $3x$ to equation $6y-3x=9$ .

$6y-3x+3x=9+3x$

$6y=9+3x$

Now, divide the above equation by $6$ .

$\fbox{\begin\\\math{y=\dfrac{x}{2}+\dfrac{1}{2}}\\\end{minispace}}$

Compare the above final equation with the general form of the slope intercept form $\fbox{\begin\\\math{y=mx+c}\\\end{minispace}}$ .

It is observed that the value of $m$ is $\dfrac{1}{2}$ and the value of $c$ is $\dfrac{3}{2}$ .

This implies that the $y$ -intercept of the line is $\dfrac{3}{2}$ so, it can be said that the line passes through the point $\fbox{\begin\\\ \left(0,\dfrac{3}{2}\right)\\\end{minispace}}$ .

To draw a line we require at least two points through which the line passes so, in order to obtain the other point substitute $0$ for $y$ in $6y=9+3x$ .

$0=9+3x$

$3x=-9$

$\fbox{\begin\\\math{x=-3}\\\end{minispace}}$

This implies that the line passes through the point $\fbox{\begin\\\ (-3,0)\\\end{minispace}}$ .

Now plot the points $(-3,0)$ and $\left(0,\dfrac{3}{2}\right)$ in the Cartesian plane and join the points to obtain the graph of the line $6y-3x=9$ .

Figure $1$ shows the graph of the equation $6y-3x=9$ .

Now to obtain the region of the inequality $6y-3x>9$ consider any point which lies below the line $6y-3x=9$ .

Consider $(0,0)$ to check if it satisfies the inequality $6y-3x>9$ .

Substitute $x=0$ and $y=0$ in $6y-3x>9$ .

$(6\times0)-(3\times0)>9$

$0>9$

The above result obtain is not true as $0$ is not greater than $9$ so, the point $(0,0)$ does not satisfies the inequality $6y-3x>9$ .

Now consider $(-2,2)$ to check if it satisfies the inequality $6y-3x>9$ .

Substitute $x=-2$ and $y=2$ in the inequality $6y-3x>9$ .

$(6\times2)-(3\times(-2))>9$

$12+6>9$

$18>9$

The result obtain is true as $18$ is greater than $9$ so, the point $(-2,2)$ satisfies the inequality $6y-3x>9$ .

The point $(-2,2)$ lies above the line so, the region for the inequality $6y-3x>9$ is the region above the line $6y-3x=9$ .

The region the for the inequality $6y-3x>9$ does not include the points on the line $6y-3x=9$ because in the given inequality the inequality sign used is $>$ .

Figure $2$ shows the region for the inequality $\fbox{\begin\\\math{6y-3x>9}\\\end{minispace}}$ .

Therefore, the statement which correctly describes the shaded region for the inequality is $\fbox{\begin\\\ Above the dashed line\\\end{minispace}}$

Learn more:

A problem to determine the range of a function brainly.com/question/3852778
A problem to determine the vertex of a curve brainly.com/question/1286775
A problem to convert degree into radians brainly.com/question/3161884

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Linear inequality

Keywords: Linear, equality, inequality, linear inequality, region, shaded region, common region, above the dashed line, graph, graph of inequality, slope, intercepts, y-intercept, 6y-3x=9, 6y-3x>9, slope intercept form.

4 0

3 years ago

Read 2 more answers

Is 11/12 greater or less than 2/3?

Sauron [17]

False beacause 2/3 is bigger than 11/12. Think about it like pizza 2/3 pieces is better cuz there bigger & 11/12 are smaller pieces.

8 0

3 years ago

Please help me find the area of this figure

Harman [31]

Answer:

=51.63 m^2

Step-by-step explanation:

First find the area of the triangle

A = 1/2 bh = 1/2(3) * 5 = 7.5

Then find the area of the rectangle

A = l*w = 5*6 = 30

Then find the area of the semi circle, which is 1/2 the area of the circle

The diameter is 6 so the radius is 3

A = 1/2 pi r^2 = 1/2 (3.14) (3) ^2 = 14.13

Add the areas together for the total area

7.5+30+14.13

=51.63

5 0

3 years ago

What is 1 and 1/4 minus 3/8?

matrenka [14]

Answer: 7/8

Step-by-step explanation:

You can change all the fractions to have equivalent denominators.

The Least Common Denominator of 1 1/4 and 3/8 is 8. Now we can change the fractions.

1 1/4 = 1 2/8 = 10/8.

3/8 = 3/8.

Now we can subtract. Subtract the numerators of the first fraction from the numerators of the second fraction, and the denominators oft he first fraction to the denominators of the second fraction.

10/8 - 3/8 = 7/8.

Therefore, 1 1/4 - 3/8 = 7/8; the fourth answer.

6 0

3 years ago