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3 years ago

How do you solve for #23

Mathematics

1 answer:

Bingel [31]3 years ago

8 0

5 is you answer because absolute value is the distance on a number line from 0

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Multiplicacion 5(3x-2)

Lena [83]

Answer: 15x-2

Step-by-step explanation: ?

7 0

1 year ago

Read 2 more answers

If a,b,c and d are positive real numbers such that logab=8/9, logbc=-3/4, logcd=2, find the value of logd(abc)

Eva8 [605]

We can expand the logarithm of a product as a sum of logarithms:

$\log_dabc=\log_da+\log_db+\log_dc$

Then using the change of base formula, we can derive the relationship

$\log_xy=\dfrac{\ln y}{\ln x}=\dfrac1{\frac{\ln x}{\ln y}}=\dfrac1{\log_yx}$

This immediately tells us that

$\log_dc=\dfrac1{\log_cd}=\dfrac12$

Notice that none of $a,b,c,d$ can be equal to 1. This is because

$\log_1x=y\implies1^{\log_1x}=1^y\implies x=1$

for any choice of $y$ . This means we can safely do the following without worrying about division by 0.

$\log_db=\dfrac{\ln b}{\ln d}=\dfrac{\frac{\ln b}{\ln c}}{\frac{\ln d}{\ln c}}=\dfrac{\log_cb}{\log_cd}=\dfrac1{\log_bc\log_cd}$

so that

$\log_db=\dfrac1{-\frac34\cdot2}=-\dfrac23$

Similarly,

$\log_da=\dfrac{\ln a}{\ln d}=\dfrac{\frac{\ln a}{\ln b}}{\frac{\ln d}{\ln b}}=\dfrac{\log_ba}{\log_bd}=\dfrac{\log_db}{\log_ab}$

so that

$\log_da=\dfrac{-\frac23}{\frac89}=-\dfrac34$

So we end up with

$\log_dabc=-\dfrac34-\dfrac23+\dfrac12=-\dfrac{11}{12}$

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Another way to do this:

$\log_ab=\dfrac89\implies a^{8/9}=b\implies a=b^{9/8}$

$\log_bc=-\dfrac34\implies b^{-3/4}=c\implies b=c^{-4/3}$

$\log_cd=2\implies c^2=d\implies\log_dc^2=1\implies\log_dc=\dfrac12$

Then

$abc=(c^{-4/3})^{9/8}c^{-4/3}c=c^{-11/6}$

So we have

$\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}$

4 0

3 years ago

I really think it’s B ...Help?

kvv77 [185]

The correct answer is c y-5=4(x-7)

7 0

3 years ago

What’s the answer to this problem?

Vinil7 [7]

×=23

:) :) :) :) :););) ;););)

5 0

3 years ago

The area of a rectangle is 30 + 12x. List at least 3 possibilities for the length and width of the rectangle.

Gala2k [10]

Answer:

Below in bold.

Step-by-step explanation:

Area = 30 + 12x and area is also = to width * length so we need to look for factors of 30 + 12x.

30 + 12x = 6(5 + 2x)

So 6 and 5 + 2x is one possible answer.

3 and 10 + 4x is another.

12 and 2.5 + x is another.

If we multiply these pairs together we see that the result is

30 + 12x in each case.

6 0

3 years ago