what is pemdas and how is it used in math

1) AC || DF; BC ≅ DE , 2) )Alternate interior angles formed by transversal BC and parallel lines AC and DF are congruent 3) Identity Property of Congruence (Any segment is congruent to itself)

what is Congruence?

In mathematics, congruence is a term used to describe the relationship between two geometric figures that have the same shape and size. Two objects are said to be congruent if they are identical in shape and size.

In the given question,

STATEMENTS

AC || DF; BC ≅ DE

<CBE ≅ <DEB

BE ≅ BE

∆DBE ≅ ∆BEC

REASONS

1)Given

2)Alternate interior angles formed by transversal BC and parallel lines AC and DF are congruent

3) Identity Property of Congruence (Any segment is congruent to itself)

4) SAS (Side-Angle-Side) Congruence Postulate (Since BC and BE are congruent and <DBE and <BEC are congruent, and BE is common to both triangles)

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Answer:

60°

120°

Step-by-step explanation:

Supplementary angle are those that sum up to a total of 180 degrees.

So, let's have 2 angles, angle A and angle B.

Angle A's measure is α so the measure of angle B is 2α.

The sum of these two angles sum up to 180 degrees, so we can say that:

α + 2α = 180°

3α = 180°

α = 60°

So, one of our angles is 60° and the other is (2*60)° which is 120°.

Answer:

Step-by-step explanation:

To calculate the interest that Margo will pay, we first need to determine how much interest she will accrue over the 17-month period.

We can use the formula:

Interest = Principal x Rate x Time

Where:

Principal is the amount borrowed, which is $700 in this case.

Rate is the annual interest rate, which is 3% or 0.03 as a decimal.

Time is the time period expressed in years, which is 17/12 or 1.4167 years in this case (since there are 12 months in a year).

Therefore, the interest that Margo will pay can be calculated as:

Interest = $700 x 0.03 x 1.4167

Interest = $29.75

So Margo will pay $29.75 in interest. Rounded to the nearest cent, the answer is $29.8.

Answer:

60

Step-by-step explanation:

Since this is a right triangle, the longest side can be solved using the Pythagorean Theorem

x^2 + y^2 = z^2

So

15^2 + 20^2 = 225 + 400 = 625 = 25^2.

So 25 is hypotenuse.

Add them all together : 25+15+20 = 60.

So your answer is 60.

Answer:

60

Step-by-step explanation:

A squared + B squared = C squared

15 squared + 20 squared = C squared

225 + 400 = C squared

625  = C squared

Use radicals to find the square root of 625

Which is 25

C = 25

25 + 15 + 20 =

60

Answer:

1 21/29

Step-by-step explanation:

Therefore, the second rectangle has a greater area than the first rectangle.

A rectangle is a quadrilateral geometric shape that has four sides and four right angles (90-degree angles). It is characterized by having opposite sides that are equal in length and parallel to each other. The rectangle's other two sides are also equal in length and parallel to each other but different in length than the opposite sides.

The area of a rectangle is calculated by multiplying its length by its width, which gives the total amount of space inside the shape. The perimeter of a rectangle is the sum of all its sides.

To find the area of a rectangle, we multiply its length by its width. Therefore, the area of the first rectangle is:

Area of first rectangle = 12 ft × 1 ft = 12 sq ft

And the area of the second rectangle is:

Area of second rectangle = 16 ft × 1 ft = 16 sq ft

Therefore, the second rectangle has a greater area than the first rectangle.

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Answer:

u = 2√3;

v = 2

Step-by-step explanation:

Use trigonometry:

[tex] \cos(60°) = \frac{v}{4} [/tex]

Cross-multiply to find v:

[tex]v = 4 \times \cos(60°) = 4 \times 0.5 = 2[/tex]

Use the Pythagorean theorem to find u:

[tex] {u}^{2} = {4}^{2} - {v}^{2} [/tex]

[tex] {u}^{2} = {4}^{2} - {2}^{2} = 16 - 4 = 12[/tex]

[tex]u > 0[/tex]

[tex]u = \sqrt{12} = \sqrt{4 \times 3} = 2 \sqrt{3} [/tex]

Imaginary Numbers are 21. (5+2i)/ 4i is  -(5/4) + (1/2)i, 22. 3i/(-2+i) is -1.5i + 0.75. 23. (3-2i)/(4-3i) is 4/5 + (1/25)i, 24. 7/(5-2i) is (14/29) + (7/29)i.

In mathematics, imaginary numbers are a type of complex number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

Imaginary numbers were first introduced in the 16th century as a solution to certain polynomial equations that did not have real solutions. They were initially met with skepticism and derision, but eventually became widely accepted as a fundamental part of complex analysis and number theory.

One of the key properties of imaginary numbers is that when they are multiplied by themselves, the result is always a negative real number. For example, i * i = -1. This property is what makes imaginary numbers useful for representing certain physical quantities, such as the amplitude and phase of an oscillating system.

21. (5+2i)/ 4i = -(5/4) + (1/2)i

To divide complex numbers, we can multiply the numerator and denominator by the conjugate of the denominator. Here, the conjugate of 4i is -4i.

(5+2i)/ 4i = (5+2i)/4i * (-4i/-4i)

= -(20i - 8)/(-16)

= -(20i - 8)/16

= -(5/4) + (1/2)i

Therefore, (5+2i)/ 4i = -(5/4) + (1/2)i.

22. 3i/(-2+i) = -1.5i + 0.75

We can again use the conjugate to simplify the division of complex numbers.

3i/(-2+i) = 3i/(-2+i) * (-2-i)/(-2-i)

= (-6i -3)/(-5)

= 3/5 + 1.5i

Therefore, 3i/(-2+i) = -1.5i + 0.75.

23. (3- 2i)/(4-3i) = (18+5i)/25

Using the conjugate:

(3-2i)/(4-3i) = (3-2i)/(4-3i) * (4+3i)/(4+3i)

= (12+9i-8i-6i²)/(16+12i+12i-9i²)

= (20+i)/25

= 20/25 + (1/25)i

= 4/5 + (1/25)i

Therefore, (3-2i)/(4-3i) = (18+5i)/25 = 4/5 + (1/25)i.

24. 7/(5-2i) = (14/29) + (7/29)i

Using the conjugate:

7/(5-2i) = 7/(5-2i) * (5+2i)/(5+2i)

= (35+14i)/(29)

= (14/29) + (7/29)i

Therefore, 7/(5-2i) = (14/29) + (7/29)i.

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(A). the current sale price of the computer system is $543.20.

Therefore, members of the store's loyalty club pay $488.88 for the computer system with their discount.

Find the current sale price. Round to the nearest cent if necessary.

• Members of the store's loyalty club get an additional 10% off their computer purchases. How much do club members pay for the computer with their discount?

To find the current sale price, we first need to calculate the markdown amount. We know that the markdown is 30% of the original selling price, which is $776, so the markdown amount is:

30% of $776 = 0.30 x $776 = $232.80

The sale price is then the original selling price minus the markdown amount:

Sale price = $776 - $232.80 = $543.20

Therefore, the current sale price of the computer system is $543.20.

Next, we need to calculate the price that club members pay after their discount. We know that club members get an additional 10% off the sale price, which is $543.20, so their discount amount is:

10% of $543.20 = 0.10 x $543.20 = $54.32

The price that club members pay is then the sale price minus their discount amount:

Price for club members = $543.20 - $54.32 = $488.88

Therefore, members of the store's loyalty club pay $488.88 for the computer system with their discount.

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The perimeter of scale drawing of Central Park is 30 centimeter.

The area of scale drawing of Central Park is 31.25 square centimeters.

What is perimeter?

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

Given that Central Park is a rectangular park in New York City

The measured length is 12.5 centimeters

The measured width is 2.5 centimeters

The perimeter of scale drawing of Central Park is given as:

Given is a rectangular park

perimeter of rectangular = 2(length + width)

perimeter of rectangular = 2(12.5 + 2.5)

perimeter of rectangular = 2(15) = 30

Thus perimeter is 30 centimeter

The area of scale drawing of Central Park is given as:

area = length x width

area = 12.5 x 2.5 = 31.25 cm²

Thus area of rectangular park is 31.25 square centimeters

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Using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

The right rectangular prism has four rectangle-shaped side faces and two parallel end faces that are perpendicular to each of the bases.

Parallelograms make up the sides of an oblique prism, a non-right rectangular prism.

A cuboid is yet another name for a right rectangle prism.

So, the volume of the right rectangular prism:

V = wlh

Insert values:

V = wlh

V = 6*8*4.5

V = 216cm³

Now, the volume of the cube:

V = a³

V = 2³

V = 8cm³

Then, the number of cubes that can be fitted in the right rectangular prism:

216/8 = 27

Therefore, using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

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Correct question:

How many cubes, with side measures of 2 cm, will fit inside a right rectangular prism with dimensions of 6 cm by 8 cm by 4 1/2 cm?

Group of answer choices

a. 24

b. 27

c. 108

d. 54

Answer:

22 * 100

Step-by-step explanation:

It would defintely be 22 * 100 because the other ones may be troubling to do mentally, especially 88 * 25. But with 22 * 100, you can easily get an answer of 2200.

Answer-

1/8 because their are 8 peices and 1 of them are blue and 2 of them are yellow so it become 1/8

Answer:

ans is 1/6

because its sure spinner not land on the yelow so two pieces neglect

so prob =favourable cases/total cases

blue has one piece only

1/6

Answer: Approximately $4,176.19 today for an investment that returns $800 each year for 6 years

Step-by-step explanation:

To calculate the present value of an investment that returns $800 each year for 6 years at a discount rate of 4 percent, we can use the formula for the present value of an annuity:

PV = C x [(1 - (1 / (1 + r)^n)) / r]

where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of years.

Plugging in the given values, we get:

PV = 800 x [(1 - (1 / (1 + 0.04)^6)) / 0.04]

PV = $4,176.19 (rounded to the nearest cent)

Therefore, if the discount rate is 4 percent, you would be willing to pay approximately $4,176.19 today for an investment that returns $800 each year for 6 years

Answer:

54

Step-by-step explanation:

16/4 + 56 - (3 + 4 - 1)

= 16/4 + 56 - (6)

= 4 + 56 - (6)

= 4 + 56 - 6

= 60 - 6

= 54

So, the answer is 54 !

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[tex] \sf \frac{16}{4} + 56 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \cancel \frac{16}{4} + 56 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \: 4 + 56 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \: 60 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \: 60 - (3 + 3)[/tex]

[tex] \: [/tex]

[tex] \sf \: 60 - 6[/tex]

[tex] \: [/tex]

[tex] \sf \fbox{ \: \sf \blue{ 54 }\: \: }[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps!:)

Answer:

then she will have 139.67 left

To solve this problem, we can use the trigonometric functions sine, cosine, and tangent.

First, let's draw a diagram:

             A (top of the mountain)

            /|

           / |

         /    |  h (height of mountain)

       /      |

     / θ     |

B /_____|

   d (distance from base)

We are given that the distance from the base of the mountain to point B is 1/2 mile, or 2640 feet (since there are 5280 feet in a mile). We are also given that the angle of elevation from point B to point A is 65 degrees, and that the angle between the ski lift and the ground is 15 degrees.

Let's start by finding the height of the mountain h. We can use the tangent function, since we know the opposite (h) and the adjacent (d) sides of the right triangle formed by points A, B, and the foot of the mountain (call it point C):

tan(65) = h / d

h = d * tan(65)

Plugging in the values, we get:

h = 2640 * tan(65)

h ≈ 7855 feet

Next, let's find the length of the ski lift. We can use the cosine function, since we know the adjacent (d) and hypotenuse (L) sides of the right triangle formed by points B, the foot of the mountain, and the base of the ski lift (call it point D):

cos(15) = d / L

L = d / cos(15)

Plugging in the values, we get:

L = 2640 / cos(15)

L ≈ 2736 feet

Therefore, the length of the ski lift from the beginning to the end is approximately 2736 feet.

Answer:

x = 8

Step-by-step explanation:

We can write the following equation to find the value of x based on above mentioned information:

10x - 20 = 7x + 4

10x - 7x = 20 + 4

3x = 24

x = 8

To find each angle measure, replace x with 8:

10x - 20 would be 10 × 8 - 20 = 60

Since angles are congruent the other one also would be 60°.

Without further context about the triangle and the lengths of its sides, it is not possible to solve for sin(B) using just the given information about cos(A).

Volume of  6 3/4 cups of water is equal to 54 cups of water.

What is Volume?

One cup is equal to 8 fluid ounces. Therefore, to convert 6 3/4 cups to fluid ounces, we can multiply by 8:

6 3/4 cups = (6 x 8) + (3/4 x 8) cups = 48 + 6 = 54 cups

So, 6 3/4 cups of water is equal to 54 cups of water.

What is fluid?

A fluid is a substance that has the ability to flow and take the shape of its container. Fluids include liquids, gases, and plasmas.

Liquids are a common type of fluid that can flow and take the shape of their container, but have a definite volume. Some examples of liquids include water, oil, and milk.

Gases are another type of fluid that can flow and fill the entire volume of their container, taking on the shape of the container. Some examples of gases include air, oxygen, and nitrogen.

Plasmas are a unique type of fluid that occurs at very high temperatures, in which some or all of the atoms or molecules have been ionized, resulting in the presence of free electrons and positive ions. Some examples of plasmas include lightning, the sun, and neon lights.

Fluids are important in many fields, including physics, engineering, and biology. They play a critical role in many processes, such as the circulation of blood in the body, the flow of water in a river, and the movement of air in the atmosphere.

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The approximate perimeter of the entire shape is 77.69 inches.

The perimeter of a figure is the sum of the whole sides of the figure.

Therefore, the perimeter of the entire shape can be calculated as follows:

The shape is made of three sides of a square and half a circle.

Therefore,

circumference of the semi circle [tex]= \pi r[/tex]

[tex]r = 17 \div 2 = 8.5 \ \text{inches}[/tex]

circumference of the semi circle [tex]= 8.5\pi[/tex]

Hence,

perimeter of the shape [tex]= 17+17+17+ 8.5\pi[/tex]

perimeter of the shape [tex]= 51 + 8.5(3.14)[/tex]

perimeter of the shape [tex]= 51 + 26.69[/tex]

Therefore,

perimeter of the shape = 77.69 inches

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A hemisphere over the cone with a radius of 10 cm and a height of 15 cm.

a) volume of the cone: V = 1570.8 cm³

b) volume of the hemisphere: V = 2093.33 cm³

c) voume of the entire figure : V= 3664.13 cm³

a) The formula V = (1/3)r2h, where r is the cone's radius and h is its height, determines the volume of the cone.

Substituting r = 10 cm and h = 15 cm, we get:

V = (1/3)π(10 cm)²(15 cm)

V ≈ 1570.8 cm³

The volume of the cone is approximately 1570.8 cm³.

b) The volume of the hemisphere is given by the formula V = (2/3)πr³, where r is the radius of the hemisphere. Since the hemisphere has the same radius as the cone, i.e., r = 10 cm, we get:

V = (2/3)π(10 cm)³

V = 2093.33 cm³

The volume of the hemisphere is approximately 2093.33 cm³.

c) The volume of the entire figure is the sum of the volume of the cone and the volume of the hemisphere. Adding the volumes of the two shapes, we get:

V = 1570.8 cm³ + 2093.33 cm³

V = 3664.13 cm³

The volume of the entire figure is approximately 5759.6 cm³.

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The width of the rectangular rug is 13 feet and the length of the rectangular rug is 26 feet.

Area of a rectangle formula: A = L * W. A

rectangle's length and width are multiplied to produce its area.

A is the area, L is the length, and W is the width or girth, where

A = L * W.

The corresponding sides of the rectangular rug and the rectangular floor must be proportional if they are alike.

Let's use "x" to represent the rug's width. The floor measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet according to the details provided. Since the rug and the surface are comparable, we can establish the following ratio:

Rug width/floor width = rug length/floor length

x / 26 = rug's length / 32

We can cross-multiply and then solve for "x" to find the answer:

32x = 26 * Rug's length

x =  (26 * Rug Length) / 32

[tex]= \frac{26 * 16}{32} \\= \frac{26}{2} \\= 13[/tex]

Therefore x ( the width of the rug) is = 13 feet.

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Complete question:

The rectangular rug is similar to the rectangular floor. If the floor of the room measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet, what is the width of the rug?

Answer:

To solve 34x23 ≡ r (mod 13), we can first calculate the product 34x23 = 782. Next, we need to find the remainder when 782 is divided by 13. To do this, we can divide 782 by 13 and find the remainder: 782 ÷ 13 = 60 remainder 2 Therefore, 782 is equivalent to 2 (mod 13). So, the solution to the original equation is r ≡ 2 (mod 13).

Original Equation:

2x + 5y = 0

Explanation:

The slope intercept form is y = mx + b, so first we have to get x onto the other side, to do that, we subtract 2x from both sides and end up getting:

5y =  - 2x

Now we divide both sides by 5 to isolate y

[tex]y = -\frac{2}{5} x[/tex]

That's our equation!

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Dοnοvan's hοurly wage than his brοther's hοurly wag wοuld be, $7.98/hοur

Average salary is the average amοunt οf mοney earned by wοrkers in a particular industry, ecοnοmy, area, etc.

Tοtal hοurs wοrked by Dοnοvan = 40 hοurs/week x 48 weeks/year = 1,920 hοurs/year

Next, we can calculate Dοnοvan's hοurly wage:

Hοurly wage οf Dοnοvan = Annual salary οf Dοnοvan / Tοtal hοurs wοrked by Dοnοvan

= $55,000 / 1,920 hοurs/year

= $28.65/hοur

Similarly, we can find the tοtal number οf hοurs that his brοther wοrks in a year:

Tοtal hοurs wοrked by Dοnοvan's brοther = 40 hοurs/week x 52 weeks/year = 2,080 hοurs/year

Hοurly wage οf Dοnοvan's brοther = Annual salary οf Dοnοvan's brοther / Tοtal hοurs wοrked by Dοnοvan's brοther

= $43,000 / 2,080 hοurs/year

= $20.67/hοur

Difference in hοurly wages = Hοurly wage οf Dοnοvan - Hοurly wage οf Dοnοvan's brοther

= $28.65/hοur - $20.67/hοur

= $7.98/hοur

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Answer: [tex]-3\sqrt{3}[/tex]

This the expression [tex]-3\times\sqrt{3}[/tex] or "-3 times the square root of 3"

[tex]\rule{300}{1.5}[/tex]

Work Shown:

Factor each term inside the square root so that a perfect square is one of the pieces. Then break up the roots and simplify as shown below.

[tex]-4\sqrt{12}+\sqrt{75}[/tex]

[tex]-4\sqrt{4\times3} +\sqrt{25\times3}[/tex]

[tex]-4\sqrt{4} \times\sqrt{3} +\sqrt{25} \times\sqrt{3}[/tex]

[tex]-4\times2\times\sqrt{3} +5\times\sqrt{3}[/tex]

[tex]-8\sqrt{3}+5\sqrt{3}[/tex]

[tex](-8+5)\sqrt{3}[/tex]

[tex]\bold{-3\sqrt{3}}[/tex]

Answer: To make "w" the subject of the formula "P+aw=b", we need to isolate "w" on one side of the equation.

First, we can subtract "P" from both sides of the equation to get:

aw = b - P

Next, we can divide both sides of the equation by "a" to get:

w = (b - P) / a

Therefore, the solution is:

w = (b - P) / a

Step-by-step explanation: