Pls help due tomorrow!!!

To verify:

cos⁴x+sin⁴x=1-2sin²xcos²x​

we have,

LHS= sin⁴x+cos⁴x

=(sin²x)²+(cos²x)² +2sin²x cos²x - 2sin² cos²x

(by adding and subtracting 2sin²x cos²x)

=(sin²x +cos²x )² - 2 sin²x cos²x

=1-2sin²x cos²x =RHS

Therefore LHS=RHS

The study of angles and the angular relationships of planar and three-dimensional figures is known as trigonometry. It is the branch of mathematics concerned with specific functions of angles and their application to calculations.

Trigonometry as the name suggests is all about triangles. More specifically, it is about right-angled triangles.

The trigonometry functions (also called the circular functions) comprising trigonometry are the cosecant, cosine(cos), secant, sine(sin), and tangent(tan).

to learn more about trigonometry refer to the link below:

https://brainly.com/question/24349828

Store of Value: people are willing to hold onto it because they're confident that it will keep its value over time.

In Economics, money can be defined as any formally recognized economic unit that is universally accepted as a medium of exchange for goods (products) and services, as well as repayment of debts such as taxes, levies, fees, and loans, across the world.

Generally speaking, money is universally accepted as a medium of exchange because it possesses six (6) essential characteristics and these include the following:

In conclusion, we can reasonably infer and logically deduce that store of value is a measure of the durability of money.

Read more on money here: brainly.com/question/11252085

#SPJ1

Eric's regular hourly pay is $14.05.

Pay is a term used to describe the compensation received for providing goods or services. It may be in the form of wages, salary, commission, bonus, tips, piece rate pay, or other forms of compensation. Pay is often based on the amount of time worked, or on the amount of work completed. Pay is a key component of the employer-employee relationship, and labor laws often regulate pay to ensure fairness and compliance.

To calculate Eric’s regular hourly pay, we can use the following equation:

Regular hourly pay = (Total pay - Overtime pay) / (Regular hours + Overtime hours)

In this case, we would plug in the following values:

Regular hourly pay = ($852.5 - (10 x 1.5 x Regular hourly pay)) / (40 + 10)

Regular hourly pay = ($852.5 - $150) / 50

Regular hourly pay = $702.5 / 50

Regular hourly pay = $14.05

Therefore, Eric's regular hourly pay is $14.05.

To know more about pay click-
https://brainly.com/question/25793394
#SPJ1

Answer:

a=-1/4

Step-by-step explanation:

a+3 1/4 =5 2/9

change to improper fraction

a+13/4 = 47/9

make sure that both fractions have the same denominator

a+(13/4)9=(47/9)4

a+117/36=108/36

make sure that variable is alone on one side

a=108/36-117/36

a=-9/36= -1/4

a=-1/4

Step-by-step explanation:

a+3 1/4 =5 2/9

change to improper fraction

a+13/4 = 47/9

make sure that both fractions have the same denominator

a+(13/4)9=(47/9)4

a+117/36=108/36

make sure that variable is alone on one side

a=108/36-117/36

a=-9/36= -1/4

Answer:

C is the corect answer

Step-by-step explanation:

12x+3=39

12x=39-3

12x=36

x=36:12

x=3

12×3=36

36+3=39

Answer:

Buffy is correct

Step-by-step explanation:

To start off, we know that if we buy 1 pen, the cost of the singular pen will be 1.5, which isn't a whole number. Therefore we can eliminate Bonnie, meaning the domain of the situation is by positive real numbers (real numbers meaning decimal, fraction AND whole numbers)

The difference between the amount paid by the company and the premium contribution is given as follows:

FRW 1 298 400.

The difference is obtained applying the proportions in the context of the problem, which is the yearly payment, for the time.

The insurance was purchased on the 25th birthday, and the person died with 65 years old, hence the time period is given as follows:

65 - 25 = 40 years.

He paid a premium of 35 740 FRW yearly, hence the total amount paid is given as follows:

40 x 35 740 = 1,429,600.

A man took a life insurance policy for 2 728 000 FRW on his 25th birthday, hence the difference is calculated as follows:

2,728,000 - 1,429,600 = FRW 1 298 400.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

After 18 ​years, the investment compounded periodically will be worth (future value) ​$534.55 more than the investment compounded annually.

The future value is the compounded present value of an investment using an interest rate.

The future value can be computed using an online finance calculator.

N (# of periods) = 72 quarters (18 years x 4)

I/Y (Interest per year) = 6%

PV (Present Value) = $8,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $23,369.26

Total Interest = $15,369.26

N (# of periods) = 18 years

I/Y (Interest per year) = 6%

PV (Present Value) = $8,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $22,834.71

Total Interest = $14,834.71

Difference in future value = $5,34.55 ($23,369.26 - $22,834.71)

Thus, compounding an investment quarterly yields a greater future value than annual compounding.

Learn more about the future value at https://brainly.com/question/24703884

#SPJ1

We can simplify the inequality |x + 3| > 2 to get the compound inequality:

-1 < x

-5 > x

Thus, the correct option is B.

Here we have the following inequality:

|x + 3| > 2

The absolute value part can be "separated" into a compound inequality, we can rewrite this as:

|x + 3| > 2

-2 > x + 3

2 < x  + 3

Now we can solve these two inequalities for x, we will get:

-2 > x + 3

-2 - 3 > x

-5 > x

The second inequality gives:

2 < x + 3

x - 3 < x

-1 < x

Then the compound inequality is:

-1 < x

-5 > x

Then the correct graph is the one in option B.

Learn more about inequalities by reading:

https://brainly.com/question/24372553

#SPJ1

The proof to show that △STU≅△QUT.

Congruency is a property which implies that two given shapes are equal in respect of their length of corresponding sides, and measure of their corresponding internal angles.

Thus, the proof to show that △STU≅△QUT are explained below;

<QRU ≅ <SRT                           (vertically opposite angle property)

QT = QR + RT          

SU = SR + RU

So that;

QT ≅ SU                                   (Reflexive property of congruent triangles)

TU ≅ UT                                   (common side of congruent triangles)

QU ≅ ST                                    

<SUT ≅ <QTU                         (Reflexive property of congruent triangles)

Therefore, it can be concluded that;

△STU≅△QUT

Learn more about properties of congruent triangles at https://brainly.com/question/30179212

#SPJ1

Answer:

12.43 pounds of chocolate with 13 pounds of trail mix

Step-by-step explanation:

To find the amount of chocolate that needs to be mixed with the trail mix, we need to set up the following equation:

(cost of chocolate per pound * pounds of chocolate) + (cost of trail mix per pound * pounds of trail mix) = cost per pound of mixture * (pounds of chocolate + pounds of trail mix)

We can plug in the given values to get the following equation:

($20.80/pound * pounds of chocolate) + ($3.50/pound * 13 pounds) = $11.80/pound * (pounds of chocolate + 13 pounds)

We can then solve this equation to find the number of pounds of chocolate that should be mixed with the trail mix.

($20.80/pound * pounds of chocolate) + $46.50 = $11.80/pound * (pounds of chocolate + 13 pounds)

$20.80/pound * pounds of chocolate = $11.80/pound * (pounds of chocolate + 13 pounds) - $46.50

$20.80/pound * pounds of chocolate = $11.80/pound * pounds of chocolate + $11.80/pound * 13 pounds - $46.50

$9.00/pound * pounds of chocolate = $158.40 - $46.50

$9.00/pound * pounds of chocolate = $111.90

pounds of chocolate = $111.90 / $9.00/pound

pounds of chocolate = 12.43 pounds

Thus, the store owner should mix 12.43 pounds of chocolate with 13 pounds of trail mix to create a mixture worth $11.80 per pound.

Answer:

12 pound of chocolate

Step-by-step explanation:

Let x pounds of chocolate costing $20.80 per pound, mixed with 13 pounds of trail mix costing $3.50 per pound to create a mixture worth $11.80,

The total quantity of trail mix = ( x + 13 ) pounds,

Also, the cost of x pounds of chocolate + the cost of 13 pounds of trail mix = the cost of the resultant trail mix.

total cost = number of pounds × price per pound

20.80x + 3.50(13) = 11.80(x + 13)

20.80x + 45.5 = 11.80x + 153.53

9x + 45.5 = 153.53

9x = 108.03

x = 12 pound

If you can, please give me a Brainliest; thank you!

57 beads out of 100 beads are brown in colour.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Brennan ordered a set of beads

He received 100 beads

57% of 100 beads were brown.

we need to find the number of beads which are brown.

Convert 57 % to the decimal value.

57/100=0.57

Now multiply 0.57 with 100

0.57×100=57

Hence, 57 beads out of 100 beads are brown in colour.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1

The equation of the line with gradient of 1 / 2 and passes through (4, -2) is  y = 1 / 2 x - 4.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line has a gradient or slope of 1 / 2 and it passes through (4, -2).

y = 1 / 2 x + b

let's find the y-intercept using (4, -2)

-2 = 1 / 2(4) + b

-2 - 2 = b

b = -4

Therefore, the equation is y = 1 / 2 x - 4

learn more on equation of a line here: https://brainly.com/question/29647048

#SPJ1

Multiple triangles are possible with three different side lengths. The relationships between the side lengths and the lengths of the sides determine the number of triangles.

For instance, only one triangle can be formed if the lengths of the three sides are the same. Two triangles can be formed if the lengths of two sides are equal. It is possible to form three triangles if the lengths of the three sides differ.

In general, it is possible to form a triangle if the three side lengths satisfy the triangle inequality theorem. The sum of any two sides of a triangle must be greater than the sum of the third side, according to this theorem. For instance, since 3 + 4 is greater than 5, a triangle can be formed if the three side lengths are 3, 4, and 5. A triangle cannot be formed if the sum of any two sides is not greater than the third side.

The angle relationships between the sides also play a role in determining how many distinct triangles can be formed.

Learn more about Triangle Inequality Theorem here:

https://brainly.com/question/309896

#SPJ4

Answer: y=mx+b

Step-by-step explanation:

The value of the t score for a 90% confidence interval if we take a sample of size 22 is 1.721.

Any member of the family of continuous probability distributions known as the Student's t-distribution (or simply the t-distribution) in probability and statistics is used to estimate the mean of a normally distributed population when the sample size is small and the population's standard deviation is unknown.

The Student's t-test for determining the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and linear regression analysis are just a few commonly used statistical analyses that make use of the t-distribution. Additionally, the Bayesian analysis of data from a typical family produces the Student's t-distribution.

To learn about T-distribution :

https://brainly.com/question/17469144

#SPJ4

The properties of exponents are (ab)^x = a^xb^x, b² × b^x = b^(2+x), and x⁻² = 1/x². Hence options A, D, E are correct.

What is the property of exponent?

When referring to a mathematical phrase that denotes that a number will be multiplied by itself n times, the terms power and exponent are frequently used interchangeably. That is a valid definition of power, however, in mathematics, the word exponent expressly refers to the amount. n that specifies the number of times it will be multiplied by itself.

There are six properties of the exponent. The properties are

Product of Powers (x^m)(x^n) = x^(m+n)

Power to a Power (x^m)^n = x^(mn)

Quotient of Powers (x^m)/(x^n) = x^(m-n)

Power of a Product (xy)^m = x^m× x^n

Power of a Quotient (x/y)^n = x^n/y^n

Negative exponent  x^(-n)= 1/x^n

According to the Power of a Product:

(ab)^x = a^xb^x

According to the Negative exponent:

7⁻³ = 1/7³

According to the Product of Powers:

b² × b^x = b^(2+x)

According to the Negative exponent:

x⁻² = 1/x².

To learn more about Power of a Quotient rule, click on the below link:

https://brainly.com/question/8826169

#SPJ1

Isosceles triangle the vertex angle is twice either base angle is the right statement. Isosceles triangle is a triangle which has two sides of equal length or value.

Isosceles triangle is a triangle that has two side of same value. It is mean that isosceles triangle has to fulfill this condition : two sides of triangle has to be congruent to each other; the third side of isosceles triangle that has not same length to the another side is called the base of the isosceles triangle; the two angles opposite has the same sides are congruent to one another.

Learn more about isosceles triangle here

brainly.com/question/13664166

#SPJ4

Answer:

0=0

Step-by-step explanation:

6(4x+3y)=6(-2)

3(8x+6y)=3(-4)

24x+18y=-12

24x+18y=-12

0=0

The values of exponent 5, √15, 2 and ∛2.

There are various exponential laws. Numerous mathematical problems involving repeated multiplication operations can be solved using all of the exponent rules. The operations of multiplication and division are made simpler and easier to solve by the laws of exponents.

Given,

The important laws of exponents are given below:

xᵃ ₓ xᵇ = x ᵃ⁺ ᵇ

xᵃ/xᵇ = x ᵃ⁻ ᵇ

(xᵃ)ᵇ = x ᵃᵇ

a⁻ⁿ = 1/aⁿ

a⁽¹/ⁿ⁾ = [tex]\sqrt[n]{a}[/tex]

1: [tex]25^{\frac{1}{2} }[/tex]

25 = 5 x 5 = 5²

[tex]( 5^{2}) ^{\frac{1}{2} }[/tex] = 5 using formula (xᵃ)ᵇ = x ᵃᵇ

2: [tex]15^{\frac{1}{2} }[/tex]

= [tex]\sqrt{15}[/tex] using a⁽¹/ⁿ⁾ = [tex]\sqrt[n]{a}[/tex]

3: [tex]8^{\frac{1}{3} }[/tex]

8 = 2 x 2 x2 = 2³

[tex]( 2^{3}) ^{\frac{1}{3} }[/tex] =  2 using formula (xᵃ)ᵇ = x ᵃᵇ

4: [tex]2^{\frac{1}{3} }[/tex]

= ∛2 using a⁽¹/ⁿ⁾ = [tex]\sqrt[n]{a}[/tex].

Hence values are 5, √15, 2 and ∛2.

Learn more about exponent;

https://brainly.com/question/15993626

#SPJ1

The side length of each square piece of fabric is 0.343 feet

From the question, we have the following parameters that can be used in our computation:

Square quilt

The readings from the quilt are given as

Using the above as a guide, we have the following:

Number of squares * Area of Individual shapes = Area of quilt

Substitute the known values in the above equation, so, we have the following representation

64 * Area of Individual shapes = seven and fifty-two hundredths feet

Rewrite as

64 * Area of Individual shapes = 7.52

Divide both sides by 64

Area of Individual shapes = 0.1175

Take the square roots

Length of square = 0.343

Hence, the length is 0.343 feet

Read more about area at

https://brainly.com/question/24487155

#SPJ1

So there are 5 raspberries in the bowl.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

We know that for every 3 raspberries, there are 5 blackberries.

We can set up an equation to represent this relationship:

5 blackberries = 3 raspberries

We also know that there are a total of 15 blackberries in the bowl.

We can use the equation to find the number of raspberries in the bowl:

15 blackberries = 3 raspberries

15 blackberries / 3 raspberries = 5 raspberries

So there are 5 raspberries in the bowl.

To learn more about unitary method visit:

brainly.com/question/28276953

#SPJ1

The two true options about the ratio between the hours he works and the neckties he produces among the given statements are (c) and (d).

Given that Diante can make 5 neckties in 4 hours. ratio

Hence,

Number of neckties Diante can make in an hour = 5/4 = 1.25 per hour.

Hence, (d) is correct.

As in (b), it is written that Diante can make 4/5 of a necktie in an hour hence it is incorrect.

We can also say that:-

Number of hours taken to make a necktie = 4/5 hour.

Hence, (c)  is correct.

As in (a), it is written that Diante can make 1 necktie in 1.25 hours, hence it is incorrect.

complete question

Diante can make 5 neckties in 4 hours.

select the two true statements about the ratio between the hours he works and the neckties he produces.

a. it takes diante 1.25 hours to make one necktie.

b. diante makes 45 of a necktie per hour.

c. it takes diante 45 hour to make a necktie.

d. diante makes 1.25 neckties per hour.

To learn more about ratio, here:-

brainly.com/question/13419413

#SPJ4

The equations of the line in slope-intercept form are listed below:

4) y = - x / 2 + 3

5) y = (5 / 2) · x + 1

6) y = - 4 · x + 5

7) y = - x + 2

8) y = 2 · x / 3 + 4

9) y = x

Lines are described by first order polynomials of the form:

y = m · x + b

Where:

Where the slope of the line is found by secant line formula:

m = Δy / Δx

Where:

The complete procedure is summarized below:

Case 4

(x₁, y₁) = (0, 3), (x₂, y₂) = (6, 0)

m = (0 - 3) / (6 - 0)

m = - 1 / 2

b = y - m · x

b = 0 - (- 1 / 2) · 6

b = 3

y = - x / 2 + 3

Case 5

(x₁, y₁) = (0, 1), (x₂, y₂) = (2, 6)

m = (6 - 1) / (2 - 0)

m = 5 / 2

b = y - m · x

b = 6 - (5 / 2) · 2

b = 6 - 5

b = 1

y = (5 / 2) · x + 1

Case 6

(x₁, y₁) = (- 2, 3), (x₂, y₂) = (0, - 5)

m = (- 5 - 3) / [0 - (- 2)]

m = - 4

b = y - m · x

b = - 5 - (- 4) · 0

b = - 5

y = - 4 · x + 5

Case 7

(x₁, y₁) = (0, 2), (x₂, y₂) = (2, 0)

m = (0 - 2) / (2 - 0)

m = - 1

b = y - m · x

b = 0 - (- 1) · 2

b = 2

y = - x + 2

Case 8

(x₁, y₁) = (0, - 4), (x₂, y₂) = (6, 0)

m = [0 - (- 4)] / (6 - 0)

m = 2 / 3

b = y - m · x

b = 0 - (2 / 3) · 6

b = 4

y = 2 · x / 3 + 4

Case 9

(x₁, y₁) = (0, 0), (x₂, y₂) = (1, 1)

m = (1 - 0) / (1 - 0)

m = 1

b = y - m · x

b = 1 - 1 · 1

b = 0

y = x

To learn more on equations of the line: https://brainly.com/question/21511618

#SPJ1

Solutions to the given inequality are numbers 4 and 5. Thus, the answer is (e) and (f).

To find the solution, first, we solve the inequality for x:

2x - 1 > x + 2

2x - x > 2 + 1

x > 3

Hence, the answer is any number that is greater than 3.

Therefore, the solutions are numbers 4 and 5.

To learn more about solving inequality:

https://brainly.com/question/11897796

The complete question is:

Which numbers are solutions to the inequality 2x - 1 > x + 2? Check all of the boxes that apply.

(a) 0

(b) 1

(c) 2

(d) 3

(e) 4

(f) 5

The height, in feet, of the fifth bounce=2.7579

On the 1st bounce, height = 6.1 feet

We were not given the initial height of the ball before the 1st bounce

2nd bounce:

height = 0.82 of the previous bounce

height = 0.82(6.1)

height=5.002

3rd bounce:

height = 0.82 of the previous bounce

previous bounce = 0.82(6.1)

height = 0.82(0.82 × 6.1)

height=4.10164

We can derive a formula for the nth bounce:

height=6.1(0.82)^n-1

h(n)=6.1(0.82)^n-1

To verify consider n=1

h(1)=6.1(0.82)^1-1

h(1)=6.1

To calculate the fifth bounce:

h(5)=6.1(0.82)^5-1

considering n=5

h(5)=6.1(0.45212176)

h(5)=2.7579

To know more about the Bounces of the ball:

https://brainly.com/question/29122461

#SPJ4