use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos^4

Determining the slopes of each side, we get the slope of [tex]\overline{AB}[/tex] is [tex]2[/tex], the slope of [tex]\overline{BC}[/tex] is -1/2, the slope of [tex]\overline{CD}[/tex] is 2, and the slope of [tex]\overline{AD}[/tex] is -1/2. Since the slopes of sides AB and CD and BC and AD are equal, it follows that [tex]\overline{AB} \parallel \overline{CD}[/tex] and [tex]\overline{BC} \parallel \overline{AD}[/tex]. Thus, ABCD is a parallelogram because it is a quadrilateral with two pairs of opposite congruent sides. However, we can also note that the slope of side AB is the negative reciprocal of that of sides BC, and thus [tex]\overline{AB} \perp \overline{BC}[/tex]. Using the fact that perpendicular lines form right angles, we can conclude that [tex]\angle ABC[/tex] is a right angle, and since ABCD is thus a parallelogram with a right angle, it must also be a rectangle.

Answer:

Answers will vary based on the method used, but the final slope-intercept form of the equation of A⁢B↔ will be the same.Let the equation of A⁢B↔ in slope-intercept form be y=m⁢x+d, where m is the slope and d is the y-intercept.The coordinates of points A and B are (1, 1) and (5, 3), respectively, so the slope of A⁢B↔ is m=yB−yAxB−xA=24=0.5.Substitute the value of m back in the equation:y = 0.5x + d.Substitute the coordinate of point A (1, 1) in the equation above, and solve for d: 1 = 0.5 + dd = 0.5.Therefore, the equation of A⁢B↔ is y = 0.5x + 0.5. To check whether C lies on A⁢B↔ substitute the x-coordinate of C into the right side of the equation: 0.5 (2.6) + 0.5 = 1.8.The result is equal to the y-coordinate of C. Thus, C satisfies the equation of A⁢B↔ which means that C lies on A⁢B↔.

Step-by-step explanation:

I did it

The number of compounding per year is[tex]N = 920(1+0.03)^4t[/tex]

This can be calculated by making use of the formular;  920(1.03)^4t and use the  compound interest equation which is N=P( 1+r/n)^nt

We know that 12% was given as the rate per year, then to get the quarter rate we divide by factor of 4, which is  12/4= 3%

The compounding for t years = n*t = 4t where n=4.

and the Initial number of cars serviced=920

Then we can substitute the values into the above equation, we have Thus [tex]N = 920(1+0.03)^4t[/tex]

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CHECK THE COMPLETE QUESTION BELOW:

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. A car repair center services 920 cars in 2012. The number of cars serviced increases quarterly at a rate of 12% per year after 2012. Create an exponential expression to model the number of cars serviced after t years. Then, match each part of the exponential expression to what it represents in the context of the situation. 920(1.03) is the number of cars multiplied by 1.03. The quarterly rate of growth is 0.03 or 3%. The compound periods multiplied by the number of years is 4t. The initial number of cars serviced is 920. The growth factor is represented by 1.03. The growth rate is 1.03. Exponent arrowRight Base arrowRight Coefficient arrowRight Rate arrowRight

Step-by-step explanation:

12 inches

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The amount of money Kim, maneet and Sutopa have is $115.6, $97.6 and $73.2 respectively.

x + (x - 18) + 3/4(x-18) = 286.40

x + x - 18 + 3/4x - 13.5 = 286.40

2 3/4x = 286.40 + 13.5 + 18

11/4x = 317.9

x = 317.9 ÷ 11/4

= 317.9 × 4 / 11

= 1,271.6 / 11

x = $115.6

So,

Kim = x

= $115.6

Maneet = x - 18

= 115.6 -18

= $97.6

Sutopa = 3/4(x-18)

= 3/4(97.6)

= $73.2

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Using linear functions, it is found that over a range of x < 10000 she will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job

A linear function is modeled by:

y = mx + b

In which:

Considering the fixed salary as the intercept and the earning per shoe sold the slope, the functions for her salaries at each situation is:

He will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job when:

C(x) > H(x)

52000 + 3.25x > 37000 + 4.75x

1.5x < 15000

x < 15000/1.5

x < 10000

The range is x < 10000.

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Answer: True.

Step-by-step explanation:

The prefix "bi-" shows that there are two terms in a binomial expression. Therefore, this statement is True.

I hope this helps! :)

Answer:

A. True.

Step-by-step explanation:

A binomial has two terms.

Think of it this way. Any object's name that starts with 'bi' has two of something. For example, a bicycle, bicycles have 2 wheels.

Hope this helps!

Answer:

6

Step-by-step explanation:

If you divide 78 by all of the numbers, only one, 6, is a whole number, making it the only factor. You can check this by multiplying 6 by 13, (you get 13 from the division) and you get 78.

I hope this helps!

Using proportions, it is found that the coordinates of point B are given as follows:

A. (1.6, 0).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Point B is 3/4 of the way from AB to AC, hence:

[tex]B - A = \frac{3}{4}(C - A)[/tex]

The points are:

Then, to find the x-coordinate:

[tex]x + 2 = \frac{3}{4}(3 + 2)[/tex]

x + 2 = 3.6.

x = 1.6.

For the y-coordinate:

[tex]y + 3 = \frac{3}{4}(1 + 3)[/tex]

y + 3 = 3

y = 0.

Hence option A is correct.

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Answer: D times 6 = 72

D= 12

Step-by-step explanation:

The term product means multiplication. Donnie's age is represented by the letter d, so if the product of d and 6 is 72, or in other words, d times 6 is 72, then d would equal 12

The number of ways pets can be arranged in group according to the species is  in a row 288 ways.

Pets can be grouped by permutation concept as follows.

Total number of pets = 10

Number of dogs = 4

Number of cats = 3

Number of alpacas = 2

Number of bunny = 1

The number of ways pets can be arranged in group according to the species in a row as,

⇒ (4!)(3!)(2!)(1!)

⇒ (24)(6)(2)(1)

⇒ 288

Hence we can conclude that the number of ways pets can be arranged in group according to the species in a row is 288 ways.

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According to my calculation the answer is 188.

If the domain of the function y=-2/3 x+7 is {-12,-6,3,15} then the range of the function is {15,11,5,-3}.

Given that the domain of the sunction y=-2/3 x+7 is {-12,-6,3,15}.

We have to find the range of the function and complete the table.

Function is relationship between two or more variables expressed in equalto form. In a function each value of x has some value of y.

To complete the table we need to find the value of the function at different values of x.Domain is basically value of  x which satisfies the function.

We have to first put the value of x=-12 in y=-2/3+7

y--2/3*-12+7

=15

Now put x=-6 in the function.

y=-2/3 *-6+7

=3

Put the value of x=3 in the function.

y=-2/3*3+7

=5

Put the value of x=15.

y=-2/3*15+7

=-41/3.

Hence the range of function is {15,11,-41/2,5}.

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Averagely, Ana practiced for a greater amount of time each day.

Mean for ana= (20 + 20 + 30 + 60 + 60 + 60 + 70 + 70 + 100 + 100 + 100 + 115 + 115 + 115)/14 = 69.6

Mean for tara= (20 + 20 + 30 + 30 + 45 + 45 + 45 + 70 + 70 + 70 + 75 + 90 + 90 + 120)/14 = 58.6

Median for ana= 70

Median for tara= (45 + 70)/2 = 57.5

Ana has the greater median and also has the greater mean.

Averagely, we can conclude that ana practiced for a greater amount of time each day.

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Answer: no, it's not similar because we cannot multiply it by any factor that the ratio will be the

Step-by-step explanation:

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer:

Hope it helps u, any questions u may ask me

x=70 [alternate interior angles]

y=60 [alternate interior angles]

a=110 [By linear pair]

b=120 [By linear pair]

The time it will take for the block of ice to melt if the temperature is 45 degrees is 3 hours.

The cost to travel 22 miles is 55 dollars.

let

time it takes for ice to melt = x

air temperature = y

Therefore,

x ∝ 1 / y

x  = k / y

when x = 2.5 hours and y = 54 degrees

Hence,

k = 2.5 × 54

k = 135

The time it will take for the block to melt at 45 degrees = 135 / 45 = 3 hours

It costs $35 for a ride from the city centre to the airport, 14 miles away.

where

c = cost

m = number of miles

Therefore, the equation is as follows:

35 / 14 = 2.5

c = 2.5m

Hence, when you travel 22 miles,

c = 22(2.5)

c = 55 dollars

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The statement that is true about Sheila's savings plan is that; C.

Sheila must save $60 per month to achieve her goal.

The price of bathroom remodeling is $ 810.

After 13 months , she has saved $ 510

This means that she has a $300 shortage to cover in 5 months.

This means that she need to save :

$300/5  = $60 / month in order to achieve her goal

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Answer: C

Step-by-step explanation: edge

The correct option is C. political affiliation.

An example of quantitative data are-

Data that expresses a definite quantity, amount, or range is known as quantitative data. In most cases, the data is accompanied with measuring units, such as metres in the case of a person's height. Setting boundaries for such data makes sense, and performing mathematical operations on the data has significance.

Types of Quantitative Data are-

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The complete question is-

8. Each of the following is an example of quantitative data, except ______.

A. weight in ounces

B. income in dollars

C. political affiliation

D. age in years

The value of x in terms of l is.

[tex]x=\sqrt{5l^{2} }[/tex]

A fundamental relationship in Euclidean geometry between  a right triangle's three sides is known as the Pythagorean theorem, or Pythagoras' theorem. The area of the square whose side is the hypotenuse is said to be equal to the total of the areas of the squares on the other two sides.

length = [tex]l[/tex]

width= [tex]2l[/tex]

diagonal = [tex]x[/tex]

We would get a right angle triangle if we were to cut a part across the diagonal. The Pythagoras Theorem can be used to solve the right angle triangle.

[tex]x^{2} =a^{2} +b^{2}[/tex]

using this formula substituting the value:

[tex]x^{2} =l^{2} +2l^{2}[/tex]

[tex]x^{2} =l^{2} +4l^{2} \\x^{2} =5l^{2} \\x=\sqrt{5l^{2}} \\[/tex]

from the above calculation we have:

[tex]x=\sqrt{5l^{2} }[/tex]

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Answer:

Below in bold.

Step-by-step explanation:

Total number of marbles = 3+4+5 = 12

P(white, red) = 4/12 * 3/11

                      = 12/132

                      = 1/11,

P(blue, white, red)  = 5/12 * 4/11* 3/10

                                 = 60/1320

                                 = 6/132

                                 = 1/22.

The range of the values are 8.3<x< 8.38

The given figure is an isosceles triangle, with none of its side equal.

Using the Pythagorean theorem, we have

[tex] {x}^{2} = \sqrt{ {8}^{2} } + \sqrt{ {2.5}^{2} } [/tex]

[tex] x = \sqrt{70.25} [/tex]

[tex]x = 8.38[/tex]

Thus, the range of the values are 8.3<x< 8.38

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There were 2.07 times as much people that applied in the fourth month than in the first month.

An exponential function is one that grows or decreases in an exponential manner. Thus, for any exponential function we can write; f(x) = ax^±n. The term a is the initial value x is the rate of change while n is the time elapsed. The positive sign is used for an exponential increase while the negative sign is used for an exponential decrease.

Thus we have;

f(x) = 27(1.2)^4

This shows us that the time elapsed is four months and f(x) = 2.07.

Therefore, there were 2.07 times as much people that applied in the fourth month than in the first month.

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There are 105 comparisons made with 15 statistically independent scenarios.

According to the statement

we have given value of n is 15.

Then r = 2. so,

we use the formula NcR then

Substitute the values in it then

15c2

we open it according to ncr formula

In this formula we arrange the terms according to the following

NcR formula = n! /r! * (n-r)!

then the terms will arrange in this way.

So,

ncr = 15! / 2! * 13!

After solving the statement some terms will be cancel with each other and remaining terms are

ncr = 15*14/2

ncr = 210/2

ncr = 105

here the value becomes 105.

So, There are 105 comparisons made with 15 statistically independent scenarios.

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The correct option is (d) cotФ.

As, cosineФ/sineФ = cotФ.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

The basic trigonometric identities are-

Solution for the given trigonometric function; (cosineФ/sineФ)

Use formula of tanФ

tanФ = sineФ/cosineФ

Also, from basic trigonometric ratios.

tanФ = 1/cotФ

Substitute sineФ/cosineФ to get the result

1/cotФ = sineФ/cosineФ

Further simplify,

cotФ = cosineФ/sineФ

Therefore, the value of cosineФ/sineФ = cotФ

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Which of the following is a simpler way to write StartFraction cosine theta Over sine theta EndFraction-

(a) tanФ

(b) secФ

(c) cosecФ

(d) cotФ

Answer: D, cot o

Step-by-step explanation:

edge :-]

Answer:

10

Step-by-step explanation:

A scale factor of 2/3 means multiplying all side lengths by 2/3

15*2/3=10

Answer:

Step-by-step explanation:

What is the length of the apothem, rounded to the nearest inch? recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon. 4 in. 5 in. 9 in. 11 in.

Answer:

9

Step-by-step explanation:

apothem (AB)

1/2 of the length (10) is 5

AB^2 + 5^2 = 10^

AB^2 = 100-25

Square root of AB^2 = square root of 75

AB = 8.66

8.66 is about 9

Answer:

0.315

Step-by-step explanation: