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4 years ago

Use the figure to identify each pair of angles as complementary angles, supplementary angles, vertical angles, or none of these.

Mathematics

1 answer:

zhenek [66]4 years ago

8 0

Answer:

a is true and becomes complimentary as they both add up to 90 degree.

b. is true it is the only vertical angle group. As points AE, and BD cross and create these angles.

c is supplementary as both 3,4 together add up to 180

but each of these do not fit other description, as 5,1 would be also supplementary if 2 was in that group.

Step-by-step explanation:

Points 3, 4 as a group and 3,2,1 as a group and 2,1,5 as a group are each supplementary as each group add up to 180 degree. 1,5 on its own is not supplementary

Points 2 is complimentary on its own and also 1,5 combined are complimentary so this is true and 1,5 on its own as a group is complimentary.

Points 3,5 become vertical angles as a group.

Angles A:B + D:E are also vertical angles this shows points 1,2 and 4 as a group of vertical angles.

Vertical Angles are the angles opposite each other when two lines cross. "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down

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Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

8 0

3 years ago

The population of Linton is 12 times as great as the population of Elmore the combined population of both towns is 9,646 people

zysi [14]

Let the population of Elmore be "X".
Since that the population of Linton is 12 times as great as the population of Elmore, then it is considered to be "12x".
Since that the sum of both Elmore and Linton is 9.646, then "X + 12x = 9464" x+12x is 13x , so it should be "13x = 9464". Now, it is easy to find the population of Elmore which is 9464 / 13 = 742. Since that the population of Linton is 12 times the population of Elmore, then the population of Linton is "742 * 12 = 8904".

6 0

4 years ago

21,300 feet = <br> miles

Rudik [331]

Answer:

4.034 miles.

Step-by-step explanation:

1 mile is: 5280

21300/5280= 4.034

Hope this helps & best of luck!

Feel free to message me if you need more help! :)

4 0