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lilavasa [31]
3 years ago
8

Which is a correct two column proof. Given <4 and

Mathematics
1 answer:
vladimir1956 [14]3 years ago
4 0

The initial statement is:    QS = SU   (1)

                                    QR = TU    (2)

 

We have to probe that:  RS = ST

 

 

Take the expression (1):                     QS       =   SU

We multiply both sides by R                (QS)R   =   (SU)R

 

 

But    (QS)R = S(QR)     Then:            S(QR)   =   (SU)R     (3)

 

From the expression (2):  QR = TU. Then, substituting it in to expression (3):

 

                                                       S(TU)   =   (SU)R     (4)

 

But  S(TU) = (ST)U  and (SU)R = (RS)U

 

Then, the expression (4) can be re-written as:

 

                                                      (ST)U    =    (RS)U

 

Eliminating U from both sides you have:     (ST) = (RS)    The proof is done.

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Directions: for questions 1 through 4, find the diagonal length of each solid figure.
Alex787 [66]
\text{The length of the diagonal is }11.2\text{ mm}

Here, we want to find the diagonal of the given solid

To do this, we need the appropriate triangle

Firstly, we need the diagonal of the base

To get this, we use Pythagoras' theorem for the base

The other measures are 6 mm and 8 mm

According ro Pythagoras' ; the square of the hypotenuse equals the sum of the squares of the two other sides

Let us have the diagonal as l

Mathematically;

\begin{gathered} l^2=6^2+8^2 \\ l^2\text{ = 36 + 64} \\ l^2\text{ =100} \\ l\text{ = }\sqrt[]{100} \\ l\text{ = 10 mm} \end{gathered}

Now, to get the diagonal, we use the triangle with height 5 mm and the base being the hypotenuse we calculated above

Thus, we calculate this using the Pytthagoras' theorem as follows;

\begin{gathered} d^2=5^2+10^2 \\ d^2\text{ = 25 + 100} \\ d^2\text{ = 125} \\ d\text{ = }\sqrt[]{125} \\ d\text{ = }11.2\text{ mm} \end{gathered}

7 0
1 year ago
Find the quotient of the quantity negative 5 times x to the 3rd power plus 20 times x to the 2nd power minus 25 times x all over
Alona [7]
Negative x squared minus 4 x plus 5
8 0
3 years ago
Read 2 more answers
Can someone please check to make sure I got this correct? I would appreciate if you showed your work so that I could compare wit
dmitriy555 [2]

Answer:

-4

Step-by-step explanation:

[√2(cos(3π/4) + i sin(3π/4))]⁴

(√2)⁴ (cos(3π/4) + i sin(3π/4))⁴

4 (cos(3π/4) + i sin(3π/4))⁴

Using De Moivre's Theorem:

4 (cos(4 × 3π/4) + i sin(4 × 3π/4))

4 (cos(3π) + i sin(3π))

3π on the unit circle is the same as π:

4 (cos(π) + i sin(π))

4 (-1 + i (0))

-4

8 0
3 years ago
The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra
Snezhnost [94]
Let X denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by X_1,\ldots,X_{36}, each independently and identically distributed with distribution X_i\sim\mathcal N(26,7.2).

You want to find

\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)

Recall that if X\sim\mathcal N(\mu,\sigma), then the sampling distribution \overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right) with n being the size of the sample.

Transforming to the standard normal distribution, you have

Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}

so that in this case,

Z=6\dfrac{\overline X-26}{7.2}

and the probability is equivalent to

\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)
=\mathbb P(Z>1.481)\approx0.0693
5 0
3 years ago
PLZ ANSWER NOW FOR BRAINLEIST ANSWER AND 30 points!!! Show all work
Darina [25.2K]
A simple method is to square all the answers 

6^2 = 36~~~( \sqrt{40} )^2 = 40 ~~5^2 = 25 ~~~~ (\sqrt{23} )^2 = 23

now arrange them
7 0
3 years ago
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