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VladimirAG [237]
3 years ago
10

.16(6x + 36) < -7 + 5

Mathematics
1 answer:
Andreas93 [3]3 years ago
3 0

Answer: x<97/12 or in decimal form x<8.083

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What are the roots of the polynomial equation x^3-5x+5=2x^2-5? Use a graphing calculator and a system of equations. Round nonint
leonid [27]

The right answer is c. –2.24, 2, 2.24


This question needs to be solved in two ways. First, using a graphing calculator. Next, using a system of equations.


1. Using a graphing calculator.


We have the following polynomial equation:

x^3-5x+5=2x^2-5


By ordering this equation we have:

x^3-2x^2-5x+10=0


So, we can say that this equation comes from a function given by:

f(x)=x^3-2x^2-5x+10


Thus, by plotting this function, we have that the graph of this function is indicated in Figure 1. By zooming, we can see, in Figure 2, that the roots of the polynomial equation are the x-intercepts of f(x) which are:


x_{1}=-2.236 \\ \\ x_{2}=2 \\ \\ x_{3}=2.236


Finally, rounding noninteger roots to the nearest hundredth we have:


\boxed{Root_{1}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=2.24}


2. Using a system of equations.


The ordered equation is:

x^3-2x^2-5x+10=0


By arranging to factor out we have:

x^3-5x-2x^2+10=0


Then, by factoring:

x(x^2-5)-2(x^2-5)=0


Term (x^2-5) is a common factor, thus:


(x-2)(x^2-5)=0 \\ \\ (x-2)(x-\sqrt{5})(x+\sqrt{5})=0 \\ \\ Finally: \\ \\ \boxed{Root_{1}=-\sqrt{5}=-2.24} \\ \\ \boxed{Root_{2}=2} \\ \\ \boxed{Root_{3}=\sqrt{5}=2.24}

6 0
3 years ago
Read 2 more answers
Circletown's limits form a perfectly circular shape. It has a population of
Iteru [2.4K]

Answer:

3.64 Km.

Step-by-step explanation:

Given,

Total population = 20,000 people

Population density = 480 people per square kilometer

Area of the circle town

A = \dfrac{20000}{480}

A = 41.667\ km^2

Radius of the circle town

\pi r^2 = 41.667

r = 3.64\ km

Hence, the radius of circle town is equal to 3.64 Km.

5 0
3 years ago
Read 2 more answers
• Use whichever method you prefer (the area model or the distributive property)
kolbaska11 [484]

Answer: 2a^2+22a+−1

Step-by-step explanation:

Let's simplify step-by-step.

2a^2−5a+(9)(3)a−1

=2a^2+−5a+27a+−1

Combine Like Terms:

=2a^2+−5a+27a+−1

=(2a^2)+(−5a+27a)+(−1)

=2a^2+22a+−1

4 0
3 years ago
There are 24 pens in a desk drawer. The pens are either red or blue. The ratio of red pens to blue pens is 5:1. How many pens ar
Flura [38]

Answer:

The number of red pens is 20.

The number of blue pens is 4.

Step-by-step explanation:

We are given that, the ratio of number of red pens to the number of blue pens is 5 : 1.

∴ Let us assume that the number of red pens be 5<em>x</em> and number of blue pens be <em>x</em>.

Total number of pens in the desk drawer = 24

Now, according to question :

Number of red pens + Number of blue pens = 24

⇒5<em>x</em> + <em>x</em> = 24

⇒6<em>x</em> = 24

⇒x=\frac{24}{6}=4

So, number of red pens in the drawer = 5<em>x</em> = 5 × 4 = 20

Number of blue pens in the drawer = <em>x</em> = 4

6 0
3 years ago
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
larisa [96]

Answer:

y = - 6x - 57

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 6, thus

y = - 6x + c ← is the partial equation

To find c substitute (- 9, - 3) into the partial equation

- 3 = 54 + c ⇒ c = - 3 - 54 = - 57

y = - 6x - 57 ← equation of line

4 0
3 years ago
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