All categories

3 years ago

What is the factoring quadratic expression for 8x^2-18=0

Mathematics

2 answers:

Rus_ich [418]3 years ago

5 0

$8x^2-18=0\\
2(4x^2-9)=0\\
2(2x-3)(2x+3)=0\\
x=\frac{3}{2} \vee x=-\frac{3}{2}$

mash [69]3 years ago

3 0

$8x^2-18=0\ /:2\\\\4x^2-9=0\ \ \ \Leftrightarrow\ \ \ (2x)^2-3^2=0\ \ \ \Leftrightarrow\ \ \ (2x-3)(2x+3)=0\\\\2x-3=0\ \ \ \ \ \ \ or\ \ \ \ 2x+3=0\\\\2x=3\ /:2\ \ \ \ \ \ or\ \ \ \ 2x=-3\ /:2\\\\x=1.5\ \ \ \ \ \ \ \ \ \ \ \ or\ \ \ \ x=-1.5$

You might be interested in

n the graph below determine how many real solutions the quadratic function has, and state them, if applicable. List solutions in

IRINA_888 [86]

Answer:

There are no real solutions.

Step-by-step explanation:

There are 3 options.

2 real solutions: This happens if in the graph, each arm intersects the x-axis, this means that there are two different values of x such that the equation:

a*x^2 + b*x + c

is equal to zero.

Another way to see this, is if the determinant:

b^2 - 4*a*c

is larger than zero.

1 real solution: This happens when the vertex of the graph intersects the x-axis. This means that there is a single value of x such that:

a*x^2 + b*x + c

is equal to zero.

Another way to see this is if the determinant:

b^2 - 4*a*c

is larger equal zero.

No real solution: if in the graph we can not see any intersection of the x-axis, then we do not have real solutions (only complex ones).

Another way to see this is if the determinant:

b^2 - 4*a*c

is smaller than zero.

Now that we know this, let's look at the graph.

We can see that the vertex is below the x-axis, and the arms of the graph go downwards. So the arms will never intersect the x-axis (and neither the vertex).

So the graph does not intersect the x-axis at any point, which means that there are no real solutions for the quadratic equation.

The correct answer would be "none"

3 0

2 years ago

2. Given the equation of a circle in standard form, identify the center, radius, and graph the circle.

Varvara68 [4.7K]

Answer:

Center: ( -1 , 2 )

Radius: 6

Step-by-step explanation:

The equation for a circle is given as follow:

$(x-h)^{2} +(y-k)^{2} =r^{2}$

Where,

the Center is: ( h , k ) (note that the signs of the number are different)

and the radius is: r

So if we compare the original circle equation to the equation in the question we can see that:

$(x+1)^{2} +(y-2)^{2} =36$

the Center is: (-1,2)

and the radius is: $\sqrt{36}$ = 6

2. To draw the graph find points that lay on the circle, it's better to take the values of x and y from the Center:

first sub y=2 in the equation to find the values for x:

$(x+1)^{2} +(y-2)^{2} =36$

$(x+1)^{2} +(2-2)^{2} =36$

$(x+1)^{2} +(0)^{2} =36$

$(x+1)^{2} =36$

$x+1 =±\sqrt{36}$

$x=6-1$ AND $x=-6-1$

$x=5$ AND $x=-7$

The points are A(5,2) and B(-7,2)

second sub x= -1 in the equation to find the values for y:

$(x+1)^{2} +(y-2)^{2} =36$

$(-1+1)^{2} +(y-2)^{2} =36$

$(0)^{2} +(y-2)^{2} =36$

$(y-2)^{2} =36$

$y-2=±\sqrt{36}$

$y=6+2$ AND $y=-6+2$

$y=8$ AND $y=-4$

The points are D(-1,8) and E(-1,-4)

After finding the points write them in the graph and match them together to get the like the circle in the picture below:

8 0

3 years ago

Find the value of x. B X+5 4 D E 2x 3 А x = [?]

Greeley [361]

Answer:

x = 3

Step-by-step explanation:

Δ BDE and Δ BAC are similar triangles, thus the ratio of corresponding sides are equal, that is

$\frac{BD}{BA}$ = $\frac{BE}{BC}$ , substitute values

$\frac{x+5}{3x+5}$ = $\frac{4}{7}$ ( cross- multiply )

4(3x + 5) = 7(x + 5) ← distribute parenthesis on both sides )

12x + 20 = 7x + 35 ( subtract 7x from both sides )

5x + 20 = 35 ( subtract 20 from both sides )

5x = 15 ( divide both sides by 5 )

x = 3

5 0

3 years ago

Given a non-zero rational number, a, and an irrational number, b, what can be said about the product of a and b?

laiz [17]

Answer:

The product of a non-zero rational number and an irrational number is irrational.

7 0

2 years ago

In making a sales forecast, the business owner can only use his best judgment to determine projected costs and revenues. True Fa

nalin [4]

The best answer between the two choices would be the second option B) FALSE because the owner doesn't have to use his ''best'' judgement to figure out costs and expenses when it comes to sales.

7 0

3 years ago

Read 2 more answers