Which congruence theorems can be used to prove △EFG ≅ △JHG? Check all that apply.
HL
SAS
SSS
ASA
AAS
Answers
Answer:
ASA and AAS
Step-by-step explanation:
We do not know if these are right triangles; therefore we cannot use HL to prove congruence.
We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.
We are given that EF is parallel to HJ. This makes EJ a transversal. This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent. We also know that ∠EGF and ∠HGJ are vertical angles and are congruent. This gives us two angles and a non-included side, which is the AAS congruence theorem.
Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent. Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.
Answer: ASA and AAS
Step-by-step explanation:
Related Questions
The length of a rectangle is twice the width. the perimeter is 32 cm more than the width. find the dimensions of the rectangle.
Answers
Length: 2x
Perimeter=2x+2x+x+x=6x
32 cm more than width means x+32
6x=x+32
5x=32
x=6.4
Dimension is 6.4×12.8 (width×length)
The dimensions of the rectangle are 6.4 and 12.8 respectively.
What is the perimeter of the rectangle?The formula for calculating the perimeter of a rectangle is given by :
P = 2 ( L + w )
The length of a rectangle is twice the width. And the perimeter is 32 cm more than the width.
L = 2w
Now substituting into the formula , we have
Width: x
Length: 2x
Perimeter P = 2 ( L + w ) = 2(3x) = 6x
Since 32 cm more than width means x+32
6x = x + 32
5x = 32
x = 6.4
Hence, Dimension is 6.4 × 12.8.
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What is solution to the system of equations? Y=5×+2 3×=-y+10
Answers
3x = y + 10
3x = y + 10
3x = 5x + 2 + 10
3x = 5x + 12
3x - 5x = 12
-2x = 12
x = -6
substitute x = -6 into y = 5x + 2
y = 5(-6) + 2
y = -30 + 2
y = -28
x = -6, y = -28
hope this helped, God bless!
Which phrase describes an unknown or changeable quantity?
Answers
If each password must contain at least one upper-case letter, one lower case letter and one number, how many passwords are there? unanswered
Answers
So it will be 26x26x10=6,760
A cotton candy vendor has 11 cones of blue cotton candy to sell. if the blue cotton candy is 25% of the total number of cones, how many total cotton candy cones does he have
Answers
11*4=44
The total number of cotton candy cones is 44.
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The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Check all that apply. $8 $9 $11 $13 $14 $15
Answers
x > = 14...this is saying the hourly wage is 14 and above
so possible values are : 8,14,15 <==
we have
[tex]x<9[/tex] ------> inequality A
The solution of the inequality A is the interval--------> (-∞,9)
All real numbers less than [tex]9[/tex]
[tex]x\geq14[/tex] -----> inequality B
The solution of the inequality B is the interval--------> [14,∞)
All real numbers greater than or equal to [tex]14[/tex]
The solution Inequality A or Inequality B is equal to
Solution A+Solution B
(-∞,9)U[14,∞)
The solution of the compound system of inequalities must satisfy inequality A or inequality B
we're going to verify every case
case A) [tex]\$8[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]8<9[/tex] -------> is true
Therefore
[tex]\$8[/tex] is a possible value for x
You don't need to check for inequality B
case B) [tex]\$9[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]9<9[/tex] -------> is not true
Verify inequality B
[tex]9\geq14[/tex] ------> is not true
Therefore
[tex]\$9[/tex] is not a possible value for x
case C) [tex]\$11[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]11<9[/tex] -------> is not true
Verify inequality B
[tex]11\geq14[/tex] ------> is not true
Therefore
[tex]\$11[/tex] is not a possible value for x
case D) [tex]\$13[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]13<9[/tex] -------> is not true
Verify inequality B
[tex]13\geq14[/tex] ------> is not true
Therefore
[tex]\$13[/tex] is not a possible value for x
case E) [tex]\$14[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]14<9[/tex] -------> is not true
Verify inequality B
[tex]14\geq14[/tex] ------> is true
Therefore
[tex]\$14[/tex] is a possible value for x
case F) [tex]\$15[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]15<9[/tex] -------> is not true
Verify inequality B
[tex]15\geq14[/tex] ------> is true
Therefore
[tex]\$15[/tex] is a possible value for x
therefore
the answer is
[tex]\$8[/tex]
[tex]\$14[/tex]
[tex]\$15[/tex]
is 2x-5y=10 a function ------is it linear or nonlinear?
Answers
It is linear when 2x- 5y = 10. A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 Or 1.
How can we tell whether a function is linear or not?Looking at a function’s graph will reveal if it is linear or not with the greatest ease. When a linear function is plotted on a graph, a straight line is formed.
A nonlinear function Is curved in some way; it does not form a straight line.
How is a function defined as linear?The graph of a linear function is a straight line. One independent variable and one dependent variable make up a linear function.
X and Y are the independent and dependent variables, respectively. The constant term, or a, is the y-intercept.
Is a function 2x-5y=10 real? Is it nonlinear or linear?Given that a linear equation is an equation of a straight line, its degree must be either 0 or 1.
For every one of its elements. In this instance, both the degree of the variables Y and X is 1.
Resolve the Y equation.
2x-5y=10
Y=-2+2x/5
Hence Given that a linear equation is an equation of a straight line, its degree must be either 0 or 1. For every one of its elements. The degree of the variable Y in this instance is 1, while the degree of the variable X is linear at 1.
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Write each mixed number as an improper fraction. 1 7/8 1 7/12 2 1/2 NEED BRAINLIEST!!!
Answers
Given that the rectangle above has a perimeter of 34 units, find . round the answer to the nearest hundredth.
Answers
NEED HELP! Thanks!
Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 70 mph and the other train travels at 80 mph.
How much time passes until the trains are 600 mi apart?
Enter your answer in the box.
Answers
How many 1-cm squares would it take to construct a square that is 3 m on each side?
Answers
A science museum charges an admission fee of $10 per adult and $6 per child. If the museum had 2,000 visitors on a particular day and the total collection was $18,800, how many adults and children visited the museum?
Answers
c = child
10a + 6c = 18,800
a + c = 2,000
In the second equation, subtract c from both sides.
a = 2000 - c
Put this into the first equation.
10(2000 - c) + 6c = 18800
Multiply everything in the parenthesis by 10.
20,000 - 10c + 6c = 18,800
Combine like terms.
20,000 - 4c = 18,800
Subtract 20,000 from both sides.
-4c = -1,200
Divide -4 on both sides.
c = 300
Put this into the second equation.
a + 300 = 2,000
Subtract 300 from both sides.
a = 1,700
Hope this helps!
∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 . What is the value of x? Enter your answer in the box.
Answers
5x+10=7x-12
10=2x-12
22=2x
11=x
What are the x and y-intercepts of the line described by the equation?
3x−9y=10.8
Enter your answers, in decimal form, in the boxes.
x-intercept =
y-intercept =
Answers
3x - 9y = 10.8
3x - 9(0) = 10.8
3x = 10.8
x = 10.8/3
x = 3.6 or (3.6,0) <== ur x int
to find the y int, sub in 0 for x and solve for y
3x - 9y = 10.8
3(0) - 9y = 10.8
-9y = 10.8
y = -10.8/9
y = - 1.2 or (0,-1.2) <== ur y int
The x-intercept and the y-intercept of the line described by the equation 3x - 9y = 10.8 are 3.6 and -1.2
The x-intercept of a line is the point where y-coordinate is zero while the y-intercept of the line is the point where the x-coordinate is zero
Given the expression 3x - 9y = 10.8
Get the x-intercept. If y = 0
3x - 9(0) = 10.8
3x = 10.8
x = 10.8/3
x = 3.6
Get the y-intercept. If x = 0
3(0) - 9y = 10.8
-9y = 10.8
y = -10.8/9
y = -1.2
Hence the x-intercept and the y-intercept of the line described by the equation 3x - 9y = 10.8 are 3.6 and -1.2
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Jason has 75 feet of wallpaper border. He wants to put up a wallpaper border around his rectangular bedroom that measures 12 feet by 14 feet. He multiplies 12 x 14 = 168 to get an exact answer of how much border he needs. He concludes that he does not have enough border for the whole job.
1. Tell how you can critique Jason’s reasoning.
2. Critique Jason’s reasoning
3. Jason uses an overestimate to decide how many rolls of wallpaper he needs for another’s room. Explain why his reasoning to use an overestimate does or does not make sense
Answers
the tape is 75 feet long
the bedroom is 12 feet by 14 feet.
1. Tell how you can critique Jason’s reasoning.
If you want to Critique Jason's reasoning, you could a) ask yourself the same questions that Jason did and see if you would come with the same answers and used the same analysis or b) analyse Jason's answer to see if he did a mistake or missed an important detail and made a thought mistake
2. Critique Jason’s reasoning
I will use the option b from above:
?
Jason first multiplied 12 x 14 = 168. This multiplication is correct, but what did he get? He needed to get the perimeter of the bedroom because it was only the wallpaper border, not the wallpaper itself - so getting the perimeter was needed, but this we get by the formula ( 2* *(length+width), not length* width - as Jason did.
So Jason made a mistake here! his actual answer should be 2*(12+14)=2*26=52, so the tape of 75 feet would have been enough!
3. Jason uses an overestimate to decide how many rolls of wallpaper he needs for another’s room. Explain why his reasoning to use an overestimate does or does not make sense
Using an overestimate is often a good idea- in case some of the tape gets damaged, he will have some left. However, since his calculations are wrong by a lot (he multiplies rather than adds and multiplies by 2), his overestimate will be a lot higher than would be practical - he would be left with a lot of leftovers and spend too much money. So his reasoning does not make sense
Alison wants to construct the perpendicular bisector of MN¯¯¯¯¯¯¯. What should Alison do for her first step? A.) Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is equal to 1/2MN . B.) Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is greater than 1/2MN. C.) Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is less than 1/2MN. D.) Use the straightedge to draw a line that intersects MN¯¯¯¯¯¯¯ at a point between M and N.
Answers
Answer:
Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is greater than 1/2MN.
Step-by-step explanation:
The site told me that correct answer was B., so it was greater than.
Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.
What is the length of one of the diagonals of the rectangle?
Enter an expression in the box for the length of the diagonal.
Answers
d(S,P) = √b^2
d(S,P) = b
so
SP = b
d(P, Q) = √(a-0)^2 + √(b-b)^2
d(P, Q) = √a^2
d(P, Q) = a
so
PQ = a
SQ = c^2 = a^2 + b^2
SQ = √(a^2 + b^2)
answer
the length of one of the diagonals of the rectangle is √(a^2 + b^2)
The length of a line with known end point coordinates is given by Pythagoras's theorem
The expression for the length of the diagonal [tex]\overline{PR}[/tex], is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]
The expression for the length of the diagonal [tex]\overline{QS}[/tex], is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]
Reason:
The given coordinates of the vertices are; P(0, b), Q(a, b), R(a, 0), and S(0, 0)
Diagonals of the rectangle are segments; [tex]\overline{PR}[/tex], and [tex]\overline{QS}[/tex]The lengths of the diagonals are given by the equation for finding the length, l, of a line given the coordinates which is [tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where:
(x₁, y₁) = P(0, b), and (x₂, y₂) = R(a, 0), we get;
[tex]Length \ of \ diagonal \ segment \ \overline{PR} = \sqrt{\left (0-b \right )^{2}+\left (a-0 \right )^{2}} = \sqrt{b^2 + a^2}[/tex]Where:
(x₁, y₁) = Q(a, b), and (x₂, y₂) = S(0, 0), we get;
[tex]Length \ of \ diagonal \ segment \ \overline{QS} = \sqrt{\left (0-b \right )^{2}+\left (0-a \right )^{2}} = \sqrt{b^2 + a^2}[/tex]Therefore,
The expression for the length of the diagonal is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]Learn more here:
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In how many games did the team score at least 70 points?
Answers
Answer: the answer is 5
Step-by-step explanation:
b
The equation of line m is 4x+5y=−2. What is the slope of a line that is perpendicular to line m?
Answers
4x + 5y = -2
5y = - 4x - 2
y = -4/5 x - 2/5
the slope of this line is -4/5 and slope of line perpendicular to it is - 1 / -4/5
= 5/4 answer
The required slope of a line will be 5/4 which is perpendicular to line m.
What are the perpendicular lines?Perpendicular lines are two lines that cross one other and create a 90-degree angle. Two lines are perpendicular if the product of their slopes is -1.
The equation of line m is given in the question below as:
⇒ 4x + 5y = −2
We have to determine the slope of a line that is perpendicular to line m
First, we need to find the slope of line m
To convert to slope-intercept form
⇒ 4x + 5y = -2
⇒ 5y = - 4x - 2
⇒ y = -4/5 x - 2/5
So the slope of this line is -4/5 and the slope of a line perpendicular to it is
⇒ - 1 / (-4/5)
Reciprocal the terms in the numerator,
⇒ 5/4
Therefore, the required slope of a line will be 5/4 which is perpendicular to line m.
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Students in a science class are divided into 6 equal groups with at least 4 students in each group for a project. write and solve an inequality that represents the number of students in the class
Answers
There are a total of 6 groups.
And each group contains at least 4 students.
So the minimum number of students is:
minimum = 6 * 4 = 24 students
Let us say that x represents the number of students, hence:
x ≥ 24
To represent the number of students in the class, we can write the inequality 24 ≤ x.
Explanation:To represent the number of students in the class, let's assume that the total number of students in the class is represented by the variable 'x'. Since the students are divided into 6 equal groups and each group has at least 4 students, we can write the inequality:
6 * 4 ≤ x
Simplifying the inequality:
24 ≤ x
This inequality represents that the total number of students in the class should be greater than or equal to 24.
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How many ways can i distribute 3 slices of pizza to 3 people of fairness doesn't matter?
Answers
Which expression is equivalent to 3x(1.05)?
A: 3x + 3x + 3x
B: 1.05x + 1.05x + 1.05x
C: x + 3.15
D: 1.05x + 3
Answers
answer
B: 1.05x + 1.05x + 1.05x
What does .9999 rounded to the thousandths?
Answers
hope this helps
tom can wash 44 plates in 3 minutes. how many seconds will it take him to wash 12 wash? show your work.
Answers
Raise to the power:
(–0.2xy)4
Answers
-0.0016 x^4 y^4. The ^ symbols just mean that it’s to the power of four. x^4 = x to the power of four.
Does the graph represent the function?
Answers
Find the axis of symmetry for this parabola : y= 2(x-7)(x+9)
Answers
y = 2x - 14x (x +9)
y = 2x^2 +18x -14x^2 + 126x
y = -12x^2 +144x
axis of symmetry = -b / 2a
= -144 / 2*-12
= 6
axis of symmetry x = 6
Economists study the way society uses its resources. One important resource studied is agriculture. The recent increase in demand for organic produce has created some interesting economic scenarios for both farmers and consumers. Click the link to learn key facts about the economics of organic produce and answer a few questions. Which is a reason that organic farming is more expensive than conventional farming? How many years must a farm be run organically before its produce can be labeled as “organic”? Why do most small organic farms pay a higher percentage of their profit for farming equipment than conventional farms?
Answers
Answer:
Which is a reason that organic farming is more expensive than conventional farming?
Organic farmers must pay for a costly certification process
How many years must a farm be run organically before its produce can be labeled as “organic”?
3
What is a benefit of crop rotation?
Rotating crops can help build healthy soil.
Step-by-step explanation:
Just took the test!
Answer:
Economists study the way society uses its resources. One important resource studied is agriculture. The recent increase in demand for organic produce has created some interesting economic scenarios for both farmers and consumers. Click the article to learn key facts about the economics of organic produce and answer a few questions.
Which is a reason that organic farming is more expensive than conventional farming?
✔ Organic farmers must pay for a costly certification process.
How many years must a farm be run organically before its produce can be labeled as “organic”?
✔ 3
What is a benefit of crop rotation?
✔ Rotating crops can help build healthy soil.
Step-by-step explanation:
just got it on edge
How do i graph y= 2x
Answers
what is the advantage of multiplying both sides of the equation by the least common multiple of the denominators in the first step?