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emmainna [20.7K]

3 years ago

9

If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the e

quation?

1 answer:

natita [175]3 years ago

7 0

Equations don't really have x intercepts, functions or curves do. They're also known as the zeros of the function. When we set a function equal to zero we get an equation to solve, and the zeros of the function become the solutions or roots of the equation.

If a quadratic equation only has one root, that's a repeated root corresponding to a discriminant of zero.

In this example our equation is something like $2(x+3)^2=0$ , or expanded

$2x^2+12x + 18 = 0$

The discriminant $d=b^2-4ac$ here is

$d = 12^2 - 4(2)(18) = 0 \quad\checkmark$

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Step-by-step explanation:

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3 years ago

What is the value of the expression (-8/9) divided by (-2/3) x (-4 1/2) ?

Law Incorporation [45]

Answer:

B) $x=-\frac{8}{27}$

Step-by-step explanation:

$-\frac{8}{9}=-\frac{2}{3}x(-4\frac{1}{2})$

To start things off, lets convert any <em>mixed numbers</em> like $-4\frac{1}{2}$ into <em>improper fractions</em>. In this case $-4\frac{1}{2}$ as an improper fraction is $-\frac{9}{2}$ .

$-\frac{8}{9}=-\frac{2}{3}x(-\frac{9}{2})$

Now let's multiply $-\frac{2}{3}x$ by $-\frac{9}{2}$ . When multiplying fractions, all you need to do is multiply the numerators and denominators separately. Your final answer should be $\frac{18}{6}x$ .
*Note: a <em>negative </em>times a <em>negative </em>is a <em>positive</em>, so that's why we now have an even number in front of $x$ instead of a negative number.

$-\frac{8}{9}=\frac{18}{6}x$

Now we want to isolate $x$ , so we'll have to divide $-\frac{8}{9}$ by $\frac{18}{6}$ , but dividing these two fractions seems like a pain. To make things a bit easier, let's turn our improper fraction into a whole number. To change this improper fraction into a whole number, we should ask ourselves what times $6$ is equal to $18$ ? In this case, the answer is 3, so $\frac{18}{6}$ is actually the same thing as the whole number $3$ .
*Note: In general, keeping fractions as either improper fractions or whole numbers will make doing math easier. Avoid mixed numbers like $-4\frac{1}{2}$ when trying to do math and simply change improper fractions into mixed numbers once you have your final solution.

$-\frac{8}{9}=3x$

Now divide $-\frac{8}{9}$ by $3$ . Think of it as multiplying the denominator of $-\frac{8}{9}$ by $3$ .

$-\frac{8}{27}=x$

6 0

4 years ago

The arc made by a sector at center is 72 degrees . Given that the length of an arc is 44cm ,calculate the radius of the circle (

lesantik [10]

Given:

Central angle of a sector = 72 degrees

Intercepted arc length = 44 cm

To find:

The radius of the circle.

Solution:

We know that, the arc length is

$s=2pi r\dfrac{\theta }{360^\circ}$

Where, r is the radius of the circle, $\theta$ is the central angle in degrees.

Putting $s=44,\pi=3.14$ and $\theta = 72^\circ$ , we get

$44=2(3.14)r\dfrac{72^\circ }{360^\circ}$

$44=6.28r(0.2)$

$44=1.256r$

Divide both sides by 1.256.

$\dfrac{44}{1.256}=r$

$35.031847=r$

$r=35.03$

Therefore, the radius of the circle is about 35.03 cm.

3 0

3 years ago