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3 years ago

Steps to solve x/8-5=-1

Mathematics

1 answer:

topjm [15]3 years ago

4 0

Answer: x = 32

Step-by-step explanation:

x/8 - 5 = -1

Add 5 both sides : x/8 = 4

Multiply both sides by four: x=4 times 8

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Can someone please help me

solniwko [45]

(-2,2) (8,2) (8,-2) (-2,-2)

7 0

3 years ago

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

If x- 2 is a factor of x^2 -bx+ b, where b is a constant, what is the value of b

KATRIN_1 [288]

$\bf x^2-\underline{b} x+b\implies \stackrel{given}{(x-2)}~(x-y)\impliedby \textit{now let's do some FOIL}\\\\
-------------------------------\\\\
\begin{cases}
-yx-2x=-\underline{b}x\implies y+2=\underline{b}\\
(-2)(-y)=b\implies 2y=b
\end{cases}
\\\\\\
\underline{b}=b\implies y+2=2y\implies 2=y$

what is b? from the first equation in the system, y + 2 = b.

4 0

3 years ago

What is 150% of 200. Show work. ASAP

zalisa [80]

150 % of 200

150 / 100 = 1.5

1.5 * 200 = 300

hope this helps!.

8 0

3 years ago

Read 2 more answers

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Juli2301 [7.4K]

Answer:

w+4 is bigger!