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3 years ago

Use the discriminant to determine the number and type of solutions the equation has.

2 answers:

6 0

$ax^2+bx+c=0\ \ \ \Rightarrow\ \ \ \Delta=b^2-4\cdot a\cdot c\\\\\Delta>0\ \ \ \Rightarrow\ \ \ two\ real\ solutions\\\Delta=0\ \ \ \Rightarrow\ \ \ one\ real\ solution\\\Delta0\ \ \ \ \Rightarrow\ \ \ two\ real\ solutions\ \ \ \Rightarrow\ \ \ Ans.\ C$

White raven [17]3 years ago

5 0

$x^2 + 8x + 12 = 0\\ \\a=1 , b= 8, c= 12 \\ \\ \Delta =b^2-4ac = 8^2 -4\cdot1\cdot12= 64-48= 16\\ \\\Delta > 0 \\ \\ Answer : \ C. \ \ two \ rational \ solutions$

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The surface area of a given cone is 1,885.7143 square inches. What is the slang height?

kap26 [50]

Answer:

If $r >> h$ , the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

$A = \pi \cdot r^{2} + 2\pi\cdot s$

Where:

$r$ - Base radius of the cone, measured in inches.

$s$ - Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

$s = \sqrt{r^{2}+h^{2}}$

Where $h$ is the altitude of the cone, measured in inches. If $r >> h$ , then:

$s \approx r$

And:

$A = \pi\cdot r^{2} +2\pi\cdot r$

Given that $A = 1885.7143\,in^{2}$ , the following second-order polynomial is obtained:

$\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2} = 0$

Roots can be found by the Quadratic Formula:

$r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}$

$r_{1,2} \approx -1\,in \pm 24.521\,in$

$r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in$

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

3 0

3 years ago

How do you find x? and how do you round to the nearest tenth?

expeople1 [14]

Hey there!

In order to solve this problem, we can use the Pythagorean Theorem, which is $c^2 = a^2 + b^2$ . Since the Pythagorean Theorem would find only half of the length of x, we'll need to double it in the end.

First, let's plug in what we know to the Pythagorean Theorem: $2.1^2 = 1.4^2 + b^2$

Next, we'll simplify to that $b^2$ is by itself:

$b^2 = 2.45$

Then, we'll find the square root of 2.45, multiply that by 2 and round to the nearest tenth:

$2(\sqrt{2.45} ) = 3.1$

Therefore, x = 3.1 ft.

How to round to the nearest tenth:

In a decimal, the tenth is the first number after the decimal point. To round to the tenth, if the number in the hundredth place is less than 5, you keep the number as it is, but if the number in the hundredth place is more than 5, you increase the number in the tenth place by 1.

Hope this helps!! :)

6 0

3 years ago

A rectangular box has faces with areas of 12,15, and 20 square units. What is the volume of the box?

miv72 [106K]

First find the side lengths of the box by factoring each area:

12: 1, 2, 3, 4, 6, 12
15: 1, 3, 5, 15
20: 1, 2, 4, 5, 10, 20

Find 3 numbers that both have 2 sides have in common and can multiply to make the areas of the faces:

12: 3 * 4
15: 3 * 5
20: 4 * 5

Sides: 3, 4, and 5

Then multiply to get the volume:

3 * 4 * 5 = 60 units^2

6 0

3 years ago

Solve this equation 53y - 55 = 42y

stiv31 [10]

53y-42y=55
11y=55
Y=55/11 =5

6 0

3 years ago

Read 2 more answers

What is the volume of the pyramid?

Assoli18 [71]

The answer should be C.

3 0

3 years ago

Read 2 more answers