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3 years ago

Sin^2x/cos^2 + sinxcscx = sec^2x Identify it, please explain so I know how you did it, thanks

Mathematics

1 answer:

max2010maxim [7]3 years ago

6 0

$\frac{sin^2x}{cos^2x} + sin x *cscx\\ tan^2x + \frac{sin x}{sin x} \\ tan^2x + 1\\ sec^2x$

$\frac{sin^2x}{cos^2x} = tan^2x$

$csc x = \frac{1}{sinx}$

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

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Find an equation of the line through these points (15,2.2) (5,1.6). Write answer in a slope-intercept form

nadya68 [22]

Answer:

$y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (15,2.2) and (5,1.6):

$m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}$

Therefore, the slope of the line is $\frac{\displaystyle 3}{\displaystyle 50}$ . Plug this into $y=mx+b$ :

$y=\frac{\displaystyle 3}{\displaystyle 50}x+b$

2) Determine the y-intercept (b)

$y=\frac{\displaystyle 3}{\displaystyle 50}x+b$

Plug in a given point and solve for b:

$1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b$

Therefore, the y-intercept is $\frac{\displaystyle 13}{\displaystyle 10}$ . Plug this back into $y=\frac{\displaystyle 3}{\displaystyle 50}x+b$ :

$y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}$

I hope this helps!

5 0

2 years ago

Another customer purchases a pack of gum for $1.25 and a candy bad for $1.10, what is yhe total of these two items before tax ?

Rzqust [24]

$1.25
+
$1.10
___
$2.35 because the 5 goes to 0 the 2 to 1 and 1 to 1 which makes $2.35

8 0

2 years ago

Kevin drew a triangle with angle measures of 30 degrees and 40 degrees and side measures of 5 cm, 7cm, and 8 cm. Explain, using

Pavel [41]

Answer:

He drew a scalene triangle

Step-by-step explanation:

A scalene triangle is where all side measure and all angle measure are different.

8 0

2 years ago

Read 2 more answers

During the season, the Rangers played 25 games. They won 14 of the games.

34kurt

Answer:

See below

Step-by-step explanation:

Out of 25 games, they won 14

Fraction won = won / total = 14 / 25

Percent won = won /total * 100 % = 14/25 * 100 = .56 * 100 % = 56 %

To find the number of games lost

25-14 = 11

Fraction won = won / total = 11 / 25

Percent won = won /total * 100 % = 11/25 * 100 = .44 * 100 % = 44 %

To check your work, the percent total should be 100

56+44 = 100

5 0

1 year ago

I'm trying to find 1, 2, & 3 but idk how? Sry if it's sideways I'm new

Vedmedyk [2.9K]

Answer:

Step-by-step explanation:

m∠1+∠2=180

2x+40+2y+40=180

2x+2y=180-80

2x+2y=100

x+y=50

x=50-y

m∠1=m∠3

2x+40=x+2y

2x-x=2y-40

x=2y-40

2y-40=50-y

2y+y=50+40

3y=90

y=30

x=50-y=50-30=20

m∠1=2x+40=2×20+40=80°

m∠2=2y+40=2×30+40=60+40=100°

m∠3=x+2y=20+2×30=80°

6 0

2 years ago