In y=3x+1, where does the line cross the y axis?

How to solve this ? I am not sure pls if you know the answer answer it I really neeed it for marks

xz_007 [3.2K]

Answer:

L.S = R.S ⇒ Proved down

Step-by-step explanation:

Let us revise some rules in trigonometry

sin²α + cos²α = 1
sin2α = 2 sin α cosα
cscα = 1/sinα

To solve the question let us find the simplest form of the right side and the left side, then show that they are equal

∵ L.S = csc2α + 1

→ By using the 3rd rule above

∴ L.S = $\frac{1}{sin2\alpha}$ + 1

→ Change 1 to $\frac{sin2\alpha}{sin2\alpha}$

∴ L.S = $\frac{1}{sin2\alpha}$ + $\frac{sin2\alpha}{sin2\alpha}$

→ The denominators are equal, then add the numerators

∴ L.S = $\frac{1+sin2\alpha}{sin2\alpha}$

∵ R. S = $\frac{(sin\alpha+cos\alpha)^{2} }{sin2\alpha}$

∵ (sinα + cosα)² = sin²α + 2 sinα cosα + cos²α

∴ (sinα + cosα)² = sin²α + cos²α + 2 sinα cosα

→ By using the 1st rule above, equate sin²α + cos²α by 1

∴ (sinα + cosα)² = 1 + 2 sinα cosα

→ By using the 2nd rule above, equate 2 sinα cosα by sin2α

∴ (sinα + cosα)² = 1 + sin2α

→ Substitute it in the R.S above

∴ R. S = $\frac{1+sin2\alpha}{sin2\alpha}$

∵ L.S = R.S

∴ csc 2α + 1 = $\frac{(sin\alpha+cos\alpha)^{2} }{sin2\alpha}$

4 0

3 years ago

Last year, 45% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indica

natka813 [3]

Answer:

a)x₁ = 24 business owners plan to provide a gift this year

b) p-value = 0,0017

c)p-value < α we have to eject H₀ And support the claim that the proportion of business owners providing gifts has decrease

Step-by-step explanation:

a) Sample size 80

proportion p₁ = 30 % p₁ = 0,3

Then x₁ = 80*0,3

x₁ = 24 business owners plan to provide a gift this year

b) Hypothesis Test

Null Hypothesis H₀ p₁ = 0,45

Alternative Hypothesis Hₐ p₁ < 0,45

p₁ = 0,3 then q₁ = 1 - 0,3 q₁ = 0,7

z(s) = ( p₁ - 0,45 )/ √p₁* q₁ / n

z(s) = - 0,15 / √0,002625

z(s) = - 0,15 / 0,05123

z(s) = - 2,9279

b)From z-table we find p-value = 0,0017

c) If α = 0,05 ( significance level ) as

p-value < α we have to eject H₀ And support the claim that the proportion of business owners providing gifts has decrease

6 0

2 years ago

.0190500 in scientific notation

arsen [322]

The answer is

1.905×10^-2

8 0

3 years ago

Write a linear equation in point-slope form for the line that goes through (1, -3) and (3,9).

dimaraw [331]

The slope of the line is 6, meaning that you can eliminate A,C. Since the point slope formula is y-y1=m(x-x1) you just need to see if the points are correct.

B. (3,9)
D. (1,-3)

While these do contain one point, substitute the coordinates to see which contain both.

B.

(1,-3): -3-9=6(1-3): -12=-12
(3,9): 9-9=6(9-3): 0= 6(6)

D.

(1,-3): -3+3=6(1-1): 0=6(0); 0=0
(3,9): 9+3=6(3-1): 12=6(2): 12=12

D is correct since the coordinate are on the line.

3 0

2 years ago

Read 2 more answers

Check all the equations that are equivalent.

Fiesta28 [93]

Answer:

the answer is a, c and d

a. a=180(n-2)

c. n=a/180+2

d. n= a+360/180

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers