Algebra 2 inequalities and quadratic equations

Mariana [72]

The only one with two obtuse and two right angles.

Trapezoid

7 0

3 years ago

Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers

Bas_tet [7]

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the $x^2$ coefficient is 1, i.e. the equation is written like $x^2+bx+c=0$ , then you can say the following about the coefficients b and c:

$b$ is the opposite of the sum of the roots
$c$ is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

$4+(-2) = 4-2 = 2 \implies b = -2$
$4 \cdot (-2) = -8 \implies c = -8$

So, the equation is $x^2-2x-8=0$

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

$\dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4}$
$\dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8}$

And so the equation is

$x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0$

In order to have integer coefficients, you can multiply both sides of the equation by 8:

$8x^2 - 10 + 3 = 0$

5 0

3 years ago

your friend says that the volume of a sphere with a radius r is four times the volume of a cone with radius r. when is this true

Ierofanga [76]

Volume of a sphere is given by the formula: $V_{\circ}=\frac43\pi r^3$

If we pull the 4 out front we have, $V_{\circ}=4\left(\frac13\pi r^3\right)$ .

Volume of a cone is given by the formula: $V_{\triangle}=\frac{1}{3}\pi r^2\cdot h$

Notice that if the height of the cone is equal to the radius, $V_{\triangle}=\frac13\pi r^2\cdot r$

then it's exactly what we see in our volume formula without the 4!

7 0

2 years ago

A campground consists of 5 square campsites arranged in a line along a beach. The distance from the edge of a campsite to the wa

Anestetic [448]

To answer this question with the choices given, you would substitute the possible answers into your work for the base and the height of each dimension on the entire campground.

To find the length of the campground, you multiply each choice by 5 because there are 5 campsites.

For the width, you add each choice to 4.

Then you multiply the total length by the total width to see if your answer is 950 square yards.

See the attached picture for all the work.

7 0

3 years ago

Solve for p: -9 + p < 15 <br> A. p > 24 B. -p > 6 C. p < 24 D. -p < -6

Soloha48 [4]

Answer:

C. In the given expression -9 + p < 15 , the value of p < 24.

Step-by-step explanation:

Here, the given expression is :

-9 + p < 15

Now, solving for the value of p.

If equals are added to both sides of inequality, the inequality remains unchanged.

Now, -9 + p < 15

⇒ -9 + p + 9 < 15 + 9 (adding +9 on both sides)

or, p < 24

Hence, in the given expression -9 + p < 15 the value of p < 24.

5 0

3 years ago