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tatuchka [14]
3 years ago
10

Write in standard form 3+4i/2-6i

Mathematics
1 answer:
ziro4ka [17]3 years ago
4 0
The answer would be 3-4i
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Julia collects colored beads for craft projects. Of julia's beads, 4/9 are silver, 1/5 are, gold and 1/4 are blue. The rest of t
klemol [59]

Answer:

19 red beads

Step-by-step explanation:

We first need to find a common denominator of 4/9, 1/5 and 1/4.

The common denominator is 180. Like in an expression, what we do to one side we have to do to the other.

Silver - 180/9 = 20 ; 20*4 = 80 so there are roughly 80 sliver beads.

Gold - 180/5 = 36 ; 36*1 = 36 so there are roughly 36 gold beads.

Blue - 180/4 = 45 ; 45*1 = 45 so there are roughly 56 blue beads.

180 - (silver+gold+blue) = red beads

180-161 = 19 red beads b/c ----->

80+36+45+19 = 180

4 0
3 years ago
X2+5xy+6y2 challenge question
saul85 [17]

Answer:

Step-by-step explanation:

x^2+5xy+6y^2\\ \\ x^2+2xy+3xy+6y^2\\ \\ x(x+2y)+3y(x+2y)\\ \\ (x+3y)(x+2y)

6 0
2 years ago
Solve the system by substitution. 4x+3y=5x=4y+6Options: A. The solution is ____B. There are infinitely many solutions. C. There
zvonat [6]

So we have the following system of equations:

\begin{gathered} 4x+3y=5 \\ x=4y+6 \end{gathered}

We need to solve it by substitution. This means that we have to take the expression for x given by the second equation and replace x with it in the first equation:

\begin{gathered} 4x+3y=5 \\ 4\cdot(4y+6)+3y=5 \\ 16y+24+3y=5 \\ 16y+3y=5-24 \\ 19y=-19 \\ y=-\frac{19}{19}=-1 \end{gathered}

So y=-1. If we use this value in the second equation:

\begin{gathered} x=4y+6 \\ x=4\cdot(-1)+6 \\ x=-4+6 \\ x=2 \end{gathered}

So we have x=2 and y=-1 which means that there's one solution. Then the correct answer is A and the solution is (2,-1).

5 0
10 months ago
Which statement describes the inverse of m(x) = x2 – 17x?
stealth61 [152]

Answer:

The correct option is;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

Step-by-step explanation:

The given information is that m(x) = x² - 17·x

The above equation can be written in the form;

y = x² - 17·x

Therefore;

0 = x² - 17·x - y

From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

By comparison to the equation,0 = x² - 17·x - y, we have;

a = 1, b = -17, and c = -y

Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;

x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}

Which can be simplified as follows;

x =  \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2}  \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}

And further simplified as follows;

x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}

Interchanging x and y in the function of the inverse, m⁻¹(x), we have;

m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;

m'(x) = 2·x - 17 = 0

x = 17/2

Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;

m''(x) = 2 > 0, therefore, the point is a minimum point on the graph

Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }} to increase m⁻¹(x) above the minimum.

8 0
2 years ago
What is the slope of the line with points (-5, -4) and (2, 7)?
jolli1 [7]

Answer:

m = 11/7

Step-by-step explanation:

m = y2-y1/x2-x1

m = 7-(-4)/2-(-5)

m = 7+4/2+5

m = 11/7

6 0
2 years ago
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