please help, the assignment is in the photos

Given:

[tex]\dfrac{1+\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{1+\sin \theta}=2\sec \theta [/tex]

To prove:

The given statement.

Proof:

We have,

[tex]\dfrac{1+\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{1+\sin \theta}=2\sec \theta[/tex]

Taking LHS, we get

[tex]\text{LHS}=\dfrac{1+\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{1+\sin \theta}[/tex]

Taking LCM, we get

[tex]\text{LHS}=\dfrac{(1+\sin \theta)^2+cos^2\theta }{\cos \theta(1+\sin \theta)}[/tex]

[tex]\text{LHS}=\dfrac{(1)^2+2\sin \theta +\sin^2 \theta+cos^2\theta }{\cos \theta(1+\sin \theta)}[/tex]    [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]

[tex]\text{LHS}=\dfrac{1+2\sin \theta +1}{\cos \theta(1+\sin \theta)}[/tex]    [tex][\because \sin^2 \theta+cos^2\theta =1][/tex]

[tex]\text{LHS}=\dfrac{2+2\sin \theta}{\cos \theta(1+\sin \theta)}[/tex]

[tex]\text{LHS}=\dfrac{2(1+\sin \theta)}{\cos \theta(1+\sin \theta)}[/tex]

[tex]\text{LHS}=\dfrac{2}{\cos \theta}[/tex]

[tex]\text{LHS}=2\sec \theta[/tex]         [tex][\because \sec\theta=\dfrac{1}{\cos \theta}][/tex]

[tex]\text{LHS}=\text{RHS}[/tex]

Hence proved.

Answer:

95% confidence interval for the population standard deviation of the lifetimes of the batteries produced by the manufacturer.

(8.889, 11.7106)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 23

Mean of the sample x⁻ = 10.3

Standard deviation of the sample (s) = 2.4

Level of significance = 0.05

Degrees of freedom = n-1 = 23-1 =22

Step(ii):-

95% confidence interval for the population standard deviation of the lifetimes of the batteries produced by the manufacturer.

[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} +t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]

[tex](10.3 - t_{\frac{0.05}{2} } \frac{2.4}{\sqrt{23} } , 10.3 +t_{\frac{0.05}{2} } \frac{2.4}{\sqrt{23} } )[/tex]

(10.3 -  2.8188 (0.50043) , 10.3 + 2.8188(0.50043)

(10.3-1.4106 , 10.3+1.4106)

(8.889, 11.7106)

final answer:-

95% confidence interval for the population standard deviation of the lifetimes of the batteries produced by the manufacturer.

(8.889, 11.7106)

Answer: m = 2b/v

Step-by-step explanation:

Answer:

∠ XWZ is a right angle.

Step-by-step explanation:

See the given diagram.

In triangle WXZ, WY is an altitude.

So, ∠ WYZ = ∠ XYW = 90°

Now, given that ∠ ZWY = ∠ WXY.

Now, from Δ XYW, since, ∠ XYW = 90° so, ∠ WXY + ∠ YWX = 90° ....... (1)

⇒  ∠ ZWY + ∠ YWX =  90° {Since, ∠ ZWY = ∠ WXY}

⇒ ∠ XWZ = 90°

Therefore, the angle XWZ is right angle. (Answer)

Answer:

B. XWZ is a right angle

Step-by-step explanation:

edge 2020 plz vote brainliest

Answer:

Option (2)

Step-by-step explanation:

Formula to get the surface area of a sphere is,

Surface area = 4πr²

Here 'r' = Radius of the sphere

We have to calculate the surface area of a sphere with radius r = 9 inches.

By substituting the value of r in the formula,

S = 4π(9)²

Therefore, Option (2) will be the correct option.

Answer:

Answer:

41

Step-by-step explanation:

i rounded the 40.5 to 41.

Answer:

A. (0, 1) and (2, -2)

B. Slope (m) = -³/2

C. y + 2 = -³/2(x - 2)

D. [tex] y = -\frac{3}{2}x + 1 [/tex]

E. [tex] \frac{3}{2}x + y = 1 [/tex]

Step-by-step explanation:

A. Two points on the line from the graph are: (0, 1) and (2, -2)

B. The slope can be calculated using two points, (0, 1) and (2, -2):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 1}{2 - 0} = \frac{-3}{2} = -\frac{3}{2} [/tex]

Slope (m) = -³/2

C. Equation in point-slope form is represented as y - b = m(x - a). Where,

(a, b) = any point on the graph.

m = slope.

Substitute (a, b) = (2, -2), and m = -³/2 into the point-slope equation, y - b = m(x - a).

Thus:

y - (-2) = -³/2(x - 2)

y + 2 = -³/2(x - 2)

D. Equation in slope-intercept form, can be written as y = mx + b.

Thus, using the equation in (C), rewrite to get the equation in slope-intercept form.

y + 2 = -³/2(x - 2)

2(y + 2) = -3(x - 2)

2y + 4 = -3x + 6

2y = -3x + 6 - 4

2y = -3x + 2

y = -3x/2 + 2/2

[tex] y = -\frac{3}{2}x + 1 [/tex]

E. Convert the equation in (D) to standard form:

[tex] y = -\frac{3}{2}x + 1 [/tex]

[tex] \frac{3}{2}x + y = 1 [/tex]

Answer: Your real answer is D

Step-by-step explanation:

The start is 7 to the right of 2

Answer:

the answer is 0

Step-by-step explanation:

Answer:

1.6 billon

Step-by-step explanation:

1.6 billon

Answer:

B

Step-by-step explanation:

i think it is

No, it cannot. You will need a microscope in order to see DNA.

One cell of DNA can not be viewed by the naked eye, but when gathered in thousand of cells, it can.

So its no

Answer:

The answer would be

Negative

Answer:

Negative

Step-by-step explanation: If there are a odd number of negative sigs, the answer is negative. If there are a even amount of negative symbols, the answer is positive and there are 3 negative symbols, so the answer is NEGATIVE

Step-by-step explanation:

is there a picture that you could put on here so i can see?

Answer: 5 sides

Step-by-step explanation:

Answer:

It look right to me

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

After adding 5 to both sides what did Michele get? Let's see

[tex]3x-5 + 5 = -10 + 5\\3x= -5[/tex]

If she wants to find the value of [tex]x[/tex] then she needs to have only the variable [tex]x[/tex] on the left hand side. What she must do so that [tex]3x[/tex] becomes just [tex]x[/tex]?  What do you have to do to the number 3 so it becomes a 1? That's right, she must divide by 3!

So, after dividing both sides by 3:

[tex]\frac{3x}{3} = \frac{-10}{3} \\\\\boxed{x=\frac{-10}{3}}[/tex]

Thus, the correct answer is letter B

Answer:

.50 cents per pound

Step-by-step explanation:

Answer:

Mark me brainliest

Answers are, they are congruent, and corresponding angles are proportional

Step-by-step explanation:

whats the answer

Step-by-step explanation:

Answer:

i think question is not clear

Answer:

v= 6km/h - 1km/h^2 * t

Step-by-step explanation:

From the information, it seems the runner is slowing down because the speed at 1st hour is 5km/h but at 3rd hour becomes 3km/h.

If v= velocity, v0= initial speed, t= time, and the a=acceleration then the function would be:  

v= v0 + a * t

To find the acceleration you need to do this equation:

acceleration= velocity1- velocity3 / t3-t1

a = (3km/h-5km/h)/ (3 hour- 1 hour)

a = (-2km/h)/2hour= -1 km/hour^2

After that, you need to find the initial speed. Try to put the 1st-hour variable into the full equation. It would look like this

v= v0 + a * t

5km/h= v0 + (-1 km/hour^2 * 1 hour)

v0= 5km/h + 1km/h

v0= 6km/h  

Then the full function would be:

v= 6km/h - 1km/h^2 * t

The graph would look like a backslash(\) from 5 gradually go down to 1.  

6                          

5 O                    

4      O                

3          O              

2              O            

1                   O      

   1   2  3  4  5

Answer:

well just give it to him

i would yell lol!!

i yell alot lol...............

Answer:

4

Step-by-step explanation:

the different planes are either negitive or positive. since one goes to positive and negative, for example, 5 is greater that -9.

Answer:

x = 4 and y = 15

Step-by-step explanation:

Opposite sides of parallelogram are equal

Opposite sides of parallelogram are equaltherefore,

13x + 15 = 19x - 9

15or 15 + 9 = 19x - 13x

or 24 = 6x

or 24÷6 = X = 4

adjacent angles = 180°

therefore,

(10y - 37) + (4y + 7) = 180

or 10y - 37 + 4y + 7 = 180

or 14y = 180 + 37 - 7

or 14y = 210

or y = 210 ÷ 14

or. y = 15

Answer: 2.70

Step-by-step explanation: 5-2.30=2.70

Answer:

$2.70

Step-by-step explanation:

alright dig this

5-2.3=2.7

my source? a calculator

also im going to assume that sales tax doesn't exist in this problem heehoo

Answer:

[tex]\frac{33}{20}[/tex]

Hope this helps!

Answer:

sin A =cos B

Step-by-step explanation:

sin A =opp/hyp =BC/AB

cos B=adj/hyp = BC/AB

Answer:

its C

Step-by-step explanation: