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2 years ago

One-step equations: integers 18=a/2

Mathematics

2 answers:

denpristay [2]2 years ago

7 0

Answer:

Step-by-step explanation:

18=a/2

2*18=a

36=a

Serjik [45]2 years ago

5 0

18= a/2

Cross multiple a= 18*2 and then a=36

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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

2 years ago

50 PTS

liubo4ka [24]

Answer:

The correct option is B.

Step-by-step explanation:

The amount of money, in dollars, in a savings account after x years is given by $M(x) = 10000(1.03)^{x}$

This above equation represents that $10000 becomes M(x) after x years at a rate of interest 3% compounded in each year.

Therefore, the value in the expression 1.03 represents that there is a 3 percent increase in the savings account each year.

So, the correct option is B. (Answer)

8 0

3 years ago

First examples pt 1 no one answer

andrew11 [14]

Answer:

It takes the second worker 11 hours to do the job alone

Step-by-step explanation:

The problem tells you how to work it.

$\dfrac{1}{11}+\dfrac{1}{x}=\dfrac{2}{11}\\\\x+11=2x \qquad\text{multiply by 11x}\\\\11=x \qquad\text{subtract x}$

x = 11 tells you the second worker takes 11 hours to do the job alone.

_____

You can also work directly with the fractions. Subtract 1/11 and you have ...

1/x = 1/11

It should not be a real stretch to see that x=11. If you need, you can multiply both sides by 11x to get 11=x.

3 0

2 years ago

I need help ASAP!!!please help

muminat

Use 6 triangles then 2 square so you will only be using a total of 4 square and 12 triangles

8 0

2 years ago

What’s the slope and y - intercept of this equation ?

zavuch27 [327]

Answer:

Slope = - $\frac{7}{3}$

Y-intercept = 4

Step-by-step explanation:

-> See attached

-> This equation is in slope-intercept form.

[] When we use y = mx + b, the m is the slope and the b is our y-intercept.

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

5 0

2 years ago

Read 2 more answers