Similar Triangles Question

Solve for x and determine the scale factor. Notice the change in angles.
X = _____
Scale Factor = _____
Write the answer as a decimal.
Example: 0.3. Must have a 0.

Answer:

Step-by-step explanation:

The simplified expression after rationalizing the denominator are:

1)  (17 + √3)/13.

2) -3(2+√5)/5.

What is rationalizing the denominator?

To rationalize the denominator with two terms, find the conjugate of the denominator. Then multiply and divide the fraction by the conjugate of the denominator.

1).

a) The conjugate of the denominator is 4 + √3.

b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:

(5/4 - √3) * (4 + √3) / (4 + √3) * (4 - √3)

Simplifying the numerator:

5(4) + 5(√3) - 4(√3) - 3 / 13

= (17 + √3)/13

Therefore, the simplified expression after rationalizing the denominator is (17 + √3)/13.

2).

a) The conjugate of the denominator is 1 - √2.

b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:

2 / (1 - √2) * (1 + √2) / (1 + 2)

Simplifying the numerator:

2(1 + √2) / (-1 + 2)

= -2(1 + √2)

Therefore, the simplified expression after rationalizing the denominator is -2(1 + √2).

a) The conjugate of the denominator is 2 + √5.

b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:

3 / (2 - √5) * (2 + √5) / (2 + √5)

Simplifying the numerator:

3(2 + √5) / (-5)

= -3(2+√5)/5.

Therefore, the simplified expression after rationalizing the denominator is -3(2+√5)/5.

Hence, the simplified expression after rationalizing the denominator are:

1)  (17 + √3)/13.

2) -3(2+√5)/5.

To learn more about rationalizing the denominator visit:

https://brainly.com/question/30603089

#SPJ1

To estimate the probability that a randomly selected person would pass the driving test on the first attempt, we can divide the number of people who passed on the first attempt (6500) by the total number of people who took the test (10,000).

Probability = Number of favorable outcomes / Total number of possible outcomes.In this case, the favorable outcome is passing the test on the first attempt, and the possible outcomes are all the people who took the test.

Probability = 6500 / 10000= 0.65

Therefore, the estimated probability that a randomly selected person would pass the driving test on the first attempt is 0.65 or 65%. This means that there is a 65% chance that a randomly selected person from the group of 10,000 would pass the driving test on their first try.

For more such questions on probability

https://brainly.com/question/24756209

#SPJ11

Equation that will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b is [tex]\frac{80+22d}{d} = 32d[/tex]

For finding the equation we will first form separate equations of both company a and company b and then we will equate the formed equation to find the number of days.

Let the number of days be d.

For company a, we will first add the service charges and per day charge multiplied with number of days, and then divide the sum with number of days.

= [tex]\frac{80+22d}{d}[/tex]

For company b, we will multiply the per day charges with the number of days.

= [tex]32d[/tex]

Now, we will equate both the formed equation

[tex]\frac{80+22d}{d} = 32d[/tex]

To know more about equation

https://brainly.com/question/29657988

#SPJ4

The equation solved for m is written as:

(y - b)/x = m

Here we have a general linear equation:

y = m*x + b

And we want to solve the equation for m, this means that we need to isolate the variable m in that equation.

We will get:

y = m*x + b

y - b = m*x

(y - b)/x = m

That is the equation solved for m.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Answer:

The data in Set A are skewed left, because the mean is less than the median. The data in set B are symmetrical, because the mean is equal to the median.

Step-by-step explanation:

For prim people, this is the answer I got it right.

The complete question:

A carpet is laid on a rectangular floor of length 12m and breadth 8m. This leaves a margin of width 1m round the carpet. What is the area of the carpet?

Solution:

The area of the carpet laid on a rectangular floor of length 12m and breadth 8m is, 56 meter²

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

The area of the carpet can be calculated by subtracting the area of the margin from the total area of the rectangular floor.

The total area of the floor is:

= 12m x 8m

= 96 square meters.

The area of the margin is:

= 2 x (12m + 8m) x 1m

= 40m.

Therefore, the area of the carpet is:

= 96m² - 40m²

= 56 meter²

To learn more about Area check:

https://brainly.com/question/16151549

#SPJ1

Answer: The least number that can be made using each digit exactly once is 123456789. The value of 4 is greater than the value of 6 because in the decimal system (base 10), the position of a digit determines its value. The leftmost digit represents the greatest place value (ones, tens, hundreds, etc.) and each subsequent digit represents a smaller place value. In the number 123456789, the 4 is in the thousands place, which has a greater value than the 6, which is in the tens place.

Therefore, the 4 has a greater value than the 6 because it represents a larger place value.

Step-by-step explanation:

On solving the provided question, we can say that in a day, the expression will be  16*24 of 10.9% = 384 od 10.9% = 41.856

In mathematics, it is pοssible to multiply, divide, add, or remove. The construction of an expression is as follows: Expressiοn, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expressiοn (such as addition, subtraction, multiplicatiοn or division etc.) Expressions and phrases can be cοntrasted.

Any mathematical statement with variables, numbers, and an arithmetic οperation between them is called an expression or an algebraic expression. Fοr instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expressiοn, all of which are separated by the arithmetic sign +.

Dr. Drew cοnsumes 16 ounces of a caffeinated beverage first thing in the mοrning

Caffeine wears off at a rate of apprοximately 10.9% an hour.

in a day, the expression will be  16*24 of 10.9% = 384 od 10.9% = 41.856

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Answer:

Step-by-step explanation: The temperature at Thabana dropped by 7 degrees, so we can calculate the night temperature by subtracting 7 from the original temperature of 6 degrees:

Step 1: Subtract 7 from 6:

6 - 7 = -1

Step 2: The night temperature will be -1 degrees.

Answer:

bro do u have a pic i will give u your points back but i need a pic to help

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's call the number of boys "b" and the number of girls "g". From the ratio, we know that b/g = 11/9.

Also, we know that b = g + 124, so we can substitute the second equation into the first:

b/g = 11/9

b = g + 124

g + 124 / g = 11/9

Cross multiply:

9g + 1112 = 11g

Solve for g:

-2g = -1112

g = 556

So there are 556 girls and 556 + 124 = 680 boys at the school.

The total number of students at the school is 556 + 680 = 1236.

Answer: Parallelogram angles add up to 360, so use angle properties and known measures.

Step-by-step explanation:

Lauren was 13 miles away from the restaurant when Aidan reached it.

Travel refers to the act of moving from one place to another, often over a distance or by means of transportation.

Lauren and Aidan both left their offices at 6:15 P.M. and traveled for 20 minutes (from 6:15 P.M. to 6:35 P.M.) before Aidan arrived at the restaurant. During this time, Lauren traveled at a speed of 39 miles per hour, so she covered a distance of:

distance = speed x time

distance = 39 miles/hour x (20 minutes / 60 minutes/hour) = 13 miles

After 20 minutes, Aidan arrived at the restaurant, having traveled for 20 minutes at a speed of 42 miles per hour. The distance he covered during this time is:

distance = speed x time

distance = 42 miles/hour x (20 minutes / 60 minutes/hour) = 14 miles

Since they both traveled the same distance to the restaurant, but Aidan arrived there first, Lauren must have been 1 mile behind him when he arrived at the restaurant.

Therefore, Lauren was 14 - 1 = 13 miles away from the restaurant when Aidan reached it.

Learn more about distance here : brainly.com/question/4931057

#SPJ1

On solving the provided question, we cans ay that inches will evaporate, the equation will be = 12x = 1/2y + 7.43

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

he water evaporates at the rate in a, for 12 hours.

inches will evaporate,

the equation will be = 12x = 1/2y + 7.43

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The ordered pair that represent the number of red beads and gold beads is A. D, and E.

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

From the table we observe that the number of red beads and the gold beads are in the proportion x : y = 4 : 3.

Using the proportion we see that:

A: (20, 15) = 20 : 15 = 4 : 3

D: (80,60) = 4: 3

E = (100, 25)= 4:3

Hence, the ordered pair that represent the number of red beads and gold beads is A. D, and E.

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ1

Answer:

I have graphed it and attached it in the explanation part.

Step-by-step explanation:

26 possible letters for each of the first two positions and 10 possible digits for each of the last 4 positions gives a total of 676,000,000 license plates.

(1) 26 possible letters for each of the first two positions and 10 possible digits for each of the last 4 positions gives a total of

26 x 26 x 10 x 10 x 10 x 10 = 676,000,000 license plates.

(2) The number of possible license plates where the digits must be different is the number of permutations of 10 items taken 4 at a time, or 10P4 = 5040. Multiplying by 26 x 26 gives a total of

5040 x 26 x 26 = 3,636,160 possible license plates.

(3) To find the number of license plates that begin with "A" and don't have a 7, we first find the number of license plates that start with "A" and don't have any restriction on the last 4 digits. This is

26 x 10 x 10 x 10 x 10 = 676,000

Then, we find the number of license plates that have a 7, which is

9 x 26 x 10 x 10 = 23,760

Subtracting this from the total number of license plates that start with "A" gives us

676,000 - 23,760 = 652,240 possible license plates.

Learn more about permutations  :

https://brainly.com/question/1216161

#SPJ4

The ratio of hours spent at soccer practice to hours spent at a birthday party are 2 for every 3.

What is a ratio?

A ratio is produced by comparing or condensing two related pieces of data. Looking at the reciprocity of the relationship allows us to calculate the number of times one quantity is equal to another. To put it simply, a ratio is a number that can be used to represent one thing as a proportion of another.

We are given that for soccer practice, Sara spends 2 hours and for birthday party, she spends 3 hours.

So, the ratio of hours spent at soccer practice to hours spent at a birthday party is  2 for every 3.

Hence, the ratio is  2 for every 3.

Learn more about ratio from the given link

https://brainly.com/question/12024093

#SPJ1

Question: The table shows how many hours Sara spent at several activities one Saturday.

Activity "Hours

Soccer practice 2

Birthday party 3

Science project 1

What is the ratio of hours spent at soccer practice to hours spent at a birthday party?

Choose 1 answer:

1 for every 2

2 for every 1

2 for every 3

3 for every 2

The 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).

We can use the conversion factor of 1 carat = 0.2 g to convert carats to grams.

Diamond weight in grams: 35.99 carats x 0.2 g/carat = 7.198 g (rounded to three decimal places)

We can use the conversion factor of 1 ounce = 28.3495 g to convert the weight in grams to ounces.

Diamond weight in ounces: 7.198 g / 28.3495 g/o z = 0.254 o z (rounded to three decimal places)

Carats are now commonly used to measure the weight of gemstones, including diamonds, and are abbreviated as "ct." A 1-carat diamond, for example, weighs 0.2 grams while a 2-carat diamond weighs 0.4 grams.

As a result, the 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).

To learn more about weight

https://brainly.com/question/1235091

#SPJ4

Answer:a=3, d=common difference=3, a2=7, a3=9

Step-by-step explanation:

firstly we have given a,d  (using the arithmetic progression formula)

                                          (  an=a+(n-1) )

so we have made a sequence a2=a+d=7  

                                                   a3=a+2d=9

Answer:

In 1 hour run:

4 4/5 miles

Step-by-step explanation:

2 4/5 = 2 + 4/5 = 10/5 + 4/5 = (10+4)/5 = 14/5

Proportions:

14/5 miles ⇒ 7/12 hour

A miles ⇒ 1 hour

A = (14/5 miles)(1hour) / (7/12 hour)

A = (14/5)/(7/12)

A = (14*12) / (5*7)

A = 168 / 35

A =  140/35 + 28/35

A = 4 + 28/35

A = 4 + 4/5

A = 4 4/5 Miles

The taste of the tomato in today's soup compared to the usual recipe is same .

We find the tomato to soup ratio for each day to compare the taste of tomato in today's soup with the usual recipe,

For the usual recipe, the soup shack uses 9 tomatoes for every 12 bowls of soup, which can be simplified to a ratio of 9:12 ⇒ 3:4 .

This means that for every 3 parts of tomato, there are 4 parts of soup.

For today's soup, the soup shack used 6 tomatoes to make 8 bowls of soup, which can be simplified to a ratio of 6:8 ⇒ 3:4.

This means that for every 3 parts of tomato, there are 4 parts of soup, which is the same as the usual recipe.

Therefore, based on the tomato to soup ratio, the taste of tomato in today's soup is same as the usual recipe.

Learn more about Ratio here

https://brainly.com/question/21358891

#SPJ4

The given question is incomplete , the complete question is

The soup shack usually makes tomato soup with 9 tomatoes for every 12 bowls of soup. today, they used 6 tomatoes to make 8 bowls of soup.

How does the tomato taste in today's soup compared to the usual recipe ?

Answer:

Let's call the length of side 1 "x". Then, the length of side 2 is 2x, and the length of side 3 is x + 4. So, the expression for the three sides of the triangle can be represented as:

x + 2x + (x + 4) = 3x + 4

This expression represents the sum of the lengths of all three sides of the triangle.

Step-by-step explanation:

Answer: x+2x+(4+x)

Step-by-step explanation:

since side one is unknown, we can substitute it with variable x, and side two is twice as much as side one so we do 2x, and side three is four cm longer than side one so we do 4+x at the end

The S = 37.2^0

Below has been attached a diagram with the meaning of this problem. So we have a right triangle whose Opposite side (s) measures 18.9 and whose Adjacent side (r) measures 24.9. So, these two sides are related in the following form:

[tex]tan(S)=\frac{\text{Opposite side}}{\text{Adjacent side}} =\frac{s}{r} \\\\tan(S)=\frac{18.9}{24.9} \\\\tan(S)=0.76\\\\S=arctan(0.76)\\\\S=37.23^o\\\\\text{Roundding off:}\\\\\boxed{S=37.2^o}[/tex]

Therefore, the S = 37.2^0

Learn more:

Angles in triangles: brainly.com/question/4400594

#SPJ4

Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice

What is a formula of area of triangle?

To calculate the area of a triangle, use the formula area = 1/2 * base * height.

To find the area of triangle ABC, we can use the formula:

Area = (1/2) * base * height

where the base and height are the dimensions of the triangle that form a right angle.

In this case, we don't have the dimensions of the triangle that form a right angle, but we know that the triangle has two angles that are 60 degrees each. This tells us that the triangle is an equilateral triangle, and all three sides are equal.

Let's call the length of each side "s". Then, we can use the formula for the area of an equilateral triangle:

[tex]Area = (\sqrt(3)/4) * s^2[/tex]

Plugging in the given value of 12 for s, we get:

[tex]Area = (\sqrt{(3)/4) * 12^2}\\\\ Area \ = (\sqrt{(3)/4) * 144} \\\\Area = 36\sqrt{(3)}[/tex]

Therefore, the area of triangle ABC is [tex]36\sqrt(3)[/tex] square units.

Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice.

To know more about area of triangle visit,

https://brainly.com/question/17335144

#SPJ1

Answer: Let's call the side length of the square pool "s". We know that the area of a square is equal to the length of one side squared, so we can set up an equation:

s^2 = 144

We can solve for s by taking the square root of both sides:

s = sqrt(144) = 12

So the side length of the pool is 12 feet.

The outside perimeter of the deck is equal to the perimeter of the square pool plus the width of the deck on each side (7 feet). So the outside perimeter is:

12 + 7 + 7 + 12 + 7 + 7 = 52 feet

So the outside perimeter of the deck is 52 feet.

Step-by-step explanation:

Answer: 52 feet

Step-by-step explanation:

First, we know this is a square. So, if the area is 144, square root of 144 is 12 (12 * 12 = 144)

Adding a width of 7 feet to each side means that we can add 12+12+7+7+7+7.

52 feet!

(っ◔◡◔)っ ♥

Hope this helps.

MM4343

The value of x is given as follows:

x = 131º.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Hence the measure of the top angle of the bottom triangle is given as follows:

a = 180 - 98

a = 82.

The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence, considering that the sum of the measures of the internal angles of a triangle is of 180º, their measures are given as follows:

2b + 82 = 180

2b = 98

b = 49.

Considering the vertical angles, the base angles of the top triangle are given as follows:

b = 49.

Hence the value of x is given as follows:

x = 180 - 49

x = 131º.

More can be learned about angle measures at https://brainly.com/question/24607467

#SPJ1

The correct statement regarding the probabilities is given as follows:

d. The experimental probability is closer to the theoretical probability for group X than group Y.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For the theoretical probability, a coin is equally as likely to be heads or tails, hence for each group they are given as follows:

p = 1/2 = 0.5 = 50%.

The experimental probabilities for obtaining heads in each group are given as follows:

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

The people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.

X = No of people having same month birth day

We need, P(X 2) ≥ 1/2

= 1-P(X ≤1) ≥ 1/2

1-P(No one having same month birth day) ≥ 1/2

P(No one having same month birth day)≤ 1/2..........................(1)

Now, k = Minimum no of people required to satisfy (1)

P(No one having same month birth day) =

[tex]\frac{11*10*9......*(12-k+1)}{12*12*12......*12}[/tex]

for k= 4

P(No one having same month birth day) =

[tex]\frac{11.10.9}{12.12.12} = 0.572 \geq 0.5[/tex]

for k= 5

P(No one having same month birth day) =

[tex]\frac{11.10.9.8}{12.12.12.12} = 0.38 \leq 0.5[/tex]

Therefore , the people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.

For more question on probability click on

https://brainly.com/question/24756209

#SPJ4

Answer:

6

Step-by-step explanation:

12 is the full length. point E marks 1/2 of the line. 12-6=6

if it's asking the length of d-e, then the answer is (6) because the entire length of line is twelve and in the top line e-f in 6 and 6-12=6