what additional information do you need to prove ABC congruent DEF by the SAS postulate

Since x, 2x, 3x contain numbers and variables, it takes two steps to find the LCM. Find the LCM for the numerical part 1; 2; 3; then find the LCM for the variable part x¹ ; x¹; x¹.

The LCM is the smallest number by which all numbers are divided without leaving a remainder.

The number 1 is not a prime number because it only has one positive factor, which is itself.

not cousin.

Since 2 has no divisors other than 1 and 2.

2 is a prime number.

Since 3 has no divisors other than 1 and 3.

3 is a prime number.

The least common multiple LCM of 1,2,3 is the result of multiplying all the prime factors the greatest number of times that appear in each term.

2 × 3

Multiply 2 by 3.

6

The factor for x¹ is x itself.

x¹ = x

The Least Common Multiple LCM of x¹ ; x¹; x¹ is the result of multiplying all the prime factors the greatest number of times that appear in each term.

x

The LCM for x;2x;3x is the numerical part 6 multiplied by the variable part.

6x ====> Answer

The measure of side IG from similar triangles DEF and GHI is 34.8 units.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two shapes are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. Hence:

IG/GH = FD/DE

x / 19 = 11/6

x = 34.8

The measure of side IG from similar triangles DEF and GHI is 34.8 units.

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Answer:

see below

Step-by-step explanation:

6 -2x + 5 +4x

Combine like terms

6 +5  -2x+4x

The 6 and 5 do not have x  only the -2 and -4 have x with them

6+5  +x(4-2)

11 +2x

Answer:

√2685 is your answer

hope this will help you

Answer:

13.82 in.

Step-by-step explanation:

To find the circumference of a circle, you multiply the diameter by pi ([tex]\pi[/tex]):

[tex](4.4)(\pi )=13.82301[/tex]

Rounded to the nearest tenth, 13.82301 is 13.82. Therefore, 13.82 is the answer.

I hope this helps!

Answer:

-sin Ф

Step-by-step explanation:

sin( O + 180) = sinФ cos180 + sin180 cosФ

                     =  sin Ф * -1 + 0 * cos Ф

                     =   -sin Ф

So

Answer:

Below in bold.

Step-by-step explanation:

This is a regular polygon so all sides are congruent, therefore:

The perimeter of the polygon = 6*34 = 204 units.

We can divide the polygon into 6 conguent triangle with height 30 and base 34.

So area of 1 triangle = 1/2*34*30 = 510.

So area of the polygon = 6 * 510 = 3060 unit^2.

Perimeter of the polygon = 6*34 = 204 units.

Step-by-step explanation:

The area of the floor of the scale drawing and the scale factor are 72 in² and 1/4 respectively

Actual Length = 36 feets

Actual width = 32 feets

Model width = 9 inches

The scale factor = 9 / 36 = 1/4

The length of the model canbe calculated thus :

Actual Length × scale factor

Model width = 32 × 1/4 = 8 inches

The Area of a rectangle can be calculated using the relation :

Area = Length × width

Area of floor = 8 inches × 9 inches = 72 inch²

Therefore, the area of the floor of the scale drawing is 72 in²

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The area of the rectangular floor in the scale drawing is A = 156 inches²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular floor in the scale drawing be A

Let the length of the rectangular floor be L = 26 feet

Now , the length of the rectangular floor in scale drawing = 13 inches = L/2

And , the width of the rectangular floor be W = 24 feet

So , the width of the rectangular floor in scale drawing = W/2 = 12 inches

Now , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

The area of the rectangular floor in the scale drawing A = 13 x 12

The area of the rectangular floor in the scale drawing A = 156 inches²

Hence , the area of rectangle is 156 inches²

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The function that has a range limited to only negative numbers is Square Root.

The function of this kind is known to be a kind of radical function that is said to have even index e.g. a square root.  and thus, this radicand  is one that can have a negative value for some or for the  values of x.

Note therefore, that The function that has a range limited to only negative numbers is Square Root and thus it is correct.

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Answer:

A or the first Graph

Step-by-step explanation:

My attachment proves this answer is true

Answer:

500

Step-by-step explanation:

Hello!

Let the smallest number be x. The next number would be x + 1, then the next would be x + 2, then x + 3.

The sum of these four is 1998.

Solve for x:

The third number is (x + 2), so simply add 2 to 498 = 500

The third number is 500.

All 4 numbers are 498, 499, 500, and 501.

The equation of a circle that contains the point (–5, -3) and has a center at (-2, 1) is (x + 2)² + (y - 1)² = 25

An equation is an expression that shows the relationship between two or more variables and numbers.

The circle contains the point (–5, -3) and has a center at (-2, 1), hence:

[tex]radius=\sqrt{(1-(-3))^2+(-2-(-5))^2}=5\ units[/tex]

The equation is:

(x - (-2))² + (y - 1)² = 5²

(x + 2)² + (y - 1)² = 25

The equation of a circle that contains the point (–5, -3) and has a center at (-2, 1) is (x + 2)² + (y - 1)² = 25

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[tex]\text{The roots are 13 and 2.}\\\\\text{Now, the quadratic function,}\\\\~~~~~~~f(x) =x^2 -(13+2)x + (13)(2)\\\\\implies f(x)= x^2 -13x-2x + 26\\ \\\implies f(x) = x^2 -15x+26[/tex]

Answer:

a is 3  and b is 10 i am pretty sure

Step-by-step explanation:

The number of people of the country which is predicted will be illiterate in the year 2025 are 1,300,700.

Percentage decrease is the amount deducted or reduced from the initial value in the percentage part.

In the year 2017, an estimated 4,347,000 people in this country are illiterate. With new incentives and funding, The country is hoping to cut that number by 14% every year.

Total year from 2017 to 2025 are 8 years. Thus, use the following formula of compound interest to find percentage decrease:

[tex]A=P\times\left(1+\dfrac{r}{100}\right)^{t}\\[/tex]

Here, A is the final population, The initial population is P, the rate is r and the time period is t. Put the values,

[tex]A=4347000\times\left(1-\dfrac{14}{100}\right)^{8}\\A\approx1300700[/tex]

Thus, the number of people of the country which is predicted will be illiterate in the year 2025 are 1,300,700.

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Answer:

D

Step-by-step explanation:

Remark

The two legs when each of them is squared = 136 by

6^2 + 10^2 = 36 + 100 = 136

The hypotenuse is 12

12^2 = 144

The answer is that it is not a right angle triangle having 2 legs and a hypotenuse. That is because both sides are not equal.

Answer:

23.88 cm squared

Step-by-step explanation:

3.6 x 5.9 = 21.24

1.1 x 4.8 x 1/2 = 2.64

21.24 + 2.64 = 23.88

Answer:

a) 55 b)=21/32 c)x=6

Step-by-step explanation:

a)Follow the PEMDAS order of operations

Calculate within parentheses

(6 +3 x 2)

(6+6)

= 12

=51+ 12 ÷ 3

Multiply and divide (left to right)

12÷ 3=4

51 +4

Add and subtract (left to right)

51 + 4=55

B)

Follow the PEMDAS order of operations

29 – 8) ÷ 32

Calculate within parentheses

(29 – 8) =21

= 21 ÷32

Multiply and divide (left to right)

21 ÷32

=21/1× 1/32

=21/32

C)let the unknown be X

6+ 5× X- 16 = 20

Group like terms

5x +6- 16 = 20

Add/Subtract the numbers:

6- 16 = -10

5x - 10= 20

Add 10 to both sides

5x- 10 + 10 =20 + 10

Simplify

5x=30

Divide both sides by 5

5x/5=30/5

x=6

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{51 + ( 6 + 3 \times 2 ) \div 3}\\\\\mathsf{= 51 + \dfrac{6+ 3\times2}{3}}\\\\\mathsf{= 51 + \dfrac{6 + 6}{3}}\\\\\mathsf{= 51 + \dfrac{12}{3}}\\\\\mathsf{= 51 + 4}\\\\\mathsf{= 55}\\\\\huge\text{Therefore, the answer is: \boxed{\mathsf{55}}}\huge\checkmark[/tex]

[tex]\mathsf{(29 - 8) \div 32}\\\\\mathsf{= \dfrac{29 - 8}{32}}\\\\\mathsf{= \dfrac{29 - 8}{32 - 0}}\\\\\mathsf{= \dfrac{21}{32}}\\\\\mathsf{= 21\div 32}\\\\\mathsf{= 0.65625}\\\\\huge\text{Therefore, the answer is: \boxed{\mathsf{0.65625}}}\huge\checkmark[/tex]

[tex]\mathsf{6 + 5 \times p - 16 = 20}\\\mathsf{\rightarrow 6 + 5p - 16 = 20}\\\mathsf{\rightarrow 5p - 10 = 20}\\\text{ADD 10 to BOTH SIDES}\\\mathsf{5p - 10 + 10 = 20 + 10}\\\text{SIMPLIFY IT!}\\\mathsf{5p = 20 + 10}\\\mathsf{5p = 30}\\\text{DIVIDE 5 to BOTH SIDES}\\\mathsf{\dfrac{5p}{5}= \dfrac{30}{5}}\\\text{SIMPLIFY IT!}\\\mathsf{p = \dfrac{30}{5}}\\\mathsf{p = 6}\\\\\huge\text{Therefore, the answer is: \boxed{{\mathsf{6}}}}\huge\checkmark[/tex]

[tex]\large\textsf{Lets check to make sure \#3 is correct!}\\\mathsf{6 + 5\times \bold{6} - 16}\\\mathsf{= 6 + 30 - 16}\\\mathsf{= 36 - 16}\\\mathsf{= 20}\\\\\huge\textsf{Thus, the answer in the blank IS: \boxed{\mathsf{6}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

$584.41

Step-by-step explanation:

From this information, we can write the following equation:

[tex]P = 500(e)^{0.039t[/tex] where t is the number of years.

To find out the amount after 4 years, we can simply plug in 4 for t:

[tex]P = 500(e)^{0.039(4))\\[/tex]

≈ $584.41

Answer:

$584.41

Step-by-step explanation:

From this information, we can write the following equation:

where t is the number of years.

To find out the amount after 4 years, we can simply plug in 4 for t:

≈ $584.41

Answer:

Tom's class had the lower score

Step-by-step explanation:

Because the range is larger for Tom's class than it is for Brad's class, it is rather likely that students in Tom's class did not do as well on the test than students in Brad's class did.

Answer:

If [tex]\displaystyle\mathsf{\overline{WS}}[/tex] ║ [tex]\displaystyle\mathsf{\overline{KV}}[/tex], and [tex]\displaystyle\mathsf{\overline{KV}}[/tex] ⊥ [tex]\displaystyle\mathsf{\overline{RT}}[/tex], then  [tex]\displaystyle\mathsf{\overline{RT}}[/tex] ⊥ [tex]\displaystyle\mathsf{\overline{WS}}[/tex]

Step-by-step explanation:

We are given the diagram of parallel lines, [tex]\displaystyle\mathsf{\overline{WS}}[/tex] and [tex]\displaystyle\mathsf{\overline{KV}}[/tex], which are intersected by line [tex]\displaystyle\mathsf{\overline{KV}}[/tex]. The prompt requires us to determine the relationship between [tex]\displaystyle\mathsf{\overline{RT}}[/tex] and [tex]\displaystyle\mathsf{\overline{RS}}[/tex].

Parallel lines are non-intersecting lines that are coplanar and have the same slope.  

Perpendicular lines: the intersection between two lines that form right angles. Perpendicular lines also have negative reciprocal slopes.    

Transversal : a line that intersects at least two distinct coplanar lines in at least two or more definite points.  

We will use the given diagram and the following theorems/postulates to prove the relationship between lines [tex]\displaystyle\mathsf{\overline{RT}}[/tex] and [tex]\displaystyle\mathsf{\overline{WS}}[/tex].

Now that we have established the necessary postulates and theorem, we can state that:  

Keywords:

Parallel Lines

Perpendicular lines

Perpendicular Transversal Theorem

____________________________

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Answer:

2.05 · 10^-1

Step-by-step explanation:

(5·10^-3)+(2·10^-1) = 2.05 × 10^-1

Answer:

acute

Step-by-step explanation:

it is an acute triangle

Step-by-step explanation:

well, what do we expect in theory ?

a coin has a 50/50 chance for beads or tails. so, a probability of 1/2 for either one.

the probability for a survival number in a die is 1/6.

remember, the probability is always desired results over total possible results.

so, the combination is a simple multiplication.

the probability to get a certain side of the coin AND a certain number on the die is

1/2 × 1/6 = 1/12

so, this is what we would expect in theory : every combination happens in 1/12 of all cases.

now, what do we see in our practical experiment ?

there were 24 events (so, the total possible results are 24).

how many of them had heads and a 3 (the desired results) ?

there was only 1 result (in fact, there was only one 3 independently from the coin result, which is surprisingly low for 24 rolls of a die).

so, our experiment shows us a ratio or experimental probability of

1/24

for the desired result of heads with a 3 on the die.

we expected to get a ratio of

1/12 = 2/24

so, in reality, we got 1/24 less than theoretically expected.

Answer:140

Step-by-step explanation:

Answer:

B) sqrt(50)

Step-by-step explanation:

c=sqrt((sqrt(10)^2+sqrt(40)^2)=sqrt(10+40)=sqrt(50)

Answer:

square millimeters

Step-by-step explanation:

The surface area will always have answer in

square millimeters / meters / centimeters, etc.

Answer:

Step-by-step explanation:

The bottom of the spinner is not flat.

Answer:

[A] The corresponding sides of the triangles are congruent.

[B] The corresponding angles of the triangles are congruent.

[C] The triangles have the same size.

[D]  The triangles have the same shape.

Step-by-step explanation:

SAS which it is stands for {side, angle, side} and the meaning of SAS is that we have two triangles where we see two sides and the included angle are equal.

In Order for two triangles to be congruent must have the following below:

Hence, base on the given all the following are correct:

A. The corresponding sides of the triangles are congruent. √

B. The corresponding angles of the triangles are congruent. √

C. The triangles have the same size. √

D. The triangles have the same shape. √

Kavinsky

Answer:

A

Step-by-step explanation:

b/c the sides are corresponding and corresponding angles are always equal