a. Prove ABD is congruent to CBD.
b. Determine whether all four triangles in the diagram are congruent.
c. Explain your reasoning.
Answers
Answer:
a. The proof is in your picture
b. Yes
c. All four triangles are congruent by the HL theorem
Step-by-step explanation:
Given AB≅CB in ∆ABC with BD⊥AC, you want to show ∆ABD≅∆CBD, and you want to know if these are congruent to ∆CEG and ∆FEG.
a. Left trianglesYour picture correctly shows a proof that ∆ABD≅∆CBD by the HL postulate.
b. Right trianglesSides CE and FE are marked congruent to each other and sides AB and CB. The altitudes BD and EG of these isosceles triangles are marked as congruent. Hence all four triangles, ∆ABD, ∆CBD, ∆CEG, and ∆FEG are congruent by the HL theorem.
c. All trianglesThe same HL theorem reasoning applies to all of the triangles.
__
Additional comment
The distance from the light to the stage is said to be the same for both lights. That would be measured perpendicular to the stage, and is the shortest such distance. We are assuming that BD and EG are those perpendicular distances, as we see no markings on the diagram indicating right angles.
Related Questions
can you solve please
Answers
Answer:
113
Step-by-step explanation:
30° + 37° + angle c = 180° (Sum of all angles of a triangle is 180°)
or, 67° + angle c = 180°
or, angle c = 180° - 67°
or, angle c = 113°
Find the sum of 6 and 18.
12
× (6 +18) = X
?
Answers
Answer:
24
Step-by-step explanation:
6 + 8 =24. You can ignore the 1/2 because it is on both sides of the equation.
Answer:
it is 24 and 24x1/2 but you can count 1/2 as 2 which will get you to 48 division 12
PLEASE HELP ASAP ITS URGENT!!!!!!!!!!!!!!!!!!
Answers
Answer:
The lie is #2
Step-by-step explanation:
Just like how dividing powers with the same bases is like subtracting exponents, multiplying them is like adding exponents.
If you substitute 4 as x in #1, you get [tex]13^2*13^4=13^6[/tex]. This is the same as saying [tex]13^2^+^4=13^6[/tex], which is true.
If you substitute 4 as x, 6 as y, and 8 as z in #2, you get [tex]m^6*m^8=m^4[/tex]. This is the same as saying [tex]m^6^+^8=m^4[/tex], which is not true.
If you substitute 6 as y in #3, you get [tex]5^6*5^6=5^1^2[/tex]. This is the same as saying [tex]5^6^+^6=5^1^2[/tex], which is true.
Two Causal Relationships and One Correlation (Two Truths and a Lie)
Create three sets of two variables so that two sets describe causal relationships and one describes a correlation between the variables.
For example, one set of two variables that represent a causal relationship would be The number of people eating at a restaurant vs. The amount of food needed.
Please reply to the prompt and respond to two other students posts. You will earn 10 points for your initial response and 5 points for each reply. Students
may earn a max of 20 points.
How to respond to other posts:
• In one response, guess which set of variables represent the correlation.
. In the second response, describe how you could alter one of their causal relationships so it instead describes a borrelation.
Answers
However, a correlation between two variables does not always imply that a change in one variable is the reason for a change in the values of the other. There is a causal link between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event.
Causal relationships between variables may consist of direct and indirect effects. Direct causal effects are effects that go directly from one variable to another. Indirect effects occur when the relationship between two variables is mediated by one or more variables.
Direct and indirect effects may make up causal connections between variables. Effects that flow directly from one variable to another are referred to as direct causal effects. When one or more factors mediate the link between two variables, indirect effects result.
What are examples of causal relationships?
Causal relationships: A causal generalization, e.g., that smoking causes lung cancer, is not about an particular smoker but states a special relationship exists between the property of smoking and the property of getting lung cancer.
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Juliet needs to rewrite 3 (x + 2) = 6 y in slope-intercept form so she can easily graph it. Which step would be correct to start the process?
She could combine the x and 2 to get 3 (2 x) = 6 y.
She could divide both sides by 3 to get x + 2 = 2 y.
She could distribute the 3 to get 3 x + 2 = 6 y.
She could subtract the 6y to get Negative 6 y = 3 (x + 2).
Answers
The first step to start the is dividing both sides by 3, so the correct option is the second one.
The linear equation in slope-intercept form is:
y = (1/2)*x + 1
How to write the line in the slope-intercept form?To do that, we need o isolate the variable y in one of the sides of the linear equation:
3*(x + 2) = 6y
We can divide both sides by 3 to get:
x + 2 = (6/3)*y
x + 2 = 2y
Now, we can divide both sides by 2, so we will get:
(x + 2)/2 = y
y = (x + 2)/2
y = (1/2)*x + 1
The equation in the slope-intercept form is:
y = (1/2)*x + 1
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Find x, y and z for the diagram below.
X =
y =
Z=
88
2x+18
y+10
3x-7
Answers
The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
The value of x is 25.
The value of y is 78.
The value of z is 24.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
From the figure given we see that,
88 and y + 10 are corresponding angles.
88 = y + 10
y = 88 - 10
y = 78
Now,
3x - 7 and 2x + 18 are oposite angles.
3x - 7 = 2x + 18
3x - 2x = 18 + 7
x = 25
Now,
(y + 10) + (3x - 7) + z = 180
78 + 10 + 3 x 25 - 7 + z = 180
88 + 75 - 7 + z = 180
z = 180 - 156
z = 24
Thus,
The value of x is 25.
The value of y is 78.
The value of z is 24.
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i need help with this.. help please?? :,))
Answers
Answer:
C: adding on the right and subtracting on the left; n = 4S: dividing on the left and subtracting on the right; y = 2J: multiplying on the left and dividing on the right; b = 512Step-by-step explanation:
You want the solutions to three equations, and the error in the work shown.
Cullen: -6n +22 = -4n +14Seraphina: 8.4y -6.8 = -3.2y +16.4Jasper: 7/8b -32 = 3/4b +32CullenThe correct solution is ...
[tex]-6n+22=-4n+14\\\\22=2n+14\qquad\text{add $6n$}\\\\8=2n\qquad\text{subtract 14}\\\\\boxed{4=n}[/tex]
Cullen's error was adding 4n to one side, and subtracting 4n from the other side of the equation. (The same operation must be done to both sides.)
SeraphinaThe correct solution is ...
[tex]8.4y -6.8 = -3.2y +16.4\\\\11.6y-6.8=16.4\qquad\text{add $3.2y$}\\\\11.6y=23.2\qquad\text{add 6.8}\\\\\boxed{y=2}[/tex]
Seraphina's error was dividing one side of the equation by 11.6 and subtracting 11.6 from the other side. (The same operation must be done to both sides.)
JasperThe correct solution is ...
[tex]\dfrac{7}{8}b -32 = \dfrac{3}{4}b +32\\\\\dfrac{1}{8}b-32=32\qquad\text{subtract $\dfrac{3}{4}b$}\\\\\dfrac{1}{8}b=64\qquad\text{add 32}\\\\\boxed{b=512}\qquad\text{multiply by 8}[/tex]
Jasper's error was multiplying one side of the equation by 8 and dividing the other side by 8. (The same operation must be done to both sides.)
A new club sent out 250 coupons to boost sales for next year's memberships. They provided 4 times as many to potential members than to existing members. How many coupons did they send to existing members?
A.
4
B.
50
C.
5
D.
54
Answers
Answer:
B. 50
Step-by-step explanation:
Let x be the number of coupons sent to existing members.
The number of coupons sent to potential members is 4 times the number of coupons sent to existing members, or 4x.
The total number of coupons sent is the sum of the number of coupons sent to existing members and the number of coupons sent to potential members, or x + 4x = 5x.
The club sent out 250 coupons, so 5x = 250.
Dividing both sides of the equation by 5, you get x = 250 / 5 = 50.
Therefore, the club sent 50 coupons to existing members.
please help:
show that two quadrilaterals are congruent
Answers
The ratio of all the corresponding sides and corresponding angles is one. Then the quadrilateral is congruent with each other.
What is a quadrilateral?The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.
The quadrilaterals are LMNP and LKJQ shown.
In quadrilaterals LMNP and LKJQ,
LK = LM = LQ = LP (Given)
JK = JQ = NM = NP (Given)
∠KJQ = ∠MNP (Given)
∠KLQ = ∠MLP (Given)
∠JKL = ∠NML (Given)
∠JQL = ∠NPL (Given)
The ratio of all the corresponding sides and corresponding angles is one. Then the quadrilateral is congruent with each other.
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Write the statement "the sum of a number and 10.7 is at most −3.2" as an inequality.
−3.2 + b > 10.7
−3.2 + b < 10.7
b + 10.7 ≥ −3.2
b + 10.7 ≤ −3.2
Answers
The inequality that represents the condition will be b + 10.7 ≥ −3.2. Then the correct option is C.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Let the number be 'b'. Then the statement "the sum of a number and 10.7 is at most −3.2" is written in mathematical form. Then we have
b + 10.7 ≥ −3.2
Thus, the inequality that represents the condition will be b + 10.7 ≥ −3.2. Then the correct option is C.
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Which subset of real numbers does
belong to?
-17/20
Answers
The number -17/20 belongs to the set of real numbers.
What is the set of real numbers?
The set of real numbers is made by combining the set of rational numbers and the set of irrational numbers. Real numbers include natural numbers or counting numbers, whole numbers, integers, rational numbers (fractions and repeating or terminating decimals), and irrational numbers.
All real numbers, including fractions and decimals, are part of the set of real numbers.
The set of real numbers includes all numbers that can be expressed on the number line, including positive and negative numbers, as well as all fractions and decimals.
This set is often denoted by the symbol "ℝ".
Hence, The number -17/20 belongs to the set of real numbers.
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Jim began a 255-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 7 hours. If Jim walks at a rate of
3 miles per hour and rides at 39 miles per hour, find the amount of time he spent on the bicycle.
Answers
The amount of time Jim spent on the bicycle is 6.5 hours.
What is distance?The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.
Given:
Total distance, d = 255 miles,
Total time, t = 7 hours,
The speed of walking, s = 3 miles / hour,
The speed of riding bicycle, S = 39 miles/hour,
Calculate the time spent on the bicycle as shown below,
Total time = Time on bicycle + Time walking
7 = Distance on bicycle/speed + Distance of walking / speed
7 = b / 39 + w / 3
Here w is the distance by walking and b is the distance covered by bicycle,
b + w = 255 (As given)
Solve both equations,
w = 1.5 miles and b = 255 - 1.5 = 253.5 miles
Calculate the time spent on a bicycle as shown below,
The time spent on the bicycle = b / 39
The time spent on the bicycle = 253.5 / 39 = 6.5 hours
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PLEASE HELP!!!!! 20 POINTS!!! The Shultz family went apple picking. Jeshua picked 16 red apples, ½ as many yellow apples as red apples and 28 green apples. How many apples dir he pick in all?
Answers
Answer:
He picked a total of 52
Step-by-step explanation:
You would add 16 (red apples), then divide 1/2 from the 16 red apples, +28 green apples which would equal 52.
~Describe each transformation in words.
11.) _____________________.
Answers
The required transformation of the given figure is given as 4 units right and 2 units down.
Given that,
To determine the trasformation of the given figure.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
here,
As shown in the figure,
The figure is translated as of the former figure to 4 units in the positive x direction and 2 units towards the negative y direction.
Thus, the required transformation of the given figure is given as 4 units right and 2 units down.
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Name two sets of alternate interior angles.
Answers
Answer:
∠ a & ∠ d
∠ b & ∠
Answer:
∠ A and ∠ D
∠ B and ∠ E
Step-by-step explanation:
(1 point) 5 dice of different colors are rolled, and the number coming up on each die is recorded. how many different outcomes are possible? your answer is :
Answers
There are 7776 different outcomes possible when 5 dice of different colors are rolled.
What is probability?The ratio of favorable outcomes to the total number of outcomes of an event is said to be the probability of that event.
P(E) = n(E)/n(S)
Calculation:It is given that, there are 5 dice with different colors.
There are 6 outcomes for each die rolling. That is the number coming up on each die when it is rolled (1, 2, 3, 4, 5, 6).
So, for five dice when rolled, the number of possible outcomes is
n = 6 × 6 × 6 × 6 × 6
⇒ n = 7776
Therefore, 7776 different outcomes are possible.
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2
Write an equation in slope-intercept form that models the situation. In order to go bowling,
you must pay a one-time fee of $10 for rental shoes, and then pay $3 per game. Let y
represent the total cost of bowling after playing x games. * (5 Points)
y=-3x+10
y=3x+10
y=10x-3
y=10x+3
y=-10x+3
Answers
The slope intercept form of the given situation is y=3x+10.
What is slope-intercept form?y = mx + b is the slope-intercept form, where m is the slope and b is the y-intercept.
What is the slope of a line?The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches.
Let x= $3 per game
and we have to add $10 for rental shoes. So slope form will ne
y= 3x+10.
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PLEASE HELP
Explain how you can identify the opposite and adjacent sides of a right triangle and explain how these can change in any given triangle. Use a diagram to support your explanation.
Answers
In a right angled triangle, the opposite and adjacent sides are the sides proportional to the two acute angles of the triangle.
How to identify the opposite and adjacent sides?In every triangle, the sum of angles is 180⁰. In a right angled triangle, one of the angles is = 90⁰.
The side facing the right angle is called the hypothenuse side.
The sum of the other two angles is 90⁰. That each of the angles is acute angle.
The sides proportional to the acute angles are the opposite and adjacent.
If an angle is given in one of the angle, the side proportional to the given angle is called the opposite while the other one is called the adjacent.
if the angle is changed to the other angle, the side proportional to the given angle becomes the opposite while the other is the adjacent.
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Chad is decorating a rectangular ballroom ceiling with decorative lights. Beginning in a corner, Chad strings the lights along the length of the ceiling, a distance of 55 feet. Next, Chad strings the lights along the width of the ceiling, a distance of 48 feet. Then Chad strings the lights straight back to the original corner. At this point, how many feet of lights has Chad used?
If necessary, round your answer to the nearest tenth.
feet
Answers
At the given point, Chad has used 176 feet of light
How to determine the number of feet of light?From the question, we have the following parameters that can be used in our computation:
Length = 55 feet
Width = 48 feet
We start by calculating the distance from the end of the width till the beginning of the length
This is represented by the following Pythagoras theorem
Distance = √(Length² + Width²)
So, we have
Distance = √(55² + 48²)
Evaluate
Distance = 73
The number of feet is then calculated as
Feet = Length + width + distance
So, we have
Feet = 55 + 48 + 73
Evaluate
Feet = 176
Hence, the total distance is 176 feet
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Which relation is a function?
Answers
A function is a relation where each conceivable input value results in exactly one potential output value. The phrase "the output is a function of the input" frequently used.
Explain about the function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
3 ,-3 is an input value of the function
0 is an output value of the function in this graph
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Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded quarterly until
April 1 of the flllowing year.
Answers
Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded is $58.83
What is compounded?
to combine into a single unit; combine: to mix medications to create a new medication. to create something by putting pieces, things, etc. together; construct: to combine elements of various previous plans to create a new one.The interest on a loan or deposit calculated based on the initial principal, and the collective interest from previous periods is called compound interest. It is basically 'interest earned on money that was previously earned as interest'.
Given that, principal=$3620, rate of interest=6.5% and time period=9 months.
Here, principal compounded quarterly
Thus, Amount
[tex]\$ 3,620 \times 6.5 \% \times \frac{1}{4}=\$ 58.83[/tex]
The first period interest is product of the principal, the annual interest rate and the interest period (expressed in years).
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Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded is $58.83
What is compounded?
To combine into a single unit; combine: to mix medications to create a new medication. to create something by putting pieces, things, etc. together; construct: to combine elements of various previous plans to create a new one.The interest on a loan or deposit calculated based on the initial principal, and the collective interest from previous periods is called compound interest. It is basically 'interest earned on money that was previously earned as interest'.
Given that, principal=$3620, rate of interest=6.5% and time period=9 months.
Here, principal compounded quarterly
Thus, Amount
$3,620x6.5%x1/4=$58.83
The first period interest is product of the principal, the annual interest rate and the interest period (expressed in years).
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Factorise 64(x²-9x+18)=4x²
Answers
Step-by-step explanation:
Here, not sure if it got the answer you were looking.
Determine the number of solutions for the equation below.
-7x + 7 + 12x = 5x + 7
A. infinite solutions
B. Two solutions
C. One solution
D. no solution
Answers
Answer:
ANS:- No solution
Step-by-step explanation:
-7x + 7 + 12x = 5x + 7
5x + 7 = 5x + 7
0 = 0
Which positive even integer, when added to the following2 consecutive odd integers, creates a sum of 40?
Answers
Answer:
Let the odd numbers be 2n + 1 and 2n + 3 where n is any positive integer. Therefore, the numbers are 19 and 21.
the probability that it will rain tomorrow is 0.2. the odds that it will rain tomorrow are 2 to . the odds that it will not rain tomorrow are to
Answers
The probability that it will rain tomorrow is 0.2. the odds that it will rain tomorrow are 2 to . The odds that it will not rain tomorrow are to 0.8.
What is probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The probability that it will rain tomorrow is 0.2
i.e.
P(it will rain tomorrow )=0.2
Now probability that it won't rain tomorrow is,
P(it won't rain tomorrow )=1- P(it will rain tomorrow)=1-0.2=0.8
Thus
P(it won't rain tomorrow)=0.8.
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Describe the graph of the system of inequalities:
Answers
The x = 5-y line passes through (0,5) and (5,0).
The y = 2x -4 line passes through (0,4) and (2,0).
What is a linear equation?
The graphs of all first-degree equations in two variables will be straight lines. This fact will be used here even though it will be much later in mathematics before you can prove this statement. Such first-degree equations are called linear equations.
Here, we have
Given inequalities
x - y < 5
y ≥ 2x - 4
We have to describe the graph of the system of inequalities.
For, x < 5+y
x = 5-y
We put y = 0, we get
x = 5
We put x =0, and we get
y = 5
Hence, the x = 5-y line passes through (0,5) and (5,0).
For, y ≥ 2x - 4
y = 2x -4
We put x = 0, and we get
y = 4
We put y = 0, we get
x = 2
Hence, the y = 2x -4 line passes through (0,4) and (2,0).
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Help……………………dldkdkldleld
Answers
Answer:
Angle DFC is complementary to angle BFC
Step-by-step explanation:
AD is a straight line passing line EB. DFE, EFA, AFB and BFD are right angles as the lines are perpendicular.
DFB is divided into 2 angles by the segment FC
therefore
DFC + BFC = 90 degrees
PLS HELP ME!!!!!! I ONLY HAVE 5 MINS!!!! 50 PTS
Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to play as many games as they can before running out of tokens. Let m represent the number of games that require 2 tokens; n represent the number of games that require 3 tokens; and p represent the number of games that require 4 tokens.
Janie plays the 3-token game four times. Write two equivalent expressions to represent the number of tokens that Janie will need to play each of the three games at least one time.
Answers
do your work buddy and dont cheat
Step-by-step explanation:
dont cheat and actually study
On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.
Complete the relative frequency table, showing all necessary calculations.
Answers
Students do not likes to fly, can drive is 0.13. Therefore, the completed relative frequency table is given below.
Given that, on a recent survey, students were asked if they like to fly and if they can drive.
What is the relative frequency?Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.
From the table
Likes to fly
Row totals = Can drive + Cannot drive
0.32+Cannot drive =0.70
Cannot drive =0.38
Can drive:
Column totals=Likes to fly + Do not likes to fly
0.32 + Do not likes to fly=0.45
Do not likes to fly=0.13
Cannot drive:
Column totals=Likes to fly + Do not likes to fly
0.38 + Do not likes to fly=0.55
Do not likes to fly=0.55-0.38
= 0.17
Row totals = 0.13 + 0.17
= 30
Students do not likes to fly, can drive is 0.13. Therefore, the completed relative frequency table is given below.
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Aeris reads the temperature of a liquid in a lab experiment. The temperature of the liquid is 7.2ºF. After 5 hours, she reads the temperature of the liquid again. The temperature of the liquid is now −1.6°F.
Aeris plots the points on a number line to determine the temperature change between these two readings.
How much did the temperature decrease?
Enter your answer as a decimal in the box.
[]
Answers
Answer:
Step-by-step explanation:
5,6