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3 years ago

Find an exact value cos 75°

Mathematics

2 answers:

Drupady [299]3 years ago

5 0

Answer:

0.2588

Step-by-step explanation:

Vikentia [17]3 years ago

4 0

Answer:

(√3 - 1) / 2√2.

Step-by-step explanation:

Using the compound angle identity

cos(A + B) = cosA cosB - sinA sinB:-

cos 75

= cos (45 + 30)

= cos 45 cos 30 - sin 45 sin 30

= 1 / √2 * √3/2 - 1 / √2 * 1 / 2

= √3 / 2√2 - 1 / 2√2

= (√3 - 1) / 2√2.

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Triangle VXW is similar to triangle ZXY. Triangle V X W. Side V W is 12 miles and side V X is 14 miles. Triangle Z X Y. Side Y Z

amid [387]

Answer: Kara should have written the proportion in step 1 as;

Start Fraction 12 Over 72 End Fraction = Start Fraction 14 Over x End Fraction (that is 12/72 = 14/x)

Step-by-step explanation: The two similar triangles are given with the following dimensions;

Triangle VXW with side VW = 12 and side VX = 14. Also Triangle ZXY with side YZ = 72 and side XZ = x.

For two triangles to be similar, then there must be a similarity ration that is consistent with all sides in both triangles. This means if in the first triangle a side measures 1 unit and the similar side in the other triangle measures 5 units, then the ratio of similarity of corresponding sides shall be ratio 1 : 5. So for every corresponding side in the second triangle the measurement shall be times five of the side that corresponds in the first triangle.

Therefore, in triangle VXW and triangle ZXY, the corresponding sides are as follows;

VX = ZX

VW = ZY

XW = XY

What Kara did was as follows;

VX/ZY = VW/ZX

Which translates to 14/72 = 12/x

This was a wrong calculation because the side that corresponds to VX is ZX and not ZY.

The correct step should therefore have been;

VW/ZY = VX/ZX

12/72 = 14/x (Step 1)

12x = (72) (14) {Step 2}

x = 1008/12 (Step 3)

x = 84 (Step 4)

5 0

3 years ago

Read 2 more answers

What is the equation of a line that contains the point (2,-5) and is parallel to the line y=3x-4

aev [14]

Answer:

$\large\boxed{y=3x-11}$

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\y=3x-4\to m_1=3\\\\\text{Therefore}\ m_2=3.\\\\\text{We have the equation:}\ y=3x+b.\\\\\text{Put the coorsdinates of the point (2, -5) to the equation of the line}\\\\-5=3(2)+b\\-5=6+b\qquad\text{subtract 6 from both sides}\\-11=b\to b=-11$

7 0

4 years ago

Given the rule: an=7(1/2)n-1 identify the first term

Shkiper50 [21]

Answer:

using the rule given: 2.5
using an exponential rule: 7

Step-by-step explanation:

Evaluating the linear rule given, for n = 1, we have ...

a1 = 7(1/2)(1) -1 = 7/2 -1 = 5/2 = 2.5

_____

We suspect you may intend the exponential function ...

an = 7(1/2)^(n-1)

Then, for n = 1, we have ...

a1 = 7(1/2)^(1 -1) = 7(1) = 7 . . . . the first term is 7

_____

When writing an exponential expression in plain text, it requires the exponential operator, a caret (^). If the exponent contains any arithmetic, as this one does, it must be enclosed in parentheses.

3 0

3 years ago

Someone help, I suck at math

attashe74 [19]

option A.55°

Answer:

Solution given:

<x+<y=<z

exterior angle of a triangle is equal to the sum of two opposite interior angle

4n-18+n+8=133-6n

5n+6n=133+10

11n=143

n=143/11

n=13

exterior angle =133-6*13=55°

option A.55°

5 0

3 years ago

Ticket for football final selling well, on Thursday 4/7 of the tickets are sold, on Friday 1/4 of the tickets are sold, What fra

sergij07 [2.7K]

Answer:

5/28

Step-by-step explanation:

1/1 represents the whole amount of tickets.

4/7 are sold on Thursday.

an additional 1/4 are did on Friday.

fraction of available tickets on Saturday are therefore

1/1 - 4/7 - 1/4 = 4/1 - 16/7 - 1/1 = 28/1 - 16/1 - 7/1 = 5/1

that means out of 28 equal parts of the total number of tickets 16+7 = 23 parts have been sold.

so, there are only 5 out of the total 28 parts available on Saturday, and the fraction of available tickets is therefore 5/28.

we could have also tried to bring both fractions to the same denominator, and found that this is 28.

and then

4/7 + 1/4 = 4/4 × 4/7 + 7/7 × 1/4 =

= 16/28 + 7/28 = 23/28

and the whole is 28/28.

so we have 28/27 - 23/28 = 5/28 left.

surprise, surprise, it is the same result ...

4 0

2 years ago