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3 years ago

3x+3y+2(2x-y) equivalent fractions to this problem

Mathematics

1 answer:

Anastaziya [24]3 years ago

6 0

Distribute the 2 into the 2x and -y

Then add “like terms” which are 3x and 4x... 3y and -2y

Which then becomes 7x+y

There are no more “like terms” so that is your final answer

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If p=(-3,-2) and q=(1,6) are the endpoints of the diameter of a circle find the equation of the circle

stira [4]

Answer:

The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²

 or 

The equation of the circle x² + 2 x + y² - 4 y = 15

Step-by-step explanation:

Given points end Points are p(-3,-2) and q( 1,6)

The distance of two points formula

P Q = $\sqrt{x_{2} - x_{1})^{2} + ((y_{2} -y_{1})^{2} }$

P Q = $\sqrt{1 - (-3)^{2} + ((6 -(-2))^{2} }$

P Q = $\sqrt{16+64} = \sqrt{80}$

The diameter 'd' = 2 r

2 r = √80

= $\sqrt{16 X 5}$

= $4 \sqrt{5}$

r = 2√5

Mid-point of two end points

$(\frac{x_{1} + x_{2} }{2} , \frac{y_{1} +y_{2} }{2} ) = (\frac{-3+1}{2} ,\frac{-2 +6}{2} )$

= (-1 ,2)

Mid-point of two end points = center of the circle

(h,k) = (-1 , 2)

The equation of the circle

(x -h )² +(y-k)² = r²

(x -(-1) )² +(y-(2))² = (2(√5))²

x² + 2 x + 1 + y² - 4 y + 4 = 20

x² + 2 x + y² - 4 y = 20 -5

x² + 2 x + y² - 4 y = 15

Final answer:-

The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²

 or 

The equation of the circle x² + 2 x + y² - 4 y = 15

6 0

3 years ago

An ice cream cone is filled with a vanilla and chocolate ice cream at a ratio of 2:

nirvana33 [79]

$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\quad 
\begin{cases}
r=radius\\
h=height\\
----------\\
diameter=2\\
r=\frac{diameter}{2}\\
\quad = 1\\
h=6
\end{cases}\implies V=\cfrac{\pi\cdot 1^2\cdot 6}{3}
\\\\\\
V=2\pi \\\\
-------------------------------$

$\bf \cfrac{\stackrel{vanilla}{volume}}{\stackrel{chocolate}{volume}}\qquad 2:1\qquad \cfrac{2}{1}\implies \cfrac{2\cdot \frac{V}{2+1}}{1\cdot \frac{V}{2+1}}\implies \cfrac{2\cdot \frac{2\pi }{2+1}}{1\cdot \frac{2\pi }{2+1}}
\\\\\\
\cfrac{2\cdot \frac{2\pi }{3}}{1\cdot \frac{2\pi }{3}}\implies \cfrac{\quad \frac{4\pi }{3}\quad }{\frac{2\pi }{3}}$

3 0

3 years ago

Read 2 more answers

What is 1 3/7 as an improper and equivalent fraction?

Alex777 [14]

Improper: multiple the 1 by the denominator 1x7 = 7 then add to numerator number.

Final answer is 10/7

And equivalent fraction could be anything as long as it’s equal to the original.

Possible could be 1 9/21

4 0

3 years ago

What is the equation of the line in slope–intercept form that passes through the point (0, 3) and is perpendicular to the line y

Liula [17]

Y = 2x - 6 => slope is 2
For perpendicular lines, m2 = -1/m1
Slope of the required line is -1/2
Required equation is (y - 3)/(x - 0) = -1/2 => y - 3 = -1/2 x => y = -1/2 x + 3

6 0

3 years ago

Read 2 more answers

The Sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.

Step2247 [10]

Answer:

8 and 17

Step-by-step explanation:

Let the number x and y

Sum of numbers, x + y = 25 -----------( 1 )

One number exceeds other by 9,

that is difference between the numbers is 9, x - y = 9

=> x = 9 + y --------- ( 2 )

Substitute ( 2 ) in ( 1 )

( 9 + y ) + y = 25

2y = 25 - 9

2y = 16

y = 8

Substitute y = 8 in ( 2 ) : x = 9 + y

= 9 + 8 = 17

Therefore the 2 numbers are 8 and 17

3 0

3 years ago

Read 2 more answers