Factor the difference of two cubes completely.

x^3-64

can anyone verify this for me?

Julio initially started with the number 20, because cubing the number and then taking the cube root returns the original number.

If Julio cubes a number and then takes the cube root of the result, and ends up with 20, then the number he started with is also 20. This is because the cube of a number n is n
to the power of 3 (n³), and the cube root of a number is the inverse operation, which will return the original number. In symbolic form, if n is cubed to get n³, then taking the cube root of n³ will return n. Since Julio ends up with 20, the number he started with must have been 20.

[tex]\frac{3}{2}x[/tex] - 4 = 16

[tex]\frac{3}{2}x[/tex]  = 20    added 4 to both sides

3x = 40       multiplied both sides by 2

x = [tex]\frac{40}{3}[/tex]     divided both sides by 3

Answer: x = [tex]\frac{40}{3}[/tex]

The answer to your problem is Substitution (A) due to y being 4.

The two of the given numbers 54.045 and 54.405 can be compared using the inequality as 54.045 < 54.405.

Given two numbers 54.045 and 54.405. If the two numbers are plotted on the graph as shown below, it can be clearly seen that 54.045 comes before 54.405 on positive axis.

Therefore, 54.045 is smaller than 54.405. So ‘<’ smaller than inequality symbol will be used in between  54.045 and  54.405.

Hence, the correct representation of the comparison is 54.045 < 54.405.

Learn more about Inequality here:
https://brainly.com/question/28823603

#SPJ6

For this question, you simply take the x value from the given chart and plug it into the equation, then if the outcome makes sense based on the chart then you use another value of x and plug the second value in and if that also makes sense then you continue plugging in all the x values from the chart until all of them match. There is only one chart which contain the correct table of values.

To start of, let’s plug in the x values from graph 1, the first two values seems to be correct. However, in the third value, it does not match, therefore the first option is in correct.

Moving on to the second option, we could already determine that this table of values is incorrect because the very first x value does not match.

Moving onto the third table of values, we determine that all of the x values are in accordance with the y-values, therefore this option is correct.

Answer: Third option

The answer is B) The initial number of bacteria is 57, and the growth rate is 31% per hour.

The expression shown is an exponential expression.  An exponential expression usually takes the form [tex]ab^{x}[/tex], as this one does.  A represents the initial value, in this case-the initial number of bacteria.  B represents the growth rate.  When it is an increasing growth rate, it will begin with 1, because it will have everything it had before, plus the percent increase, the decimal portion.  In this case, a=57, and b=0.31.

Hope this makes sense!

Answer:

$35

Step-by-step explanation:

Rounding to the nearest dollar which would be 4 so in that case you would use the 5 in .57 and because 5 is a large number it would make the 4 into a five thus making it $35. Hope this helped :)

Here is the equation:

[tex]f(x)=4x+1[/tex]

You need to find f(3). To do that, substitute all the x's with 3:

[tex]f(x)=4x+1 \rightarrow f(3)=4\times3 + 1[/tex]

The first thing you need to do is multiply 4 by 3. Multiply:

[tex]4 \times 3 = 12[/tex]

Here is your new equation:

[tex]f(3)=12+1[/tex]

To get your answer, you need to add 12 and 1. Add:

[tex]12+1 = 13[/tex]

That means:

[tex]\bf f(3)=13[/tex]

If you have any questions, feel free to ask in the comments! :)

F(x)= 4x+1

To find f(3) you substitute it into x.

F(3)= 4(3)+1

F(3)=12+1

F(3)=13

Divide total miles between airports by the airplane's speed to find the time it took to travel by plane:

1450 miles / 350 mph = 4.142 hours = 4 hours 9 minutes

Then add the time the bus traveled:

4 hours 9 minutes  + 20 minutes = 4 hours 29 minutes

Answer:

4 hours and 29 mins

Step-by-step explanation:

The answer is B. 2

Hope it helps

If you consider the logarithm base 3 of both sides, you have

[tex] \log_3(3^c) = \log_3(27) [/tex]

You can use a rule of logarithms that allow you to turn exponents into multiplicative factors:

[tex] \log_a(b^c) = c\log_a(b) [/tex]

So the equation becomes

[tex] c\log_3(3)=\log_3(27) [/tex]

Now, by definition, you have

[tex] \log_a(b)=c \iff a^c=b [/tex]

So, you have

[tex] \log_3(3)=x \iff 3^x=3 \iff x = 1,\quad \log_3(27)=y \iff 3^y=27\iff y=3 [/tex]

So, the equation becomes

[tex] 1\cdot c = 3 \iff c=3 [/tex]

[tex]log_{3}[/tex]27 = c

using the law of logs : [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

given [tex]3^{c}[/tex] = 27 then

[tex]log_{3}[/tex] 27 = c

y = 8/5( x - 9 ) + 16

8/5 = 1.6

y = 1.6x - 14.4 + 16

y = 1.6x + 1.6

The slope is therefore 1.6 and

The y-intercept is 1.6

Answer: First portion is greater than second portion.

Step-by-step explanation:

Time taken to hiked down a trail = 10 minutes

Change in elevation = (-) 170 feet

Speed is given by

[tex]Speed=\frac{Distance}{Time}\\\\Speed=\frac{170}{10}\\\\Speed=17\text{ feet per minute}[/tex]

Similarly,

Time taken to hiked down a trail = 20 minutes

Change in elevation = (-)220 feet

Speed is given by

[tex]Speed=\frac{Distance}{Time}[/tex]

[tex]Speed=\frac{220}{20}\\\\Speed=11\text{ feet per minutes}[/tex]

So, we can see that first portion of the hike where he hiked down a trail at a steady rate for 10 minutes and her change in elevation was (-) 170 feet, was her rate of change in elevation greater.

As 17 feet per minutes is greater than 11 feet per minutes.

Answer:

The amount of her commission is $1,324.952

Step-by-step explanation:

1. You have the following information given in the problem above:

- Erin has $45,688 in sales.

- Erin's commission rate is 2.9% (0.029).

2. Therefore, to solve this exercise you must multiply the commission rate by her sales, as following:

[tex](45,688)(0.029)=1,324.952[/tex] dollars

–31.7 + 4.5x, when x = 2.1.

-31.7 + 4.5(2.1)

-31.7 + 9.45

Myra should have multiplied 4.5 and 2.1 first.

Answer:

B.Myra should have multiplied 4.5 and 2.1 first.

Step-by-step explanation:

We are given that Myra is evaluating the expression

-31.7+4.5 x when x=21.

We have to find the error in Myra's calculation

When x=2.1

-31.7+4.5(2.1)

-31.7+9.45

=-22.25

By using DMAS rule

D=Divide

M=Multiply

A=Addition

S=Subtraction

But Myra first add  -3.7 to 4.5 then multiply

Hence, Myra should have multiplied 4.5 and 2.1 first instead of add.

Answer:B.Myra should have multiplied 4.5 and 2.1 first.

[tex]y = e^{-sin(x)}[/tex]

[tex]y' = -e^{-sin(x)}(cos(x))[/tex]

[tex]0 = -e^{-sin(x)}(cos(x))[/tex]

When is cos (x) = 0?  at 90° (aka π/2)

Answer: [tex]\frac{\pi}{2}[/tex]

Answer: Hello there!

We have the function f(x) = exp(-sin(x)) and we want to see in wich point the slope is 0.

This is equivalent to see when f'(x) = 0

where f'(x) is the derivative of f(x)

Then the first step is derivate the function f(x)

if we have a function of the form g(h(x)), his derivate is:

g'(h(x))*h'(x)

In our case, g(x) = exp(x) and h(x) = - sin(x)

then f'(x) = exp(-sin(x))*(-cos(x))

Now we know that exp(-sin(x)) is never equal to 0, then we need to se when the cosine is equal to zero.

cos(90°) = 0, and 90° is equivalent to pi/2

Then f'(pi/2) = exp(-sin(pi/2))*(-cos(pi/2)) = 0

this means that the function f(x) has a slope of 0 in the point x = pi/2

*(Answer)*= (2,1)

*(Information)*= There is an attachment of the graph

The coordinates of the other endpoint L are (-19, 13).

If K is the midpoint of segment HL, we can use the midpoint formula to find the coordinates of point L.

The midpoint formula states that if you have the coordinates of two endpoints of a line segment and the coordinates of the midpoint, you can find the missing endpoint.

Let's denote the coordinates of point L as (x, y).

The midpoint formula is:

Midpoint =[tex]\(\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\)[/tex]

Given:

Coordinates of K = (-9, 3)

Coordinates of H = (1, -7)

Let (x, y) be the coordinates of point L.

Using the midpoint formula for x-coordinates:

[tex]\(\frac{{1 + x}}{2} = -9\)[/tex]

Solving for x:

[tex]\(1 + x = -18\)[/tex]

[tex]\(x = -19\)[/tex]

Using the midpoint formula for y-coordinates:

[tex]\(\frac{{-7 + y}}{2} = 3\)[/tex]

Solving for y:

[tex]\(-7 + y = 6\)[/tex]

[tex]\(y = 13\)[/tex]

Therefore, the coordinates of the other endpoint L are (-19, 13).

ANSWER

The correct answer is A

[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]

EXPLANATION

Given [tex]f(x)=ax-b[/tex].

We can find the inverse by taking the steps.

1. Let  [tex]y=ax-b[/tex]

2. Interchange x and y

[tex]x=ay-b[/tex]

3. Make y the subject

[tex]x+b=ay[/tex]

[tex]\frac{x+b}{a}=y[/tex]

The new function we got now is the inverse of f(x)

[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]

x + b/a Replace f(x) with y, interchange x and y and solve for y.

D. y = 50x + 200 is your answer

[tex]-7k < 63\qquad|\text{change the signs}\\\\7k > -63\qquad|\text{divide both sides by 7}\\\\k >-9\\\\Answer:\ c)\ k > -9.[/tex]

the answer is 5k^2+6k+1

Keep in mind both of these angles are equal to each other meaning the equation will have a = So...

4x+7=5(x-4)

Now multiply 5 to x and 4

4x+7=5x-20

Now subtract 4x from 5x

7=1x-20

Now add  20 to both sides

27=x

So x=27