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2 years ago

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6x+7y=4x+4y6x+7y=4x+4y6, x, plus, 7, y, equals, 4, x, plus, 4, y Complete the missing value in the solution to the equation. (((

,-4),−4)

1 answer:

Dmitrij [34]2 years ago

8 0

Answer:

<h3>The missing value in the given solution is x=6</h3><h3>Therefore the solution is (6,-4)</h3>

Step-by-step explanation:

Given equation is $6x+7y=4x+4y\hfill (1)$

<h3>To find the missing value in the solution to the equation :</h3>

Let missing value in the solution be x
Then the solution of the given equation is (x,-4)

Substitute the value of y=-4 in the given equation (1) we get

$6x+7(-4)=4x+4(-4)$

$6x-28=4x-16$

$6x-28-(4x-16)=4x-16-(4x-16)$

$6x-28-4x+16=4x-16-4x+16$ ( adding the like terms )

$2x-12=0$

$2x=12$

$x=\frac{12}{2}$

Therefore x=6

<h3>Therefore the missing value in the given solution is x=6</h3><h3>Therefore the solution is (6,-4)</h3>

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timama [110]

Use the change-of-basis identity,

$\log_x(y) = \dfrac{\ln(y)}{\ln(x)}$

to write

$xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}$

Use the product-to-sum identity,

$\log_x(yz) = \log_x(y) + \log_x(z)$

to write

$xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}$

Redistribute the factors on the left side as

$xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}$

and simplify to

$xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)$

Now expand the right side:

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}$

Simplify and rewrite using the logarithm properties mentioned earlier.

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1$

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

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1 year ago

A bag has 5 blue marbles, 3 red marbles, and 2 green marbles. We draw two marbles, one at a time, with replacement. What is the

VMariaS [17]

Answer: $\frac{1}{10}$

<u>Step-by-step explanation:</u>

Blue = 5, Red = 3, Green = 2, Total = 10

Probability = First draw and Second draw

= $\frac{5}{10}$ x $\frac{2}{10}$

= $\frac{10}{100}$

= $\frac{1}{10}$

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2 years ago

What is the standard form of 0.0005?

mash [69]

5 * 10 raise to power of - 4

7 0

2 years ago

Which ordered pair is a solution to the equation?

Mama L [17]

Answer:

y=4/5x-3 - (-5, -7)

Step-by-step explanation:

So to solve this, lets just plug in each value for x, and see if the y value we get is equal to one of our answers.

So we have (-10, 5)

Well plug in -10 for 4/5x we get:

-40/5=-8

Next we take that value and solve:

y=-8-3

y=-11

The answer for this was 5, not -11.

Ill skip a few steps:

(10, -11):

Plug in 10 we get:

y=8-3 which is y=5. This is not right, for it needed to be -11.

Next we have (5, -1)

This gets us y=4-3 this is y=1 which is not -1. So thats not right.

Finally we have (-5, -7):

This gets us y=-4-3 this is y=-7. What was our y value? -7!

So the answer is (-5, -7)

I hope this helps! :)

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2 years ago

What is the volume of the right rectangular prism? Enter your answer in the box.

Nutka1998 [239]

Answer:

1000 cm²

Step-by-step explanation:

Given:

Length = 10 cm
Width = 12.5 cm
Height = 8 cm

<u>Formula:</u>

$\text{Volume = Length} \times \text{Width} \times \text{Height}$

Substitute the length, width, and the height of the prism to determine the volume of the prism.

$\implies \text{Volume = 10} \times 12.5 \times 8$

Simplify the right hand side of the equation, as needed;

$\implies \text{Volume = 10} \times 12.5 \times 8$

$\implies \text{Volume =}\ 125 \times 8$

$\implies \boxed{\text{Volume =}\ 1000 \ \text{cm}^{2} }$

Therefore, the volume of the prism is 1000 cm².

7 0

1 year ago