Consider the diagram.
Triangles B A E and C A D are connected at point A. Angle B A E is a right angle. Sides B A and A C are congruent. Sides B E and C D are congruent.
The congruence theorem that can be used to prove △BAE ≅ △CAD is
SSS.
ASA.
SAS.
HL.
Answers
The congruence theorem that proves that △BAE ≅ △CAD is: HL.
What is the HL Congruence Theorem?The HL congruence theorem states that, if the hypotenuse and one leg of a right triangle is congruent to the hypotenuse and a corresponding leg of another right triangle, then they are congruent triangles.
△BAE and △CAD have:
Congruent hypotenuses: BE ≅ CD.
Congruent legs: BA ≅ CA
Therefore, the congruence theorem that proves they are congruent is: HL.
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Answer: Option 4 or D. HL
Step-by-step explanation:
Related Questions
Select the correct answer.
The product of two numbers is 21. If the first number is-3, which equation represents this situation and what is the second number?
OA The equation that represents this situation is x-3=21. The second number is 24.
OB. The equation that represents this situation is 3x=21. The second number is 7.
OC. The equation that represents this situation is-3x=21. The second number is-7.
OD. The equation that represents this situation is -3+x=21. The second number is 18.
Answers
Option B is correct
Why
3x=21
3(7) =21
21=21
Step-by-step explanation:
Answer:
[tex]-3x=21 , -7[/tex]
Step-by-step explanation:
[tex]-3x=21\\x=\frac{21}{-3} =-7[/tex]
Casey was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:
−8, which represents the depth of water in the swimming pool
+7, which represents the height of the slide at the pool
Part A: What does 0 represent in this situation? (3 points)
Part B: Describe the height of the slide in relation to 0 in the situation. (3 points)
Part C: Casey held a pole in the swimming pool. The bottom of the pole was at a depth of 2 feet. How should Casey mark the level of the bottom of the pole on the number line? Explain how you determined this. (4 points)
Answers
The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that −8 represents the depth of water in the swimming pool. Hence:
The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.
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A company earns a profit of $100 the first month it is in business. Every month after that, the company earns a profit that is 1.5 times the previous month's profit. What will the company's profit be in the fith month?
Answers
The company's profit in fifth month will be $506.25
Profit : The gain in an expenditure, that is when the return is higher than the original amount, then the gained extra amount is called profit.
Example : If someone sell a toy of $10 in $15, then he gained profit & his profit is $(15-10) = $5.
A company earns a profit of $100 the first month it is in business.
Every month after that, the company earns a profit that is 1.5 times the previous month's profit.
In 1st Month,
Profit = $100
In 2nd Month,
Profit = 1.5 times of profit of 1st month
= 1.5 × $100
= $150
In 3rd Month,
Profit = 1.5 times of the profit of 2nd month
= 1.5 × $150
= $225
In 4th Month,
Profit = 1.5 times of the profit of 3rd month
= 1.5 × $225
= $337.5
In 5th Month,
Profit = 1.5 times of the profit of 4th month
= 1.5 × $337.5
= $506.25
So, the profit of 5th month = $506.25
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A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points)
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answers
Considering the definition of an inequality and system of inequalities, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
System of inequalitiesA system of inequalities is made up of two or more inequalities.
The solution will be formed by the intersection of the half-planes of each of the inequalities, that is, it will be the enclosure that all the inequalities have in common. That is, the solution of the system is given by the region of the common plane of the half-planes that define each one of the inequalities.
System of inequality in this caseIn this case:
c represents child bikes.a represents adult bikes.Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. The company is able to have up to 120 hours of building time and 100 hours of testing time for a week.Then, the system of inequality is:
[tex]\left \{ {{4c+6a\leq 120} \atop {4c+4a\leq 100}} \right.[/tex]
On the other hand, the company can build 20 child bikes and 6 adult bikes in the week. So, checking the equations, for given c=20 and a=6:
4×20 + 6×6= 116 < 120
4×20 + 4×6= 104 >100
Finally, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."
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If x is inversely proportional to y, then as x decreases, y decreases.
Answers
Answer:
Yes
Step-by-step explanation:
Let's assume that x=1/y.
For y=1, x=1
For y=2, x=0.5
For y=4, x=0.25
And so on
Fill the empty slots by dragging tiles from the left to show the next step for solving the equation. Solve the two-step equation. -9x + 0.4 = 4
Which operation must be performed to move all the constants to the right side of the equation?
Answers
In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation.
What are the constant terms?In an equation, the constant terms are those terms that do not have any alphabet attached to them. In this case, 4 and 0.4 are constant terms.
In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation thus;
-9x + 0.4 - 0.4 = 4 - 0.4
-9x = 3.6
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A farmer has 45 horses and 20 cows.
(i) Write this as a ratio horses : cows.
Give your answer in its simplest form.
Answers
Answer: 9 : 4
Step-by-step explanation:
45 : 20
simplify
9 : 4
Find the midpoint of points A(10,-7) and B(6, 1) graphically.
Answers
Answer:
(8,-3)
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x^{1}+x^{2} }{2}, \frac{y^{1} +y^{2} }{{2} } )[/tex]
Plug in your numbers from the coordinates:
(10+6/2, -7+1/2)
(16/2, -6/2)
(8,-3)
The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the decision rule
Answers
Using the p-value method, the decision rule is:
|z| < 1.645: do not reject the null hypothesis.|z| > 1.645: reject the null hypothesis.What is the relation between the p-value and the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.If it is less, it is rejected.In this problem, we have a two-tailed test, as we are testing if the mean is different of a value. For a significance level of 0.1, the critical value of z(when a p-value of 0.1 is obtained) is of |z| = 1.645, hence the decision rule is:
|z| < 1.645: do not reject the null hypothesis.|z| > 1.645: reject the null hypothesis.More can be learned about p-values at https://brainly.com/question/13873630
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what is n divided by 2 plus five minus n
Answers
The Simplified algebraic expression for the statement "n divided by 2 plus five minus n" is given by 5-(n/2).
Algebraic Expression is a mathematical expression involving variables, Numbers, other mathematical quantities, and mathematical operations and combinations of them.
Here given statement is "n divided by 2 plus five minus n"
Now we have to write the above given statement as simplified algebraic expression.
"n divided by 2" is given by = n/2
then "n divided by 2 plus five" is given by = (n/2)+5
there after "n divided by 2 plus five minus n" is given by = (n/2)+5-n
Simplifying the total algebraic expression we get,
(n/2)+5-n = 5-{n-(n/2)} = 5-((2n-n)/2) = 5-(n/2)
Hence the suitable Simplified algebraic expression for the given statement is given by = 5-(n/2)
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The area and one side of a rectangle are given. Determine the missing dimension
Answers
The missing dimension is x + 4
How to determine the missing dimension?The given parameters are:
Area = 4x^2 + 13x - 12
Length = 4x - 3
The width is calculated using:
Width = Area/Length
This gives
Width = (4x^2 + 13x - 12)/(4x - 3)
Expand
Width = (4x^2 + 16x - 3x - 12)/(4x - 3)
Factorize
Width = (4x(x + 4) - 3(x + 4)/(4x - 3)
Factor out x + 4
Width = (4x - 3)(x + 4)/(4x - 3)
Cancel out the common factor
Width = x + 4
Hence, the missing dimension is x + 4
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If the zeros of a quadratic equation are 7 and - 4 , what would be the factors?
Answers
Answer:
(x - 7) , (x + 4)
Step-by-step explanation:
given the zeros of a quadratic equation x = a and x = b , then
the corresponding factors are (x - a) and (x - b)
here the zeros are x = 7 and x = - 4 then factors are
(x - 7) and (x - (- 4) ) , that is
(x - 7) and (x + 4)
The surface area of a rectangular prism is increased by a factor of 16.
By what factor is the volume of the figure increased?
04
08
O 32
O 64
Answers
Answer:
The volume of the prism increased by a factor of 64.
Step-by-step explanation:
Given that the original prism and the increased prism are similar, we have that the scale factor is:
Area ∝ (length of side) x (length of side)
If the area increases by a factor of 16, each side increases by a scale factor of √16 = 4. Regarding the volume:
Volume ∝ (length of side) x (length of side) x (length of side)
Thus the increase factor for the volume, in this case, is 4 x 4 x 4 = 64.
An article marked to give 120% profit originally cost $60. what is the marked price?
Answers
Reason
We know cost is $60
We know profit percent is 120%
So 60x 120% = $72 marked price
A shopkeeper had 3sacks of sugar each weighing a mass of 90kg.he repacked the sugar in 0.00025tonnes packets.how many packets did he obtain?
Answers
Answer:
1080.
Step-by-step explanation:
0.00025 tonnes = 0.00025 * 1000 = 0.25 kg.
Total number of packets
(3 *90) / 0.25
= 12*90
= 1080.
At a meeting attended by 23 people, the females exceeds the males by 7. how many males were there?
Answers
Number of males in the meet were 8.
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
Let the number of males be x.
∴ Number of females = x + 7
Total number of people attending meet = Number of male +
Number of females
23 = x + x + 7
23 = 2x + 7
16 = 2x
x = 8.
Thus number of males in the meet were 8.
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Suppose that $x$ is a multiple of 6 (not necessarily positive). If the square of $x$ is less than 200, how many possible values of $x$ are there
Answers
All multiple of 6 under 14 are: -12, -6, 0, 6, 12
How do we get 14 here:
√200= 14.142 (Round to thousandth place)
This is how many x we have found.
A multiple in math is the number you get when you multiply a certain number by using an integer. for example, multiples of 5 are: 10, 15, 20, 25, 30…, and so forth. Multiples of 7 are 14, 21, 28, 35, 42, 49…and many others.
In math, the meaning of a multiple is the product result of one number multiplied by another number. Here, 56 is a multiple of the integer 7. Here is an example of multiples: Fun facts. 0 is a multiple of every number as the product of 0 multiplied by any number is 0.
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An architect's sketch of plans for the front of a garage in the shape of pentagon is shown below. What is the approximate perimeter of the
front of the garage?
-8
-6 -4 -2
A. about 36 ft
B. about 21 ft
C. about 10 ft
D. about 77 ft
Answers
Using it's concept, it is found that the approximate perimeter of the front of the garage is:
A. about 36 ft.
What is the perimeter of a figure?The perimeter of a figure is given by the total length of it's boundary.
In this problem, we have that:
The bottom boundary has length of 10 units.The two lateral boundaries have lengths of 7 units.There are two top boundaries, which are the hypotenuses of a right triangle with legs 3 and 5, hence:[tex]t = \sqrt{3^2 + 5^2} = 5.83[/tex]
Hence the perimeter of the figure is:
P = 10 + 2 x 7 + 2 x 5.83 = 35.66.
Rounding, it is of about 36 ft, hence option A is correct.
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A survey of 150 people at a local high school about playing video games was conducted, and the results are posted in the table.
Play Video Games Do Not Play Video Games
Juniors 48 12
Seniors 45 25
Teachers 6 14
What is the probability of choosing a person at random who is a teacher and plays video games? Are these independent events?
The P(teacher and video games) = 4%; the two events are not independent.
The P(teacher and video games) = 4%; the two events are independent.
The P(teacher and video games) = 9%; the two events are not independent.
The P(teacher and video games) = 9%; the two events are independent.
Answers
The P(teacher and video games) = 4%; the two events are not independent.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
P(teacher and video games) = number of teachers who play video game / total number of respondents
6/150 = 0.04 = 4%
Independents events are events whose occurrence do not depend on each other. They are random events.
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Answer:
The P(junior and video games) = 32%; the two events are not independent.
Step-by-step explanation:
i got it right aswell
If 3x + 7 =22, what is the value of x
Answers
Answer:
x=5
Step-by-step explanation:
solution,
3x+7=22
or,3x=22-7
or,3x=15
or,x=15/3
:×=5
The value of x in the equation 3x + 7 = 22 is x = 5.
To find the value of x in the equation 3x + 7 = 22, we can solve for x as follows:
Subtract 7 from both sides of the equation:
3x + 7 - 7 = 22 - 7
3x = 15
Divide both sides of the equation by 3 to isolate x:
(3x)/3 = 15/3
x = 5
Therefore, the value of x in the equation 3x + 7 = 22 is x = 5.
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What is the length of the hypotenuse of right ΔDEF shown? A) √5041 B) √2545 C) √497 D) √1063
Answers
The length of the hypotenuse of right triangle ΔDEF is 50.44 units
How to find hypotenuse of a right triangle?The hypotenuse side can be found using Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenusea and b are the other legs.Therefore,
x² = 39² + 32²
x² = 1521 + 1024
x = √2545
x = 50.4479930225
x = 50.44
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A suitcase measures 24 inches long and the diagonal is 30 inches long. What is the area of material that is needed to cover one side of the suitcase
Answers
Answer:
706.858347
Step-by-step explanation:
Determine whether the stated conclusion is valid based on the given information. If not,
write invalid. In either case, explain your reasoning.
A. Given: If a point is the midpoint of a segment, then it divides the segment into two
congruent segments. R is the midpoint of QS
Conclusion: QR = RS.
Answers
Both the given statements are true. The figure is given below.
We need to determine whether the stated conclusion is valid based on the given information.
What is the midpoint of the line segment?In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. R is the midpoint of QS.
Conclusion: QR=RS.
Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. AB=BC
Conclusion: B divides AC into two congruent segments
Both the given statements are true. The figure is given below.
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Triangles F G H and F J H share common side F H. Sides F G and G H are congruent. Sides F J and J H are congruent.
Which explains whether ΔFGH is congruent to ΔFJH?
They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
They are congruent because opposite sides of a parallelogram are congruent.
They are not congruent because only one pair of corresponding sides is congruent.
They are not congruent because only two pairs of corresponding sides are congruent.
Answers
Answer:
They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
Step-by-step explanation:
ABC is an equilateral triangle whose vertex A has the co-ordinates (0, √3). Find the co- ordinates of B and C.
Answers
Answer:
B = (-1, 0)
C = (1, 0)
Step-by-step explanation:
Properties of an Equilateral Triangle
Three sides of equal lengthAll interior angles are 60°Given:
ΔABC is an equilateral triangleVertex A is at (0, √3)Drawing an altitude from vertex A divides the triangle into two 30-60-90 triangles.
A 30-60-90 triangle is special right-angled triangle where:
Angles are in the ratio 1 : 2 : 3Sides are in the ratio 1 : √3 : 2Therefore, the formula for the sides is: b : b√3 : 2b, where:
b = shortest side opposite the 30° angleb√3 = side opposite the 60° angle2b = longest side (hypotenuse) is opposite the right angleAs Vertex A has the co-ordinates (0, √3), the side opposite the 60° angle is √3 units.
Using the ratios to find b (shortest side length):
b√3 = √3 ⇒ b = 1
As the altitude divides BC into two equal line segments, and the length of the shortest side of the right triangles is 1 unit, the coordinates of B are C are:
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A tire on a car has an outside diameter of 36.30 in. Through what angle (in radians) does the tire turn while traveling 1 mile?
Answers
Answer: 3491.91 radians
Step-by-step explanation:
The total distance in inches traveled by car = 63,360 inches (1 mile)
Total Revolution made by tire through traveling =
[tex]=\frac{63360}{\pi *36.30}[/tex]
We know 1 revolution angle made by tire = 2π radian (360 degrees/1 revolution of unit circle)
In [tex]\frac{63360}{\pi *36.30}[/tex] ,
the revolution angle made by the tire =
[tex]=2\pi * \frac{63360}{\pi 36.60}[/tex]
[tex]=2 * \frac{63360}{ 36.60}[/tex]
[tex]= 3491.91[/tex] radian
Eight years ago, Marilyn invested $1000 in a stock. The table shows the
value of the stock over time.
Year
0
1
2
3
4
5
6
7
8
Value
$1000
$1095
$1200
$1314
$1440
$1580
$1730
$1890
$2070
Which is closest to the rate of change modeled by the function?
Leaming Inc.
Helo 13
Answers
Answer: 1.095
Step-by-step explanation:
The function is increasing, so the rate of change must be greater than 1.
The weight of an apple is 150g, rounded to the nearest 5g. what is the lower bound and upper bound?
Answers
The lower bound is 147.5 and the upper bound is 152.5.
Given the weight of an apple 150 g rounded to the nearest 5g.
We have to find lower bound and upper bound.
Lower bound is an element less than or equal to all the elements in a given set.
Upper bound is an element greater than all the elements in a given set.
Lower bound= Number 1- (Number nearest to which number 1 is rounded)/2
Upper bound=Number 1+(number nearest to which number 1 is rounded)/2
Weight of an apple =150 g
Lower bound=150-5/2
=150-2.5
=147.5
Upper bound=150+5/2
=150+2.5
=152.5
Hence the lower bound is 147.5 and upper bound is 152.5.
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Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answers
Answer:
10
Step-by-step explanation:
2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.
The answer will be either 8 or 4 or 0.
What is a riddle?
A riddle is an intentionally framed ambiguous question or statement that requires ingenuity and critical thinking to solve or understand.
In the given riddle, all the two dogs, four horses, one giraffe and a duck are lying on the bed. Three chickens are flying over a chair.
Assumptions:
1) Bed is placed on the ground.
2) Bed and chair considered are of standard type.
case1:
If we consider the legs of only living organisms, the number of legs on the ground at the given instant will be 0.
case2:
If that's not the case, then a typical chair will have four legs, and a standard bed will also have four legs. So a total of 8 legs will be on the ground or floor of the room.
case3:
And if we consider the possibility of the chair being placed on the bed, then the legs of the chair will not touch the ground. So a total of 4 legs will be on the ground or floor of the room.
∴ From different perspectives, the number of legs on the ground will be either 8 or 4 or 0.
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John lives in Vermont and Julie lives in Florida. One January day, it was 52°F in Florida and 9°F in Vermont. What was the difference in temperature.
Answers
Answer:
43
Step-by-step explanation:
52-9=43