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3 years ago

What is the sum of 12x^2+3x+6 and -7x^2-4x-2

Mathematics

1 answer:

GrogVix [38]3 years ago

7 0

Answer: $5x^2-x+4$

Step-by-step explanation:

In addition of polynomials, you only have to add the like terms.

Remember the multiplication of signs:

$(+)(+)=+\\(-)(-)=+\\(-)(+)=-$

Then, given the polynomial $12x^2+3x+6$ and the polynomial $-7x^2-4x-2$ , you can find the sum of them by adding the like terms.

Observe the procedure below:

$(12x^2+3x+6)+(-7x^2-4x-2)=12x^2+3x+6-7x^2-4x-2=5x^2-x+4$

Therefore, the sum is:

$5x^2-x+4$

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What is the area of a circle?<br><br> The answer is A=πr2, but I want you to show the work.

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2 years ago

What percentage of 340 is 425?

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Answer:

125%

Step-by-step explanation:

1. Set up the equation

425/340 = x/100

(percentages are out of 100 so this equation means 425 out of 340 is equal to a number out of 100)

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340x = 42500

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3 years ago

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Question 26 pleaseee

LuckyWell [14K]

Answer:

The inequality is $55+10x\leq 105$

The greatest length of time Jeremy can rent the jet ski is 5 and Jeremy can rent maximum of 135 minutes.

Step-by-step explanation:

Given: Cost of first hour rent of jet ski is $55

Cost of each additional 15 minutes of jet ski is $10

Jeremy can spend no more than $105

Assuming the number of additional 15-minutes increment be "x"

Jeremy´s total spending would be first hour rental fees and additional charges for each 15-minutes of jet ski.

Lets put up an expression for total spending of Jeremy.

$\$55+ \$ 10\times x$

We also know that Jeremy can not spend more than $105

∴ Putting up the total spending of Jeremy in an inequality.

$\$ 55+\$10x\leq \$ 105$

Now solving the inequality to find the greatest number of time Jeremy can rent the jet ski,

⇒ $\$ 55+\$10x\leq \$105$

Subtracting both side by 55

⇒ $\$ 10x\leq \$50$

Dividing both side by 10

⇒ $x\leq \frac{50}{10}$

∴ $x\leq 5$

Therefore, Jeremy can rent for $60\ minutes + 5\times 15\\= 60\ minutes + 75= 135\ minutes$

Jeremy can rent maximum of 135 minutes.

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3 years ago

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:

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

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3 years ago

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