Which ratio is equivalent to 21:56

Four time a number r plus half a number s equals 12. Twice the number r plus one fourth of the numbers s equals 8. What are the

Snezhnost [94]

The system of equations have no solution.

Explanation:

The equations are $4r+\frac{1}{2}s=12$ and $2r+\frac{1}{4} s=8$

To find the two numbers, let us solve the equations using substitution method.

From the equation $2r+\frac{1}{4} s=8$ , let us determine the value of r,

$\begin{aligned} 2 r+\frac{1}{4} s &=8 \\ 2 r &=8-\frac{1}{4} s \\ r &=\frac{1}{2}\left(8-\frac{1}{4} s\right) \\ r &=4-\frac{1}{8} s \end{aligned}$

Let us substitute the value of r in $4r+\frac{1}{2}s=12$ , we get,

$\begin{aligned} 4\left(4-\frac{1}{8} s\right)+\frac{1}{2} s &=12 \\ 16-\frac{1}{2} s+\frac{1}{2} s &=12 \\ 16 &=12 \end{aligned}$

which is not possible.

This means that the system has no solution.

6 0

4 years ago

#23-6: The pool concession stand made $5,800 in June and $6,300 in July. What is the percent of increase in sales? Round the ans

katrin [286]

Answer:

8.6%

Step-by-step explanation:

To find the percent change, you will need to compute the positive difference and then divide the difference by the original (the older amount).

So the positive difference will be obtain by doing larger minus smaller:

6300

- 5800

-----------

500

The older amount was 5800.

So 500/5800 is the answer as a un-reduced fraction.

I'm going to reduce it by dividing top and bottom by 100:

500/5800 = 5/58

5/58 is the answer as a reduced fraction.

5 divided by 58 gives=0.086206897 in the calculator .

Approximately 0.0862 is the answer as a decimal.

To convert this to a percentage, multiply it by a 100:

8.62%

Rounded to the nearest tenths is 8.6%

-------------

So 5800+5800(.0862) should be pretty close to 6300 (not exactly though since we rounded).

5800+5800(.0862)=6299.96 using the calculator.

8 0

3 years ago

Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.

frutty [35]

<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

$2^n\leq 2^{n+1}-2^{n-1}-1$

where n is a positive integer.

Let us take n=1

then we have:

$2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2$

Hence, the result is true for n=1.

Let us assume that the result is true for n=k

i.e.

$2^k\leq 2^{k+1}-2^{k-1}-1$

Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u> $2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Let us take n=k+1

Hence, we have:

$2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)$

( Since, the result was true for n=k )

Hence, we have:

$2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2$

Also, we know that:

$-2$

(

Since, for n=k+1 being a positive integer we have:

$2^{(k+1)+1}-2^{(k+1)-1}>0$ )

Hence, we have finally,

$2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

$2^n\leq 2^{n+1}-2^{n-1}-1$ where n is a positive integer.

6 0

3 years ago

If △ABC ≅ △DEF, then what corresponding side is congruent to side BA? (Enter answer using segment letters only.)

sdas [7]

<h3>Answer is ED</h3>

note: ED is the same as DE. The order of the segment letters does not matter.

============================================

Explanation:

In the sequence ABC, the letter B is the second letter and A is the first.

So the corresponding segment to BA will have its first slot be the second letter of DEF, and its second slot be the first letter of DEF. That's how I'm getting ED for the answer. It is the same as DE because it's the same segment.

The corresponding sides are congruent due to the CPCTC which stands for "corresponding parts of congruent triangles are congruent".

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Csqrt%7B8%7D%2B%5Csqrt%7B18%7D-%5Csqrt%7B32%7D" id="TexFormula1" title="\sqrt{8}+\sqrt{18}-\

eduard

√8+√18−√32
√2^2·2+√3^2·2−√2^4·2
√2^ 2·√2+√3^2·√2−√2^4·√2

√2 is the answer

7 0

3 years ago