PS Unit 02: Prove These Triangles are Congruent

please help I need this ASAP

a) An equation representing the situation where x represents the number of months when Plan A and Plan B cost the same is 80x = 630 + 45x.

b) Using inverse operations, we can state that 80x - 45x = 630 or 35x = 630, and x = 18.

c) From this equation, we determine that x is 18 months.

An equation is a mathematical statement that shows that two or more mathematical expressions are equal or equivalent.

Equations use the equation symbol (=) to depict the equality of the expressions.

                             Plan A      Plan B

Monthly charge      $80          $45

Free phone              $0         $630

Let Plan A = 0 + 80x

Let Plan B = 630 + 45x

The month the two plans' costs are equal can be derived by equating the two expressions above:

80x = 630 + 45x

80x - 45x = 630

35x = 630

x = 18 months

Thus, solving the equation, we can conclude that choosing Plan B will take 18 months to equal the cost of Plan A and thereafter, be considered cheaper than Plan A.

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Answer:

a = 16.51

angle A = 54

angle B = 63

Step-by-step explanation:

Recall the law of sines:

sinA/a = sinB/b = sinC/c

We know c is 20, and angle C is 63. Since b is also 20, angle B must also be 20. We know have two of the 3 angles, summing to 126, and we can find the last angle from that. 180-126=54, so angle A must be 54.

To solve for a, we need to know the ratio of the other two terms. Sin(63) is around 0.99, and 0.99/20 is 0.049. So we have 0.049=sin(54)/a. To solve for a, we divide by sin(54) and take the reciprocal of both sides, giving a = (sin54)/0.049, which is about 16.51, which is the length of the side a.

Answer:

C. 33

Step-by-step explanation:

Given:

[tex]\sqrt{x+3}=6[/tex]

Solution:

(square both sides)

[tex]x+3=6^{2}[/tex]

[tex]x+3=36[/tex]

[tex]x=36-3[/tex]

[tex]x=33[/tex]

Answer is 33

option C

Answer: 0.65=13/20

Step-by-step explanation: First, rewrite the decimal number as a fraction and put 1 in the denominator's place. 0.65/1
Then, multiply to get rid of 2 decimal places. Then, multiply top and bottom by 10^2 which equals 100

0.65/1 × 100/100= 65/100

Find the Greatest Common Factor or GCF of 65 and 100, and reduce the fraction by dividing both the numerator and denominator by GCF = 5,

[tex]\frac{65/5}{100/5}[/tex]=13/20

Hope this helps!

Answer: ya

Step-by-step explanation:bc

The unknown angle in the parallelogram is as follows:

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

In other words, a parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other. Opposite sides are equal in length. Opposite angles are equal. The sum of any two adjacent angles of a parallelogram is equal to 180°

The sum of angles in a parallelogram is 360 degrees.

Therefore,

∠1 = 25 degrees

Hence,

Adjacent angles in a parallelogram are supplementary. This means adjacent angles sum up to 180 degrees.

Therefore,

∠2 + ∠1 = 180

∠2 + 25 = 180

∠2 = 180 - 25

∠2 = 155 degrees

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Answer:

y = -x + 4

Step-by-step explanation:

m = y2-y1 / x2-x1

m = 4-6/ 0-(-2)

m = -2/2

m = -1

y = -x + b

4 = -(0) + b

b = 4

y = -x + 4

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Answer: n= 9 and n=11

Step-by-step explanation:

Assume that x is the lesser of the two numbers. The second figure must be x+2.

Since x*(x+2) = 99, we know that

x^2 + 2x - 99 = 0

We obtain x = 11 and 9 by searching for the roots of this equation.

This can also be resolved in the following ways:

We are aware that the two numbers (x and x +2) are consecutive odd numbers. Since x * (x + 2) = x2 + 2x, the value of x must be near to the square root of 99.

The squares 81 and 100 are the ones closest to the number 99. Additionally, we know that x * (x+2) is bigger than x2 (by a factor of 2x), therefore x must equal 9 and x+2 must equal 11.

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Wouldn't the answer be 1 and 4?

The time it would take the two sisters to paint 80 mugs is 8 hours.

From the question, we are to determine how long it would take the sisters to paint 80 mugs

From the given information,

"The younger sister can paint 2 mugs every half hour"

That is,

The younger sister can paint 4 mugs every hour

Also

"The older sister can paint 6 mugs every hour?"

Let x represent the number of hours it would take them to paint 80 mugs.

Then, we can write that

4x + 6x = 80

10x = 80

x = 80/10

x = 8

Hence, the time it would take is 8 hours

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Answer:

D

Step-by-step explanation:

A and C are equations. B is an inequality.

An expression does not have an inequality or equal sign.

Hence, D is the answer.

Answer:

10^3.

Step-by-step explanation:

You can represent 1,000 as 10^3. 10 x 10 x 10 = 1000. is read as “10 to the third power” or “10 cubed.”

all numbers are base 10 unless the teacher says to use another base so

there are 3 zeroes so

10^3 is the answer

Carleen owns a Dog as her pet.

The logical thinking definition is analysing a situation or problem using reason and coming up with potential solutions.

Given that, Amy, Brenda and Carleen own a cat, a dog and a fish, but not necessarily in that order.

It is saying that Amy hats a cat, which ca be meant she has a pet cat

Therefore, Amy owns a pet cat.

Now, Brenda can not have a hairy pet because she has allergic conditions, so the only pet in the given list with no hair is the fish

Therefore, Brenda owns a pet fish.

Now, only Carleen is left, and a pet dog is left.

Therefore, Carleen owns a pet dog.

Hence, Carleen owns a Dog as her pet.

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The conjecture and rephrased statement of proof to demonstrate that the diagonals of a parallelogram cross each other, taking into account the provided figure, is: DE and EB are congruent to one another in the parallelogram EFGH, while AE is congruent to EC.

A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

The parallelogram's diagonals are the lines connecting its two opposed ends. Sharing into two equal portions is known as bisecting. Congruent refers to a copy that has the same dimensions as the original and may therefore be used in place of it. When the diagonals of a parallelogram bisect one another, it signifies that they split into two equal pieces that are congruent with one another.

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Answer:11.20*168=$1 881.6

Step-by-step explanation:

The exact values for sin(2x), cos(2x) and tan(2x) without solving for x  4√5 /9, -1/9 and -4√5  respectively

Given:  cos(x)= 2/3 and x is in quadrant IIn trigonometry, cos(x) = adjacent/hypotenuse = 2/3.

adjacent = 2

hypotenuse = 3

Here, we will find the opposite

opposite =√(3²-2²) = √5

sin(x) = (√5)/3   (opp./hyp.)cos(x) = 2/3    

(adj./hyp.)tan(x) = (√5)/2 (opp./adj.)

Using trigonometry identity:

sin(2x)  = 2sin(x)cos(x) sin(2x)  

= 2× (√5)/3 × 2/3sin(2x)  

=  4√5 /9cos(2x) = 2cos²(x) - 1

cos(2x) = 2(2/3)² -1cos(2x) = -1/9

Also, we will find the exact value for tan.

tan(2x) = 2tan(x) / 1-tan²(x)tan(2x) = (2(√5))/2 / 1-((√5)/2)²

tan(2x) = √5 / (-1/4)

tan(2x) = -4√5

Therefore, the exact values are given above.

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Group 1: 1, 2, 3, 4, 5

Group 2: 6, 7, 8, 9

In this case, the sum of the numbers in Group 1 is 1 + 2 + 3 + 4 + 5 = 15, and the sum of the numbers in Group 2 is 6 + 7 + 8 + 9 = 30. The sum of the numbers in both groups is 15 + 30 = 45, which is the same.

Alternatively, we could create the following two groups:

Group 1: 1, 2, 3, 4

Group 2: 5, 6, 7, 8, 9

In this case, the sum of the numbers in Group 1 is 1 + 2 + 3 + 4 = 10, and the sum of the numbers in Group 2 is 5 + 6 + 7 + 8 + 9 = 35. The sum of the numbers in both groups is 10 + 35 = 45, which is the same.

There are many other ways to create two groups of cards with the same sum using as many cards as possible. The key is to use all of the numbe

Answer:

group 1: 1,2,3,4,5

Group 2: 6,7,8,9

Step-by-step explanation:

my brain

Answer:

Step-by-step explanation:

i think it's black people x chicken = happy

The percentage decrease of the depth of the lake from January to August is 20%.

The difference between the initial and final numbers is shown as a percentage reduction. It displays a percentage loss of value compared to the original regardless of the units. The decrease is equal to the initial amount less the final amount.

Given,

The depth of lake in January = 943 feet

The depth of lake in August = 754.4 feet

The difference is = (943-754.4) feet

                             = 186.6 feet

So, the percentage decrease of the depth of the lake from January to August will be =  (186.6 ÷ 943) × 100

                        = 20%

Therefore, the answer is 20%.

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The information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.

From the information given, it was stated that the real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 2000,000 altogether.

It was further depicted that he sold the land in the shape of a quadrilateral at Rs 1,500,000. In their case, the sale is less than the cost and therefore, there's a loss.

The loss will be:

= 2,000,000 - 1,500,000

= 500,000

Therefore, the information illustrated a loss of RS 500,000.

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Complete question

Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur

Answer:

10

Step-by-step explanation:

The 2 subtracting signs become addition, which is 4 + 6

Answer:

take wholesale cost and multiply it by 95%, then add to the original value

another way, just multiply by 1.95

Retail cost:  1.95*($99.50) = $194.03

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

So the sales price of the sled is   100%  + 95 % = 195 % of the cost

   = 1.95 * cost     =     1.95 * 99.50 = 194.03 dollars

Answer:

5 1/2 + 3/4

11/2 + 3/4

22+3/4

25/4

=6 1/4

Answer:

Step-by-step explanation: the answer is 90

the answer is 3 x 3 x 10 because she has 3 boxes and 30 shells in each box. 30 divided by 3 is 10 therefore you would multiply 3 by 3 to get 9 then multiply 9 times 10 to get 90.

Using z-score calculations, we can say that around 13.14%of the young women have a BMI (Body Mass Index) of less than 18.5 and are underweight.

The formula for z-score is;

z = (x' - μ)/σ

We are given;

Population Mean; μ = 26.8

Population standard deviation; σ = 7.4

Average BMI; x' = 18.5

Thus;

z = (18.5 - 26.8)/7.4

z = -1.12

From online p-value from z-score calculator, we have;

p-value = 0.1314 = 13.14%

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Complete question is;

Your body mass index (BMI) is your weight by kilograms divided by the square of your height in meters. Online BMI calculators allow you to enter weight in pounds and height in inches. High BMI is a common but controversial indicator of being overweight or obese. A study by the National Center for Health Statistics found that the BMI of American young women (ages 20-29) is approximately Normally distributed with mean 26.8 and standard deviation 7.4

People with BMI less than 18.5 are often classed as “underweight.” What percent of young women are underweight by this criterion?

Answer:

<

Step-by-step explanation:

On a number line, -42 is to the left of -19.

When you compare two numbers on a number line, the number to the left is smaller.

-42 is less than -19

-42 < -19

There is enough storage in the truck. The volume of the septic tank is about 30,164 gallons.

Given that:

Your company uses a truck with a storage tank capable of holding 30,500 gallons of waste.

A full septic tank in the shape of a cube measuring 191 inches on each side.

First, calculate the volume of the septic tank:

Volume of septic tank (V) = S³

where S is the side length of the septic tank

S =  191 inches

V = S³

V = 191³ = 6967871 cubic inches

Since we have 231 cubic inches in 1 gallon:

V = 6967871 / 231 = 30,164 gallons

Thus, the capacity of the full septic tank is 30,164 gallons

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