On Monday, Jack bought 2 burgers and 3 fries for $11.25. On Tuesday, he bought 7 burgers and 5 fries
for $32.50. Find the price of each item.
The burgers is sold each for 3.75 dollars , while the fries is solde for 1.25 dollars each
How to solve for the equationWe would have to solve for the price of each of the items using the simultaneous linear equation method
2 burgers and 3 fries for $11.25
we would have:
Use the elimination method to solve the system of equations:
2 x+ 3 y = 11.25
7 x + 5 y = 32.50
Step 1 - Multiply Equation 1 by 7:
7 * (2x+3y=11.25) --> 14x + 21y = 78.75
Step 2 - Multiply Equation 2 by 2:
2 * (7x+5y=32.50) --> 14x + 10y = 65
Step 3 - s
14x + 21y = 78.75
-(14x + 10y = 65)
------------------------------
21y - 10y = 78.75 - 65
Step 4 - simplify and solve for y:
11y = 13.75
y = 13.75 / 11
y = 1.25
Step 5 - now that we have solved for y, let's rearrange Equation 1 to solve for x:
2x = 11.25 - 3y
Divide each side by 2
2x / 2 = 11.25 - 3y / 2
x = 11.25 - 3y / 2
Step 6 - we determined y = 1.25. Plug it into our Rearranged equation 1:
x = 11.25 - 3(1.25) / 2
x = 11.25 - 3.75 / 2
x = 7.5 / 2
x = 3.75
Since x is the burgers which is 3.75 dollars while y is the fries which is 1.25 dollars
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Using the last of my points please help as fast as possible 6th grade math!!! HELP ASAPPPPP!!!!!! PLEASEEE
A student has a rectangular bedroom. If listed as ordered pairs, the corners of the bedroom are (21, 18), (21, −7), (−12, 18), and (−12, −7). What is the perimeter in feet?
116 feet
58 feet
33 feet
25 feet
The perimeter of the rectangular bedroom is: A. 116 feet.
What is the Perimeter of a Rectangle?Perimeter of a rectangle = 2(length + width)
To find the perimeter of the rectangular bedroom, we need to calculate the sum of the lengths of its four sides.
Let's start by finding the length of the horizontal sides of the rectangle. The two horizontal sides are defined by the points (21, 18) and (21, −7), which are 25 feet apart in the vertical direction (18 − (−7) = 25). Therefore, the length of each horizontal side is 25 feet.
Next, let's find the length of the vertical sides of the rectangle. The two vertical sides are defined by the points (21, 18) and (−12, 18), which are 33 feet apart in the horizontal direction (21 − (−12) = 33). Therefore, the length of each vertical side is 33 feet.
Now we can add up the four side lengths to get the perimeter:
Perimeter = 2(Length of horizontal sides) + 2(Length of vertical sides)
= 2(25 feet) + 2(33 feet)
= 50 feet + 66 feet
Perimeter = 116 feet
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Suppose a certain baseball diamond is a square 80 feet on a side. The pitching Fubber is located 55.5 feet from home plate on a line joining home plate and second base. a) How far is it from the pitching rubber to first base? b) How far is it from the pitching rubber to second base? c) If a pitcher faces home plate, through what angle does he need to turn to face
The distance from the pitching rubber to first base is 98.7ft, B - the distance from the pitching rubber to first base is 96.6ft and C - A pitcher must pivot to face in a 45-degree angle if he is facing home plate.
(a) To find the distance from the pitching rubber to first base, we can use the Pythagorean theorem, since the distance forms the hypotenuse of a right triangle with legs of length 80ft (the length of a side of the square) and 55.5ft (the distance from the pitching rubber to home plate along a diagonal line). Thus, we have:
distance to first base = [tex]\sqrt{ 80^{2} + 55.5^{2}[/tex] = 98.7ft
(b) To find the distance from the pitching rubber to second base, we can use the fact that second base is located at a distance of 80ft from home plate along a line perpendicular to the line connecting the pitching rubber and home plate. Using the Pythagorean theorem, we have:
distance to second base = [tex]\sqrt{55.5^{2} + 80^{2} }[/tex] = 96.6ft
(c) If a pitcher faces home plate, he needs to turn through an angle of 45 degrees to face second base. This is because second base is located at one corner of the square, and the angle formed by the lines connecting the pitching rubber to home plate and second base is a right angle (since the sides of the square are perpendicular).
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12.
to maitsig
Which of the following pairings is INCORRECT?
(ة)
فه
First Amendment-freedom of speech
Second Amendment-right to bear arms
First Amendment-freedom of the press
Fourth Amendment-freedom
of religion
con
noaliW w
The pairing that is incorrect is D. Fourth Amendment-freedom of religion.
What does the Fourth Amendment do ?The Fourth Amendment to the United States Constitution protects citizens from unreasonable searches and seizures and requires that search warrants be issued only with probable cause and based on specific information. It does not address freedom of religion.
The First Amendment protects a number of individual rights, including freedom of speech, freedom of the press, freedom of religion, and the right to assemble and petition the government.
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Calculate the Mean Absolute Deviation (MAD) for the months of January through April using the following data:Month Actual Sales Forecast JAN 1000 600 FEB 1600 2500 MAR 2000 1500 APR 1800 2000
The Mean Absolute Deviation (MAD) for actual sales is 300 and for forecast is 600.
Mean Absolute Deviation evaluates the absolute difference between each data point to its mean. Mean Absolute Deviation can be calculated using formula:
MAD = ∑|x - x bar|
n
where:
x = data point
x bar = data mean
n = number of data
Based on the given data, we know that:
Mean Actual sales = (1,000 + 1,600 + 2,000 + 1,800) / 4
Mean actual sales = 1,600
MAD = |1,000 - 1,600| + |1,600 - 1,600| + | 2,000 - 1,600| + |1,800 - 1,600|
4
MAD = (600 + 0 + 400 + 200) / 4
MAD = 300
Mean Forecast = (600 + 2,500 + 1,500 + 2,000) / 4
Mean forecast = 1,650
MAD Frc = |600 - 1,650| + |2,500 - 1,650| + |1,500 - 1,650| + |2,000 - 1,650|
4
MAD Forecast = (1,050 + 850 + 150 + 350) / 4
MAD Forecast = 600
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Stephen has a rectangular rug with a perimeter of 16 feet the width of the rug is 5 feet what is the length of the rug
The length of Stephen's rug is 3 feet.
How can you use the perimeter and width of Stephen's rug to find the length?To find the length of Stephen's rug, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. In this case, we know that the perimeter of the rug is 16 feet and the width is 5 feet. So, we can plug in these values into the formula and solve for L:
Let's use the formula for the perimeter of a rectangle to solve the problem: Perimeter = 2 x (Length + Width)
We know that the perimeter of the rug is 16 feet and the width is 5 feet. Plugging those values into the formula, we get: 16 = 2 x (Length + 5)
Simplifying the equation, we can divide both sides by 2:
8 = Length + 5
16 = 2L + 2(5)
16 = 2L + 10
2L = 6
L = 3
Therefore, the length of Stephen's rug is 3 feet.
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Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = x y = 0 x = 6 (a) the x-axis (b) the y-axis (c) the line x = 6 (d) the line x = 9
The volume of the solid is 72π. of the x-axis, the volume of the solid is 72π of y axis, the volume of the solid is 192π of the line x=6 and the volume of the solid is 99π of the line x=9.
(a) Spinning the locale about the x-hub will make a strong with a round and hollow shape. The volume of the strong can be tracked down utilizing the equation:
[tex]V = ∫[a,b] πy^2 dx[/tex]
where an and b are the x-directions of the marks of convergence of the bends y=x and y=0.
The convergence focuses are (0,0) and (6,6). In this way, the restrictions of coordination are 0 and 6.
V = [tex]V = ∫[a,b] πy^2 dx[/tex]
=[tex]π(6^3)/3[/tex]
= 72π
The volume of the strong is 72π.
(b) Spinning the locale about the y-hub will make a strong with a round and hollow shape. The volume of the strong can be tracked down utilizing the equation:
V = [tex]∫[a,b] πx^2 dy[/tex]
where an and b are the y-directions of the marks of convergence of the bends y=x and y=0.
The convergence focuses are (0,0) and (6,6). In this way, the restrictions of coordination are 0 and 6.
V = [tex]∫[0,6] πy^2 dy[/tex]
= [tex]π(6^3)/3[/tex]
= 72π
The volume of the strong is 72π.
(c) Rotating the district about the line x=6 will make a strong with a washer shape. The volume of the strong can be tracked down utilizing the recipe:
V = [tex]∫[a,b] π(R^2 - r^2) dx[/tex]
where an and b are the x-directions of the marks of convergence of the bends y=x and y=0, R is the separation from the line of upheaval to the external edge of the strong (y=x), and r is the separation from the line of transformation to the internal edge of the strong (y=0).
The convergence focuses are (0,0) and (6,6). R=6 and r=0, since the strong stretches out from the line of insurgency to the bend y=x.
V =[tex]∫[0,6] π(6^2 - x^2) dx[/tex]
= [tex]π(6^3 - 2(6^3)/3)[/tex]
= 32π(6)
The volume of the strong is 192π.
(d) Rotating the locale about the line x=9 will make a strong with a washer shape. The volume of the strong can be tracked down utilizing the recipe:
V =[tex]∫[a,b] π(R^2 - r^2) dx[/tex]
where an and b are the x-directions of the marks of convergence of the bends y=x and y=0, R is the separation from the line of upheaval to the external edge of the strong (y=x), and r is the separation from the line of transformation to the internal edge of the strong (y=0).
The convergence focuses are (0,0) and (6,6). R=3, since the separation from the line x=9 to the bend y=x is 3 units. r=0, since the strong reaches out from the line of transformation to the bend y=x.
V = [tex]∫[0,6] π(3^2 - x^2) dx[/tex]
= [tex]π(3^3 - 2(6^2)(3) + 6^3/3)[/tex]
= 18π(6) - 27π
= 99π
The volume of the strong is 99π.
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n²-n-56 factoring trinomials
Answer:
(n - 8)(n + 7)
--------------------
Given trinomial:
n² - n - 56Apply Viet's theorem.
The sum of the roots is 1 and the product of the roots is - 56.
This is achieved when the roots are 8 and - 7.
n² - n - 56 = (n - 8)(n - (-7)) = (n - 8)(n + 7)The radius y (in millimeters) of a chemical spill after x days is represented by the equation y=6x+50 .
a. Graph the linear equation
This function y = 6x + 50 has a graph that is a straight line with a 50-point y-intercept.
What is the slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is its graph or the rate of change is large.
Given, The radius y after x days is represented by the equation y = 6x + 50.
Here, The initial radius was 50 mm and it is growing at a rate of 6 mm per day.
The graph of this function will be a straight line having a y-intercept at 50.
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prime factorization of 107
The heights of men (in inches) in the United States follow approximately N(69, 2.25). The heights of women (in inches) in the United States follow approximately N(64,2). A female volleyball player at your college is 6 feet 2 inches tall, and a male college soccer player is also 6 feet 2 inches tall. Based on the distribution above, who is taller in relation to the distribution of heights based on gender?
According to the distribution shown above, the heights of female is taller according to the gender based distribution of heights.
What exactly is normal distribution?
The normal distribution, also called the Gaussian distribution, is a probability distribution that is symmetric about the mean, demonstrating that data close to the mean occur more frequently than data distant from the mean. The normal distribution looks like a "bell curve" when represented graphically.
Considering the information provided,
The United States' average male population is 69.
In the US, men's standard deviation is 2.25.
In the US, the average gender distribution is 64.
Women in the US experience a 2 standard deviation.
Now z-score for,
Female players = [tex]\frac{74-64}{2}[/tex] = 5
Playing men = [tex]\frac{74-69}{2.25}[/tex] = 2.22
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Adjust the number into correct standard form. 59 × 10^-7
Answer:
Given: Find the standard for of 59 × 10^-7 ( 0.0000059 ).
= 5.9 × 10-6.
The conservation club coordinator is recruiting volunteers to help build a shed for recycling. She knows that finishing the shed will take 120 work hours. She figures out that if she can find one more person to help, the project will take a half hour less per volunteer. How many volunteers have already signed up?
please help asap I need this lesson passed.
The area of the triangle will be 1 square foot.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Calculate the value of x of the small right-angle triangle.
4² = ( 3 + x )² + (2 / 3 )²
16 + 9 + 6x + x² + 4 / 9
7 = x² + 6x + 4 / 9
9x² + 54x - 59 = 0
x = 0.9 ft
The area of the triangle will be calculated as:-
Area = ( 1/2 ) x 3.9 x ( 2 / 3 ) - (1/2 ) x 0.9 x ( 2 / 3 )
Area = ( 1 / 2 x 2 / 3 ) ( 3.9 - 0.9 )
Area = ( 1 / 3 ) x 3
Area = 1 square ft
Therefore, the triangle's area will be one square foot.
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Do the ratios 8-16 and 3/6 form a proportion
Yes, The ratios 8/16 and 3/6 form a proportion.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The ratios are,
⇒ 8/16 and 3/6
Now, We know that;
Two ratio are equivalent to each other then, it is form a proportional relation.
Hence, We can check as;
⇒ 8 / 16 = 1/2
⇒ 3/6 = 1/2
Thus, The ratios 8/16 and 3/6 form a proportion.
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Javier has been saving to purchase a beach home for 20 years. Monthly deposits of $500 are made into an annuity that earns 3.5% annual interest, compounded monthly. According to account documents, after these 20 years, there is a balance of $173,434.63 in the account. How much of this balance did Javier contribute?
Javier contribute $12,000 of his balance in the bank account.
What is Compound interest?Compound interest is the interest which is calculated on both the initial principal and the accumulated interest from previous periods. It can be easily understood as interest on interest.
[tex]A= P(1+\frac{r}{n})} ^{nt}[/tex]
Javier has been saving to purchase a beach home for 20 years.
Monthly deposits of $500 are made into an annuity that earns 3.5% annual interest, compounded monthly.
Javier contribute= monthly deposit* number of months* time period
Javier contribute = 500*12*20
= $12000
Hence, Javier contribute $12,000.
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Answer:
Step-by-step explanation:
Javier contributes $500 each month, for 20 years. To find the amount that was contributed, we multiply those pieces together (12 months in each year).
500⋅12⋅20=$120,000
Estimate the mean of the number of eagles spotted during a tour group hike given in the following grouped frequency table. • Round the final answer to one decimal place. Value Interval Frequency 3-6 13 7-10 21 11-14 6 Provide your answer below:
The mean of the number of eagles spotted is 7.8
In our daily life, we encounter a lot of information in the form of numbers, tables, graphics, etc. This information can refer to goals, temperatures in different cities, most popular articles in student classes, etc. Data is collected information
Order refers to the frequency with which an event or value occurs. A frequency table is a table that lists items and indicates how often they occur.
Then, find the sum of all frequencies and multiply each class frequency by the midpoint for that class. Then find the mean of the frequency distribution using the formula where the mean of the clustered frequency distribution is given as ¯x=∑fixi∑fi.
here for rage 3-6 first find mean = (3+6)/2= 4.5 frequency =13
here for rage 7-10 first find mean =(7+10)/2=8.5 frequency =21
here for rage 11-14 first find mean =(11+14)/2=12.5 frequency 6
mean = (4.5*13+8.5*21+12.5*6)/(13+21+6)
=7.8
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At a high school, the probability that a student is a senior is 0.25. The
probability that a student plays a sport is 0.20. The probability that a student
is a senior and plays a sport is 0.08.
What is the probability that a randomly selected student plays a sport, given
that the student is a senior?
O A. 0.32
• B. 0.08
O C. 0.17
O D. 0.25
The probability that a randomly selected student plays a sport, given
that the student is a senior is A. 0.32
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
This is a case of conditional probability and we know,
Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Given, At a high school, the probability that a student is a senior is 0.25
and the probability that a student is a senior and plays a sport is 0.08.
Therefore, The probability that a randomly selected student plays a sport, given that the student is a senior is,
= 0.08/0.25.
= 0.32
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Let X have probability mass function
x 1 2 3 4 5
px(x) 1/7 1/14 3/14 2/7 2/7a. Calculate P(X≤3).
b. Calculate P(X<3).
c. Calculate P(X<4.12|X>1.638).
d. Find the cumulative distribution function of X.
The formula for X's cumulative distribution function (CDF) is
a. Probability P(X≤3) = P(X=1) + P(X=2) + P(X=3) = 1/7 + 1/14 + 3/14 = 5/14
b. P(X<3) = P(X=1) + P(X=2) = 1/7 + 1/14 = 3/14
c. P(X<4.12|X>1.638) = P(2<X<4.12)/P(X>1.638) = [P(X=3)+P(X=4)]/[1-P(X=1)] = (3/14)/(11/14) = 3/11
d. The cumulative distribution function of X, for x = 5, F(5) = 1
a. Probability P(X≤3) = P(X=1) + P(X=2) + P(X=3) = 1/7 + 1/14 + 3/14 = 5/14
b. P(X<3) = P(X=1) + P(X=2) = 1/7 + 1/14 = 3/14
c. P(X<4.12|X>1.638) = P(2<X<4.12)/P(X>1.638) = [P(X=3)+P(X=4)]/[1-P(X=1)] = (3/14)/(11/14) = 3/11
d. The formula for X's cumulative distribution function (CDF) is
F(x) = P(X < x)
For x = 1, F(1) = 1/7
For x = 2, F(2) = 1/7 + 1/14 = 3/14
For x = 3, F(3) = 1/7 + 1/14 + 3/14 = 5/14
For x = 4, F(4) = 1/7 + 1/14 + 3/14 + 2/7 = 11/14
For x = 5, F(5) = 1
As a result, X's CDF is:
F(x) = {1/7, x < 1
3/14, 1 ≤ x < 2
5/14, 2 ≤ x < 3
11/14, 3 ≤ x < 4
1, x ≥ 4}
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The probability for event A is 0.3, the probability for event B is 0.5, and the probability of events A and
the events independent?
because
The required probability that events A and B both occur is 0.15.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
The probability that events A and B both occur is given by the product of their individual probabilities if they are independent. Independence means that the occurrence of one event does not affect the probability of the other event.
In this case, the probability that events A and B both occur is given by:
0.3 × 0.5 = 0.15
So, the probability that events A and B both occur is 0.15.
It's important to note that without further information, we cannot determine if events A and B are independent. The probabilities of 0.3 and 0.5 are the individual probabilities of each event, but we would need to know if their occurrence affects each other to determine if they are independent.
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Nate knew that most mobile phones also included music players. In 2012, the number of mobile phones in Italy was 147.4% of the population. If the number of mobile phones was 88,6000,000 in Italy in 2012, what was the approximate population?
The approximate population in Italy in 2012 was about 60,045,678.74.
What do we mean by approximate?We mean close in value or amount but not precise. an approximate solution. a rough date.
We can begin by establishing a ratio between the number of mobile phones and the population:
code:
147.4% = 1.474 (because 147.4% is the decimal equivalent of 1.474)
1.474 = number of mobile phones / population
We can solve for the population by substituting the given values:
code:
88,600,000 / population = 1.474
88,600,000 / 1.474 = population
The population is 60,045,678.74 people.
As a result, the approximate population of Italy in 2012 was 60,045,678.74.
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select all that apply standard deviations can be compared multiple select question. for data sets with different measurement units. for data sets with the same measurement units but greatly different magnitudes. only for data sets with the same measurement units and similar magnitude. only for data sets with the same measurement units.
The statement of option a "for data sets with different measurement units" and the statement of option b "for data sets with the same measurement units but greatly different magnitudes." is true about comparing standard deviations. So the option a and b is correct.
When comparing standard deviations, it is important to consider the context in which the data was collected. For example, if two datasets have similar means but different standard deviations, the one with the larger standard deviation may indicate more variability or a wider range of values.
On the other hand, if two datasets have different means but similar standard deviations, the one with the larger mean may be more representative of the population as a whole. In either case, it is important to look at the context of the data to make a more informed comparison.
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The complete question is:
Which of the following is true about comparing standard deviations? (Select all that apply)
a. For data sets with different measurement units
b. For data sets with the same measurement units but greatly different magnitudes
c. For data sets with the same measurement units and similar magnitude
d. For data sets with the same measurement units
Use the commutative property of addition to collect like terms
Answer: The commutative property of addition states that changing the order of the terms being added does not change the sum. Therefore, we can rearrange the terms in an expression in any order we choose without changing the result.
For example, if we have the expression:
3x + 2y + 4x + 5y
We can use the commutative property of addition to rearrange the terms as:
3x + 4x + 2y + 5y
Then, we can collect the like terms (terms with the same variable and exponent) by combining the coefficients:
7x + 7y
So the simplified expression is 7x + 7y.
Step-by-step explanation:
Dakota earned $14.00 in interest in Account A and $15.75 in interest in Account B after 21 months. If the simple interest rate is 4% for Account A and 3% for Account B, which account has the greater principal?
The account with the greater principle is Account B
How to find the account ?First, find the principle on Account A to be :
= Interest earned in 14 months / Interest rate for 21 months
= 14 / ( 4 % / 12 months x 21 months )
= 14 / 7 %
= $ 200
Then find the principle on Account B using the same method :
= Interest earned in 14 months / Interest rate for 21 months
= 15.75 / ( 3 % / 12 months x 21 months )
= 15. 75 / 5. 25 %
= $ 300
Account B has the greater principal.
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Help me simplify it pls
The simplest term is [tex]\frac{(2x-5)}{(x-3)(x-2)}[/tex].
what is factorization?Factorization of a number or an algebraic expression means writing the given number or given expression as a product of its factors. For algebraic expressions these factors can be numbers, variables, or an algebraic expression
Given,[tex]\frac{x-1}{x^{2} -3x+2} +\frac{x-2}{x^{2} -5x+6}[/tex]
By factorizing the denominator we get,
[tex]\frac{x-1}{(x-2)(x-1)} +\frac{x-2}{(x-2)(x-3)}[/tex]
By cancelling the common terms we get,
[tex]\frac{1}{(x-2)} +\frac{1}{(x-3)}[/tex]
Taking LCM we get,
[tex]\frac{(x-2)+(x-3)}{(x-3)(x-2)}[/tex]
By simplifying, we get,
[tex]\frac{(2x-5)}{(x-3)(x-2)}[/tex]
Hence, the simplest term is [tex]\frac{(2x-5)}{(x-3)(x-2)}[/tex]
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I GIVE BRAINLIEST.In the graph above, determine a system of only three transformations that will map ∆XYZ to the other three triangles.
Step-by-step explanation:
Rotation, reflection, translation
Hope this helps :)
Find the domain and the range of the following function.
f(x) =
x+3, for x≤-5
-1,
1
3x,
for -5
for x ≥ 6
The domain and the range for the function in this problem are given as follows:
Domain: All real values.Range: (∞, -2] U {-1} U [2, ∞).How to find the domain and the range of a function?The domain of a function is the set that contains all the values assumed by the values of x of the function.The range of a function is the set that contains all the values assumed by the values of y of the function.For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.
The range is obtained as follows:
Up to x = -5: values of x from negative infinity to -5 + 3 = -2.Between x = -5 and x = 6: constant value of 1.x = 6 and greater: Minimum value of 6/3 = 2.Hence the composition of these three intervals is given as follows:
(∞, -2] U {-1} U [2, ∞).
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Lola has 4
1
2
cups of rice. She uses
3
4
of the rice to make sushi rolls for dinner. She uses the rest of the rice to make rice pudding for dessert. How much rice does Lola use for the rice pudding?
Lola used 15/4 cups of rice to make rice pudding.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Given is that Lola has 4[tex]\frac{1}{2}[/tex] cups of rice. She uses 3/4 of the rice to make sushi rolls for dinner. She uses the rest of the rice to make rice pudding for dessert.
Amount used by Lola for the rice pudding -
{x} = 4[tex]\frac{1}{2}[/tex] - 3/4
{x} = 9/2 - 3/4
{x} = 18/4 - 3/4
{x} = 15/4
Therefore, Lola used 15/4 cups of rice to make rice pudding.
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{Complete question -
Lola has 4[tex]\frac{1}{2}[/tex] cups of rice. She uses 3/4 of the rice to make sushi rolls for dinner. She uses the rest of the rice to make rice pudding for dessert. How much rice does Lola use for the rice pudding?}
Find two different linear mappings that map the square with vertices 0, 1, 1 + i, and i, onto the square with vertices −1, 0, i, −1 + i.
The linear Mapping of the square with vertices
1: x = -1 + (2/2)(x + iy), y = -1 + (2/2)(x - iy)
2: x = -1 + (2/2)(x + y), y = -1 + (2/2)(-x + y)
The first linear mapping can be found by using the following matrix:
M = [a b]
[c d]
where, a = 2/2, b = -1, c = -2/2, d = 1.
By multiplying the matrix M with the vector [x, y]T, the linear mapping can be obtained.
For example, for the point (0, 1):
M * [0, 1]T = [-1, 1]
Similarly, for the point (1 + i, i):
M * [1 + i, i]T = [-1 + i, -1 + i]
Therefore, we get the linear mapping:
x = -1 + (2/2)(x + iy), y = -1 + (2/2)(x - iy)
The second linear mapping can be found by using the following matrix:
N = [e f]
[g h]
where, e = 2/2, f = -1, g = 2/2, h = 1.
By multiplying the matrix N with the vector
[x, y]T, the linear mapping can be obtained.
For example, for the point (0, 1):
N * [0, 1]T = [-1, 1]
Similarly, for the point (1 + i, i):
N * [1 + i, i]T = [i, -1 + i]
Therefore, we get the linear mapping:
x = -1 + (2/2)(x + y), y = -1 + (2/2)(-x + y)
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which of these existential quantifications are true, where the domain of x is the positive integers?
Two out of the three given existential quantifications are true, while one is false.
In mathematics, quantifiers are used to describe the properties of a set or a domain. One such quantifier is the existential quantifier, which is used to indicate the existence of at least one element in a set that satisfies a given property. In this case, we are interested in finding out which of the given existential quantifications are true, where the domain of x is restricted to positive integers. Let's explore this in more detail.
The domain of x is the set of positive integers, which means that x can only take on values such as 1, 2, 3, 4, and so on. The given existential quantifications are as follows:
∃x(x²=9)
∃x(x+3=5)
∃x(x²=2)
Let's examine each of these in turn.
∃x(x²=9)
This existential quantification is true. To see why, we need to find an integer value of x such that x² equals 9. We can easily see that x=3 satisfies this property, since 3² = 9. As 3 is an integer and satisfies the condition, the statement is true.
∃x(x+3=5)
This existential quantification is also true. We need to find an integer value of x such that x+3 equals 5. This can be easily done by subtracting 3 from both sides of the equation to get x=2. As 2 is an integer and satisfies the condition, the statement is true.
∃x(x²=2)
This existential quantification is false. We need to find an integer value of x such that x² equals 2. However, there is no such integer value of x. This can be proven using the fact that the square of any integer is always a non-negative integer. Therefore, the statement is false.
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Complete Question:
Which of these existential quantifications are true, where the domain of x is the positive integers?
∃x(x²=9)
∃x(x+3=5)
∃x(x²=2)