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3 years ago

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Mathematics

1 answer:

Andre45 [30]3 years ago

7 0

Answer:

the one real zero is in the interval (-1, 0)

Step-by-step explanation:

Descartes' rule of signs tells you there are 0 or 2 positive real zeros. Changing the signs of the odd-degree terms and applying that rule again tells you there is one negative real zero. At the same time, those coefficients (-3, -5, -5, +7) have a negative sum, so you know ...

f(-1) = -6

f(0) = +7

so there is a zero in the interval (-1, 0).

You can try a few values between x=0 and x=10 to see what the function does in that part of the graph. You find ...

f(1) = 10

f(2) = 21

f(3) = 58

So, it is safe to conclude that there are no real zeros for x > 0.

The only real zero of f(x) is in the interval (-1, 0).

_____

I like to use a graphing calculator for problems like this.

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Marcus wants to know if students at his school like to sing in the shower. He polled 40 students who were not part of the school

telo118 [61]

Answer:

Step-by-step explanation:

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3 years ago

HELLOOOO HELP PLEASE

MA_775_DIABLO [31]

Answer:

$2*log(x)+log(y)$

Step-by-step explanation:

So, there are two logarithmic identities you're going to need to know.

<em>Logarithm of a power</em>:

$log_ba^c=c*log_ba$

So to provide a quick proof and intuition as to why this works, let's consider the following logarithm: $log_ba=x\implies b^x=a$

Now if we raise both sides to the power of c, we get the following equation: $(b^x)^c=a^c$

Using the exponential identity: $(x^a)^c=x^{a*c}$

We get the equation: $b^{xc}=a^c$

If we convert this back into logarithmic form we get: $log_ba^c=x*c$

Since x was the basic logarithm we started with, we substitute it back in, to get the equation: $log_ba^c=c*log_ba$

Now the second logarithmic property you need to know is

<em>The Logarithm of a Product</em>:

$log_b{ac}=log_ba+log_bc$

Now for a quick proof, let's just say: $x=log_ba\text{ and }y=log_bc$

Now rewriting them both in exponential form, we get the equations:

$b^x=a\\b^y=c$

We can multiply a * c, and since b^x = a, and b^y = c, we can substitute that in for a * c, to get the following equation:

$b^x*b^y=a*c$

Using the exponential identity: $x^{a}*x^b=x^{a+b}$ , we can rewrite the equation as:

$b^{x+y}=ac$

taking the logarithm of both sides, we get:

$log_bac=x+y$

Since x and y are just the logarithms we started with, we can substitute them back in to get: $log_bac=log_ba+log_bc$

Now let's use these identities to rewrite the equation you gave

$log(x^2y)$

As you can see, this is a log of products, so we can separate it into two logarithms (with the same base)

$log(x^2)+log(y)$

Now using the logarithm of a power to rewrite the log(x^2) we get:

$2*log(x)+log(y)$

3 0

2 years ago

If 5 sips +4 gulps = 1 glass and 13 sips +7 gulps = 2 glasses, how many sips equal a gulp?

nataly862011 [7]

Answer:

3 sips equal a gulp

Step-by-step explanation:

we have

$5sips+4gulps=1glass$ ----> equation A

$13sips+7gulps=2glass$

Divide by 2 both sides

$6.5sips+3.5gulps=1glass$ ----> equation B

equate equation A and equation B

$5sips+4gulps=6.5sips+3.5gulps$

Group terms that contain the same variable

$4gulps-3.5gulps=6.5sips-5sips$

$0.5gulps=1.5sips$

$gulps=(1.5/0.5)sips$

$gulps=3sips$

therefore

3 sips equal a gulp

3 0

3 years ago

If X - A = B, what is X?

sineoko [7]

Answer:

x=a+b

Step-by-step explanation:

Just move a to the other side (by adding it)

6 0

2 years ago

Read 2 more answers

What’s the slope of (-3, 6), (2, 6)?

IRINA_888 [86]

Answer:

Step-by-step explanation:

(y2-y1)/(x2-x1)

6(y2)-6(y1)= 0

2(x2)- -3(x1)=5

0/5=0

4 0

3 years ago