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2 years ago

Elimination Method: 6x - 4y = -24 and 4x + 5y = -2

Mathematics

1 answer:

nirvana33 [79]2 years ago

4 0

Answer:

$(-2;-6)$

Step-by-step explanation:

First of all, let's rewrite the first one after dividing both sides by 2.

$\left \{ {{3x-2y=-12\atop {4x+5y=-2}} \right.$

Now, let's pick one you want to eliminate.

<u>Eliminating x:</u> Let's multiply the first one by 4, the second by 3, and subtract one from the other. Rest is simply solving an equation in one variable

$4I-3II : 12x-8y-12x+15y = -48 - (-6)\\7y = -42 \rightarrow y= -6$

<u>Eliminating y:</u> Let's multiply the first by 5, the second by 2, and add them together. Rest is simply solving an equation in one variable

$5I+2II: 15x -10y +8x +10y = -60 +4\\23x = -56 \rightarrow x=-2$

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In the local frisbee league, teams have 7 members and each of the 4 teams takes turns hosting tournaments. At each tournament, e

mars1129 [50]

There are 4 teams in total and each team has 7 members. One of the team will be the host team.

Tournament committee will be made from 3 members from the host team and 2 members from each of the three remaining teams. Selecting the members for tournament committee is a combinations problem. We have to select 3 members out 7 for host team and 2 members out of 7 from each of the remaining 3 teams.

So total number of possible 9 member tournament committees will be equal to:

$7C3 \times 7C2 \times 7C2 \times 7C2\\ \\ = 324135$

This is the case when a host team is fixed. Since any team can be the host team, there are 4 possible ways to select a host team. So the total number of possible 9 member tournament committee will be:

$9 \times 324135\\ \\ =2917215$

Therefore, there are 2917215 possible 9 member tournament committees

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3 years ago

What are the domain and range of f(x) = (1/6)x + 2? domain: ; range: {y | y > 0} domain: ; range: {y | y > 2} domain: {x |

Trava [24]

Sir you posted question and answer? or are providing examples of preferred format?

7 0

3 years ago

Read 2 more answers

Ann is using a recipe that serves 20 people. The recipe requires 1/2 of a cup of sugar. How many cups of sugar does Ann need to

nikitadnepr [17]

Answer:

Step-by-step explanation:

x/70=0.5/20

x=35/20

x=1.75

Ann will need 1.75 cups of sugar.

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3 years ago

ACTIVITY 2

Harlamova29_29 [7]

Answer:

1.False

2.False

3.True

4.True

5.not sure, it could be true or false because adjacent angles can add up to 180 or even 360 as long as they have the same vertex

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3 years ago

Find three positive numbers whose sum is 140 and whose product is a maximum. (Enter your answers as a comma-separated list.)

Paladinen [302]

Answer:

$\frac{140}{3}, \frac{140}{3}, \frac{140}{3}$

Step-by-step explanation:

Let the numbers be $x, y\ and\ z.$

Such that:

$x + y + z = 140$

Make z the subject

$z = 140 -x - y$

For their product to be maximum, we have:

$f(x,y,z) = xyz$

Substitute $z = 140 -x - y$ in $f(x,y,z) = xyz$

$f(x,y) = xy(140 - x - y)$

Open bracket

$f(x,y) = 140xy - x^2y - xy^2$

Differentiate w.r.t x and y

$f_x=140y - 2xy - y^2$

$f_y=140x - x^2 - 2xy$

Since the products are maximum, then $f_x = f_y = 0$

For $f_x=140y - 2xy - y^2$

$140y - 2xy - y^2 = 0$

Factorize:

$y(140 - 2x - y) = 0$

Split

$y = 0\ or\ 140 - 2x - y = 0$

Make y the subject

$y = 0\ or\ y = 140 - 2x$

For $f_y=140x - x^2 - 2xy$

$140x - x^2 - 2xy = 0$

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

Substitute y = 0

$140x - x^2 -2x*0 = 0$

$140x - x^2 = 0$

Factorize

$x(140 - x)= 0$

$x = 0\ or\ 140-x = 0$

$x = 0\ or\ x = 140$

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

Substitute $y = 140 - 2x$

$140x - x^2 - 2xy = 0$

$140x - x^2 - 2x(140 - 2x) = 0$

$140x - x^2 - 280x + 4x^2 = 0$

Re-arrange

$4x^2 -x^2 +140x - 280x = 0$

$3x^2 -140x = 0$

Factor x out

$x(3x - 140) = 0$

Divide through by x

$3x - 140 = 0$

$3x = 140$

$x = \frac{140}{3}$

Recall that: $y = 140 - 2x$

$y = 140 - 2 * \frac{140}{3}$

$y = 140 - \frac{280}{3}$

Take LCM

$y = \frac{140*3-280}{3}$

$y = \frac{140}{3}$

Recall that:

$z = 140 -x - y$

$z = 140 - \frac{140}{3} - \frac{140}{3}$

Take LCM

$z = \frac{3 * 140- 140 - 140}{3}$

$z = \frac{140}{3}$

Hence, the numbers are:

$\frac{140}{3}, \frac{140}{3}, \frac{140}{3}$

8 0

3 years ago