cos^4x - sin^4x +1 = 2cos^2x
prove
​

[tex] \: \huge \tt{\pink{A}{\orange{N}S{\green{W}{\blue{E}{\purple{R}}}}}} \\ \\ \: \: \: \tt \rightarrow {\blue{\fbox{147 \: sets}}} (approx)[/tex]

Step-by-step explanation:

Fixed costs = $ 1329.50 per month

Variable cost are $3.70 per set of napkins

Total cost she set aside = $1870 for monthly costs

Amount left for napkins = Total cost - Fixed Cost

= 1870 - 1329.50

= $540.50

Cost for one set = $3.70

Let set of napkins = x

Total cost for napkins = $540.50

Therefore , she can afford to make 147 (approx) sets of napkins per month.

Answer:

3/2

Step-by-step explanation:

6/4 = 1.5

3/2 = 1.5

So we know 1.5 is the scale and it asks for it in fraction form which would be 3/2.

The values of the missing variables from the areas of rectangle and square are;

17) x = 4

18) y = 5

19) x = 4

17) The formula for area of rectangle is;

A = Length * Width

Formula for area of square is;

A = side * side

Thus;

A_rect = (x - 1)(x + 2) = x² + x - 2

A_sq = x²

The area of the rectangle shown exceeds the area of the square by

2 cm². Thus;

x² + x - 2 - x² = 2

x - 2 = 2

x = 4

18) Area of the square; A_sq = y²

Area of the rectangle; A_rect = (y - 3)(y + 1) = y² - 2y - 3

The area of the square exceeds the area of the rectangle by 13 m². Thus;

y² - y² + 2y + 3 = 13

2y = 10

y = 5

19) The area of the square is half the area of the rectangle. Thus;

x² = ¹/₂(2(x² + 2x - 8))

x² = x² + 2x - 8

2x - 8 = 0

x = 4

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Answer:

Answer in photo!!! :))

Step-by-step explanation:

The fraction of hour that remained is 1/2 hour.

It is given in the question that three students were scheduled to give book reports in 1 hour.

After the first report, 2/3 hour remained. The next report took 1/6 hour.

We have to find the fraction of hour that remained.

We know that,

Total time for reports = time taken for first report + time taken for second report + time remained for third report

Hence, we can write,

Time taken for first report =  1-2/3 = 1/3 hour

Time taken for second report = 1/6 hour

1 = 1/3 + 1/6 + time remained for third report

1 = 2/6 + 1/6 + time remained for third report

1 = 3/6 + time remained for third report

1-3/6 = time remained for third report

3/6 = 1/2 = time remained for third report

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Answer:

2  legos were green

Step-by-step explanation:

Given- in an assorted colored lego box, 5/6 of the legos were red, and 2/3 of the remaining legos were green. if there were 18 legos,

let->

x number of the red ball then probability= x/18=5/6

=>x=15

then, 3 balls are other in which the green +remaining ball is present according to the question.

2/3 times of 3 are green legos==>

(2/3)*3=2 are green legos;

and the last ball 1 lego is remain.

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56x raise to power minus 4 divided by 14x raise to power minus 8​ has its answer calculated as 4[tex]x^2[/tex] by solving through formulas of exponents and powers.

A mark placed exactly or right above a mathematical equation or a numeral that helps to denote the action of raising to a power of something.

Exponent is also defined as one of the methods of expressing many large numbers in terms of powers. This means that exponent refers to how many times a single number or an equation is multiplied by itself.

The statement 56x raise to power minus 4 divided by 14x raise to power minus 8​ can be simplified in equational terms as

[tex]\frac{56x^-{4}}{14x^{-8}}[/tex]

which can be further simplified as [tex]4x^{4}[/tex]

Exponentiation is a type of mathematical operation that can be written as bⁿ, involving two numbers. The base b and then the exponent or power n is included in it and pronounced as "b to the power n".

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Answer:

[tex]\frac{15-6-6}{2}[/tex] = x

You should have 1.5 feet of space between each picture.

Step-by-step explanation:

Let x be the spacing between the pictures

[tex]\frac{15-6-6}{2}[/tex] = x The total length - end spacing - the width of the posters.  What is left is the blank spaces between the posters.  Since there are 2 blank spaces, we will divide by 2 to find out the spacing between the two pictures.  Which is 1.5 feet.

The trigonometric ratio which can be used to find the measurement of F using only the lengths is: D. tangent only.

In geometry, a tangent is also known as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.

Mathematically, the tangent of an angle is given by this expression:

Cosθ = Adj/Hyp

Where:

Since both the opposite side and adjacent side of this right-angled triangle are given, cosine is the trigonometric ratio which can be used.

For this right-angled triangle, the cosine of the angle (θ) is given by:

Cosθ = 9/F

F = 9/Cosθ

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Answer:

Because these probabilities are independent, the friend was supposed to multiply them, not add them. So the probability of rain this weekend is

.35 × .65, or .2275, meaning that the probability of rain this weekend is 22.75%

Cost of one hot dog is and potato chips is

As per the given problem a customer buys 3 hot dogs and 3 bags of potato chips for $8.25. we have to find the cost of each item.

let price of one hot dog is x nd price of potato chips is y.

Formulating the Equation we get

3x+3y=$8.25

another customer buys 5 hot dogs and 3 bags of potato chips for $11.25.

Formulting the Equation we get

5x+3y=$11.25.

we get two linear equation with two unknowns.

solving both equation we get $8.25-3x=$11.25-5x

or 2x=$3

x=$1.5

y=$1.25

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At 32 cm^2/s rate the area of the square is increasing when the area of the square is 64 [tex]cm^{2}[/tex]

As per given problem each side of a square is increasing at a rate of 2 cm/s. let side of square is x.so the area of it is A= [tex]x^{2}[/tex].now differentiating w.r.t time A

[tex]\frac{dA}{dt}[/tex]= 2x[tex]\frac{dx}{dt}[/tex]

when A=64 [tex]cm^{2}[/tex] x=8 cm

also given [tex]\frac{dx}{dt}[/tex]=2cm/s

so [tex]\frac{dA}{dt}[/tex]=2×2×8=32

So at 32 cm^2/s rate the area of the square is increasing when the area of the square is 64 [tex]cm^{2}[/tex]

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Answer:

Step-by-step explanation:

Answer:

б) не более трех раз

The time it would take the cost to be 4 times the current cost of a gallon of milk at an annual inflation rate of 6% is calculated to be 23.8 years.

To determine the time for the cost to be 4 times the current cost of a gallon of milk, we use the compound interest formula as follows;

A(t) = A(0) (1 + r)^t

Here A(t) is the cost of 4 times the current cost at time t

A(0) is the current cost

r is the interest rate

t is the time period

Therefore;

2.70 × 4 = 2.70( 1 + 0.06)^t

2.70 × 4 / 2.70 = (1.06)^t

4 = (1.06)^t

Taking log on both sides;

t × log(1.06) = log 4

t = log 4 / log(1.06)

t = 23.791 = 23.8 years

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The numbers are 26 and 9 respectively.

An algebraic expression can best be defined as an arithmetic or mathematical expression that is known to consist of variables, coefficients, constants, factors as well as terms.

These expressions said to contain numerous arithmetic operations, which includes;

From the information given, we have that

Let the small number be x

The large number be y

y < 3x    (1)

Also,

x + y = 35    equation 2

x = 35 - y

Substitute the value of x in equation 1

y < 3(35 - y)

expand the bracket

y < 105 - 3y

collect like terms

y + 3y < 105

4y < 105

Make 'y' the subject

y < 105/4

y < 26. 25

y = 26

substitute the value of y

x + y = 35

x + 26 = 35

x = 9

Hence, the values are 26 and 9

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If the given mathematical expression 12−{1+2[−1(3−8)]2} is been evaluated , then it will become -18.

The mathematical expression can be simplified by first simplify the expression in the inner bracket one after the other.

The given mathematical expression is 12−{1+2[−1(3−8)]2}

then we can simplify one after the order by following the bracket one after the other, as :

12−{1+2[−1(3−8)]2}

12 - {1+2[-1(-5)]2}

Then we can further simplify the expression as :

12 - {3 [ 5 ] 2}

Then this can be further simplified as :

12 - {30}

This can be further  simplified as :

-18

Therefore, the value of the expression given is -18

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The number of miles in day at which the rental cost for the company A and Company B are the same is 200 miles

The Company A rented the truck for $40 a day plus $0.40 per miles

The expression will be

40+0.40x

Where x  is the number of miles

The company B rented the truck for $20 a day plus $0.50 per miles

20+0.50x

To find the number of miles in a day at which the rental costs for Company A and Company B are the same, the linear equation will be

40+0.40x = 20+0.50x

40-20 = 0.50x-0.40x

0.1x = 20

x = 200 miles

Hence, the number of miles in day at which the rental cost for the company A and Company B are the same is 200 miles

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Answer:

2x + 7y

Step-by-step explanation:

3x + 5y - x + 2y ← collect like terms

= (3x - x) + (5y + 2y)

= 2x + 7y

By Simplifying 3x + 5y - x + 2y, we get 2x + 7y

More Explanation

The simplification here follows the basic method of addition and subtraction in algebra.

Given : 3x + 5y - x + 2y

Step 1: align the numbers with similar variables.

Therefore, we get, 3x - x + 5y + 2y

Step 2: Solve by addition and subtraction.

Therefore, we get, 2x + 7y

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The values of k for which the line y = 2x + k + 2 cuts the curve y = 2x² + (k + 2) + 8 at two distinct points are; k > -12 or k < 4

We are given the equation of the line as;

y = 2x + k + 2

Equation of the curve is;

y = 2x² + (k + 2) + 8

Now, to find the the values of k for which the line y = 2x + k + 2 cuts the curve y = 2x² + (k + 2) + 8 at two distinct points, we will just equate both equations to get;

2x + k + 2 =  2x² + (k + 2) + 8

2x + k + 2 =  2x² + kx + 2x + 8

2x² + kx + (-k + 6) = 0

Now, Two distinct solutions is the same as having a positive discriminant.

b² - 4ac > 0

k² - 4(2 * (-k + 6)) > 0

k²  + 8k - 48 > 0

Solving using quadratic equation calculator gives;

k > -12 or k < 4

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The expression z raised to the twentieth power over y raised to the twentieth power is equivalent to the expression given in the question.

y raised to the negative second power = [tex]y^{-2}[/tex]

z raised to the seventh power = [tex]z^{7}[/tex]

Thus, in the numerator we have the expression- [tex]y^{-2} z^{7}[/tex]

In the denominator, we will have-

z raised to the negative third power = [tex]z^{-3}[/tex]

y raised to the eighth power = [tex]y^{8}[/tex]

denominator will be = [tex]z^{-3} y^{8}[/tex]

Thus, the expression becomes-

[tex](\frac{y^{-2 }z^{7} }{z^{-3} y^{8} })^{-2}[/tex]

Now, that we've decoded the expression, let us solve it-

[tex]({y^{-2 }y^{-8} z^{7} z^{3} )^{-2}[/tex]

= [tex]({y^{(-2-8) } z^{(7+3)})^{-2}[/tex]

= [tex]({y^{(-10) } z^{(10)})^{-2}[/tex]

= [tex]{y^{(-10*-2) } z^{(10*-2)}[/tex]

= [tex]{y^{(20) } z^{(-20)}[/tex]

= [tex]\frac{z^{20} }{y^{20} }[/tex]

= [tex](\frac{z}{y} )^{20}[/tex]

Thus, the expression z raised to the twentieth power over y raised to the twentieth power is equivalent to the expression given in the question above.

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Answer:

Step-by-step explanation: 0.00489296636 if you divided by 40 to 8175 but if you wanted 8175 divided 40 it would equal 204.375 just letting you know i used a calculator so if these aren't it then i'm not sure

Using the expected value of a discrete distribution, the correct option is given as follows:

E(penny) = 1.75 and E(nickel) = 1.5, so she should play with the pennies.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

When 3 coins are tossed, the probabilities are given as follows:

Hence the distribution for the penny points is:

The expected value for the penny points is:

-2 x 0.25 + 3 x 0.75 = 1.75.

When 2 coins are tossed, the probabilities are given as follows:

Hence the distribution for the nickel points is:

The expected value of nickel points is:

E(X) = -2 x 0.5 + 5 x 0.5 = 1.5.

Due to the higher expected value, she should play with the pennies and the third option is correct.

The complete problem is given by the image at the end of the answer;

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Answer:

The answer is C

Step-by-step explanation:

edge

The equation of the line graph in slope intercept form is gotten as;

y = x + 3

The general formula for the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, from the given straight line equation graph, we can see that the line crosses the x-intercept at x = -3 and crosses the y-intercept at y = 3. Thus;

When x = 0, y = 3

When y = 0, x = -3

Slope is gotten by using two points and their coordinates to get;

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

m = 3/3

m = 1

Thus, the equation of the line is y = x + 3

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Answer:

C = F(0.20) + F

Step-by-step explanation:

C is the total cost. F(0.20) will reduce the value of the food to the tip amount required, and then adds the tip value to the price of the food, F.

Example inputs: let F be equal to 10
C = F(0.20) + F turns into C = 10(0.20) + 10

10(0.20) will cause 10 to be multiplied by the tip value, 20%, and 20% is equivalent to 0.20. Once you multiply 10 by 0.20, you get 2. After that, you add 2 to the price of food, which is 10, and you get a total cost of 12.

12 = 10(0.20) + 10

5 to the power of -3 in its simplest form without any indices is 1/125 or 0.008.

Exponents

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as [tex]6^4[/tex]. Here, 4 is the exponent and 6 is the base. This can be read as 6 is raised to power 4.

We know that,

[tex]a^{-b}=\frac{1}{a^b}[/tex]

Hence, we can write,

[tex]5^{-3}=\frac{1}{5^3}[/tex]

We know that the cube of 5 is 125.

Hence, we can write,

[tex]\frac{1}{5^3}[/tex] = 1/125

1/125 is the simplest form of fraction and is equal to 0.008 in decimal form.

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If the second and third cards have a spade then the probability that the first card drawn is a spade is 21.2%.

Probability can be described as a field of mathematics that determines how likely a thing is to happen. When there is uncertainty about the outcome of an event we consider the probabilities of certain results or outcomes.

There are a total of 13 spades in a deck of 52 playing cards. So if the second and third cards have spades then there are 11 spades remaining.

The formula for probability can be given as;

probability = number of favorable outcomes or events ÷ total number of outcomes or events

probability = 11 / 52 = 0.212

Converting it into percentage;

probability = 0.212 × 100 = 21.2%

Therefore, the probability that the first card drawn is a spade is calculated to be 21.2%.

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The truth statements about the transformations are:

There are four types of transformation, and they are:

The representation of the types of transformation are:

Of the above transformation, only the dilation transformation do not preserve side lengths or distance

Hence, the categories of the transformations are

(a), (c) and (d) ⇒ Preserve

(b) and (e) ⇒ Do not preserve

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