Answers
If UV≅PM then UV≅PM → Definition of congruence, EF≅EF → Reflexive property of congruence, If AB≅LM and LM≅ST then AB≅ST → Transitive property of congruence.
What are postulates?A statement that is accepted as true without evidence, also referred to as an axiom. Lemmas and theorems are deduced from postulates, which serve as their fundamental building block. For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry.
A) If and only if two segments have equal amounts of each, they are congruent.
If UV≅PM then UV≅PM → Definition of congruence
B) An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.
EF≅EF → Reflexive property of congruence
C) According to the transitive characteristic of congruence, "all sides are congruent to each other if two sides are congruent to the third side."
If AB≅LM and LM≅ST then AB≅ST → Transitive property of congruence
D) Actually fairly straightforward, equality has the symmetric condition. According to this criterion, if a = b, then b must also be a. In other words, even if two equations' sides are switched, the equation still makes sense.
If AB=XY then XY =AB → Symmetric property of equality
E) The additive property of equality in an equation asserts that the sides stay equal whether we add or subtract the same amount from both sides of the equation. For entire numbers as well, this property is valid.
If 2x-3=13 then 2x=16 → Addition property of equality
Add 3 on both the sides of equation we get
2x-3+3=13+3
⇒ 2x=16
Therefore, the statement If 2x-3=13 then 2x=16 follows addition property of equality.
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Related Questions
In this triangle, what is the value of x?
Answers
Answer: 4.46cm
Step-by-step explanation:
Use [SOH CAH TOA]
We have two sides that are labeled. Use 85cm and x.
Using the angle 63 degrees would mean you are using SOH.
SOH = Opposite/Hypotenuse.
If the above is true, then: Sin63 = x/85
Since we don't know what x is, you want to move 85 to the other side.
85(Sin63) = x
Now, you can find x. Multiply 85 and Sin63. Your answer should be 4.46 (if rounded to 2 decimals).
BASED ON BEN’S WORK SHOWN, HOW WOULD HE RESPOND?
The point IS a solution to the system. Only one of the equations resulted in anidentity.
The point isNOT a solution to the system. Both equations resulted in identities.
The point is NOT a solution to the system. Only one of the equations resulted in an identity.
The point IS a solution to the system. Both equations resulted in identities.
Answers
The point is NOT to fix the system. There was just one equation that produced an identity. The right answer option 3
Equation: What is it?An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
X = 6 and Y = -8 are the points in BEN'S WORK SHOWN's 2x + y = 4 equation, and after solving it, we have the verification.
However, for x + 3y = -20, the points x = 6 and y = -8 are not solved, and since points here only fulfill one equation,
The point is NOT a solution to the system. Only one of the equations resulted in an identity.
if both the solution would have been then we can say that point is a solution to the system. but this is not true as one equation is not satisfy
The point is NOT a solution to the system. Both equations resulted in identities. this is also not true as one is identities not both.
The point IS a solution to the system. Both equations resulted in identities. this is also not true as both are not identities as only one is identities.
Thus option 3 is correct
The point is NOT a solution to the system. Only one of the equations resulted in an identity.
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Emma grew 6 plants with 3 seed packets. How many seed packets does Emma need to have a total of 16 plants in her backyard? Solve using unit rates.
Answers
8 seed packets
Step-by-step explanation:First, we need to figure out how many plants Emma can grow with each seed packet. To do this, divide 6 plants (the number of plants Emma currently has) by 3 seed packets (the number Emma had to begin with). This will give us a unit rate of "2 plants per seed packet".
Now that we know the unit rate, we can use it to figure out how many seed packets Emma needs to have 16 plants in her backyard. Divide 16 plants (the number of plants Emma wants to have) by 2 plants per seed packet (the unit rate). This will give us 8 seed packets.
Therefore, Emma needs 8 seed packets to have a total of 16 plants in her backyard.
If you have any additional questions or need further assistance, please let me know.
Which of the following is equal to the square root of the cube root of 6? (4 points)
A. 6 to the power of one sixth
B. 6 to the power of one third
C. 6 to the power of two thirds
D. 6 to the power of three halves
Answers
Answer:
A. 6 to the power of one sixth
Step-by-step explanation:
To find the square root of the cube root of 6, you need to first find the cube root of 6, which is equal to 2. Then, you need to take the square root of 2, which is equal to 1.4142135623730951. Therefore, the square root of the cube root of 6 is equal to 1.4142135623730951.
To express this value using exponents, you can use the property that the square root of x is equal to x to the power of one half. Therefore, the square root of the cube root of 6 is equal to 6 to the power of one half of one third, which simplifies to 6 to the power of one sixth.
The ratio of the angles in a triangle is 3:5:8 what is the measure of the largest angle
Answers
The measure of the largest angle is 96 degrees.
What is a ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3
The measure of the largest angle in the triangle is 96 degrees.
To find the measure of the largest angle, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's call the measures of the three angles x, y, and z, where x is the measure of the smallest angle, y is the measure of the middle angle, and z is the measure of the largest angle.
We are given that the ratio of the angles is 3:5:8, which means that x:y:z = 3:5:8.
We can set up the following equation to represent the sum of the measures of the angles in the triangle:
x + y + z = 180
We can also set up the following equation to represent the ratio of the angles:
x : y : z = 3 : 5 : 8
We can use these two equations to find the measure of the largest angle.
First, let's multiply the second equation by 3, 5, and 8 to get:
3x = 15y = 24z
Then, we can substitute these equations into the first equation to get:
15y + 24z = 180
Solving for z, we get:
z = 180 / (15+24) = 180 / 39 = 96
Therefore, the measure of the largest angle is 96 degrees.
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Need help with this question
Answers
The value of the angle m∠BDC is 105°.
What is third angle theorem?If the other two sets are both congruent, then the third angles are equal.The third pair of angles must be congruent if two angles in one triangle are congruent with two angles in another triangle. The Third Angle Theorem refers to this.The Triangle Sum Theorem can be thought of as an extension of the Third Angle Theorem. The Triangle Sum Theorem states that once two angles in a triangle are known, you automatically know the third. This indicates that if you have two triangles with two pairs of congruent angles between them, you will receive the same result both times when you apply the Triangle Sum Theorem to each triangle to determine the third angle. The third pair of angles must therefore likewise be similar.Let separate the triangles and find missing angle in triangle with given angles.
CAD = 45°
CDA = 30°
Then, CAD+CDA+ACD = 180°
45°+30°+ACD=180°
ACD=180°-75°
=105°
by applying third angle theorem,
∠CAD=∠DBC=45°
∠ADC=∠BCD=30°
Then, ∠DBC+∠BCD+∠BDC=180°
45°+30°+BCD=180°
BCD=180°-75°
=105°
Hence, The value of the angle m∠BDC is 105°.
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Evelyn need to add 3 1/3 cup of ugar to her cookie dough. She only ha a 2/3-cup meaure. How many coop of ugar doe Evelyn need to add?
Answers
The required fraction cup of sugar do Evelyn need to add is 8/3.
How to deal with fraction?Multiply the numerators and denominators independently to track down the item. At the point when you need to duplicate divisions, increase the 2 numerators together first and compose it on top. Then increase the denominators together and compose it on the lower part of the portion. Improve on your response on the off chance that you would be able so it is in the least terms.
According to question:As question says Evelyn need 3(1/3) cup og sugar
To find many cup of sugar do Evelyn need to add.
Let the required sugar be x
Then,
2/3 + x = 3(1/3)
x = 10/3 - 2/3
x = 8/3 cup of sugar need.
Thus, required cup of sugar is 8/3.
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(35 POINTS!!)
The height of a hot air balloon over time is given in the following table.
The height of a blimp over time is given by y = 250x, where y represents the height in feet and a represents the time in minutes.
How fast is the hot air balloon rising? How fast is the blimp rising?
Hot air balloon: (?) feet per minute.
Blimp: (?) feet per minute.
Answers
The hot air balloon is rising at 600 feet per minute and the blimp are rising at 250 feet per minute
How to determine how fast the hot air balloon and the blimp are rising?How fast is the hot air balloon rising?
From the question, we have the following parameters that can be used in our computation:
The height of a balloon over time is represented by the graph
On the graph, we have the following points
(x, y) = (0, 0) and (2, 1200)
The rate is calculated as
Rate = (1200 - 0)/(2 - 0)
Evaluate
Rate = 600
Hence, the rate of rising is 600 feet per minute
How fast is the blimp rising?
From the question, we have the following parameters that can be used in our computation:
The height of a blimp over time is given by y = 250x
The above equation is a linear equation
A linear equation can be represented as
y = mx + c
Where
slope = m
This means that the slope of y = 250x is 250
The slope represents the rate
Hence, the rate of rising is 250 feet per minute
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Suzanne has 12 jars of beads. some of her jars have 15 beads, and the others have 9 beads. she has 126 beads in all. How many of her jars have 9 beads?
A 3 jars
B 6 jars
C 9 jars
Answers
The number of Suzanne jars that have 9 beads is 9.
How to find the number of jars that have 9 beads?Suzanne has 12 jars of beads. some of her jars have 15 beads, and the others have 9 beads. she has 126 beads in all.
The number of jars that have 9 beads can be calculated as follows:
let
the number of jars that have 15 beads = x
the number of jars that have 9 beads = y
Hence,
x + y = 12
15x + 9y = 126
multiply equation(i) by 15
15x + 15y = 180
15x + 9y = 126
subtract equation(i) from equation(ii)
6y = 54
divide both sides by 6
y = 54 / 6
y = 9
Therefore,
jars with 9 beads = 9
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Help me please unit plsss
Answers
The possible elevation of Salton city will be;
⇒ x < - 2 feet
Where, x is the elevation of Salton city.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
New Orleans is 2 feet below sea level.
And, Salton City has an elevation that is lower than New Orleans.
Now,
New Orleans is 2 feet below sea level.
And, Salton City has an elevation that is lower than New Orleans.
Let the elevation of Salton city = x feet
Thus, We get;
The possible elevation of Salton city will be;
⇒ x < - 2 feet
Where, x is the elevation of Salton city.
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Log base 28 of 7 plus log base 28 of 4
Answers
Answer:
log base 28 of (7x4)
log base 28 of (28)
which equals 1
Can someone help me with this
Answers
Answer:
y=-3/1x-2
y=9/3x+8
Step-by-step explanation:
Slope is -3/1 using rise over run, it's just negative because the graph is slanted down. The slope is 9/3 using rise over run. Then the y-intercepts are -2 and 8.
-Hope this helped & Happy Holidays!
Jasmine made fancy red costume decorations for each of the dancers in her year-end dance performance. She used 1/4 of a meter of ribbon for each decoration, which she got by cutting 1/2 of a meter of ribbon into equal pieces. How many decorations did Jasmine make?
Answers
There are 2 decorations that Jasmine makes.
What are word problems?
A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
You can tackle any word problem by following these five steps:
Read through the problem carefully, and figure out what it's about.Represent unknown numbers with variables.Translate the rest of the problem into a mathematical expression.Solve the problem.Check your work.Since we have given that
Length of a meter of ribbon used = 1/4
[tex]\frac{1}{4} = \frac{1}{4}.100 = 25[/tex]
Length of a meter cut into equal pieces = 1/2
[tex]\frac{1}{2} =\frac{1}{2}.100= 50[/tex]
So, Number of decorations that Eli make is given by
Length of total ribbon / Length of ribbon used
= 50 / 25
= 2
Hence, there are 2 decorations that Jasmine makes.
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please help i have to make a discussion topic doesn’t have to be long just simple but still answering the question
Answers
You would add 5x + 2x = 7x
Substitute 5 for x and that = 5(5)= 35 +2(5)= 10= 45
and do it for 7(5)= 35-1 = 34 too
You can't make them equal
Following the pattern in (5)(3)+(2)(3) = (5+2)(3), we could do the same thing with 5x+2x = (5+2)x. We're basically un-distributing the common factor from each term.
And now with (5+2)x, we can add the 5 and 2 to get 7x.
If we substitute different values into 5x+2x, it works out to add up to 7 times that same substituted value. For example:
(5)(9)+(2)(9)=45+18=63
(7)(9)=63
If we substitute 9 into 7x-1, then we end up with 63-1 = 62.
In fact, any number we put into 5x+2x will always be one more than 7x-1. So, no, there doesn't seem to be any value of x that would make these equal. Since 5x+2x=7x, then 7x-1 will always be one less than 7x.
Workers are loading boxes onto a truck. So far, they have loaded 48 boxes onto the truck. According to their inventory, they still need to load 96% of the boxes on the truck. What is the total number of boxes the workers are loading on the truck?
Answers
The total number of boxes of inventory which is loading on the truck by the workers are 1,200 boxes.
What is percentage of a number?
Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
Workers are loading boxes onto a truck . So far, they have loaded 48 boxes onto the truck.
According to their inventory, they still need to load 96% of boxes on the truck. There must be 100% box at the start of the loading. Thus, the percentage of boxes they have load,
p=100-96 = 4%
Thus the percentage of boxes they have load in the truck is 4%. This is equal to the 48 boxes they have loaded.
Let suppose there is x number of total boxes. Thus the 4 percent of x will be equal to the 48.
(4/100)x=48
x = 4800/4 = 1200
Thus, the total number of boxes of inventory which is loading on the truck by the workers are 1,200 boxes.
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2X-3Y=4
X+Y=6
please explain each step
Answers
Answer:
Step-by-step explanation:
Rewrite equations: x+y=6;2x−3y=4
Solve x+y=6 for x: x+y+−y=6+−y (Add -y to both sides)
x=−y+6
Substitute −y+6 for x in2x−3y=4: 2x−3y=4
2(−y+6)−3y=4
−5y+12=4 (Simplify both sides of the equation)
−5y+12+−12=4+−12 (Add -12 to both sides)
−5y=−8
−5y/−5=−8/−5 (Divide both sides by -5)
y=8/5
Substitute 8/5 for y in x=−y+6:
x=−y+6
x=−8/5 +6
x=22/5 (Simplify both sides of the equation)
Answer: x=22/5 and y=8/5
One weekend, a shop had 850 customers. 375 were men and the rest were women. What is the ratio of men to women customers in its simplest form?.
Answers
When there were 375 men and 475 women, the simple ratio of men to women clients was 15/19.
What is ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Here,
Total customers=850
Total number of men=375
Total number of women,
=850-375
=475
The ratio of men to women customers,
=375/475
Divide both terms by the GCF 25,
375 ÷ 25 = 15
475 ÷ 25 = 19
=15/19
The ratio of men to women customers in its simplest form is 15/19 when there were 375 men and 475 women.
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Sinx+1 =cos x
Hint: square both sides
Answers
Answer:
1 – cos²x = Sin²x
Step-by-step explanation:
Sinx + 1 = cos x
by squaring both sides
(Sinx + 1)² = (cos x )²
Sin²x + 1 = cos²x
1 – cos²x = Sin²x
i hope this helped
The length of a rectangle is 15 cm. What width will make the area at least 315 cm^2
Answers
Answer:
At least 16 cm
Step-by-step explanation:
315cm/15 = 16cm
9th grade math need help asp
Answers
Answer:
10
Step-by-step explanation:
look at where the 2 lines meet and then look at the minutes
Please help it's urgent!
part a) says write an equation and solve for x
Answers
Answer: look at explanation
Step-by-step explanation:
1. Since those are congruent you equal them to eachother: 6x-8=4x+2
2. Then you solve (steps are shown below)
a) 6x-8=4x+2
b) 2x-8=2
c) 2x=10
d) x=5
3. Answer should be x=5
hope this helps!
Find the length of AB.
8 m
80°
AB =[? ]m
Round your answer to the nearest hundredth.
Answers
Answer:11.17
Step-by-step explanation:
pi x D x angle /360
pi x 8x2x80/360
=11.170
A rectangular poter ha an area of 504 quare centimeter. The width of the poter 14 centimeter. How long i the poter? Write equation to how your work
Answers
Answer:
36 cm.
Step-by-step explanation:
In the question, we have been given ,
Area of the rectangle=504cm2
The width of the rectangle=14cm
The length of the rectangle=?
The formula for the area of the area of the rectangle is L×B. Thus A=L×B(W).
So 504cm2= L×14.
Now divide both sides by 14
504cm2/14=14L/14
Therefore L= 36cm
triangle A"B"C" is formed using the translation (x+1,y+1) and the dilation by a scale factor of 3 from the origin. Which equation explains the relationship between BC and B"C"
Answers
Answer:
the equation that explains the relationship between BC and B"C" is:
BC = 2 * B"C"
This equation states that the length of BC is equal to twice the length of B"C".
Step-by-step explanation:
If triangle A"B"C" is formed using the translation (x+1,y+1) and the dilation by a scale factor of 3 from the origin, then the coordinates of the vertices of triangle A"B"C" can be expressed as follows:
A" (x+1, y+1)
B" (3x+3, 3y+3)
C" (3x+6, 3y+6)
To find the equation that explains the relationship between BC and B"C", we can use the distance formula to find the length of both segments. The distance formula is:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the distance formula, we can find the length of BC as follows:
BC = √((3x - x)^2 + (3y - y)^2)
= √((2x)^2 + (2y)^2)
= √(4x^2 + 4y^2)
= 2√(x^2 + y^2)
We can also find the length of B"C" as follows:
B"C" = √((3x+6 - 3x-3)^2 + (3y+6 - 3y-3)^2)
= √((3)^2 + (3)^2)
= √(9 + 9)
= √(18)
= 3√(2)
How can you show that these two circles are similar?
Answers
well, similarity on circles is a phony business
in essence, all circles are similar by definition, I mean, hell they're all circular, what's so unsimilar about that?
however, the silly proof asks to translate it about and then dilate it to be superimposed on the other.
On Wednesday 28% of the customers who bought gas at a gas station made additional purchases. There were 300 customers who bought gas. How many of these 300 customers made additional purchases?
Answers
Answer:70 i think srry if its wrong
Step-by-step explanation:
Find the equation of the line in tandard form that pae through the point (1, -3) and (-2, -1)
Answers
The equation of line in standard form that pass through the point (1, -3) and (-2, -1) is (-2x/3)-y=7/3 where -2/3 is x-intercept and -1 is the y-intercept.
What does the straight line equation mean?A straight line's equation is given by y=mx+c, where c is the height at which the line intersects the y-axis (often referred to as the y-intercept) and m is the gradient.
Why is there an equation of a line?The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.
we are given with;
x1=1, y1=-3
x2=-2, y2=-1
equation of line in standard form:
Ax+By=C
so using formula:
(y−y1)=(y2−y1)(x−x1)/(x2−x1)
(y−(-3))=((-1)−(-3))(x-1)/(-2−1)
(y+3)=(2)(x−1)/(-3)
(y+3)=(2x−2)/(-3)
y+3=(-2x/3)+(2/3)
y=(-2x/3)+(2/3)-3
y=(-2x+2-9)/3
y=(-2x-7)/3
(2x/3)+y=-7/3
rearranging;
(-2x/3)-y=7/3
This is our required answer.
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1. Which expression is equivalent to 10x – 5 + 8x - 7?
Answers
Answer: 18x-12
Step-by-step explanation:
Add 10x +8x (because they both have x at the end so its fine to add them
then do -5-7= -12
-35+12=
Could someone help me pls
Answers
Answer: -23
Step-by-step explanation:
When you're adding to a negative the negative number decreases, so if you're adding 12 from negative 35, you're taking away 12 negative numbers, hence why the answer is -23
hope that helped :)
If you flip a coin 300 times,how many times would you expect it to land on tails (same question for heads) Heads Frequency:35 Tails frequency:65
Answers
I flip a coin 300 times.
So the possibility of head :
The formula for probability is
Probability=
\frac{number of total events}{number of favorable events}
From the given data in the question,
The coin is tossed total 300 times,
We got head 35 times in 300 times,
So the probability of getting a head is =
[tex] \frac{300}{35} [/tex]
Same do as Tails