Mathematics High School

Prove the identity and include the rule

Answers

Answer 1

Hi there!

To begin, we can distribute sec²x with (1 - sin²x):

= sec²x - sec²xsin²x

Which simplifies to:

= sec²x - tan²x

Recall the Pythagorean identity:

1 + tan²x = sec²x

Rearrange alike to the solved for expression above:

1 = sec²x - tan²x

Thus, using the Pythagorean Identity, sec²x(1 - sin²x) = 1.

Related Questions

Emily has 2 cups. Amilia has 26 cups. Amilia has how many times as many cups as Emily?

Answers

Answer:

Step-by-step explanation:

The correct answer is 13

can someone help me with this pleaseee ill give you brainliest and points :)

Answers

Enter in order; 1800, 40, 2

PLEASE HELP FAST ILL GIVE BRAINLEST Match each function with corresponding restrictions to its domain when p(x)2x and q(x)=2^x

Answers

Answer:

1. r(x) = [q(x)]/[p(x)] is x ≠ 0

2. r(x) = p(x) * q(x) is All real numbers

3. r(x) = [1]/[p(x) + 16q(x)] is x ≠ -2

4. r(x) = [q(x)]/[p(x) + 2] is x ≠ -1

5. r(x) = [1]/[p(x) - q(x)] is x ≠ 1, 2

check all that apply
which of the following circles have their centers on the y axis

Answers

Answer:

ABD

Step-by-step explanation:

Please help- will give brainlist. I would appreciate if you told me how you got the answer but you don’t have to

Answers

Answer:

14 units

Step-by-step explanation:

Area is l*w and since the length is known, solve for width

182/13=13w/13

w=14

Answer:

14 units

Step-by-step explanation:

Given, the area of rectangle = 182 square units

length = 13 units

width = ?

By using the formula to find the area of a rectangle, we have

area of rectangle = length * width

182 = 13 * width

182/13 = width

14 units = width

What equation can be used to solve for x

Answers

Not sure but maybe x=180-(58.2)
x=180-116
x=63

Jimmy invests $2,936 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 18 years?

A) $6,599.86

C) $6,534.19

B) $7,221.39

D) $6,869.20

Answers

Answer:

B) $7,221.39

Step-by-step explanation:

Given data

Principal=$2,936

Rate=5%

n=12

Time = 18 years

The expression for compound interest is

A=P(1+r/n)^nt

substitute

A= 2936(1+0.05/12)^12*18

A= 2936(1+0.00416)^12*18

A= 2936(1.00416)^12*18

A= 2936(1.00416)^216

A= 2936*2.45149

A=7197.57464

Hence the approximate amount is B) $7,221.39

Name the polygon. Then tell whether it is a regular polygon or not a regular polygon.

Answers

Answer:

not a regular polygon

Step-by-step explanation:

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center

Evaluate the expression

Answers

Answer:

Step-by-step explanation:

b=3 and its the same question on other side except the expression is in multiplication parenthesis.

Omar is driving to Denver. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Omar has 55 miles to his destination after 44 minutes of driving, and he has 41.5 miles to his destination after 62 minutes of driving. How many miles will he have to his destination after 74 minutes of driving?

Answers

Answer:

After 74 minutes of driving, he still has 32.5 miles to his destination.

Step-by-step explanation:

A linear relationship can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that a line passes through the points (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ - x₁)

Now let's go to the question.

We know that the distance to his destination is a linear function of his total driving time.

We know that he has 55 miles to his destination after 44 minutes of driving. We can write this as the point (44 min, 55mi)

We know that he has 41.5 miles to his destination after 62 minutes of driving, we can write this as (62 min, 41.5mi)

Then the slope of this equation will be:

a = (41.5mi - 55mi)/(62min - 44min) = -0.75 mi/min.

Then the linear equation is something like:

y = (-0.75 mi/min)*x + b

to find the value of b we can use the fact that this line passes through the point (44 min, 55mi)

This means that when x = 44 min, we must have y = 55mi

Then:

55mi = (-0.75 mi/min)*44min + b

55mi + (0.75 mi/min)*44min = b

88mi = b

Then the equation is:

y = (-0.75 mi/min)*x + 88mi

Now we want to know how many miles will he have to his destination after 74 minutes of driving, then we need to replace x by 74 min.

y = (-0.75 mi/min)*74min + 88mi

y = 32.5mi

After 74 minutes of driving, he still has 32.5 miles to his destination.

5. Each of 5 gift bags contains x pencils. Tyler adds 3 more pencils to each bag.
Altogether, the gift bags contain 20 pencils. Create an equation comparing the
number of pencils in each gift bag to the total. Then find the original number of
pencils in each bag before Tyler added 3 more.

Answers

Answer:

Answer: x=20-3

Step-by-step explanation:

Please help me out please

Answers

Answer:

Your answer is 8.06.

Step-by-step explanation:

Since you're finding the hypotenuse of the triangle through Pythagorean theorem, you need to use the formula:

a² + b² = c²

Here, you have to remember that x is the same as c in the formula. c is the hypotenuse and x.

a is going to be your smallest leg, so in this case a = 4.

b is going to be your longest leg, so it is b = 7.

Now, you don't know what c yet is so you simply write it as:

4² + 7² = c²

Do the exponents.

16 + 49 = c²

Add.

65 = c²

Now you need to get the exponent away from the c. To do that, all you have to do is square root both sides.

√65 = √c2

Once you do that, you have your answer!

8.0622577483 = c

Now just simplify and you're done :)

8.06

Might sound hard now but you'll get the hang of it.

Please answer asap!!
chad bought a pair of jeans that cost 54$ plus 4.32 sales tax. What percent sales tax did he pay?

Answers

Answer:

2.3328

Step-by-step explanation:

Explain your answer please ;w; : Change -2Y - 2X = -6 to the slope intercept form of the equation of a line.

Answers

Answer:

y = -x + 2

Step-by-step explanation:

The desired equation must have the form y = mx + b.

Start with -2Y - 2X = -6 and solve for y: y + x = 2

Now solve this result for y:

y = -x + 2

What is 62 remainder 3 as a whole number

Answers

Answer:

623

Step-by-step explanation:

Answer:

20 2/3

Step-by-step explanation:

In the diagram, m∠G = 95°. What is m∠E?

Answers

Answer:

85*

Step-by-step explanation:

Its really complicated but manage to find it

If you have 2x - 4 list three input and their output values.

Answers

With 2x-4 given to you, you can substitute x (input) and solve with that input to get y (output).

Ex. 2(0)-4=-4, (0, -4)

2(1)-4=-2, (1, -2)

2(2)-4=0, (2, 0)

What is the probability of throwing 2 dice and getting the sum of 12?

Answers

Answer:

1/36

Step-by-step explanation:

P(6,6) = 1/6 x 1/6 = 1/36

What is the solution to this equation?
- 4
A. Y = 4
B. X= 8
C. X= 2
D. X= 16

Answers

Answer:

The correct answer is C. X= 2

And I also need help in this one.

Answers

Hey bestie I’m pretty sure it’s 1:3

Complete the equation for the circle with center (-2,-4) and radius 9?

Answers

Answer:

Step-by-step explanation:

55654

Find the surface area of the triangular prism.

WILL GIVE BRAINLIEST!!

Answers

Answer:

462.99

Step-by-step explanation:

Help quickly!!
A class of 50 students elected a class president.
Candidate A received 15 votes.
Candidate B received 25 votes.
The remaining students did not vote.

Which expression gives the percent of voters who voted for Candidate B?

Answers

Answer:

the answer is 25/15+25 ×100

step by step explanation:

its only 15+25 because not everyone voted so you only count those who voted

Answer:

25/50x100

Step-by-step explanation:

25/50x100

=25x2

=50

2. Find the length of the missing side. (1 point)
600
12
The triangle is not drawn to scale.
02
O 12
2
063

Answers

Answer:

x²+6²=12²

x²+36=144

x²=144-36

x²=108

x=√108

A class has 40 students. Their are 22 girls in the class. Express the number of boys in the class as a fraction.

Answers

Answer:

18/40

Step-by-step explanation:

18/40

Apologies if this is incorrect.

Matt earns $5 for each lawn he does. He wants to earn at least $100. Which inequality represents his situation?

Answers

Answer:

$100 is less than or equal to x

X is greater than or equal to $100.
The reason x is more is because he wants to earn $100 but could always earn more money because more money is always great. So x being the money he earns- could either be MORE or EQUAL to $100.

The side length of a triangle or 12.5 inch 4.4 inch and 11.72 which statement best describes the triangle formed using these
side lengths

Answers

Answer:

scalene

Step-by-step explanation:

12.5, 4.4, and 11.72 are all different measurements

i hope this helped

Graph the
equation.
y = 3x+4

Answers

Answer:

Plot the following points:

(-2,-2)

(-1,1)

(0,4)

(1,7)

(2,10)

Step-by-step explanation:

Just plug any random number in for x to solve for y.

PLEASE HELP I WILL MARK BRAINLIEST

Answers

Answer:

19 square cm

Step-by-step explanation:

4 + 2.5 = 6.5

4 × 6.5 = 26

Since the shape is half of the product above, we're going to divide it by 2

26 ÷ 2 = 13

4 × 3 = 12

12 ÷ 2 = 6

Now to add them together

13 + 6 = 19

i want derivative for (x+1)^2×e^x
please help

Answers

Answer:

(x + 1)(x + 3)eˣ

Step-by-step explanation:

Since f(x) = (x + 1)²eˣ

df(x)/dx = d[(x + 1)²eˣ]/dx

By the product rule, duv/dx = udv/dx + vdu/dx

where u = (x + 1)² and v = eˣ

So, df(x)/dx = d[(x + 1)²eˣ]/dx

= (x + 1)²deˣ/dx + eˣd(x + 1)²/dx

= (x + 1)²eˣ + eˣd(x + 1)²/d(x + 1) × d(x + 1)/dx (by the chain-rule dy/dx = dy/du × du/dx)

= (x + 1)²eˣ + eˣ[2(x + 1) × 1]

= (x + 1)²eˣ + 2eˣ(x + 1)

= (x + 1)eˣ(x + 1 + 2)

= (x + 1)eˣ(x + 3)

= (x + 1)(x + 3)eˣ

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