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3 years ago

What is the side length , in inches, of the pet shop sign ?

Mathematics

2 answers:

rusak2 [61]3 years ago

7 0

Could i see a picture please

tamaranim1 [39]3 years ago

6 0

Include a picture and I will answer this for you

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Expand (2x+2)^6 How would you find the answer using the binomial theorem?

Yanka [14]

Answer:

Step-by-step explanation:

$\displaystyle\\\sum\limits _{k=0}^n\frac{n!}{k!*(n-k)!}a^{n-k}b^k .\\\\k=0\\\frac{n!}{0!*(n-0)!}a^{n-0}b^0=C_n^0a^n*1=C_n^0a^n.\\\\ k=1\\\frac{n!}{1!*(n-1)!} a^{n-1}b^1=C_n^1a^{n-1}b^1.\\\\k=2\\\frac{n!}{2!*(n-2)!} a^{n-2}b^2=C_n^2a^{n-2}b^2.\\\\k=n\\\frac{n!}{n!*(n-n)!} a^{n-n}b^n=C_n^na^0b^n=C_n^nb^n.\\\\C_n^0a^n+C_n^1a^{n-1}b^1+C_n^2a^{n-2}b^2+...+C_n^nb^n=(a+b)^n.$

$\displaystyle\\(2x+2)^6=\frac{6!}{(6-0)!*0!} (2x)^62^0+\frac{6!}{(6-1)!*1!} (2x)^{6-1}2^1+\frac{6!}{(6-2)!*2!}(2x)^{6-2}2^2+\\\\ +\frac{6!}{(6-3)!*3!} (2a)^{6-3}2^3+\frac{6!}{(6-4)*4!} (2x)^{6-4}b^4+\frac{6!}{(6-5)!*5!}(2x)^{6-5} b^5+\frac{6!}{(6-6)!*6!}(2x)^{6-6}b^6. \\\\$

$(2x+2)^6=\frac{6!}{6!*1} 2^6*x^6*1+\frac{5!*6}{5!*1}2^5*x^5*2+\\\\+\frac{4!*5*6}{4!*1*2}2^4*x^4*2^2+ \frac{3!*4*5*6}{3!*1*2*3} 2^3*x^3*2^3+\frac{4!*5*6}{2!*4!}2^2*x^2*2^4+\\\\+\frac{5!*6}{1!*5!} 2^1*x^1*2^5+\frac{6!}{0!*6!} x^02^6\\\\(2x+2)^6=64x^6+384x^5+960x^4+1280x^3+960x^2+384x+64.$

8 0

1 year ago

guajiro [1.7K]

Answer and Step-by-step explanation: Standard form of a quadratic equation is expressed as: y=ax²+bx+c, while vertex form is written as:

y=a(x-h)²+k.

The similarities between standard and vertex forms is that they show if the graph of the equation has a minimum (when a>0) or maximum (a<0) and it's easier to determine the y-intercept: for standard, the value of c is the intercept; for vertex, the value k is the intercept.

The advantage of standard form is that you can determine the product and sum of the equation's roots, which is a method to determine them.

The advantages of vertex form are: easier to find the vertex of the graph, which is the pair (h,k) and the axis of symmetry, which is the value of h.

8 0

3 years ago

If f(x)=5x-7,what isf(3)?

ArbitrLikvidat [17]

Answer:

Explanation:

f ( − 3 ) basically means substitute − 3 for x in the function − 5 x

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Step-by-step explanation:

4 0

2 years ago

What is the constant term in the expansion of the binomial (x − 2)^4?

Marianna [84]

Answer:

the answer is a i think

3 0

3 years ago

What is the domain of f(x) = √x – 4 over the set of real numbers?

nikklg [1K]

Answer:

(2) x $\geq \\$ 4

Step-by-step explanation:

Given the sqrt(x), x $\geq \\$ zero

So, given sqrt(x -4), x -4 $\geq \\$ 0

Now solve for x

x - 4 $\geq \\$ 0

x $\geq \\$ 4

6 0

2 years ago