The relationship between equality and congruence is established by three key theorems. If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
What is triangle?In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.
All triangles are contained in a single plane if all geometry is on the Euclidean plane, but in higher-dimensional Euclidean spaces, this is no longer the case.
The definition of the terminology used to classify triangles can be found on the first page of Euclid's Elements, which dates back more than two thousand years. In modern classification, names are either directly transliterated from Euclid's Greek or translated from Latin.
hence, The relationship between equality and congruence is established by three key theorems. If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
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FIND A:B IF A:C=4:5 A:D=2:3 B:D=1:2
Answer:
Step-by-step explanation:
The sixth grade students are going on a field trip. All 188 students will ride on buses. Each bus has 28 seats that will be filled by students before the next bus in line is used. What fraction of the student seats on the last bus will be filled?
Answer:
5/7
Step-by-step explanation:
188 : 28 = 6
reminder = 188 - 6 x 28 = 188 - 168 = 20
20/28
(20:4)/(28:4)
5/7
What is the length of the radius of a circle given the equation x² y² 8?
The length of the radius of the given circle with the equation x² + y² = 8 is 2√2 units.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
In the center of a circle, equal chords subtend equal angles.
The chord is divided in half by the radius drawn perpendicular to it.
So, the length of the radius of the circle is:
The formula for the circle's general equation is: (x - h)² + (y - k)² = r²
Where, the center is (h, k) and the radius is represented by r.
The equation we have: x² + y² = 8
Then, r² = 8
Taking square root as follows:
r = √8
r = √2*2*2
r = 2√2
Therefore, the length of the radius of the given circle with the equation x² + y² = 8 is 2√2 units.
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Correct question:
What is the radius of the circle whose equation is x² + y² = 8?
What is a parent in a graph?
A parent graph is the graph of a relatively simple function. By transforming the function in various ways, the graph can be translated, reflected, or otherwise changed.
What is a Parent Function?
A parent function is an equation in the simplest form of a family of functions. A family of functions is a collection of functions that represent similar characteristics and/or transformations of its parent function. A parent function can be represented with different degree values such as degrees 1, 2, or 3.
The most basic parent function is called a constant function. A constant function is one such that y = b, where b is the constant value. A constant function creates a straight horizontal line that will intersect the y -axis.
Hence the answer is A parent graph is the graph of a relatively simple function. By transforming the function in various ways, the graph can be translated, reflected, or otherwise changed.
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You roll a six sided die. What is the
probability of rolling a given number three times in a row?
Answer:
Answer: 1/216
Step-by-step explanation:
Explanation: There are 216 possible outcomes.
First roll: 6 possible outcomes
Second roll: 6 possible outcomes
Third roll: 6 possible outcomes
1/216 = 1/6 * 1/6 * 1/6
How can dilations and similarity be modeled in real-world examples?
Answer:
It is common to dilate photos to fit the space that you want it to fit. In police work and crime investigation. Detectives and police dilate photos to see smaller details and evidence. In architecture.
Step-by-step explanation:
What are the 4 steps to solve a Punnett square?
Answer step-by-step explanation:
Step 1: Write out the cross T = tall, t = short Tt x Tt.
Step 2: Draw 2 by 2 Punnett square.
Step 3: Write the alleles for parent 1 on.
the left side of the Punnett square.
Step 4: Write the alleles from parent 2.
above the Punnett square.
I need help with this
The units of the slope is dollars per unit.
How to find the slope of a line?A linear function can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the phone company charges for service as follows:
C(n) = 27 + 0.08n
where
n is the number of minutes talked, and C(n) is the monthly charge in dollars.
Therefore, the units of the slope in dollars per minutes.
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What the 20% of 64,000
Answer: 12,800
Step-by-step explanation:
To find 20% of 64,000, we will turn 20% into a decimal and then multiply. In math, the term "of" usually means multiplication.
20% / 100 = 0.2
64,000 * 0.2 = 12,800
20% of 64,000 is 12,800.
Determine which set of side measurements could be used to form a triangle.
9, 13, 21
8, 9, 18
3, 18, 21
2, 5, 9
None of the measurement of the sides of the triangle forms a right triangle.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The measurement of the side of a right triangle can be found using Pythagoras's theorem.
Therefore,
c²= a² + b²
where
c = hypotenuse sidea and b are the other legs.Therefore, the measurement of the triangles that forms a right triangle is none of the options
9² + 13² ≠ 21²8² + 9² ≠ 18²3² + 18² ≠ 21²2² + 5² ≠ 9²learn more on right triangle here: https://brainly.com/question/4364353
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2. Show that you get the same prime factorization of 220 with 220=2 \times 110 or with 220=10 times 22
3. What numbers might be in the following form when numbers? Give 2 or 3 answers.
This is 224's prime factorization. This is the method of repeated division, and the prime factorization of 224 is 2 2 2 2 7.
What is the 220 factorization in terms of primes?Image for number 2. Show that the prime factorization of 220 is the same when 220 is multiplied by 2 times 110 or 10 times 22. What numbers might possibly be in the next form when numbers? Give two or three responses.
Therefore, 22 51 111, where 2, 5, and 11, can be expressed as 220's prime factorization.
220 has three prime factors, which are 22; 51; and 111. Here, the pair does not contain the prime factor 5. Consequently, 220 is not a square perfectly.
Consequently, the first ten multiples of 220 are as follows: 220, 440, 660, 880, 1100, 1320, 1540, 1760, 1980, and 2200.
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what is the solution a b to this system of linear equations 3a6b45 2a 2b 12
Solution of the system of linear equation 3a + 6b = 45 , 2a -2b = -12 is equal to a = 1 and b =7.
As given in the question,
System of linear equation are:
3a + 6b = 45 __( 1 )
2a - 2b = -12 __(2 )
Solution of the linear equation by elimination method is given by:
Multiply ( 2 ) by 3 and add it to (1) we get,
3a + 6b = 45
6a - 6b = -36
9a = 9
⇒ a = 1
Substitute the value of a = 1 in (1) we get,
3( 1 ) + 6b = 45
⇒ 6b = 42
⇒ b = 7
Therefore, the solution of the system of linear equation is a = 1 and
b =7.
The complete question is :
What is the solution (a, b) to this system of linear equations?
3a+6b = 45 , 2a-2b = -12
a. (-27, 6)
b. (-1, 7)
c. (1, 7)
d. (27, -6)
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{Question 8} Please help! Need this by tonight! {Click on picture}
The cost per message is $0.025.
What is cost?
A cost is the worth of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.
Raw materials, labour expenditures, and other production-related expenses are all considered direct costs. A product, division, or project can simply be linked to the cost. As an illustration, Ford Motor Company (F) produces vehicles and trucks. A automobile is built by a factory employee in eight hours.
Let, Jerry's messaging phone plan is, he paid $0.75 for every 30 messages he send.
So, the cost of each message is,
[tex]\frac{0.75}{30} = 0.025[/tex].
Hence, the per message is, $0.025.
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0.9 + 3.706 + 54.23 + .1637 =
Answer: i think its 58.9997
Step-by-step explanation:
HELP ME QUICK PLEASE!!!!!
Which inequality is a true statement?
Select each correct answer.
-3>-1
-3 ≥ -1
-3=-1
-3≤-1
-3 <-1
Answer:
-3 <-1
-3 is less than -1.
What are the examples of ASA congruence?
Example 1: For Δ ABC, show that AB = AC and Δ ABC is isosceles if the bisector AD of ∠ A is perpendicular to side BC. Also, this condition satisfies the properties of the isosceles triangles.
thus, Δ ABC is an isosceles triangle.
Example 2: Prove that △ACF≅△AEB, if ∠C=∠E and AC=AE.
How do you tell if a triangle is SAS or ASA?
SAS - side angle side ,ASA - angle side angle
What is congruence of triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. The symbol of congruence is’ ≅’.
What we have been asked
how we tell if the triangle is SAS or ASA
SAS is for if two side and in between them the angle is equal for both the triangle.
ASA is for if two angle and in between them the side is equal for both the triangle.
look at the figure
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A baseball player has 746 plate appearances in his first year, 727 plate appearances
in his second year, and 512 plate appearances in his third year. How many plate
has the player had in three years?
appearances
O 2,075
O 1,975
O 1,885
O 1,985
The player has a total plate of 1985 plate appearances (optionD)
What is addition?Addition is a way of combining things and counting them together as one large group. Addition is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum. For example if there a 5oranges, 6 bananas and 9 pineapple Ina basket. The total fruit in the basket is 5+6+9= 20 fruits
The baseball player has 746 plate appearances in his first year and 727 plate appearances in the second year and 512 in his third year.
The total plate appearances = 746+727+512=1985 plate appearances
Therefore the plate appearance the player had in three years is 1985 plate appearances.
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Find the sum of 3/4 and 5/7
3/4 add to 5/7 is 1 and 13/28
What is the rate of change for the equation y = 4x + 100?
The rate of change is .
The rate of change for the given equation is 4.
What Is the Rate of Change Formula?The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity. The rate of change from the coordinates of y to coordinates of x can found out as
Δy/ Δx = (y2 - y1 )/ (x2 - x1).
Given an equation, y = 4x + 100
Slope = 4
Hence, The rate of change for the given equation is 4.
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A soda container holds 5 gallons of soda. How many ounces of soda does this container hold?
1 quart = 32 ounces
1 gallon = 4 quarts
1)44
2)176
3)640
4)704
determine if the two triangles are congruent if they are state how you know
Two triangles are congruent if they satisfy SSS or ASA or SAS or AAS or RHS criteria.
What is the meaning of congruent triangles?
If two triangles have both the same shape and the same size then it is said that the two triangles are congruent. In other words, two triangles are congruent if they are copies of each other.
We can prove that two triangles are congruent if they satisfy any one of the following criteria:-
SSS (side side side ):- If three sides of one triangle are equal to the corresponding three sides of the other triangle.
SAS ( side angle side ):- If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle.
ASA ( angle side angle ):- If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle.
AAS ( angle angle side ):- If two angles and a none included side of a triangle are equal to the corresponding angles and side of another triangle.
RHS (right hypotenuse side ):- If the hypotenuse and one side of the right triangle are equal to the corresponding side and the hypotenuse of another triangle.
Hence, two triangles are congruent if they satisfy any one of the criteria of congruence (SSS, ASA, SAS, AAS or RHS).
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This is not multiple choice
60 points
A spinner used in a game is fun and rotated 930° on the first spin.
The distance from the point of rotation of of a spinner to the tip of the spinner is 3.5 inches.
A) what is the angle of rotation for the first been measured in radians?
B) what distance did the tip of the spinner travel during the first spin to the nearest 10th of an inch?
Part a
There are [tex]\frac{\pi}{180}[/tex] radians in a degree, so the angle of rotation in radians is [tex]\frac{930\pi}{180}=\frac{31\pi}{6}[/tex].
Part b
Using the arc length formula, the distance is [tex](31\pi/6)(3.5)=\frac{217\pi}{12}[/tex] inches.
What is an equation of the line that passes through the points (-6,6) and (-3,1)?
Answer:
y=-[tex]\frac{5}{3}[/tex]x-4
Step-by-step explanation:
find the slope m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{1-6}{-3+6}[/tex]
m=-[tex]\frac{5}{3}[/tex]
Use the slope and one of the points to solve for the y-intercept
y1=mx1+b
6=-[tex]\frac{5}{3}[/tex](-6)+b
6=10+b
b=6-10
b=-4
plug the values for m and b into y=mx+b
y=-[tex]\frac{5}{3}[/tex]x-4
Answer:
y= -1.6x+12Step-by-step explanation:First find the slope.
m=y2-y1 / x2-x1
m= 1-6
-3-(-6)
m=-5
-3+6
m=-5
3
m= -1.6
y-y1=m(x-x1)
y-6= -1.6(x-(-6))
y-6= -1.6x+6
y=-1.6x+12How do you isolate the variable by dividing each side by factors that don't contain the variable?
We isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.
According to the question,
We have the following information:
Isolating a variable by dividing each side of the equation in which one side does not contain any variable.
Now, in this case, it is clearly stated that the first step to isolate the variable from the equation is to perform division.
Now, this can be done as follows in the given equation:
2x = 14
Now, the variable x can be isolated by dividing both sides of the equation by 2:
x = 14/2
x = 7
Hence, we isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.
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For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
Answer:
x ≈ 15.62
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² = 12² + 10² = 144 + 100 = 244 ( take square root of both sides )
x = [tex]\sqrt{244}[/tex] ≈ 15.62 ( to the nearest hundredth )
PLEASE HELP ASAP!!! FULL ANSWER!!!
A person standing close to the edge on top of a 40-foot building throws a ball vertically upward. The quadratic function h = − 16t^2 + 72t + 40 models the ball's height above the ground, h , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? _____________ feet
b) How many seconds does it take until the ball hits the ground? _____________ seconds
Answer:
a) 121 feet ; b) 5 seconds
Step-by-step explanation:
maximum height = y coordinare of vertex
x coordinate = -72/2 * -16
-72/-32 = 9/4 = 2.25
y coordinate =
-16(2.25)^2 + 72(2.25) + 40
-81 + 162 + 40
-81 + 202 = 121 feet
The ball hits the ground when y = 0
-16t^2 + 72t + 40 = 0
-2t^2 + 9t + 5 = 0
discriminant = 81 -4 (-2 * 5) = 81 -4(-10) = 81 + 40 = 121
We are searching only positive value
t = (-9 -11)/-4 = -20/-4 = 5 seconds
HURRY PLS!!
Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
A. Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of buckets of popcorn and the other axis to represent the number of drinks.
Explain your graph.
B. Graph the absolute value function.
C. (a) Graph a linear function of your choice. On the same graph, graph a linear function transformed 2 units up and 3 units down.
(b) What was the equation of your linear function in slope-intercept form?
(c) What was the equation of the transformed function in slope-intercept form?
The equation of Kevin's scenario is 4x + 2y = 45
The absolute equation is y = 2|x - 3| + 5The equation of the linear function in slope-intercept form is y = 2x + 3The equation of the transformed function in slope-intercept form is y = 2x - 1How to determine Kevin's equationFrom the question, we have the following parameters
Amount = $45Bucket of popcorn = $4Bucket of each drink= Half the bucket of popcorn = $2Represent the buckets of popcorn with x and the number of drinks with y
So, we have the following equation
4x + 2y = total amount
This gives
4x + 2y = 45
See attachment for the graph
The graph of an absolute functionAn absolute function is represented as
y = a|x - h| + k
Where the vertex is (h, k)
So, we make use of the following function
y = 2|x - 3| + 5
See attachment 2 for the graph
The graph of a linear functionHere, we are to make use of any equation
A linear equation is represented as
y = mx + b
Where
slope = m
y-intercept = b
So, we make use of
m = 2 and b = 3
This gives
y = 2x + 3
When transformed 2 units up and 3 units down, the resulting equation is
y = 2x + 2 - 3
Evaluate
y = 2x - 1
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Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house. One- half of the comission goes to the broker, and one- half of the remainder to another salesperson. Stevenson receives the rest. Find the amount she receives.
Danielle Stevenson receives $2600.
What is a total amount?
A total is the sum of several numbers or the number of items in a group, as determined by addition or counting.
Here, we have
Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house.
One-half of the commission goes to the broker and one-half of the remainder to another salesperson.
We have to find out how much amount she receives.
Danielle has a 6.5% × $160,000 = $10400
Then, Danielle half of $10400 to the broker so she remains $10400 × 1/2 = $5200
Now,
Danielle one-half of the $5200 to another salesperson. so she gets $5200 × 1/2 = $2600
Hence, Danielle Stevenson receives $2600.
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Compare the graph to the graph of f(x)=|x| and m(x)=|x+1|
The graph of f(x)=|x| and m(x)=|x+1| is 1 unit left translation
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = |x|
m(x) = |x + 1|
First, we have the transformation to be:
From f(x) = |x| to m(x) = |x + 1|
This means the function is translated left by 1 unit
So, we can conclude that
The graph function is translated left by 1 unit
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