Answers
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
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Related Questions
Helppppp meeeee guyssss
Answers
25.) 4•4•4•4•4 = 1024
27.) 1/3^7= 1/2187
29.) 476500
31.) 4.26 x 10^7
Brainly pls
Madelyn and Kaia are competing to see who can sell the most tickets for the Winter Dance. On Monday, Madelyn sold 22 and then sold 30 per day after that.
Kaia sold 53 on Monday and then sold 20 per day after that.
Write an equation to represent the number of tickets that Madelyn sold.
Write an equation to represent the number of tickets that Kaia sold.
Write a system of equations. What is the appropriate method for solving the system?
Solve the system of equations. Explain the meaning of your solution.
Answers
The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;
Tickets sold by Madelyn is; y = 22 + 30·x
Tickets sold by Kaia is; y = 53 + 20·x
A system of equation obtained from the details in the question can be presented as follows
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.
The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.
What is an equation?An equation consists of two expressions that are joined by the 'equals to' (=) sign.
The number of tickets for the Winter Dance Madelyn sold = 22
Number of tickets per day Madelyn sold after that = 30 per day
Number of tickets Kaia sold on Monday = 53
Number of tickets per day Kaia sold after that = 20 per day
Let x represent the number of days since Monday, and let y represent the number of tickets sold
Therefore;
The number of tickets Madelyn sold, y = 22 + 30·x
The number of tickets Kaia sold, y = 53 + 20·x
The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x
30·x - 20·x = 53 - 22 = 31
10·x = 31
x = 31 ÷ 10 = 3.1
The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days
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Here is the graph for one equation in a system of equations:
a) Write a second equation for the system so it has infinitely many solutions.
b) Write a second equation whose graph goes through (0, 1) so the system so it has no
solutions.
Answers
The answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.What is the general form of a straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line equation is given byy = mx + c
where -
[m] : slope of line
[c] : y - intercept
Given is the graph of a straight line as shown.
[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -
(0, 4) and (4, 1)
Let the line be -
y = mx + c
m = (1 - 4)/(4 - 0) = -3/4
m = -3/4
So, the equation will be -
y = (-3/4)x + 4
[B] -
For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.
Therefore, the answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.To solve more questions on functions, expressions and polynomials, visit the link below -
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7. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the
rocket's height after 3 seconds?
h(t) = -5t² +42t + 54
Answers
The rocket's height after 3 seconds is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
[tex]xvertex = -b / 2a[/tex]
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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What is transpose of matrix
Answers
Step-by-step explanation:
it is the process of changing rows to columb
maria has type b blood. she can safely receive blood transfusions from people with blood types o and b. what is the probability that a randomly chosen person from the united states can donate blood to maria?
Answers
The probability that a randomly chosen person from the united states can donate blood to maria is 0.50
considering blood to be of types A,B,AB and O
further all blood groups are equi probable
Probability of blood type A = probability of blood type B = probability of blood type AB = probability of blood type O = x
Probability of blood type A + probability of blood type B + probability of blood type AB + probability of blood type O = 1
⇒ 4x = 1
⇒ x = 1/4
Probability that a random person will have blood of type B or O = x+x
= 1/4 + 1/4
= 1/2
= 0.50
Hence we get the required answer.
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Which parent function is represented by the graph?
O A. An exponential parent function
• B. The quadratic parent function
• C. The absolute value parent function
O D. The linear parent function
Answers
Parent function is represented by the graph is
B. The quadratic parent function
What is Parent function?
A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.
A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.
The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.
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Someone please help me with this!! I’ll give u a brainless or whatever it’s called!
Answers
Answer:
New price = 0.06 x Original price
New price $1,968
In triangle LMN, m∠L = (3c + 66)°. If the exterior angle to ∠L measures 72°, determine the value of c.
c = 72
c = 46
c = 14
c = 2
Answers
72 ° + (3c + 66 °) = 180 °
180 ° - 72 ° - 66 ° = 42 °
42 ° / 3c
14 ° = c
Answer:
c = 14
Step-by-step explanation:
Jeremy spent a total of $79.16 on a shirt and one pair of jeans. He knows the jeans cost $49.95 but he does not know the cost of the shirt, s. He created the model shown to find the cost of the shirt.
Answers
The model to show the cost of the shirt is x+49.95=79.16. Therefore, the cost of shirt is $29.21.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Jeremy spent a total of $79.16 on a shirt and one pair of jeans.
Let the cost of shirt be x.
The jeans cost is $49.95
Now, the cost of shirt + the cost of jeans = Total cost
⇒ x+49.95=79.16
⇒ x=79.16-49.95
⇒ x=$29.21
Therefore, the cost of shirt is $29.21.
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please help, this is my finals & i don’t know it
Answers
Answer:
i think that answer is correct
Step-by-step explanation:
one number is 4 less than 3 times a second number. Two times the first number decreased by two times the second is 8. what is the value of the larger number?
A.4
B.12
C.8
D.2
E.14
Answers
Answer:
Step-by-step explanation: To solve the problem, we can use the given information to set up a system of equations and solve for the values of $x$ and $y$. Specifically, we are given that one number is 4 less than 3 times a second number, and that two times the first number decreased by two times the second is 8.
Let $x$ represent the larger number, and $y$ represent the second number. We can write the given information as a system of equations as follows:
x &= 3y - 4
2x - 2y &= 8
Solving this system of equations, we find that $x = 12$ and $y = 2$. Therefore, the value of the larger number is 12
Which of the following best describes the second law passed under the Morrill Act?
Eastern schools had to research which crops were suitable for farms in Midwestern America.
Answers
Answer:
Step-by-step explanation:
Davina charges $15 an hour to weed gardens. What does she charge to weed a garden for 1, 2, 3, and 4 hours?
Answers
Answer:
1 - $15
2- $30
3 - $45
4 - $60
Step-by-step explanation:
$15/hour
1 - $15 =1*15
2- $30 =2*15
3 - $45 =3*15
4 - $60=4*15
make g the subject of 3e+4g=7+9eg
Answers
Answer:
the answer is g = (7 - 3e) / (4 - 9e)
Step-by-step explanation:
The subject of an equation is the value or values being solved for. An equation typically consists of two parts: an expression on the left side of an equal sign and an expression on the right side of the equal sign.
The given equation subject of equation is 3e + 4g = 7 + 9eg
Subtraction of 9eg from both sides of the equation
3e + 4g - 9eg = 7 + 9eg - 9eg
3e + 4g - 9eg = 7
Subtract 3e on both sides of the equation
3e + 4g - 9eg - 3e = 7 - 3e
4g - 9eg = 7 - 3e
Factorize g on left side of the equation,
g (4 - 9e) = 7 - 3e
Then divide (4 - 9e) on both sides of the equation,
g = (7 - 3e) / (4 - 9e)
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What is the interest earned in a savings
account after 12 months on a balance of
$3500 if the interest rate is 1.5% APY
compounded yearly?
Answers
Answer:
The interest earned on a savings account with a balance of $3500 and an interest rate of 1.5% per year compounded yearly would be $52.50 after 12 months.
Step-by-step explanation:
To calculate the interest earned on a savings account, you need to know the interest rate, the length of time the money is deposited, and the starting balance. Based on the information provided, it appears that the interest rate is 1.5% per year, the money is deposited for 12 months, and the starting balance is $3500.
To calculate the interest earned, you would first need to convert the interest rate to a decimal by dividing it by 100. In this case, the interest rate would be 0.015. You would then multiply the interest rate by the starting balance to get the amount of interest earned in a year. In this case, the interest earned would be $3500 * 0.015 = $52.50.
Since the interest is compounded yearly, the total balance after one year would be the starting balance plus the interest earned. In this case, the total balance would be $3500 + $52.50 = $3552.50. Therefore, the interest earned on a savings account with a balance of $3500 and an interest rate of 1.5% per year compounded yearly would be $52.50 after 12 months.
Assume that when adults with smartphones are randomlyselected, 45% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in meetings or classes. Round to 4 decimals
Answers
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
what is probability?The possibility or likelihood of an event occurring is expressed numerically as probability. Probabilities are expressed as ratios (0 to 1) and percentages (0 to 100). It is founded on the likelihood that something will occur. The theoretical probability is built on the fundamental principle of probability justification. For instance, there is a 12 percent chance of receiving heads while flipping a coin.
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
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If you vertically compress the absolute value parent function, F(x) = |x|, by multiplying by 3/4, what is the equation of the new function?
A. G(x) = | 3/4 x |
B. G(x) = |x| - 3/4
C. G(x) = 3/4 |x|
D. G(x) = | x + 3/4 |
Answers
Answer:G(x) = 3/4 |x|, nevertheless that is the same that G(x) = |3/4x|.
Step-by-step explanation:
Note that given that 3/4 is less than 1 the original function is compressed.
- Take care <3
Given the functions f(x) = x3 + x2 – 3x + 4 and g(x) = 2x – 4, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
Answers
1. f(x) - cubic function -- polynomial , g(x) - linear function
similar
domain all real numbers (?)range is all real number, end behavior is the sameThe function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.
Domain: -∞ < x < ∞
Range: -∞ < y < ∞
y-intercept = 4
x - intercepts = -2.68
Function g(x)
Domain: x > 0
Range: -4 < y < ∞
y - intercept = -4
x - intercepts = none
By comparing the key features above, we can conclude that the common features in both functions are their range
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the perimeter of a square is 48 centimeters, what is the area in square centimeters
Answers
Answer:
144cm²
Step-by-step explanation:
If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.
48/4 = 12cm
Then, to find the area, you need to multiply 12 by 12.
12 cm x 12 cm = 144cm²
Hope this helps :)
HELP ME PLEASE!!!!!!!!!
The length of a cell phone is 1.41.4 inches and the width is 3.43.4 inches. The company making the cell phone wants to make a new version whose length will be 1.541.54 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answers
Answer:
Step-by-step explanation:7.48521878104
The teacher grades 16 of the 48 quizzes before school.
If the teacher grades 15 of the remaining quizzes after school, how many quizzes still need to be graded?
Responses
8 quizzes
8 quizzes
23 quizzes
23 quizzes
25 quizzes
25 quizzes
40 quizzes
Answers
The number of quizzes still need to be graded is 17quizzes.
What is an algebraic equation?There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.
For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.
Algebraic equations in mathematics frequently have one or more variables.
It is given that,
grades of the teacher out of 48 quizzes before school = 16
grades of the teacher of the remaining quizzes after school = 15
Let us assume 'X' as the number of quizzes still need to be graded.
then X= 48-16+15
=48-31
=17
Hence, The number of quizzes still need to be graded is 17quizzes.
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The number of quizzes still need to be graded is 17 quizzes.
What is an algebraic equation?There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.Algebraic equations in mathematics frequently have one or more variables.It is given that,grades of the teacher out of 48 quizzes before school = 16, grades of the teacher of the remaining quizzes after school = 15.Let us assume 'X' as the number of quizzes still need to be graded.then X= 48-=48-31
=17
Hence, The number of quizzes still need to be graded is 17 quizzes.
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In a group of 500 people determine how many are suspects in the following scenario.
A wallet was stolen from an office in a building with 500 employees. The suspect was wearing black pants, a white button-down shirt, and a multicolored tie. In one of the offices in the building, the following data was collected.
30 people total in the office
22 wearing a white button down shirts
16 wearing black pants
7 wearing a multicolored tie
Using the data, how many suspects are there?
Answers
Using the given data, the number of suspects is; 7
How to find the intersection of mathematical sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.
However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.
Now, we are told that;
Total number of people in the office = 30 people
Number of people wearing a white button down shirts = 22
Number of people wearing black pants = 16
Number of people wearing a multicolored tie = 7
Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;
The number of suspects = A ∩ B ∩ C = 7 people
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Question 1 of 7 ✓
Question 1
>
The relationship between the amount of time a car is parked, in hours, and the cost of parking, in dollars, can be described with a function. Which
statements about the function are true? Select all that apply.
A
Answers
The parking cost is the function of the amount of time the car is parked and for 1 hour the cost of parking is $3 with a maximum amount of $12 for parking. The correct statements are C and D.
What is a function?A function is a relationship between the dependent and independent variables. The independent variables are function inputs, while the dependent variables are function outputs. The value of a dependent variable is determined by the input.
Here in the graph, the cost of parking is varying with time. It means that the cost of parking is dependent on the time of parking but the maximum amount for parking is $12 for any number of hours of car parking.
Hence, the correct statements are C and D.
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solve for x.
enter your answer as a mixed number in simplest form in the box.
x =
Answers
Answer:
x + x - x = x
explanation:
give us the actual formula lol
Question 1
Find the midpoint of the line segment with these
endpoints: (7,-6), (-6, -8)
A) (-18, -10)
B) (6.5, 1)
C) (0,5)
D) (.5, -7)
OB
OC
OA
OD
10 pts
Answers
Answer:
D
Step-by-step explanation:
(7+-6)/2
(7-6)/2
1/2
(-6+(-8)/2
(-6-8)/2
-14/2
-7
(.5,-7)
each student at william elementary can only participate in one fall activity. there are 65 students on the football team and twice that number in band. there are 61 students on each of the two soccer teams. how many students participate in fall activities
Answers
Answer:191
Step-by-step explanation:
65x2=130
130+61=191
Write the answer in the blank.
What number is 280 more than 220?
Answers
Answer: 500
Step-by-step explanation:
280 + 220 is 500
Answer:
The number is 500.
Step-by-step explanation:
Let's assume that,
→ Missing number = x
Forming the equation,
→ x = 220 + 280
Now the value of x will be,
→ x = 220 + 280
→ [ x = 500 ]
Hence, the number is 500.
the owners of a supermarket chain are looking into the effectiveness of the supermarket's loyalty card program. specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014. chloe works in the marketing department of the chain and is assigned to answer the owners' inquiry. she randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. what are the null and alternative hypotheses for this hypothesis test?
Answers
The null and different hypotheses for hypothesis test are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
Null hypotheses
Null hypothesis is usually what researchers or scientists try and confute, and if the null hypothesis is accepted, we have a tendency should modification our opinion, i.e., we have a tendency should modification our original opinion or statement so as to match the null hypothesis. H0 denotes the null hypothesis.Given that:
sample size (η)= 196
sample proposition (p^) = 114/196
Let p denote the population proportion of people who use a loyalty card.
The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]
Hence, the null and alternative hypothesis are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
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. Stanley needs to get 12 gallons of gas. He finds a gas station that is advertising their price at $3.479/gallon.
A. What will the cost be if the gas station rounds the final cost of gas (to the nearest hundredth) after all calculations?
B. What will the cost be if the gas station rounds their price per gallon (to the nearest hundredth) and then calculates the total price?
C. Which option will save Stanley money?
Answers
In case A:
The amount to be paid = $41.75
In case B :
The amount to be paid = $41.76
So, the Case A is better option.
Finding the right answer using the round off to nearest hundredth.
How to change any value to it's nearest hundredth ?
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.
Steps to find nearest hundredth of any value:
Step 1:
Since we need to round the given decimal number to the nearest hundredth, we mark the digit at the hundredths place.
Step 2:
Then, we observe the 'thousandths' place digit, which lies to the right of the hundredths column.
Step 3:
If the digit at the thousandths place is less than 5, we write the hundredths place digit as it is and remove all the digits to its right.
Step 4:
If the digit at the thousandths place is 5 or more than 5, we add 1 to the digit at the hundredths place, that is, we increase the hundredths place by 1 and remove all the digits to its right.
Case A :
The price for each gallon = $3.479
So, the total price for 12 gallon = $41.748
In case A total amount is rounded off
So, the price = $41.75
Case B :
The price for each gallon = $3.479
Rounding off the price for each gallon = $3.48
So, the total amount for 12 gallon = $41.76.
So, the case A is better option.
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