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3 years ago

Suppose y varies directly with x. If y = -4 when x = 8, what is the equation of direct variation?

2 answers:

8 0

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that }~~ \begin{cases} y=-4\\ x=8 \end{cases}\implies -4=k(8)\implies \cfrac{-4}{8}=k\implies -\cfrac{1}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{2}x~\hfill$

____ [38]3 years ago

6 0

Answer:

k = -1/2

y= -1/2x

Step-by-step explanation:

y = kx

We know y = -4 and x=8

-4 = k*8

Divide each side by 9

-4/8 = 8k/8

-1/2 =k

y= -1/2x

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The ratio of green M&Ms to

saveliy_v [14]

Answer:

the ratio is 2 to 5, all M&M's in total 28

Step-by-step explanation:

2 green to 5 yellow.

if there are 28 M&M's

you will count by 2 every 5

2 , 4 , 6 , 8 , 10

5 , 10 , 15 , 20 , 25

There are 10 green M&M's

4 0

2 years ago

Ax+by=(a-b) , bx - ay =(a+b) simultaneous linear equations using cross multiplication

Molodets [167]

Answer:

$x=1\,,\,y=-1$

Step-by-step explanation:

Given: $ax+by=a-b\,,\,bx-ay=a+b$

To solve: the given linear equations

Solution:

Consider the equations:

$A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0$

By method of cross multiplication:

$\frac{x}{B_1C_2-B_2C_1}=\frac{y}{C_1A_2-C_2A_1}=\frac{1}{A_1B_2-A_2B_1}$

For equations: $ax+by=a-b\,,\,bx-ay=a+b$

$ax+by-(a-b)=0\\bx-ay-(a+b)=0$

Take $A_1=a\,,\,B_1=b\,,\,C_1=-(a-b)\,,\,A_2=b\,,\,B_2=-a\,,\,C_2=-(a+b)$

So,

$\frac{x}{-b(a+b)-a(a-b)}=\frac{y}{-b(a-b)+a(a+b)}=\frac{1}{-a^2-b^2}\\\frac{x}{-ab-b^2-a^2+ab}=\frac{y}{-ab+b^2+a^2+ab}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{1}{-(a^2+b^2)}\,,\,\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\x=1\,,\,y=-1$

6 0

2 years ago

Find the surface area of the cylinder to the nearest tenth. Use 3.14 for n

zaharov [31]

Remember: The formula for surface area for cylinders are S= 2πrh + 2πr²
The 2πr² represents the circular parts of the cylinder.

First, let's find the lateral side of the cylinder.
→ 2 (3.14)(6)(15) = 565.2
Next, find the circular parts.
→ 2 (3.14)(6²)
→ 2 (3.14)(36) = 226.08
Add the two answers together.
→565.2 + 226.08 = 791.28
Round.
Your final answer is 791.3 in²
I hope this helps!

5 0

2 years ago

What is the answer to this

olasank [31]

Three times the variable m minus four is equal to fourteen.

Another way could be:

Four less than three multiplied by m is equivalent to fourteen.

The first way I put it is simpler but if you really want to impress your teacher then I suggest going with the second way.

Also if you are looking to solve the equation then it would be:

3m - 4 = 14

+4 +4

------------

3m = 18

----- -----

3 3

m = 5

Hope that helped :-)

8 0

2 years ago

Covert 2/3 years to months

natali 33 [55]

Multiply by 12 so 8

thank you hope this helps

3 0

2 years ago

Read 2 more answers