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3 years ago

Solve the system of equations 3x-4y=18 -2x-3y=5

Mathematics

2 answers:

oksian1 [2.3K]3 years ago

6 0

$\left\{\begin{array}{ccc}3x-4y=18&/\cdot2\\-2x-3y=5&/\cdot3\end{array}\right\\\\+\left\{\begin{array}{ccc}6x-8y=36\\-6x-9y=15\end{array}\right\\-------------\\.\ \ \ \ \ \ \ -17y=51\ \ \ \ |:(-17)\\.\ \ \ \ \ \ \ \ \ y=-3\\\\3x-4(-3)=18\\3x+12=18\\3x=18-12\\3x=6\ \ \ \ |:3\\x=2\\\\Answer:x=2\ and\ y=-3\to(2;-3)$

Dmitry [639]3 years ago

5 0

$\left \{ {\big{ 3x-4y=18\ /\cdot2} \atop\big {-2x-3y=5\ /\cdot3}} \right.\\\\ \left \{ {\big{ 6x-8y=36} \atop\big {-6x-9y=15}} \right.\\---------\\-17y=51\ /:(-17)\\.\ \ \ \ \ \ y=-3\\\\3x-4y=18\\\Rightarrow\ \ 3x-4\cdot(-3)=18\ \ \ \Rightarrow\ \ 3x+12=18\ \ \ \Rightarrow\ \ 3x=6\ \ \ \Rightarrow\ \ x=2\\\\ \left \{ {\big{ x=2\ \ \ } \atop\big {y=-3}} \right.$

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Readings on a thermometer are normally distributed with a mean of 0C° and a standard deviation of 1.00. What is the probability

hichkok12 [17]

Given mean = 0 C and standard deviation = 1.00

To find probability that a random selected thermometer read less than 0.53, we need to find z-value corresponding to 0.53 first.

z= $\frac{x-mean}{standard deviation} = \frac{0.53-0}{1.00} = 0.53$

So, P(x<0.53) = P(z<0.53) = 0.701944

Similarly P(x>-1.11)=P(z>-1.11) = 1-P(z<-1.11) = 0.8665

For finding probability for in between values, we have to subtract smaller one from larger one.

P(1.00<x<2.25) = P(1.00<z<2.25) = P(z<2.25)- P(z<1.00) = 0.9878 - 0.8413 = 0.1465

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3 years ago

The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and

NemiM [27]

Answer:

5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

$60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120$

Let's find h with the quadratic formula:

$\fbox {Quadratic formula:} \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}$

h = 8 or h = -7.5

But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

Now we can calculate the hypotenuse with the Pythagorean equation

$\fbox {Pythagorean equation:}$ <em>The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle). </em>

The base and the height are our legs. We will use "H" for the hypotenuse

$H^2 = b^2 + h^2 = 15^2 + 8^2 = 289\\ H = \sqrt {289} = 17$

H = 17

If we decrease the base and the height by 2 centimeters, we have

b' = 15 - 2 = 13 and h' = 8 - 2 = 6

With this, let's calculate the new hypotenuse:

$H'^2 = b'^2 + h'^2 = 13^2 + 6^2 = 205\\ H' = \sqrt {205} \approx 14.3$

$H' \approx 14.3$

So, the hypotenuse decreases $H - H' \approx 17 - 14.3 = 2.7$

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AlexFokin [52]

Answer:

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Hope this helps!

Step-by-step explanation:

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