For triangles to be congruent, they must have the same angles and same three sides, irrespective of what direction they are pointing to.
Following are the ways to find if two triangles are congruent:
1. SSS (side, side, side): If all three sides of a triangle are equal to the three sides of another triangle, the triangles are congruent.
2. SAS (side, angle, side): If the two sides and the included angle of a triangle are equal to the corresponding sides and the angle of another triangle, the triangles are congruent.
3. ASA (angle, side, angle): If the two angles and their shared side is equal to the corresponding angles and shared side of another triangle, the triangles are congruent.
4. AAS (angle, angle, side): If two angles and the non-included side of a triangle are equal to the corresponding angles and non-included side of another triangle, the triangles are congruent.
5. HL (hypotenuse, leg): If the hypotenuse and one leg (side other than hypotenuse) of a right angle triangle are equal to the corresponding hypotenuse and the leg of another right angle triangle, then the two triangles are congruent.
Congruent triangles are used in real world for construction purposes to ensure that the man-made structures are strong and stable enough.
Final answer:
There are multiple ways to prove triangle congruency, including SSS, SAS, ASA, AAS, and RHS. These concepts are important in real-world applications such as architecture and engineering for ensuring precision and safety in structures and components.
Explanation:
There are several methods to prove that two triangles are congruent, each based on different sets of information about the triangles' sides and angles. The following are commonly used:
Side-Side-Side (SSS) Congruence: If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent (Theorem 16).Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent (Theorem 11).Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.Angle-Angle-Side (AAS) Congruence: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, the triangles are congruent.Right Angle-Hypotenuse-Side (RHS) Congruence (also known as HL): If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the triangles are congruent.These concepts are utilized in various real-world applications, such as architectural design, engineering, manufacturing, and construction, where precise measurements and shapes are critical for the safety and fit of structures and components.
Some one pleasseee help xx
A.
600 : 2 = 300
300 : 2 = 150
150 : 2 = 75
75 : 5 = 15
15 : 5 = 3
3 : 3 = 1
600 = 2 · 2 · 2 · 5 · 5 · 3 = 2³ · 5² · 3
B.
1050 : 2 = 525
525 : 5 = 105
105 : 5 = 21
21 : 3 = 7
7 : 7 = 1
1050 = 2 · 5 · 5 · 3 · 7 = 2 · 5² · 3 · 7
600 = 2 · 2 · 2 · 5 · 5 · 3
HCF(600, 1050) = 2 · 3 · 5 · 5 = 150
Identify the property that justifies the statement.
∠XYZ≅∠PDQ and ∠PDQ≅∠ABC, so ∠XYZ≅∠ABC.
Answer: Transitive property of Equality.
Therefore if ∠XYZ≅∠PDQ and ∠PDQ≅∠ABC then by transitive property of equality we have ∠XYZ≅∠ABC.
The law of transitivity tells that if a equals to b and b equals to c then a equals to c.
For example If Jane has same height of Susan and Susan has same height of Tina then Jane has same height of Tina.
The statement "∠XYZ ≅ ∠PDQ and ∠PDQ ≅ ∠ABC, so ∠XYZ ≅ ∠ABC" is justified by the Transitive Property of Equality, which indicates that the congruence of the first and third angle is established through their mutual congruence to the second angle.
Explanation:The property that justifies the statement "∠XYZ ≅ ∠PDQ and ∠PDQ ≅ ∠ABC, so ∠XYZ ≅ ∠ABC" is the Transitive Property of Equality. This property states that if a first thing is equal to a second thing, and the second thing is equal to a third thing, then the first thing is also equal to the third thing.
In the context of angles, if ∠XYZ is congruent to ∠PDQ, and ∠PDQ is congruent to ∠ABC, then by the Transitive Property, ∠XYZ must be congruent to ∠ABC.
What is the equation in point−slope form of the line passing through (0, 6) and (1, 3)? (5 points)
The slope-point formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have (0, 6) and (1, 3),
Substitute:
[tex]m=\dfrac{3-6}{1-0}=\dfrac{-3}{1}=-3\\\\y-6=-3(x-0)[/tex]
Someone know the answer?
Answer: Choice A) (5+a)/(a-1)
Step-by-step explanation:
In the numerator, we originally have 3+x. Replace the x with a+2 and we get 3+x = 3+a+2 = 5+a. So the answer will have a numerator of 5+a.
The denominator in the answer will be x-3 = a+2-3 = a-1
Overall that's how the answer is (5+a)/(a-1)
5 times a number, subtracted from six, is triple the number
Final answer:
The algebraic equation based on the statement '5 times a number, subtracted from six, is triple the number' is 6 - 5x = 3x. Solving for 'x' gives us x = 3/4.
Explanation:
The student's question involves creating an algebraic equation based on a verbal statement. To translate the statement '5 times a number, subtracted from six, is triple the number' into an equation, let's use 'x' to represent the unknown number. The statement can be written as: 6 - 5x = 3x. To solve for 'x', we need to get all terms involving 'x' on one side and constants on the other. Here's how you can do it:
Add 5x to both sides of the equation to get: 6 = 3x + 5x
Combine like terms: 6 = 8x
Divide both sides by 8 to get the value of x: x = 6/8
Simplify the fraction: x = 3/4
Therefore, the number in question is 3/4.
is this work right?
Idk if I followed the PEMDAS right
yes you did a very good job
If x > 0 and y > 0, where is the point (x, y) located? On a coordinate plane
Answer:
its y
Step-by-step explanation:
The registration period for the race is under way, and as the word is getting out, the number of participants registering is growing exponentially. The numbers from the first two days of registration are shown in the table.
Use the data in the table and the general form of an exponential growth equation, y= a(1 +r)^x, to write an equation modeling the exponential growth of registrations, where x is the number of days since registration opened, a is the initial number of registrations, r is the rate of growth of registrations per day, and y is the total number of registrations.
y = a(1 + r)ˣ
a = 15 "initial" means what you started with on the first day
r = 6 the rate it increased is the slope ([tex](\frac{21 - 15}{2 - 1})[/tex]
y = 15(1 + 6)ˣ
Answer: y = 15(7)ˣ
Determine whether the given function is a polynomial function. If it's a polynomial function, state the degree. If not, state the reason why.
k(x) = –3x6 – 0.7x + x3
A. Yes; degree 10
B. No, because some range elements correspond to more than one domain element
C. No, because 0.7 isn't an integer
D. Yes; degree 6
ANSWER
The correct answer is option D.
EXPLANATION
The given function is
[tex]k(x)=-3x^6-0.7x+x^3[/tex]
This a polynomial function. All degrees are greater than or equal to zero.
The coefficient being decimals does not disqualify it from being a polynomial.
The highest degree of this polynomial is 6.
Therefore the correct answer is D
Jordan bought 6 apples priced 3 for $2.89 and 5 pears priced 5 for $4.50 how much did he pay in all
Which is the best estimate for the number of items that customers bought during a trip to the grocery store one day?
The histogram shows the number of items that customers bought during a trip to the grocery store one day. Four hundred customers took a trip to the grocery store that day.
Options are:
15 (I think it is this one)
20
34
65
The answer is 65! Just took the test
Please help asap 30 pts
7x > -35 |divide both sides by 7
x > -5
---------------------
3x ≤ 30 |divide both sides by 3
x ≤ 10
-5 < x ≤ 10
Answer: b.
Heidi's mom made flower arrangements for a party. She made 4 times as many rose arrangements as tulip arrangements. Heidi's mom made a total of 40 arrangements. How many flower arrangements of each type did Heidi's mom make?
32 rose arrangements and 8 tulip arrangements
8 times 4 = 32
8 + 32 = 40
Heidi's mom made 8 tulip arrangements and 32 rose arrangements. This was determined by setting up equations based on the given information and solving for the number of each type of arrangement.
With 4 times as many rose arrangements as tulip arrangements. Let's denote the number of tulip arrangements as T and the number of rose arrangements as R. According to the information, R = 4T and R + T = 40.
Substituting R in the second equation gives 4T + T = 40, which simplifies to 5T = 40. Solving for T, we find T = 8. Therefore, the number of tulip arrangements is 8. Substituting T = 8 into the equation R = 4T gives R = 32, meaning that there are 32 rose arrangements. Thus, Heidi's mom made 8 tulip arrangements and 32 rose arrangements for the party.
During the summer, payton and James mow the lawns in their subdivision. On each lawn they spend $3.50 on gas and $1.20 on leaf bags. If they charge $22.00 for each lawn ,how much profit do they make?
Answer:
17.30 dollars
Step-by-step explanation:
Given that Payton and James mow the lawns.
They do this during summer.
The amount they spend are:
Gas cost = 3.50
Leaf bags = 1.20
Add these to get total costs
Total cost = 4.70
Charge they get per lawn = 22.00
Profit = Revenue - cost
Here revenue per lawn = 22 and cost per lawn = 4.70
Hence profit = 22-4.70 = 17.30 dollars.
Answer is they make 17.30 dollars per lawn.
Answer:
The answer is B
Step-by-step explanation:
solve the formula V = bh for h
V = bh Dividing both sides by "b" we get
(V / b) = h
Solving for h means to isolate h by move everything else to the other side of the equal sign.
V = b * h
[tex]\frac{V}{b} = \frac{b*h}{b}[/tex] divide both sides by b
[tex]\frac{V}{b} = h[/tex] h is now isolated
Mrs.Bell has a 256-ounce bag of potting soil.What is greatest number 6-ounce pots she can completely fill with soil?
One way that a company can raise money for expansion is to sell stock. When you buy a share of a company's stock, you become a shareholder, or part owner, of that company. The cost of a share is often represented in points, where each points represents one dollar. When a stock gains points, its shares increase in value, and when a stock loses points, its shares decrease in value. For instance, if a stock gains three points one day, each share of its stock is worth three dollars more than it was the day before. Positive decimal numbers are used to represent gains, and negative decimal numbers are used to represent losses.
On Monday, the closing value of a share of stock in Company ABC, was 74.01. On Tuesday, it closed at 73.67, and on Wednesday, it closed at 74.32. On Thursday, the change in stock value was -1.48. And, on Friday, Company ABC's stock gained 0.89 points. Answer the following questions based on Company ABC's stock performance this week.
If a shareholder owns 75 shares of Company ABC's stock, by what amount did their total stock value change on Wednesday?
well if he started his day on Wednesday with 75 end he ended with 74.32 he lost -0.68
of his share hope this helped theres alot of extra information in the question
Answer:
-0.68
Step-by-step explanation:
The price of wheat in 1997 was 3.38 per bushel. In 1998,the price was 2.65 per bushel. Round the price per bushel of wheat for each year to the nearest tenth of a dollar
1997 = 3.40
1998 = 2.70
In math what does it mean by Define the varible?
Final answer:
To define the variable in mathematics means to assign symbols to represent quantities that can take various values, either as numerical variables measurable in the same units or as categorical variables for classification purposes. This allows for the exploration of relationships and predictions of outcomes.
Explanation:
In mathematics, the term 'define the variable' refers to the process of assigning a symbol, typically a letter such as X or Y, to represent a quantity that can take on various values. Variables can be of different types, such as numerical variables which represent values measurable in the same units like time in hours or weight in pounds, and categorical variables which classify individuals or items into categories, such as political affiliation.
For example, in the equation of a line y=mx+b, x and y are variables with x usually representing the independent variable plotted along the horizontal axis, and y as the dependent variable plotted on the vertical axis. The variable m represents the slope of the line, and b represents the y-intercept, or the point where the line crosses the y-axis. By defining each variable, a mathematician or an economist can explore the relationship between quantities and predict outcomes.
An example in statistics would be letting X represent the number of children in a family, making it a numerical variable, where each specific number of children would be represented by a lowercase x (0, 1, 2, 3, etc.). Conversely, if Y represents someone's political party, each category (Republican, Democrat, Independent, etc.) is an example of a categorical variable, which does not make sense to average mathematically like numerical variables.
A cheetah can go from a state of testing to running at 20 m/s in just 2 seconds. What is the cheetahs average acceleration?
if f(x)=4x^2-6 and g(x)=x^2-4x-8,find (f-g)(x)
a.(f-g)(x)=x^2-14
b.(f-g)(x)=5x^2-4x-14
c.(f-g)(x)=3x^2+4x+2
d.(f-g)(x)=3x^2-4x-2
c. Due to c. and the equation above would be equal just in a different arrangement
Answer:
[tex](f-g)(x)=3x^2+4x+2[/tex]
C is correct
Step-by-step explanation:
Given: [tex]f(x)=4x^2-6[/tex]
[tex]g(x)=x^2-4x-8[/tex]
To find : (f-g)(x)
[tex](f-g)(x)=f(x)-g(x)[/tex]
[tex]\Rightarrow (4x^2-6)-(x^2-4x-8)[/tex]
using Distributive property
[tex]\Rightarrow 4x^2-6-x^2+4x+8[/tex]
[tex]\Rightarrow 4x^2-x^2+4x+8-6[/tex]
Combine like term
[tex]\Rightarrow 3x^2+4x+2[/tex]
[tex](f-g)(x)=3x^2+4x+2[/tex]
Hence, The composite function is [tex](f-g)(x)=3x^2+4x+2[/tex]
Which statement is true? A.27/19<11/30 b.17/31>19/14 c.16/26>30/31 d.35/30<22/12
is this true 27/19<11/30
In order to check if a comparison such as this is true, you can use this logical equivalence:
[tex] \dfrac{a}{b} > \dfrac{c}{d} \iff ad > bc,\quad \dfrac{a}{b} < \dfrac{c}{d} \iff ad < bc [/tex]
Anyway, it's not always necessary to make this check. We know that every proper fraction represents a number between 0 and 1, and any improper fraction represents a number greater than 1. So, every proper fraction is less than every improper fraction.
So, the first two options are surely wrong, because they ask for a proper fraction to be more than an improper fraction.
The third option compares two proper fractions, so we actually have to check:
[tex] \dfrac{16}{26}>\dfrac{30}{31} \iff 16 \cdot 31 > 26 \cdot 30 \iff 496 > 780[/tex]
which is false.
Last option:
[tex] \dfrac{35}{30}<\dfrac{22}{12} \iff 35 \cdot 12 < 30 \cdot 22 \iff 420 < 660[/tex]
Which is true.
My favorite songstress gives away 25% of the sales of her signature fragrance collection to her charity. Last month her sales was $ 1,200. How much of her total sales did she donate?
Since she donates 25%, take 25% and multiply it by 1,200
[tex].25 * 1,200 = 300[/tex]
or,
[tex]\frac{1}{4} * 1,200 = 300[/tex]
Cameron adds 4 new hats to his collection each year. He started with only 3. Find slope and the y intercept.
The slope is 4. The y intercept is 3.
plz give brainliest if possible
Please help asap 27pts
[tex]7x\geq-56\qquad|\text{divide both sides by 7}\\\\x\geq-8\\-------------------------------\\9x < 54\qquad|\text{divide both sides by 9}\\\\x < 6\\\\Answer:\ d)\ -8\leq x < 6[/tex]
Please show work and help!! Will give brainliest!!
Step 1. Since the power of 2 is even, the result will be positive
(3j^2k^3)^2(2j^2k)^3
Step 2. Use Multiplication Distributive Property
3^2(j^2)^2(k^3)^2(2j^2k)^3
Step 3. Simplify 3^2 to 9
9(j^2)^2(k^3)^2(2j^2k)^3
Step 4. Use the Power Rule
9j^4(k^3)^2(2j^2k)^3
Step 5. Use the Power Rule
9j^4k^6(2j^2k)^3
Step 6. Use Multiplication Distributive Property
9j^4k^6 * 2^3(j^2)^3 k^3
Step 7. Simplify 2^3 to 8
9j^4k^6 * 8(j^2)^3 k^3
Step 8. Use the Power Rule
9j^4k^6 * 8j^6k^3
Step 9. Take out the constants
(9 * 8)j^4j^6k^6k^3
Step 10. Simplify 9 * 8 to 72
72j^4k^6k^3
Step 11. Use the Product Rule
72j^4+6k^6+3
Step 12. Simplify 4 + 6 to 10
72j^10k^6 + 3
Step 13. Simplify 6 + 3 to 9
72j^10k^9
Select the slope-intercept form of an equation for a line with y-intercept –5 and slope 2.
Gayle is saving to buy a bicycle. The bicycle costs $119.90 she has saved 0.7 of what she needs how much has she saved so far?
Let the amount saved by Gayle be = x
Cost of the bicycle = $119.90
Gayle's saving till now = 0.7% of 119.90
[tex]\frac{0.7}{100}\times119.90=x[/tex]
[tex]x=0.83[/tex]
Hence, Gayle has saved $0.83 so far.
Answer:
She has saved $83.93.
Step-by-step explanation:
Gayle is saving to buy a bicycle.
The cost of bicycle = $119.90
She has saved = 0.7 of $119.90
= 0.7 × 119.90
= $83.93
The amount she needs more = 119.90 - 83.93
= $35.97
She has saved $83.93.
Your friend is 1.25 times taller than you. Your friend is 64.5 inches tall. How tall are you?
To do a problem like this, multiply the base height by the rate. So here is how you do it:
64.5 times 1.25
The easiest way is to get a calculator and plug in the equation
Your answer should be 80.625
*If you multiply by hand, remember to move the decimal back to the left three places.*
The 6 in 63 represents how many times the value of the 6 in 46?
In 63, 6 is in the tenths place, meaning it represrents the number 60.
In 46, 6 is in the ones place, meaning it represents the number 6.
So, given that, in the first example 6 is x times the value of 6 in the second example:
x = 60 / 6
x = 10
Hope it helped,
BioTeacher101
The value of the digit 6 in the number 63 is 10 times the value of the digit 6 in the number 46.
Explanation:In the number 63, the 6 is in the tens place, meaning it represents 60 (6 tens). In the number 46, the 6 is in the ones place, meaning it simply represents 6 (6 ones). Therefore, the 6 in 63 is 10 times the value of the 6 in 46.
Learn more about Place Value here:https://brainly.com/question/35447631
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