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Taya2010 [7]
2 years ago
9

Solve 3x² + 4x = 2. (2 points)

Mathematics
1 answer:
uysha [10]2 years ago
6 0

Answer:

Step-by-step explanation:

As it is a second order equation, it means that it has two possible answers and they are x_1 and x_2.

The famous quadratic formula for solving any second order equation is the following:

x_{1} = \frac{-b + \sqrt{b^2 - 4 ac}}{2a}\\x_{2}=\frac{-b - \sqrt{b^2 - 4 ac}}{2a}

Where a is the coefficient of x^2, b is the coefficient of x, and c is the free term. In other words,

a = 3\\b=4\\c=-2

as the equation should be in the following form:

a x^2 + bx+c = 0

Therefore the possible answer should be the following,

\frac{-4 + \sqrt{4^2 - 4*3*(-2)}}{2*3}=\frac{-4 +\sqrt{16 + 24}}{6} =\frac{-4 + \sqrt{40}}{6}=\\ \frac{-4 + \sqrt{4*10}}{6} = \frac{-4 + 2\sqrt{10}}{6}\frac{2*(-2 + \sqrt{10})}{2*3} = \frac{-2 + \sqrt{10}}{3}

by dividing the numerator and denominator by 2, we can deduce the following,

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the second one.

Step-by-step explanation:

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3 years ago
Gary just started a new job as a nurse. he is given a starting salary of $58,550 per year. he is also told that his salary will
IRINA_888 [86]

Firts we need to find the rate of change, or in other words, the slope of the line.

Question 1:

a)

For this we can take two points in the form (years, salary). Then we can define as year 0 the year when Gary starts to work. In this year the salary is $58,550. The first point is (0, $58,550)

The next point we can take is at the year 10, when the salary of Gary will be $71,950. The second point is (10, $71,950)

b) Now that we have the two points, we can use the slope formula to get the rate of change. The slope formula is, for two points A and B:

\begin{gathered} \begin{cases}A(x_a,y_a) \\ B(x_b,y_b)\end{cases} \\ m=\frac{y_a-y_b}{x_a-x_b} \end{gathered}

In this case, we can call the points A(0, $58,550) and B(10, $71,950). Using the formula:

m=\frac{58,550-71,950}{0-10}=\frac{-13400}{-10}=1340

c) "The rate of change in Gary's salary is $1340 per year."

Question 2:

a) The slope intercept form of a line is:

y-y_1=m(x_{}-x_1)

Where:

y is the output of the function.

x is the input of the function. (we provide the function with a value for x and the function give us a value of y)

m is the slope of the line. We calculate it in question 1.

x1 is the x coordinate of a point we choose.

y1 is the y-coordinate of the same point of x1.

In this case, we know:

m = 1340;

And we can take the point (0, $58,550), thus:

x1 = 0

y1 = 58,550

b) Now we need to use all this values and use the slope-intercept form:

y-58,550=1340(x-0)

And solve to get:

y=1340x+58,550

Question 3:

a) Now we have a equation for the salary, we can use this to find the salary in 13 years. We just need to replace x = 13 in the equation:

\begin{gathered} \begin{cases}y=1340x+58,550 \\ x=13\end{cases} \\ y=1340\cdot13+58,550 \\ y=75,970 \end{gathered}

B) The salary of Gary in 13 years will be $75,970.

6 0
1 year ago
If fghi is a square slove for x
Korolek [52]

Answer:multiply by y

Step-by-step explanation:

5 0
3 years ago
I am very confused on what they are asking may you please help me
Akimi4 [234]
$133.5 dollars i think
7 0
3 years ago
Read 2 more answers
What number must you add to complete the square <br> x^2+x<br><br>A. 1/2<br>B. 2<br>C. 1/4<br>D. 1
Irina-Kira [14]

for ax^2+bx+c

when a=1, then the value of c that will make the quadratic a perfect square (allows you to complete the square) is (\frac{b}{2})^2


given x^2+x

b=1

so c=(\frac{1}{2})^2=\frac{1}{4}

answer is C

8 0
3 years ago
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