How are these shortcuts (SSS, SAS, ASA, and AAS) similar to or different from those for proving triangle congruence?

Answers

Answer 1

This shortcuts (SSS, SAS, ASA, and AAS) is only a concept to determine is the triangle has a All sides, Side-Angle-Side, Angle-Side-Angle, or Angle-Angle-Side. It is not different from those proving triangle congruence because if the two triangles are congruent, all three corresponding sides are congruent and all three corresponding angles are congruent. ASA and AAS are important when solving proofs.

Related Questions

Madison wants to make cookies for her little sisters birthday party. She is cutting a roll of cookie dough into pieces that are 1/2 inch thick. If the roll is 13 inche long, how many cookies can she make

Answers

If the roll is 13 inches long and Madison is cutting the dough into 1/2 inch thick slices, then she will have 26 cookies. Cross multiply 1/2 and 13/1.

Answer:

26 cookies

Step-by-step explanation:

13 times 2

Describe how the graph of y= [tex]x^{2} [/tex] can be transformed to the graph of the given equation.

y = [tex](x-12) ^{2} [/tex] + 3

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\\\ % left side templates \begin{array}{llll} f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ y=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}} \end{array}\\\\ --------------------[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]

with that template in mind, let's see

[tex]\bf y=(x-12)^2+3\implies y=\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{-12})^2\stackrel{D}{+3}[/tex]

A = 1, so no change there from the parent.

B = 1, no change there either

C = -12, now, C/B is -12/1 or -12, that means a horizontal right shift of 12

D = +3, this means, going up by 3 units.

Which function represents the graph of f(x)=|2x| after it is translated 5 units to the left?

Answers

Answer:

Here are the options to the questions:

a.) g(x)=|2(x−5)|

b.) g(x)=|2(x+5)|

c.) g(x)=|2x+5|

d.) g(x)=|2x−5|

The answer is b.) g(x)=|2(x+5)|

Step-by-step explanation:

The function F(x) = |2x| has the vertex at point (0,0)

The rule of translation is (x,y) -------- (x - 5, y)

The translation of the point (0,0)is equal to

(x,y) -------- (0 - 5,0)

(x,y) -------- (-5,0)

The function g(x) has the vertex at point (-5,0)

So therefore, the function g(x) is equal to g(x)=|2(x+5)|

Determine the exponential function that satisfies the given conditions:
The initial mass is 1.4g and it is halving every 4 days.

Answers

The function is represented by the below symbols if x stands for days. f(x) = (1/2)^(x)*1.4 From x = 0 - 4

Final answer:

To determine the exponential function, use the general form of an exponential function and substitute the given values. The equation is y = 1.4 * (1/2)^(x/4).

Explanation:

An exponential function represents exponential growth or decay. In this case, the given information states that the initial mass is 1.4g, and it is halving every 4 days. We can use the general form of an exponential function, y = ab^x, where a is the initial value, b is the growth/decay factor, and x is the time in days.

Since the mass is halving every 4 days, the decay factor is 1/2, since the mass is halving. The equation becomes y = 1.4 * (1/2)^(x/4).

This equation represents the exponential function that satisfies the given conditions.

convert 0.000064 to scientific notation

Answers

the answer is 6.4×10−5

it is 6.4 times 10 to the -5 power

Find the greatest possible value of the product xy, given that x and y are both positive and x + 2y = 30

Answers

greatest value of xy
x + 2y = 30, x = 30 - 2y
xy = (30-2y)y = 30y-2y^2
so if -2y^2+30y = 100, then we can take out a (-2), so: y^2-15y=-50, y^2-15y+50=0
(y-5)(y-10)=0
y-5=0, y=5
y-10=0, y=10
Now we can "plug n play": plug each into x = 30-2y
x = 30-2(5) = 30-10 = 20
x = 30-2(10) = 30-20 = 10
So if we make x=20, y=5... xy = 100
And if x=10, y=10... xy = 100
Now we need to try other number variations to see if they can make xy > 100
if y=6, then x = 30-2 (6) = 30-12 = 18
xy = (18)(6) = 108. Ooh! there's a better choice, but let's keep going
if y=7, then x = 30-2(7) = 16, xy = 7*16 = 112
Even higher! But let's check others
If y=8, then x = 30-16=14, so xy = 112
But from here, the higher y gets the product of xy starts to decrease again
So the greatest possible value comes from 7*16 and 8*14, in which x*y was the maximum it could be at 112

Answer: The maximum value of the product x*y is 112.5

Step-by-step explanation:

We have that x + 2y = 30

so we can isolate one of the variables and get:

x = 30 - 2y

now, the product of x*y can be written as:

x*y = (30 - 2y)*y = 30y - 2y^2

now, we want to find the maximum of 30y - 2y^2

because the leading coeficient is negative (-2), we know that the hands of the quadratic function will go downwards, so the zero of the derivate of this quadratic equation will give us the value where the equation has a maximum:

f(y) = -2*y^2 + 30*y

f'(y) = -4*y + 30 = 0

y = -30/4 = 7.5

So the maximum value is:

f(7.5) = -2*7.5^2 + 30*7.5 = 112.5

Find the 5th term of a sequence represented by f(n) = 5n-2

Answers

Literally just plug in 5 for f(n) to get f(5)=5*5-2=25-2=23

Since you want to know what the 5th term, you substitute 5 for n and solve: f(n) = 5n-2
5n - 5
5(5) - 5 25 - 5
f(n) = 5

PLS HELP!!! WILL MAKE BRAINLIEST!!!

Answers

Calculation with Distribution
First, start by distributing the six by each fraction. (Multiply 6 by each number inside the parenthesis)
6*1/2= 3
6*2/3= 4
6*3/4= 4 1/2
Then add all of the solutions together.
3+4+4.5= 11 1/2

Calculation without Distribution
Add all the fractions together then multiply by 6.
1/2+2/3+3/4= 1 11/12
1 11/12* 6= 11 1/2

Hopefully, I could help!

Evaluate 32 + (7 − 2) ⋅ 4 − 6 / 3.
a. 24
b.54
c.27
d.28

Answers

For some reason I keep getting the result 50.

Annette drives her car 120120 miles and has a mean of a certain speed. if the mean speed had been 3mph3⁢mph more, she could have traveled 128128 miles in the same length of time. what was her mean speed?

Answers

So Annette's speed was 45 mph.

Let's make 2 equations to represent Annette's speed.

T*S = 120
Where
T = the time Annette has been driving.
S = her mean speed.
120 = number of miles she's traveled.

and another equation that's
T*(S+3) = 128

So we now have 2 equations with 2 unknowns. They are
T*S = 120
T*(S+3) = 128

Let's divide the top equation by S on both sides and the bottom equation by (S+3) on both sides giving
T = 120/S
T = 128/(S+3)

So we now know that 120/S is equal to 128/(S+3). So let's make that equation and solve for S
120/S = 128/(S+3)

Multiply both sides by S(S+3)
120(S+3) = 128S

Distribute the 120 on the left
120S + 360 = 128S

Subtract 120S from both sides
360 = 8S

And divide both sides by 8
45 = S

So Annette's speed was 45 mph.

What is equal to 3log2 + log4

Answers

Log Rule #1: log(x*y) = log(x)+log(y)
Log Rule #2: log(x^y) = y*log(x)

Using those log rules, we can say...

3*log(2) + log(4) = log(2^3) + log(4) <-- use log rule #2
3*log(2) + log(4) = log(8) + log(4) <-- simplify 2^3 to get 8
3*log(2) + log(4) = log(8*4) <-- use log rule #1
3*log(2) + log(4) = log(32) <-- simplify 8*4 to get 32

So the expression simplifies to log(32)

12/25 x 5/18 !!!!!!!!!!

Answers

To multiply fractions together you times the top and bottom numbers together and simplify:
(12*5)/(25*18) = 60/450

Then to simply you find a common number, the largest number you can divide into 60 and 450 and still be left with a interger (whole number), in this case it is 30. Then you divide the top and bottom by it:
(60/30)/(450/30) = 2/15

Hope this helps! :)

Value of 12/25 x 5/18 in the simplest form is 2/15.

What is Simplification?

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given a equation 12/25 x 5/18 we need to simplify this

Using PEMDAS

12/25 * 5/ 18

=> (12 * 5)/ 25 *18

=> 2 / (5 * 3)

=> 2/15

Therefore, Value of 12/25 x 5/18 in the simplest form is 2/15.

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For anyone taking or has taken vlacs algebra one, I really need a paragraph describing what was in module #1 for a discussion based assessment. Please help :!

Answers

i have that class i need to know the name of all the different titles in module one. so basically everything inside it. and then i can let you know

How can I tell if they are none transversal?

Answers

Final answer:

A non-transversal line in geometry is a line that does not intersect two or more lines at distinct points. Similarly, in geology, folds with a horizontal axial line, called non-plunging folds, can be analogous to non-transversal lines as they don't intersect with another structure at a distinct point.

Explanation:

In mathematics, specifcally in geometry, transversal is a line that passes through two lines in the same plane at two distinct points. If a line does not intersect two or more lines at distinct points, it can be considered as a non-transversal line.

According to the information provided, in the context of folds in geology, the axial line becomes a key concept. The axial line refers to an imaginary line drawn along the crest of a fold. If the axial line is horizontal, the fold is referred to as a non-plunging fold and it could be analogous to a non-transversal line in geometry, as it doesn't intersect with another structure at a distinct point.

However, if the axial line is tilted (plunging), it might be considered as a transversal in the sense that it 'intersects' the horizontal plane at a distinct angle. Similarly, if a line in geometry is tilted and intersects two or more lines at distinct points, it is a transversal line.

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what’s the slope for x+5=y

Answers

The slope is 1, because the slope form is:
[tex]y = mx+b[/tex]

Where the m is the slope. Here, m=1.

Drive-in movies were popular in the 1930s and 1940s. In 1933, there were 100 drive-in theater in the U.S by 1945 there were 2200. What was the percent of increase from 1933 to 1945?

Answers

2,100% increase from 1933 to 1945.

Final answer:

To find the percent of increase in the number of drive-in theaters from 1933 to 1945, subtract the initial number from the final number, divide by the initial number, and multiply by 100, resulting in a 2100% increase.

Explanation:

The question asks how to calculate the percent of increase in the number of drive-in theaters in the U.S. from 1933 to 1945. To find the percent of increase you subtract the original number from the new number divide by the original number, and then multiply by 100 to convert to a percentage.

Original number (1933) = 100 drive-in theatersNew number (1945) = 2200 drive-in theatersPercent of increase = ((2200 - 100) ÷ 100) × 100Percent of increase = ((2100) ÷ 100) × 100 = 2100%

Therefore, the percent of increase from 1933 to 1945 was 2100%.

The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?

Answers

This question has already been solved by another person. I'll list their answer here.

Perimeter is the sum of all sides of a polygon. For this case, the perimeter is expressed as: P=a+b+c. It has been said that the longest side is twice that of the shortest side. Let's assume that a is the longest side and b is the shortest side. So, the equation for the shortest side is,

6.2 = 2c
c = 3.1

14.5 = 6.2 + 3.1 + b
14.5 = 9.3 + b

I take no credit for this answer. It was solved by Taskmasters.

Which of the following demonstrates the commutative property across multiplication for 2 × 10 × 7 A. 2 + 10 × 7 B. 2 × (10 × 7) C. 10 ×7 × 2 D. (2 × 10) × 7

Answers

The correct answer is C. 10×7×2

Answer:

Option C is correct

[tex]10 \times 7 \times 2[/tex]

Step-by-step explanation:

Commutative property of multiplication states that you can multiply number in any order.

For example:

[tex]2 \times 3 = 3 \times 2[/tex]

[tex]3 \times 4 \times 5 = 4 \times 5 \times 2[/tex]

Given that:

2 × 10 × 7

By definition Commutative property of multiplication,

⇒[tex]10 \times 7 \times 2[/tex]

Therefore, [tex]10 \times 7 \times 2[/tex] demonstrates the commutative property across multiplication for 2 × 10 × 7

Put the numbers in order from least to greatest.
17
, 4.12, 41
10
, 42
15
A) 17
, 4.12, 41
10
, 42
15

B) 41
10
, 17
, 4.12, 42
15

C) 41
10
, 4.12, 17
, 42
15

D) 42
15
, 4.12, 17
, 41

Answers

none of the answers are correct because it would be 4, 10, 12, 17, then 41

Which property justifies this statement?

x−4=x−4

A. Substitution Property of Equality

B. Transitive Property of Equality

C. Reflexive Property of Equality

D. Symmetric Property of Equality

Answers

D. Symmetric Property of Equality

Answer:

C. Reflexive Property of Equality

Step-by-step explanation:

[tex]x-4=x-4[/tex]

A. Substitution Property of Equality

Some value is substituted for any variables. In the given equation, the value for x is not substituted.

B. Transitive Property of Equality

If [tex]c=b+1 \ and \ b+1=4[/tex] then c=4. Given equation does not represent transitive property.

C. Reflexive Property of Equality

When both sides are equal , then it is reflexive property

[tex]x-4=x-4[/tex] represents reflexive property of equality

D. Symmetric Property of Equality

If [tex]1+2=a[/tex] then [tex]a=1+2[/tex]

Given equation does not represents symmetric property

What is the value of x? Enter your answer in the box.

Answers

The value of x from the equilateral triangle is x = 12 and the side is 38

What is an Equilateral Triangle?

An equilateral triangle is a triangle in which all three sides have the same length.

Let the triangle be ΔABC , and

∠A = ∠B = ∠C = 60° and AB = BC = CA

Given data ,

Let the triangle be represented as ABC

Now , the triangle ABC is an equilateral triangle with

∠A = ∠B = ∠C = 60°

The measure of side AB = 4x - 10

The measure of side BC = 3x + 2

The measure of side AC = 5x - 22

And , the sides of the triangle will also be the same

So ,

Side AB = Side BC = Side CA

Substitute the values in the equation , we get

4x - 10 = 3x + 2 be equation (1)

On simplifying the equation , we get

Adding 10 on both sides of the equation , we get

4x = 3x + 12

Subtracting 3x on both sides of the equation , we get

x = 12

And ,

5x - 22 = 3x + 2

Adding 22 on both sides of the equation , we get

5x = 3x + 24

Subtracting 3x on both sides of the equation , we get

2x = 24

Divide by 2 on both sides of the equation , we get

x = 12

Hence , the value of x is 12

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Using the order of precedence for arithmetic operators, these two formulas will calculate the same result: =22/2*5 =22/(2*5).

Answers

It is false. These two formula will not give the same result.
22/2 x 5 = 11 x 5 = 55
22/(2 x 5) = 22 / 10 = 2.2
So, you see both have different answers.

HELP ME WITH MATH PLEASEEEEEEEEEEEEE

Answers

(1/2)^2x = 32

(1^2x)/(2^2x) = 32

1^2x = 1

1/2^2x = 32

32 = 2^5

2^-2x = 2^5

take out the base, (since they are the same. You are left with...)
-2x = 5

-2x = 5 is your answer in this case

hope this helps :D

1.The state fair charges and entry fee plus $0.75 per ticket needed for the rides. Sally spent her money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.

(a)Sally spent a total of $31.25 on the entry fee plus 25 ride tickets. How much did Sally pay for the entry fee?
Answer:

(b)Joe has $26 he can spend at the fair on the entry fee and tickets. How many tickets can Joe buy?
Answer:

(c)Let x represent the number of ride tickets purchased and y represent the total cost of fair entry fee and ride tickets. Write an equation to calculate the total cost of the entry fee and fair admission for a person who purchases x tickets.
Answer:

Answers

Final answer:

Sally paid a $12.50 entry fee to the fair. Joe can buy 18 tickets after paying the entry fee with his $26. The equation to represent the total cost of entry fee and tickets based on the number of tickets purchased is y = 12.50 + 0.75x.

Explanation:

(a) We are told Sally spent a total of $31.25 on the entry fee plus 25 ride tickets. Since each ticket costs $0.75, we can multiply 25 tickets by $0.75 to find the total cost of the tickets alone. That is 25 tickets × $0.75 per ticket = $18.75. Subtracting this amount from the total cost of $31.25 gives us the entry fee. The entry fee is $31.25 - $18.75 = $12.50.

(b) Joe has $26 to spend on the entry fee and tickets. We found out earlier that the entry fee is $12.50. Subtracting the entry fee from the total amount Joe has, we get $26 - $12.50 = $13.50. Now, divide this by the cost of one ticket, $0.75, to determine the number of tickets he can buy: $13.50 / $0.75 = 18 tickets.

(c) Let x represent the number of ride tickets purchased and y represent the total cost of fair entry fee and ride tickets. The total cost is the sum of the fixed entry fee and the variable cost of x tickets at $0.75 each. The equation is y = 12.50 + 0.75x.

Mike and Julie surveyed students to determine how many had a grade of A in math. They recorded their findings for each survey in the table below.

Students with an A in Math
Number of A grades Number of students surveyed
20
4
40
8
60
12
80
16

What is the constant of proportionality of the ratio of students surveyed to the number of A grades?
0.2
0.5
2
5

Answers

20/4 = 5

40/8 = 5

60/12 = 5

80/16 = 5

Answer is 5

Answer:

Option D 5

Step-by-step explanation:

Mike and Julie surveyed students to determine how many had a grade of A in math as given in the table.

We have to find the proportionality constant of the ratio of students surveyed to the number of A grades.

Since proportionality constant = [tex]\frac{\text{Students Surveyed}}{\text{number of A grades}}[/tex]

=[tex]\frac{20}{4}=5[/tex]

Similarly we can get the constant form other data which is equal to 5.

Therefore, Option D. 5 is the correct option.

Graph this equation on this graph

Answers

Plot these points (0,5) (1,-1) (2,-3) (3,-1) (4,5) and then make the parabola from there

Well you have that y-int=5 which is a good start

Now let's solve for the vertex form.
y=2x^2-8x+5
y-5=2x^2-8x
y-5=2(x^2-4x)
y-5+8=2(x^2-4+4)
y+3=2(x-2)^2

Thus the vertex is at (2,-3)
Now that you know this, plug in values(-1,0,1,2,3,4,5) to get (15,5,-1,-3,-1,5,15) respectively

What is the 8th term in the sequence?

an=25−3n

Enter your answer in the box.

Answers

The 8th term is of the sequence is1.

Answer:

Hence, the 8th term of the sequence is:

[tex]a_8=1[/tex]

Step-by-step explanation:

We are defined the nth term in the sequence with the help of the relation or expression as:

[tex]a_n=25-3n-------(1)[/tex]

We are asked to find the 8th term of the sequence i.e. we are asked to find the value of [tex]a_n[/tex] when n=8.

so, we will put n=8 in the given expression (1).

[tex]a_8=25-3\times 8\\\\a_8=25-24\\\\a_8=1[/tex]

Hence, the 8th term of the sequence is:

[tex]a_8=1[/tex]

Which value is the best estimate of 26% of 259?

A: 50
B: 52
C: 65
D: 88

Answers

C
PROOF
just multiply
259×0.26=67.34

26% of 259 is 67.34 so you would pick C. 65 since it's the closest

Megan's DVD club membership, which is $8, is deducted automatically from her bank account every month. Which expression shows the total deductions for the year?
1. (−$8) ÷ 12
2. (−$8) ⋅ 12
3. (−$8) − 12
4. (−$8) + 12

Answers

-8 * 12 = -96....she gets $ 96 deducted every year for the DVD membership

Hello,

100% Correct

The correct answer is B) (-$8) × 12

Hope this helps!!!! :)

(Took the Math test)

**(Vanessa)**

Find the point where the line crosses the x-axis. y = –5x + 5

Answers

Every point on the x-axis has y-coordinate 0.
Let y = 0, and solve for x.

y = -5x + 5

0 = -5x + 5

5x = 5

x = 1

The line crosses the x-axis at x = 1.

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