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3 years ago

6

Solve for x.

1 answer:

Artyom0805 [142]3 years ago

5 0

Answer:

x = - 4

Step-by-step explanation:

Given

5x - 11 = 7x - 3 ( subtract 7x from both sides )

- 2x - 11 = - 3 ( add 11 to both sides )

- 2x = 8 ( divide both sides by - 2 )

x = - 4

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Given that 3^x = 4^y = 12^z, show that z = (xy)/(x+y).

irinina [24]

$3^{x} = 4^{y} = 12^{z}$
$3^{x} = 4^{y} = (4 \cdot 3)^{z}$
$3^{x} = 4^{y} = 4^{z} \cdot 3^{z}$

$\text{Let a } = 3^{x} = 4^{y} = 4^{z} \cdot 3^{z}$
$log_3a = x$
$log_4a = y$
$log_{(4 \cdot 3)}a = z$

Using change of base:
$x = \frac{lna}{ln3}$
$y = \frac{lna}{ln4}$
$z = \frac{lna}{ln(4 \cdot 3)}$

$ln3 = \frac{lna}{x}$
$ln4 = \frac{lna}{y}$
$ln(4 \cdot 3) = \frac{lna}{z}$

Now, ln(4 · 3) = ln(4) + ln(3)

$\frac{lna}{z} = \frac{lna}{x} + \frac{lna}{y}$
$\frac{1}{z} = \frac{1}{x} + \frac{1}{y}$
$\frac{1}{z} = \frac{x + y}{xy}$

$\therefore z = \frac{xy}{x + y}$

8 0

4 years ago

What is the volume of the composite figure?<br> 12in<br> 4 in<br> 3 in.<br> 7 in.

Minchanka [31]

Answer:

Step-by-step explanation:

$V_p = b \cdot h \cdot w$ , where b, h, w are base, height and width respectively.

$V_{sp} = \frac{1}{3} \cdot {A_b} \cdot h$ , where h is the height, and A_b is the area of the base.

First let's calculate the volume of the paralelipiped by the first formula.

$V_p = 7 \cdot 4 \cdot 3 = 84 in^2$

Then let's find out the height of the pyramid, which is 12 - 4 = 8 in.(See drawing)

Then the area of the base of the square pyramid is simply.

$A_r = 3 \cdot 7 = 21 in^2$

Now we can find the volume of the pyramid.

$V_{sp} = \frac{1}{3} \cdot 21 \cdot 8 = 56 in^3$

To find the total volume, let's add both volumes.

$V_T = 84 + 56 = 140 in^3$

5 0

3 years ago

The sum of two numbers is 92. Their difference is 20. Find the numbers

Nikolay [14]

Answer:

72

Step-by-step explanation:

you just subtract.

8 0

3 years ago

Read 2 more answers

I NEED HELP IM CONFUSED

mihalych1998 [28]

Answer:

<h2>x=-2 or x=8</h2>

Step-by-step explanation:

Isolate by the x from one side of the equation.

|x-3|=5

x-3=-5 and x-3=5

1. x-3=-5

Add 3 from both sides.

x-3+3=-5+3

Solve.

-5+3=(-2)

x=-2

2. x-3=5

Add 3 from both sides.

x-3+3=5+3

Solve.

5+3=8

x=8

Therefore, the correct answer is x=-2 or x=8.

3 0

3 years ago

PLS HELP ITS DUE TODAY!!

dezoksy [38]

Answer:

y=20x75 is the answer

Step-by-step explanation:

You can basically eliminate other two choices since they are division

8 0

3 years ago