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Blababa [14]
2 years ago
15

If it takes 8 inches of ribbon to make a bow,how many bows can be made from 3 feet of ribbon (1 foot = 12 inches)? Will any ribb

on be left over? If so, how much?
Mathematics
1 answer:
Aloiza [94]2 years ago
8 0

First, find out how much ribbon there is.

3 x 12 = 36

Now, see how many times you can divde that by 8.

36 can only be divided by 8 four times, and there would be 4 inches of ribbon left.

So, you would be able to make 4 bows, with 4 inches of ribbon remaining.

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Solve equations -8x=88
Alexxx [7]
ANSWER:X=-11

Explanation

3 0
3 years ago
If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.
Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have S_1=3\times2^{1-1}+2(-1)^1=3-2=1, which agrees with the initial value <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}

and

S_k=3\times2^{k-1}+2(-1)^k

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}

From the given recurrence, we know

S_{k+1}=S_k+2S_{k-1}

so that

S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)

S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}

S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)

S_{k+1}=3\times2^k-2(-1)^k

S_{k+1}=3\times2^k+2(-1)(-1)^k

\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}

which is what we needed. QED

6 0
2 years ago
Evaluate: (8/27)^-2/3 <br><br> add: sqroot(27) + sqroot (75)
vredina [299]
The answer to the first question
is 2 1/4.
The answer to the second question is 8 sqroot 3. Hope I was able to help

3 0
3 years ago
F(x)=12x2-4x-8. G(x)=11x-6
AlekseyPX

Answer: Second option.

Step-by-step explanation:

Given the functions f(x) and g(x):

f(x)=12x^2-4x-8\\\\g(x)=11x-6

You need to divide them in order to find (\frac{f}{g})(x) asked in the exercise. Then:

(\frac{f}{g})(x) =\frac{12x^2-4x-8}{11x-6}

Now, it is important to remember that, by definition, the division by zero is not defined. Therefore, the denominator of the function cannot be zero.

Let's find the value of "x" for which the denominator of the function would be zero:

1. You need to make the denominator equal to zero:

11x-6=0

2. Finally, you must solve for "x":

11x=6\\\\x=\frac{6}{11}

Therefore, as you can see, the answer is:

 (\frac{f}{g})(x) =\frac{12x^2-4x-8}{11x-6}, x=\frac{6}{11}

4 0
3 years ago
What is the cost of a $19,500 plus a 6% sales tax?
vova2212 [387]
1% of 19,500= 195

6% = 1%x6 = 195x6 = 1170

19500+1170=20670
3 0
3 years ago
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