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ipn [44]
3 years ago
8

2x + 5 = 4 (5/4 - 1/2 x)

Mathematics
1 answer:
ruslelena [56]3 years ago
6 0

Answer:

x=0

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2x+5=−2x+5

Step 2: Add 2x to both sides.

2x+5+2x=−2x+5+2x

Step 3: Subtract 5 from both sides.

4x+5−5=5−5

4x=0

Step 4: Divide both sides by 4.

4x/4=0/4

X=0

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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}

###

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
3 question problem, plz HELP!!!!!!
pav-90 [236]

Answer:

the four point cannot be on the same line , but they have to be on the plane.

A D C E

collinear means on the same line

so ABC

non-coplanar means the point do not lie on the same plane so you can include point F

F A D B

3 0
3 years ago
Standard form of y=7x+10
Ugo [173]

Answer: 7x-y=10

Step-by-step explanation:

4 0
3 years ago
PLEASE HELP ASAP
zaharov [31]
Wouldn’t it be 0, as that’s when their values are both equal to each other, making the equation true?
4 0
3 years ago
Given sin x=13/85 and tan x=13/84 .
olga55 [171]

ANSWER:

We know that,

  • tanΘ = sinΘ/cosΘ

cosΘ = sinΘ/tanΘ

So, cosΘ = 13/85 ÷ 13/84

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7 0
3 years ago
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