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3 years ago

Find the measure of each angel if m angle 8 = 115º

Mathematics

1 answer:

zalisa [80]3 years ago

7 0

Lines p and q are parallel.
Corresponding angles are congruent.
Each two adjacent angles are supplementary.
Vertical angles are congruent.

Angles 7 and 8 are adjacent, supplementary angles.
m<7 + m<8 = 180
m<7 + 115 = 180
m<7 = 65

Angles 6 and 8 are corresponding angles and congruent.
m<6 = m<8
m<6 = 115

Angles 1 and 6 are vertical angles and congruent.
m<1 = m<6
m<1 = 115

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Write an equation for the n th term of the arithmetic seqeuence. Then find a{10}. 100,110,120,130

lord [1]

Answer:

100+10n

Step-by-step explanation: a(10)

100+10(10)

100+100 = 200

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3 years ago

Which inequality is represented by the accompanying graph? Thank you!!!

yan [13]

Answer:

y<3

Step-by-step explanation:

It is y<3 because all areas below y=3 are shaded.

In addition, the line y=3 is dotted, which means it is not part of the inequality (i.e. strict inequality).

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3 years ago

find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8)

frutty [35]

Answer:

cosФ = $\frac{1}{\sqrt{65}}$ , sinФ = $-\frac{8}{\sqrt{65}}$ , tanФ = -8, secФ = $\sqrt{65}$ , cscФ = $-\frac{\sqrt{65}}{8}$ , cotФ = $-\frac{1}{8}$

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

cosФ = $\frac{x}{r}$
sinФ = $\frac{y}{r}$
tanФ = $\frac{y}{x}$
secФ = $\frac{r}{x}$
cscФ = $\frac{r}{y}$
cotФ = $\frac{x}{y}$

Where r = $\sqrt{x^{2}+y^{2} }$ (the length of the terminal side from the origin to point (x, y)

You should find the quadrant of (x, y) to adjust the sign of each function

∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = $\sqrt{x^{2}+y^{2} }$

∵ x = 1 and y = -8

∴ r = $\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}$

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = $\frac{x}{r}$

∴ cosФ = $\frac{1}{\sqrt{65}}$

∵ sinФ = $\frac{y}{r}$

∴ sinФ = $-\frac{8}{\sqrt{65}}$

∵ tanФ = $\frac{y}{x}$

∴ tanФ = $-\frac{8}{1}$ = -8

∵ secФ = $\frac{r}{x}$

∴ secФ = $\frac{\sqrt{65}}{1}$ = $\sqrt{65}$

∵ cscФ = $\frac{r}{y}$

∴ cscФ = $-\frac{\sqrt{65}}{8}$

∵ cotФ = $\frac{x}{y}$

∴ cotФ = $-\frac{1}{8}$

8 0

3 years ago

Rewrite the following multiplication problem using the associative property and then show that both results will be the same.

densk [106]

Answer:

The answer is the same i. e., 4.375 in all the cases as shown below.

Step-by-step explanation:

$\frac {3}{7} \times \frac {5}{6} \times \frac {1}{4}$

= $\frac {35}{8}$

= $\frac {3}{7} \times \frac {1}{4} \times \frac {5}{6}$

= $\frac {5}{6} \times \frac {1}{4} \times \frac {3}{7}$

= $\frac {5}{6} \times \frac {3}{7} \times \frac {1}{4}$

= $\frac {1}{4} \times \frac {5}{6} \times \frac {3}{7}$

= $\frac {1}{4} \times \frac {3}{7} \times {5}{6}$

= 4.375 (answer)

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nirvana33 [79]

Answer:

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Step-by-step explanation:

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