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2 years ago

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

Mathematics

2 answers:

oksian1 [2.3K]2 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]2 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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2 years ago

Jeremy walked 6/8 of the way to school and ran the rest of the way. What fraction in simplest form shows the part of the way tha

Leno4ka [110]

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Find the area of an isosceles triangle with perimeter of 40 feet and a base of 12 feet. Round to the nearest whole number.

Aleksandr [31]

Answer: 76 ft2

Step-by-step explanation:

Perimeter = 2 side length +base length

40 = 2s +12

Solving for s:

40-12 =2s

28 =2s

28/2=s

14ft =side

Since the line which bisects and isosceles triangles is at a right angle to the base we can use the Pythagorean Theorem to find the height (see attachment)

c^2 = a^2 + b^2

Where c is the hypotenuse of the triangle (in this case 14) and a and b are the other sides. (Base divided by 2 is one side, the other side is the height)

Replacing with the values given:

14^2= 6^2 + x^2

196 = 36 + x^2

196-36 = x^2

160 = x^2

√160 = x

x = 12.64 (height)

Area of an isosceles triangle = 1/2 x base x height

A = 1/2 x 12 x 12.64 = 76 ft2

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2 years ago