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BlackZzzverrR [31]

3 years ago

6

Which student wrote an expression equivalent to 6x + 4x to the third power? Choose all that apply.

1 answer:

FinnZ [79.3K]3 years ago

7 0

Bart and David are correct.
Bart
6x(1+2/3^3)
6x * 1 = 6x
6x *2/3^3 = 4x^3
6x * 4x^3

David
x(6+4x^2)
x*6 = 6x
x*4x^2 = 4x^3
6x+4x^3

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If 16 cups equals one gallon than one 1/4 gallon equal cups

hoa [83]

Well...this is a proportion problwm. for every 16 cups I have 1 gallon, so I can write that as:

16 cups
-----------
1 gallon

this value will be proportional to 1/4 a gallon equal "so many" cups. let's equal the unknown about of cups to x.

16 cups______ x cups
-----------.... = ..... ----------
1 gallon _____ 1/4 gallons

I can cross multiply to find x.

1 gallon • x cups = 16 cups • 1/4 gallons

16 times 1/4 is the same as 16/4, which equals 4.

1 gallon • x cups = 4 cups gallons

divide both sides by gallons

x cups = 4 cups

so! 1/4 of a gallon equals 4 cups.

8 0

4 years ago

Find the 14th term of the geometric sequence 7, 28, 112,

Fed [463]

Answer:

a(14)=469762048

Step-by-step explanation:

geometric sequence= a(n)=a*r^(n-1)

we have:

a=7

r=28/7=4

So:

a(14)=7*4^(14-1)

=7*4^(13)

=469762048

hope this helps

6 0

3 years ago

56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

$\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2$

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ <em> </em> $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

8 0

2 years ago

–45 • –3 = please i need hep

sesenic [268]

Answer:

135

Step-by-step explanation:

3 0

3 years ago

Using a tree diagram and assuming that all options are equally likely, what is the probability of using sprinkles?

tester [92]

Some are said more than once but they is 10 different choices together so it’s be ‘1/10 probability’

6 0

3 years ago