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3 years ago

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The sum of 17 and a number x is expand to 20 (Write an equation for the decription)

1 answer:

Rudiy273 years ago

3 0

So the sum of 17 and a number x means to add them on one side of the equals sign. The other side would be your 20.

17 + x = 20

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You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is shuffled, and you draw again. Fin

AlladinOne [14]

Answer:

3/52

Step-by-step explanation:

The picture card are j,q k and there are 4 of each so there are 12 picture cards

P( picture card) = picture card/ total

12/52 = 3/13

Then replace the card

There are 13 clubs

P( club) = club/ total

13/52 = 1/4

P(picture,replace,club) = 3/13*1/4 = 3/52

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3 years ago

Solve the following systems: 3x+4y=0 2x+3y=1

yanalaym [24]

Answer:

Answer is x= -4 and y= 3

Step-by-step explanation:

$given \: equations \: are \\ 3x + 4y = 0 \: \: and \: 2x + 3y = 1 \\ multiply \: by \: 2 \: in \: first \: equation \\ 6x + 8y = 0 \\ multiply \: by \: 3 \: in \: second \: equation \\ 6x + 9y = 3 \\ subtracting \: the \: above \: mentioned \: equation \: \\ we \: get \: - y = - 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 3 \\ substitute \: y = 3 \: in \: first \: equation \\ 3x + 4(3) = 0 \\ 3x = - 12 \\ x = - 4$

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<em>THANKS FOR GIVING ME THE OPPORTUNITY</em><em> </em><em>TO ANSWER YOUR QUESTION</em><em>. </em>

7 0

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:

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

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3 years ago

Use the substitution method to solve the system of equations. Please help me get this question right

vaieri [72.5K]

Answer: B (2,1)

You know what y is (x-1) so you substitute that for y in the other equation.

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3x+4x-4=10

7x=14

x=2

Then put x=2 into y=x-1

y=2-1

y=1

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3 years ago

Give the domain and range of G={(6.0),(-9,-3),(1,-3)}

VashaNatasha [74]

Answer:

Step-by-step explanation:

D={ 6 , -9 , 1 }

R={ 0 ,-3 }

7 0

3 years ago