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schepotkina [342]
3 years ago
10

6x^2-5x+1 Factor polynomial

Mathematics
1 answer:
Tamiku [17]3 years ago
8 0
6x²-5x+1
=6x²-3x-2x+1
=3x(2x-1)-1(2x-1)
=(3x-1)(2x-1)
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Nick has designed a diamond shaped kite as shown below. The measures of some sides of the kite are marked in the figure. Find th
Zepler [3.9K]

Answer:

<h2>x = 3.499 in</h2>

Step-by-step explanation:

       In a kite, the diagonals are perpendicular. Hence \Delta DOC is a right angled triangle.

       DC=7\text{ }in,\text{ }OC=5\text{ }in

From Pythagoras theorem, since \Delta DOC is a right angled triangle, DO^{2}+OC^{2}=DC^{2}.

      Area of \Delta DOC = \frac{1}{2}\times base\times height

=\frac{1}{2}\times DO\times OC=\frac{1}{2}\times OP\times DC\\(2\sqrt{6})\times(5)=(7)\times(OP)\\OP=3.499\text{ }in

From diagram OP=x

∴ x=3.499\text{ }in

7 0
3 years ago
The daily average temperature in Santiago, Chile, varies over time in a periodic way that can be modeled approximately by a trig
natali 33 [55]

Answer:

a) the trigonometric function is;

y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5

b) y = 28.36^0 \ C    ( to two decimal places)

Step-by-step explanation:

This data can be represented by the sinusoidal function of the form :

\mathbf{y = A sin (Bt -C)+D}

where A = amplitude and which can be determined via the formula:

A = \dfrac{largest \ temperature -  lowest \ temperature}{2}

A = \dfrac{29-14}{2}

A = \dfrac{15}{2}

A = 7.5° C

where B = the frequency;

Since the data covers a period of 3 days ; then \dfrac{2 \pi}{B } =365

B = \dfrac{2 \pi}{365}   ( where 365 is the time period )

The vertical shift is found by the equation D;

D =  \frac{largest \ temperature + lowest \ temperature}{2}

D = \frac{29+14}{2}

D = 21.5

Replacing the values of A ; B and D into the above sinusoidal function; we have :

y = 7.5 sin (\frac{2 \pi}{365}t -C) + 21.5

From the question; when it is 7th of the year ( i.e January 7);

t =  7 and the temperature (y) = 29° C

replacing that too into the above equation; we have:

29= 7.5 sin (\frac{2 \pi}{365}*7 -C) + 21.5

29= 7.5 sin (\frac{14 \pi}{365} -C) + 21.5

\frac{29-21.5}{7.5}=  sin (\frac{14 \pi}{365} -C)

1=  sin (\frac{14 \pi}{365} -C)

sin^{-1}(1)=   (\frac{14 \pi}{365} -C)

\frac{\pi}{2}=   (\frac{14 \pi}{365} -C)

C=   (\frac{14 \pi}{365} -\frac{\pi}{2})

C=   (\frac{28 \pi- 365 \pi}{730} )

C=  \frac{-337 \pi}{730}

Thus; the trigonometric function is;

y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5

Similarly; to determine the temperature o Jan 31; i.e when t= 31 ; we have :

y = 7.5 sin ( \frac{2 \pi}{365}*31+ \frac{337 \pi}{730})+ 21.5

y = 7.5 sin ( \frac{62 \pi}{365}+ \frac{337 \pi}{730})+ 21.5

y = 7.5 sin ( \frac{124 \pi+ 337 \pi }{730})+ 21.5

y = 7.5 sin ( \frac{461 \pi }{730})+ 21.5

y = 7.5 *( 0.915)+ 21.5

y = 6.8689+ 21.5

y = 28.36^0 \ C    ( to two decimal places)

7 0
3 years ago
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Pls I need help with this
tigry1 [53]

Answer:

umm I think I know hold on

6 0
3 years ago
How do you divide 3/8 by 6/7 in simplest form
Ipatiy [6.2K]

Answer:

7/16

Step-by-step explanation:

First, it is good to know that when you divide fractions, you are <em>multiplying it's reciprocal</em>.

<em>6/7's reciprocal is 7/6, since the reciprocal is \frac{1}{6/7}</em>

3/8 / 6/7 =

<u>3/8 * 7/6</u>

Now that we have that, we can just multiply the two:

3/8 * 7/6 =

21/48 =

<u>7/16</u>

Hope this helped :)

8 0
3 years ago
Solve for x and then find the measure ​
Afina-wow [57]

Answer:

A= 148

Step-by-step explanation:

Angles A and B are Alt. Ext. Angles which makes them congruent. You set them equal to each other and solve for x.

4 0
3 years ago
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