Help Please? GEOMETRY Use the word bank to help you with possible answers (there are extra options that are not to be used)
Word Bank:
definition of a midpoint
triangle RSX is congruent to triangle RXT
Definition of right angles
right angles are congruent
CPCTC
Reflexive property
Answers
Answer for part A: Definition of perpendicular
Answer for part B: Right Angle Congruence Theorem
Answer for part C: Reflexive Property of Congruence
Answer for part D: Definition of Midpoint
Answer for part E: [tex]\triangle SXR \cong \triangle TXR[/tex]
Answer for part F: CPCTC
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Explanations:
Part A:
We are given that [tex]\overline{RX} \perp \overline{ST}[/tex] which means, in english, "line segment RX is perpendicular to line segment ST"
By the very definition of perpendicular, this means that the two line segments form a right angle. This is visually shown as the red square angle marker for angle RXT. Angle RXS is also a right angle as well.
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Part B:
The Right Angle Congruence Theorem (aka Right Angle Theorem) is the idea that if we have two right angles, then we know that they are both 90 degrees so they must be congruent to one another.
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Part C:
Any line segment is congruent to itself. This is because any line segment will have the same length as itself. It seems silly to even mention something so trivial but it helps establish what we need for the proof.
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Part D:
We are given "X is the midpoint of segment ST" so by definition, X is in the very exact middle of ST. Midpoints cut segments exactly in half. SX is one half while TX is the other half. The two halves are congruent which is why SX = TX
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Part E:
Writing [tex]\triangle SXR \cong \triangle TXR[/tex] means "triangle SXR is congruent to triangle TXR". These two triangles are the smaller triangles that form when you draw in segment RX
Side Note: SAS stands for "side angle side". The angle must be between the two sides. The pairing RX and RX forms one of the 'S' letters (see part C), while the pairing SX and TX forms the other 'S' (see part D). The angles between the sides are RXS and RXT (see part B).
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Part F:
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"
It means that if we have two congruent triangles, then the corresponding parts are congruent. Back in part E, we proved the triangles congruent. For this part, we look at the pieces RS and RT (which correspond to one another; they are the hypotenuse of each triangle). They are proven congruent by CPCTC
If CPCTC is an odd concept to think about, then try thinking about something like this: you have two houses which are completely identical in every way. We can say that those two houses are congruent. If the houses are identical, then surely every piece that makes up the house is identical to its corresponding piece to the other house. For example, the front door to each house is both the same size, shape, color, made of the same material, designed in the same pattern, etc. So the two doors are congruent as well.
Related Questions
Andrew lives 1.7 kilometers from soccer field. He rode his bike 0.9 of the distance to the field. How much farther does Andrew need to ride to reach the soccer field. Include an area model in your answer.
Answers
10% of 1.7 km is 0.17 km
Hope this helps!
Which state's ratification guaranteed the constitution's approval?
Answers
After a 90% reduction, you purchase a new soft drink machine on sale for 72$. What was the original price of the soft drink machine?
Answers
Original price = Sale price/(1 - percentage reduction)
$72/(1-.90) = $720
So, the original price for the drink machine was $720.
Find the percent of each number 350% of 96
Answers
Steven recorded the growth of a plant over 10 weeks for his science project. He made a graph that shows how much the plant grew each week. The plant was 2 in. tall when Steven started his project. At week 5, the plant was 8 in. tall.
Which equation represents Steven’s situation, where x is the number of weeks and y is the height of the plant?
A. y= 8/5x+2
B. y= 6/5x+2
C. y= 5/8x+2
D. y= 5/6x+2
Answers
If you substitute the points (5,8) you get:
8 = 6/5 × 5 + 2
8 = 6 + 2
Answer:
Answer is option B.
Step-by-step explanation:
Given information:
Assume the growth of plant is linear
When Steven started his project [tex](x_1=0)[/tex] , growth of plant is[tex](y_1=2 \rm in)[/tex]
At week 5,[tex](x_2=5)[/tex], growth of plant is [tex](y_2=8 \rm in)[/tex]
We know, equation of line is,
[tex](y-y_1)=m\times (x-x_1)[/tex],where [tex]m[/tex] is the slope of equation
[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{8-2}{5-0}=\frac{6}{5}[/tex]
On substituting [tex]m[/tex],
[tex](y-2)=\frac{6}{5}\times (x-0)[/tex]
[tex]y=\frac{6}{5}x +2[/tex]
So, answer is option B.
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probabiltiy can be used to determine the likelihood of specific ---------------- ( a:games,b:occurrences,c:questions,d:opportunities
Answers
6 times the sum of 12 and 8
Answers
12 + 8 = 20
6 × 20 = 120
6 × (12 + 8) = 120
What is the solution to the inequality 2(x + 3) ≥ –10 – 4x? solve step by step, please.
Answers
Here are the steps:
2(x + 3) ≥ –10 – 4x
=2x+6≥-10-4x
=2x+6-6≥-10-4x-6
=2x≥-4x-16
=2x+4x≥-4x-16+4x
=6x≥-16
=6x/6≥16/6
=x=-8/3
Help now get lots of points
Answers
-2/3x + y = 3
2x - 3y = -9
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6 - y = -5x + 8
5x - y = 8 - 6
5x - y = 2
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y - 3 = 4(x - 3)
y - 3 = 4x - 12
y = 4x - 12 + 3
y = 4x - 9
-4x + y = -9
4x - y = 9
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-7/6x + 1 = y
-7/6x - y = -1
7x + 6y = 6
Answer:
A. y = 2/3x + 3 --> 2x - 3y = -9
B. 6 - y = -5x + 8 --> 5x - y = 2
C. y - 3 = 4(x - 3) --> 4x - 9 = y
D. -7/6x + 1 = y --> 7x + 6y = 6
math question down below
Answers
To do this you flip the second fraction (3/1) around and you multiply:
3/1 = 1/3
- 4*1/5*3 = - 4/15
This means he went - 4/15 miles down,
Hope this helps! :)
What is the procedure for multiplying by a one digit number?
Answers
You and your friends decide to take a survey to try to convince mall managers to add a new store. You split up to survey parts A, B, and C of the mall. If you survey part B what percent of the will you survey
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Write a real-word problem where you have to multiply 120 and 75.
Please help best answer will be marked as braniiest
Answers
He makes $120 a day and Bob needs to make a certain amount of money to pay his bills at the end of three months. Bob has to pay $8675 for his bills. If Bob worked 75 days, does he have enough to pay his bills?
(answer)
Yes.
(work)
120 x 75 = 9000
9000-8675
I hope this helped!
In a cinema with 120 rows and 75 seats in each row, we can find the total number of seats by multiplying these two numbers together. This results in 9000 total seats.
Explanation:The subject of this question is related to a real-world mathematical problem. Suppose there is a cinema having 120 rows and each row consists of 75 seats. We want to find out the total number of seats in the cinema hall.
To solve this, we need to use multiplication. In mathematics, multiplication is one of the four elementary mathematical operations, with the other three being addition, subtraction, and division. By multiplying 120 (the number of rows) with 75 (the number of seats in each row), you can find out the total number of seats in the cinema hall.
So, 120 * 75 = 9000. Hence, there are 9000 seats in the cinema.
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what is the simplest form of 12/18
Answers
Hope this helps
Let's look at the fraction 12/18. What greatest common factor do they both share? They both share factors of 1, 2, 3, and 6. The GCF is 6.
So we'll divide the fraction by 6. 12 ÷ 6 is 2, and 18 ÷ 6 is 3.
The simplest form of 12/18 is 2/3.
Hope this helps.
May
There are 16,925 bottles of red paint packed in a box. There are 21,775 bottles of blue paint packed in another box.
How many more bottles of blue paint than red paint are there?
(insert something here) more bottles
Answers
21775-16925=4850
Yep. Go do some studying, it might help you. Also, this isn't middle school math, please post it under the relative category (that being kindergarten).
How many times greater is 7,000 than 70
Answers
To find out how many times greater 7,000 is than 70, one needs to perform a division operation. In this case, it would be 7,000 divided by 70 which equals 100. Hence, 7,000 is 100 times greater than 70.
Explanation:To determine how many times greater 7,000 is than 70, one must use division. This is done by dividing 7,000 by 70. The equation would look like this: 7,000 ÷ 70. If you solve the equation, the answer is 100. Therefore, 7,000 is 100 times greater than 70.
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sophie is trying to see how thick her pile of paper is. She has 50 pieces of paper that are each 4.5×10^-4. How thick is the whole stack?
Answers
50x4.5x10^-4
=225x10^-4
Move decimal two times to the left
=2.25x10^-2
A blue print for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building?
Answers
3 inches = (3 * 10) = 30 ft long <==
5.5 inches = (5.5 * 10) = 55 ft wide <==
Answer:
Length= 30 feet, breadth = 55 feet.
Step-by-step explanation:
Length of building in blue print= 3 inches
Breadth of building in blue print= 5.5 inches
It is given that 1 inch on the blue print is equivalent to 10 feet in actual building
We have to convert the dimensions
So Length of building in blue print in feet= 3 inches= 3×10=30 feet
Breadth of building in blue print in feet= 5.5 inches= 5.5×10= 55 feet
Hence the correct answer is Length= 30 feet, breadth = 55 feet.
The slope-intercept form of the equation of a line that passes through point (–3, 8) is y = –x + 6. What is the point-slope form of the equation for this line?
y – 3 = –(x + 8)y + 3 = –(x – 8)y + 8 = –(x – 3)y – 8 = –(x + 3)
Answers
Answer:
Option 4 - [tex]y-8=-(x+3)[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of a line that passes through point (–3, 8) is [tex]y =-x+ 6[/tex].
The general form of slope intercept is [tex]y=mx+c[/tex]
where, m is the slope and c is the y-intercept.
On comparing,
m=-1 and c=6
The point slope form of the equation of a straight line is
[tex]y-y_1=m(x-x_1)[/tex]
Point is [tex](x_1,y_1)=(-3,8)[/tex]
Substitute the values,
[tex]y-8=-1(x-(-3))[/tex]
[tex]y-8=-(x+3)[/tex]
The point-slope form of the equation for this line is [tex]y-8=-(x+3)[/tex]
Therefore, Option 4 is correct.
i need some help with solving inequalitys 9x-9 greater thab or equal to 2(8x-15)
Answers
help with geometry please
Answers
Add 3 to both sides to get 2x=x+7.
Subtract x from both sides to get x=7.
To set up the equation, you would do: 2x - 3 = x + 4.
Let's add 3 from the left side to the right, it would then be: 2x = x + 7.
We then want that "x" from the right side to be with the "2x", so we will subtract "x" from the right to cancel it out, and then we will subtract "x" to other side too.
After you do that, the equation should be: x=7. This is the final answer. Hope this helps!
May
Carmen has 18 connecting cubes. She wants to model a house shaped like a rectangle. If the model has a height of one connecting cube, how many different ways can Carmen model the house using all 18 connecting cubes?
Answers
To determine the number of ways Carmen can model the house using all 18 connecting cubes, considering them as distinguishable objects and applying permutations is essential.
Explanation:Carmen has 18 connecting cubes and wants to model a house shaped like a rectangle with a height of one connecting cube. To find the number of ways to model the house using all 18 cubes, we can approach it using combinatorics. One way to visualize this is by considering the cubes as distinguishable objects and applying permutations.
One approach could involve fixing the base of the rectangle, which will have a length of 16 cubes, leaving 2 cubes for the width. The 2 remaining cubes can be placed in 2! = 2 ways. So, the total number of ways to model the house would be 16!×2.
Answer:
There are 3 ways.
Step-by-step explanation:
Let each cube be 1 cm on the side.
The volume of each cube is 1 cm³.
volume = length × width × height
We are told the height is 1.
The volume is 18 cubes, so volume = 18 cm³.
length × width × height = 18 cm³
length × width × 1 cm = 18 cm³
length × width = 18 cm³
There are 3 ways to factor 18 into integer factors:
1, 18
2, 9
3, 6
Carmen can make the model 18 cubes long by 1 cube wide,
or 9 cubes long by 2 cubes wide, or 6 cubes long by 3 cubes wide.
Answer: There are 3 ways.
when is the diffrence of two decimals an interger
Answers
Answer:
The diffrence is that 2 placed decimals are not a whole number being contained into an equation/expression.
Step-by-step explanation:
12.45 - 7.33 = 5.12
12-7=5
Please Hurry!!
6 x 10^4 is how many times greater than 3 x 10^-5
A 2 × 10^9
B 4 × 10^−1
C 4 × 10^1
D 2 × 10^−9
Answers
10^4/10^-5 = 10^9
so it's 2 x 10^9
answer
A 2 × 10^9
Simplify negative 2 over 3 ÷ negative 7 over 4.
a. negative 7 over 6
b. negative 8 over 21
c. 8 over 21
d. 7 over 6
Answers
Answer:
B 8/21
Step-by-step explanation:
the volume of 10 000 drops of liquid is 1 fluid ounce. what is the volume of 1000
Answers
JAYDEN HELP PLZ !!!!!!Select from the drop-down menu to correctly complete the statement about the given figures.
Triangles ABC and DEF are Similar or not similar
Answers
Answer:
hello can you give the other person brainliest
Step-by-step explanation:
Relationship A has a lesser rate than Relationship B. This table represents Relationship B.
Hours worked 2 4 5 8
Amount paid ($) 36.50 73 91.25 146
Which equation could represent Relationship A?
Hours worked is represented by x and Amount paid is represented by y.
Select each correct answer.
y = 18.1x
y = 18.6x
y = 18.3x
y = 18x
Answers
Answer:
y = 18.1x ; and y = 18x
Explanation:
The rate of change in Relationship B can be found by using the formula for slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the first two points, we have
[tex]m=\frac{73-36.50}{4-2}=\frac{36.50}{2}=18.25[/tex]
We know that Relationship A has a lesser rate than this. The choices given for Relationship A are written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept (in this case b = 0).
The slope of the first equation is 18.1; this is less than 18.25.
The slope of the second equation is 18.6; this is greater than 18.25.
The slope of the third equation is 18.3; this is greater than 18.25.
The slope of the fourth equation is 18; this is less than 18.25.
Answer:
Option A and D.
Step-by-step explanation:
If a linear function passes through two points, then the rate of change is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given table it is clear that the Relationship B have two ordered pairs (2,36.50) and (4,73). So, the rate of Relationship B is
[tex]m=\dfrac{73-36.50}{4-2}[/tex]
[tex]m=\dfrac{36.50}{2}[/tex]
[tex]m=18.25[/tex]
The rate of relation B is 18.25.
Let hours worked is represented by x and amount paid is represented by y. So the Relationship B is defined as
[tex]y=kx[/tex]
Where, k is the rate of relationship A.
It is given that Relationship A has a lesser rate than Relationship B.
[tex]k<18.25[/tex]
We know that
[tex]18.1<18.25[/tex], [tex]18.6>18.25[/tex], [tex]18.3>18.25[/tex] and [tex]18<18.25[/tex].
The relationship A could be
[tex]y=18.1x[/tex] and [tex]y=18x[/tex]
Therefore, the correct options are A and D.
in order for terms to be like terms they must have?
Answers
Roscoe rides his bike at least 10 miles but not more than 30 miles. He rides at an average rate of 10.5 miles per hour. The amount of time it takes for Roscoe to ride his bike m miles is represented by a function. t(m) = m/10.5 What is the practical domain of the function?
Answers
Answer:
all real numbers from 10 to 30, inclusive
Step-by-step explanation:
The practical domain of function is , Roscoe can ride his bike only from 10 miles to 30 miles.
Domain of function is defined as the set of input values for which the function is defined i.e. the set of its possible inputs,
The amount of time it takes for Roscoe to ride his bike m miles is represented by a function.
[tex]t(m) = m/10.5[/tex]
Where m represent, number of miles he can ride.
Above function is defined for every value of m . But in question it is mention that Roscoe rides his bike at least 10 miles but not more than 30 miles.
Therefore, Domain of function is from 10 miles to 30 miles.
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