Ask question

Ask question

All categories

3 years ago

14

10. Write quadratic function with zeros -4, -7

1 answer:

Rashid [163]3 years ago

7 0

Hope that kinda helps.

You might be interested in

A 5-lb bag of apples costs $4.50, and an 8-lb bag of the same type of apples costs $7.52. Greg found the unit price, which is th

Sedaia [141]

Answer:

4 cents

Step-by-step explanation:

4.50 divide by is .9 and 7.52 divide by 8 is .94

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

2 years ago

Combine the like terms to create an equivalent expression.<br> 4n+6+n-2

NemiM [27]

5n+4 seems to be the answer

3 0

3 years ago

Read 2 more answers

The ratio of dogs to cats at an animal center 4to3. There are 16 dogs at the animal shelter. How many cats are their

WINSTONCH [101]

Answer:

yo wassup

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

HELP ASAP , WILL GIVE MOST BRAINIEST

stepladder [879]

The pink is $y>2x +4$ and the purple is $x+y\leq 6$ . Have a great day!

4 0

2 years ago