HELP PLS ILL GIVE BRAINLIEST ANSWER HELP ASAP!!

777dan777 [17]

Answer:

The last answer is correct. (x: 1,2,3,4 ; y: -5,0,5,10)

Step-by-step explanation:

In a linear function, the rate of increase/decrease is constant (the same). For the last answer, since for every x increase, y increases by 5, it is linear and has a constant rate of change.

3 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

3 years ago

Which expression is equivalent to 5^4(5^-^3)^2? 5^1 5^2 1/5^1 1/5^2

inessss [21]

Answer:

1 5th ^2.

Step-by-step explanation:

8 0

3 years ago

How do you show abc translation 5 units to the right and 2 units up

ankoles [38]

X + 5 , y + 2 when you are translating and if you are going up or right it’s going to be positive and it’s going to be negative if you’re going down or left

5 0

3 years ago

Plz help I will mark you brainlist plz help

lakkis [162]

Answer

1.) 50 mistakes per test

2.) 8 girls per group

3.) 27 pages per hour

4.) $1.30 per banana

5.) $0.50 per pencils

6.) 13 points per game

7.) $1.25 per cup of tea

8.) 65 liters per hour

9.) 25 calls per hour

10.) 35 words per minute

11.) 8 miles per liter of gas

12.) 0.4 eggs per day

13.) $28 per hour

14.) 3.5 miles per hour

Step-by-step explanation:

*Hope this helped*

8 0

3 years ago

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