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3 years ago

CAN SOMEONE PLEASE SOLVE THIS?????????? NEED HELP!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

Kipish [7]3 years ago

5 0

Answer:

x = 9, GH = 21, CD = 17

Step-by-step explanation:

Quadrilateral CDEF is a trapezoid in which G and H are mid points of the sides CF and DE respectively.

In a trapezoid, segment joining the mid points is equal to the half of the sum of the parallel sides.

$\therefore \: GH = \frac{1}{2} (CD + FE) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x - 1 + 25) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x + 24) \\ \\ \therefore \:3x - 6 =\frac{1}{2} \times 2 (x + 12) \\ \\ \therefore \:3x - 6 = x + 12 \\ \\ \therefore \:3x - x = 12 + 6 \\ \\ \therefore \:2x = 18 \\ \\ \therefore \:x = \frac{18}{2} \\ \\ \huge\red{ \boxed{\therefore \:x = 9}} \\\\ \because \overline{GH} = 3x - 6 \\ \\\therefore \:\overline{GH} =3 \times 9 - 6 \\ \\ \therefore \:\overline{GH} =27 - 6 \\ \\ \huge\purple{ \boxed{\therefore \:\overline{GH} =21}} \\ \\ \because\overline{CD} = 2x - 1 \\\\ \therefore \:\overline{CD} =2 \times 9 - 1 \\ \\ \therefore \:\overline{CD} =18 - 1 \\ \\ \huge\pink{ \boxed{\therefore \:\overline{CD} =17}} \\ \\$

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A falcon flew 70 miles in three hours what was the speed of the falcon

Evgen [1.6K]

70 mi / 3 h = 23.33 miles / hour

6 0

4 years ago

The starting salary at a company is $42,000 per year. The company automatically gives a raise of 3% per year. Write a recursive

cricket20 [7]

To solve this, we are going to use the recursive formula for a geometric sequence: $a_{n}=a_{1}r^{n-1}$
where
$a_{n}$ is the nth term of the geometric sequence.
$a_{1}$ is the first term of the geometric sequence.
$r$ is the common ratio
$n$ is the position of the term in the sequence.

We know that the starting salary is $42,000, so $a_{1}=42000$ . Now, to find the common ratio $r$ , we need to find the next term in the sequence first:
We know from our problem that t<span>he company automatically gives a raise of 3% per year, so the next term in the sequence will be 42000 + 3%(42000) = 42000 + 1260 = 43260. Remember that the common ratio is the current term of the geometric sequence divided by the previous term of the sequence; we know that our current term is 43260 and the previous term is 42000, so:
</span> $r= \frac{43260}{42000}$
$r=1.03$
<span>Now we can plug the values in our recursive formula:
</span> $a_{n}=a_{1}r^{n-1}$
$a_{n}=42000(1.03)^{n-1}$

We can conclude that the recursive definition for the geometric sequence formed by the salary increase is: $a_{n}=42000(1.03)^{n-1}$

8 0

3 years ago

A triangle has sides with lengths of 11 miles, 15 miles, and 17 miles. Is it a right triangle?

dybincka [34]

Answer:

Below.

Step-by-step explanation:

If its a right triangle it will obey the Pythagoras theorem.

17^2 = 289

11^2 + 15^2 = 121 + 225 = 346

- so NOT a right triangle.

3 0

3 years ago

"At $1.29 million, they closed last month for...26 percent above what they paid in 2007." How much did they pay in 2007?

Morgarella [4.7K]

Answer: Amount that they paid in 2007 is 1.01 millions.

Step-by-step explanation:

Since we have given that

Number of millions paid last month = $1.29 millions

According to question, it was 26% above what they paid in 2007.

Let the amount paid in 2007 be x

So, our equation becomes,

$\frac{100+27}{100}\times x=1.29\\\\\frac{127}{100}\times x=1.29\\\\1.27\times x=1.29\\\\x=\frac{1.29}{1.27}\\\\x=1.01\ millions$

Hence, Amount that they paid in 2007 is 1.01 millions.

7 0

4 years ago

Read 2 more answers

Proof by induction on the number of horses: Basis Step. There is only one horse. Then clearly all horses have the same color. In

Novosadov [1.4K]

Answer:

Claiming mathematical induction, of the statement: "all horses are the same color", the theorem is a counterfeit paradox sustained by mistaken demonstrations.

Step-by-step explanation:

”that is a horse of a different color” was a familiar expression in the middle of the last century, meaning that something is quite different from normal or common expectation, but George Polya, a great mathematician provided proof that there is no horse of a different color:

Theorem: "All horses are the same color"

Proof (by induction on the number of horses):

- Base Case: P(1) is undoubtedly true, as having only one horse, then all horses have the same color.

- Inductive Hypothesis: Assume P(n), which is the statement that n horses all have the same color.

- Inductive Step: Given a set of n+1 horses {h1,h2,...,hn+1}, we can eliminate the last horse in the serie and use the inductive hypothesis onlky to the first n horses {h1,...,hn}, deducing that they all have the same color. The same way, the conclusion may be that the last n horses {h2,...,hn+1} all have the same color. But the “middle” horses {h2,...,hn} (i.e., all but the first and the last) belong to both of these series, so they have the same color as horse h1 and horse hn+1. It follows, therefore, that all n+1 horses have the same color. Therefore, using the principle of induction, all horses have the same color.

It is clear that, it is not true that all horses are of the same color, so where is the mistake in our induction proof? It is tempting to blame the induction hypothesis. But even though the induction hypothesis is false (for n ≥ 2), that is not the mistaken reasoning. The real flaw in the proof is that the induction step is valid for a “typical” value of n, say, n = 3. The flaw, however, is in the induction step when n = 1. In this case, for n+1 = 2 horses, there are no “middle” horses, this makes the argument to collapse.

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3 years ago