I need help please and thank you

Solve the equation: 5(r + 4) = -12 + 7r*

sveticcg [70]

Answer:

$r=16$

Step-by-step explanation:

$5(r + 4) = -12 + 7r$

➠ Use the distributive property to multiply 5 by r +4:

$5r+20=-12+7r$

➠ Subtract 7r from both sides:

$5r+20-7r=-12$

➠ Combin 5r and -7r to get -2r:

$-2r+20=-12$

➠ Subtract 20 from both sides:

$-2r=-32$

➠ Divide both sides by -2:

$r=\frac{-32}{-2}$

$r=16$

OAmalOHopeO

5 0

3 years ago

Are the lines in the figure parallel, perpendicular, or neither?

icang [17]

Answer:

Perpendicular

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 6x(1/3) + 3x(4/3). You must justi

stealth61 [152]

Applying our power rule gets us our first derivative,

$\rm f'(x)=6\frac13x^{-2/3}+3\cdot\frac43x^{1/3}$

simplifying a little bit,

$\rm f'(x)=2x^{-2/3}+4x^{1/3}$

looking for critical points,

$\rm 0=2x^{-2/3}+4x^{1/3}$

We can apply more factoring.
I hope this next step isn't too confusing.
We want to factor out the smallest power of x from both terms,
and also the 2 from each.

$0=2x^{-2/3}\left(1+2x\right)$

When you divide x^(-2/3) out of x^(1/3),
it leaves you with x^(3/3) or simply x.

Then apply your Zero-Factor Property,

$\rm 0=2x^{-2/3}\qquad\qquad\qquad 0=(1+2x)$

and solve for x in each case to find your critical points.

Apply your First Derivative Test to further classify these points. You should end up finding that x=-1/2 is an relative extreme value, while x=0 is not.

Let's come back to this,

$\rm f'(x)=2x^{-2/3}+4x^{1/3}$

and take our second derivative.

$\rm f''(x)=-\frac43x^{-5/3}+\frac43x^{-2/3}$

Looking for inflection points,

$\rm 0=-\frac43x^{-5/3}+\frac43x^{-2/3}$

Again, pulling out the smaller power of x, and fractional part,

$\rm 0=-\frac43x^{-5/3}\left(1-x\right)$

And again, apply your Zero-Factor Property, setting each factor to zero and solving for x in each case. You should find that x=0 and x=1 are possible inflection points.

Applying your Second Derivative Test should verify that both points are in fact inflection points, locations where the function changes concavity.

8 0

4 years ago

E. What was the population in 1995? (the initial population for this situation) *

MaRussiya [10]

Answer:

Part e) $501,170\ people$

Part f) The decay factor is 0.98

Part g) Decreasing

Part h) $y=25,400(1+0.11)^x$

Part i) $345,071\ people$

Step-by-step explanation:

we have

$f(x)=501,170(0.98)^x$

where

x ----> is the number of years since 1995

f(x) ----> is the population of a Texas city

Part e) What was the population in 1995?

we know that

The equation of a exponential function decay is of the form

$y=a(1-r)^x$

where

a represent the initial value (y-intercept of the function)

therefore

In the given function

The initial value is the value of the function when the value of x is equal to zero

so

For x=0

$f(x)=501,170(0.98)^0=501,170\ people$

Part f) What is the growth/decay factor?

we know that

The equation of a exponential decay function is of the form

$y=a(1-r)^x$

where

(1-r) ----> is the decay factor

In this problem we have

$f(x)=501,170(0.98)^x$

(1-r)=0.98

therefore

The decay factor is 0.98

Part g) Is the population increasing or decreasing?

we know that

If the factor is greater than 1 then the population is increasing

If the factor is less than 1 and greater than zero, then the population is decreasing

In this problem

the factor is less than 1

0.98< 1 ----> is a decay factor

therefore

The population is decreasing

In the year 1995, the population of a town in Texas was recorded as 25,400 people. Each year since 1995, the population has increased on average by 11% each year

Part h) Write an exponential function to represent the town's population, y, based on the number of years that pass, x after 1995

we know that

The equation of a exponential growth function is of the form

$y=a(1+r)^x$

we have

$a=25,400\\r=11\%=11/100=0.11$

substitute

$y=25,400(1+0.11)^x$

$y=25,400(1.11)^x$

Part i) Based on the function, what is the population predicted to be in the year 2020?

Remember that the number of years is since 1995

so

x=2020-1995=25 years

substitute the value of x in the exponential function

$y=25,400(1.11)^25=345,071\ people$

3 0

4 years ago

Read 2 more answers

A rocket generates a net force (F) of 2,050,000 newtons, and the rocket mass (m) is 40,000 kilograms

SVEN [57.7K]

From the given equation above, F = ma, acceleration may be calculated by slightly modifying the equation into a = F / m. Substituting the known values for force and mass,

a = 2,050,000 N / 40,000 kg = 51.25 m/s²

Thus, the acceleration achieved is 51.25 m/s².

6 0

3 years ago