What is AAA congruence rule?
Answers
AAA ( Angle - Angle - Angle) congruence rule is one of congruence postulate but not preferable, for showing the similarity in two triangles
Two triangles are said to be congruent if one can be superimposed on the other exactly by rigid body motion, and the congruence theorem gives the conditions under which this occurs.
SAS (side-angle-side)SSS (side-side-side)ASA (angle-side-angle)AAA( angle-ange-angle)AAS (angle-angle-side)RHS( right angle-hypotenuse-side)AAA Congruence rule:
It is stands for angle-angle-angle Congruence rule. When all three angles of one triangle is equals to the corresponding angles of another triangle. but it is possible if and only if the corresponding sides of both triangles are equal and when all three sides of two triangles are equal to each other then we use SSS Congruence rule. So, it not considered as preferable congruence rule . For example, In ∆ABC and ∆PQR
all three angles of ∆ABC is equal to corresponding angles of ∆PQR. So,∆ABC and ∆PQR are congruent.
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Related Questions
6. Which of these is closest to 0.049 kg? A. ½ kg B. 1/20 kg C. 1/50 kg D. 2/50 kg
Answers
Answer:
B
Step-by-step explanation:
A = 0.5kg (Not close)
B = 0.05
C = 0.02 ( Not close)
D = 0.04
(Explanation why answer is B and not D)
B is closet because even we round off to two decimal places 0.05kg answer comes not 0.04kg
Plus 0.05 is 0.01kg away from 0.049, While 0.04kg is 0.09kg away from 0.049kg.
I hope my answer helps you.
1/20 kg is closest to 0.049 kg among the given choices. So, correct option is B.
To determine which option is closest to 0.049 kg, we can compare the given options to the target value and find the option with the smallest absolute difference.
A. ½ kg = 0.5 kg (Difference = |0.5 kg - 0.049 kg| ≈ 0.451 kg)
B. 1/20 kg = 0.05 kg (Difference = |0.05 kg - 0.049 kg| = 0.001 kg)
C. 1/50 kg = 0.02 kg (Difference = |0.02 kg - 0.049 kg| ≈ 0.029 kg)
D. 2/50 kg = 0.04 kg (Difference = |0.04 kg - 0.049 kg| = 0.009 kg)
Comparing the absolute differences, we can see that option B (1/20 kg = 0.05 kg) has the smallest difference from 0.049 kg, which is only 0.001 kg.
Therefore, option B (1/20 kg) is closest to 0.049 kg among the given choices.
When dealing with questions like this, it is helpful to compare the values using the absolute difference from the target value. The option with the smallest absolute difference is the closest approximation to the target value. In this case, 1/20 kg provides the closest value to 0.049 kg, making it the correct choice.
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After reviewing the generated schedule on Wednesday, you notice your Pharmacy Technician, Abigail Gibson, isn't being scheduled at all during the week. Which of the following would cause this?
O Minimum Base Hours set to 10
O Availability is not entered
O Workstation Proficiencies are set to "low" for all Workstations
Answers
After reviewing the generated schedule on Wednesday, you notice your Pharmacy Technician, Abigail Gibson, isn't being scheduled at all during the week. The option that will cause this is B. Availability is not entered
Who are Pharmacy technicians?Pharmacy technicians check inventory and fill prescriptions. Pharmacy assistants assist pharmacists in dispensing prescription drugs to patients or medical professionals. Hospitals and retail pharmacies are where they primarily work.
In order to assist and support patients and guarantee they receive the best care, pharmacists collaborate with pharmacy technicians, who are medical professionals.
In addition to primary care, educational, military, or veterinary practices, pharmacy technicians can work in community (retail) pharmacies, hospital pharmacies, pharmaceutical production or sales in the pharmaceutical industry, prisons, and community (retail) pharmacies.
Based on the information illustrated, the correct option is B.
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How do you find the missing length of a rectangular pyramid?
Answers
You can extrapolate the volume formula to get the missing length of a pyramid with a rectangular base.
Explain the term rectangular pyramid?A solid having a rectangular base and triangle lateral faces is called to as a rectangular pyramid. The lateral faces of the a rectangular pyramid are triangular, however its base is rectangular. A pyramid's base may well be square as well as hexagonal in shape, but its sides are often triangular.Determine the volume of a pyramid with a rectangular base using this formula.
Volume (V) is determined by multiplying the base area by the height by one-third (H). Base area equals width (W) times length (L). V= 1/3 x. (LxWxH).Thus, using your algebraic skills, determine the formula again for missing length of a pyramid with a rectangular base.
L = V / (H x W) / 3.
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What are the terms of expression 4x² 3xy?
Answers
The terms of expression 4x² - 3xy are
(a) 4x² and -3xy
(b) 4x² and 3xy
(c) 4x² and -xy
(d) x² and xy
What are the terms of an expression?A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 4 x + y, the two terms are 4 x and y. It is to be noted here that terms add up to form the expression.
What are the constant terms in the expression?Terms: a2,6a,and 9.
Variables: a2,a
Constants:9
Factors: a,a are the factors of term 1,-6 and a are the factors of term 2,and 9 is the factor of term 3.
Coefficients:1 is the coefficient of a2,-6 is the coefficient of a,and 9 is the coefficient of the constant term
Operators:- and+
Given, the expression is 4x² - 3xy.
We have to find the terms of the expression.
The terms are the numbers or the variables added together.
Each term in an algebraic expression is separated by a + sign or - sign.
Therefore, the terms in the given expression are 4x² and -3xy.
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Points E, D, and H are the midpoints of the sides of TUV, UV = 50, TV = 64, and HD = 50, Find TU
Answers
Applying the triangle midsegment theorem, the length of segment TU = 100 units.
What is the Triangle Midsegment Theorem?If a line connects the midpoints of two sides of a triangle, it is parallel to the third side, and according to the triangle midsegment theorem, it has a length that is half the measure of the third side of that triangle.
Given the triangle, TUV, where:
Segment TU is a third side to the midsegment HD = 50 units.
Thus, apply the triangle midsegment theorem to find the length of segment TU.
HD = 1/2(TU)
Substitute:
50 = 1/2(TU)
2(50) = TU
100 = TU
TU = 100 units
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which expression represents the total number of hours driven? responses x y x y, y 70 y 70, 300 x 300 x, 70x 55y
Answers
The total number of hours driven can be represented by the expression "x + y." This represents the sum of the hours driven in one car (x) and the hours driven in another car (y).
The other expressions do not represent the total number of hours driven. "x y" is not a valid mathematical expression. "y 70" and "300 x" represent the number of miles driven by one car and the number of miles driven by another car, respectively, but do not represent the total number of hours driven. "70x" and "55y" represent the number of miles driven by one car and the number of miles driven by another car, respectively, but do not represent the total number of hours driven.
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1, Class - 12, Question, In any triangle ABC, if, A=30° B= 90 find. a:b:c.
Answers
Answer:
1:3:2
Step-by-step explanation:
Sum of triangle is 180°
A : B : C
30 : 90 : (180 -90 - 30)
30 : 90 : 60
1 : 3 : 2
I hope my answer helps you.
a variable x is normally distributed with mean 21 and standard deviation 5. round your answers to the nearest hundredth as needed. a) determine the z -score for x
Answers
The formula for determining a z-score is z = (x-μ)/σ, where x is the raw score, z is the population mean, and z is the population standard deviation.
How to calculate a raw score when a z-score ?The raw score less the population mean, divided by the population standard deviation, is what the calculation reveals to be the z-score.We occasionally need to locate the raw score that corresponds to a z-score that we are aware of. A sample's z-score can be converted into a raw score using the following formula:X=(z)(SD) + mean
The formula demonstrates how to multiply the z-score by the standard deviation, then add that result to the mean.Verify if your response is logical: The raw score that corresponds to a negative z-score should be lower than the mean, and the raw score that corresponds to a positive z-score must be higher than the mean.To Learn more About z-score refer to:
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What is the surface area of a 5 cm cube?
Answers
Answer:
A=6a2=6×(5)2=6×25=150cm2.
Step-by-step explanation:
How to learn 13 table fast?
Answers
The trick for table 13 are as follows.
What is multiplication table?A multiplication chart is a table that displays the products of two numbers. One set of numbers is typically written in the left column, while another set is written in the top row. The numbers in the products are listed in a rectangular array. Addition is repeated when you multiply.
To learn table fast follow points,
1. To learn the 13 times table, we must first learn the 3 times table. 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the multiples of 3.
2. Add natural numbers to the tenth digit of the multiples of 3 to get the multiples of 13. As a result, the 13 times table can be derived as follows: 1+0)3, (2+0)6, (3+0)9, (4+1)2, (5+1)5, (6+1)8, (7+2)1, (8+2)4, (9+2)7, (10+3)0 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130.
3. The 13 multiplication table does not have any rules that make it easy to remember, but there is a pattern for every ten multiples of three: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130. Students can remember these digits to help them with the 13 times table because the last digit of these multiples always repeats.
Hence, follow the steps to learn table of 13.
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How do you find the domain and vertical asymptotes?
Answers
The domain of a function as described by the question, can be found by solving a given function for x such that the values of x satisfy the equation. And the vertical asymptotes can be found by solving for x values which make the equation go towards positive or negative infinity.
What is an asymptote?A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. To put it another way, an asymptote is a line that a curve travels towards as it approaches infinity.
What is domain of a function?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x) make up this set x.
As asked by the question, the domain of a function can be found by solving the equation f(x) = y for values of x such that the values of x give out a single value y. Similarly, the vertical asymptotes can be found from a rational function [tex]\frac{p(x)}{q(x)}[/tex] by equating the denominator q(x) to 0 and solving for x. i.e q(x) = 0.
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Right triangles ABC and DEF are drawn to measure the slope of the line.
Answers
Right triangles ABC and DEF are drawn to measure the slope of the line is:
a) run = 2 rise = 3 slope = 3/2
b) run = 6 rise = 9 slope = 9/6 = 3/2
c) Yes, they are similar because the 2 triangles are similar.
Two triangles are similar if they meet one of the following criteria. : Two pairs of corresponding angles are equal.
What is Right triangles?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
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Is equidistant to the poles is called Equator?
Answers
Answer:
In astronomy, the celestial equator is the great circle in which the plane of the terrestrial Equator intersects the celestial sphere; it consequently is equidistant from the celestial poles. When the Sun lies in its plane, day and night are everywhere of equal length, a twice-per-year occurrence known as equinox.
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Step-by-step explanation:
What do the x-intercept and y-intercept represent in terms of the units on the axes?
Answers
The x-intercept and y-intercept on the graph will cross the x and y axes accordingly.
In order to find the x-intercept and y-intercept represent in terms of the units on the axes, we must know the definition of each of them.
In math the x-intercept is defined as the value of the x coordinate of a point where the value of y coordinate is equal to zero.
Similarly, the y intercept in math is referred as the point where the graph intersects the y-axis.
While looking into the given definition, we have identified that intercept refer the intersecting point of the graph.
Based on these we have concluded that x and y intercept are the intersecting point of the graph.
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A landscape contractor bids on jobs where he can make $3250 profit. The probabilities of getting 1, 2, 3, or 4 jobs per month are shown. Find the contractor's expected profit per month. The contractor's expected profit per month is $
Answers
The profit per month for the contractor is obtained as $9425.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
The profit of the contractor per job is given as $3250.
As per the given table the expected value can be obtained as,
E(x) = [tex]\sum_{x = 1}^{4} xP(x)[/tex]
⇒ E(x) = 1 × 0.1 + 2 × 0.2 + 3 × 0.4 + 4 × 0.3
⇒ 2.9
Then, the expected profit of is given as 3250 × 2.9 = $9425
Hence, the profit per month is obtained as $9425.
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How do you classify the type of discontinuity?
Answers
There are three types of discontinuity.
Jump DiscontinuityInfinite DiscontinuityRemovable DiscontinuityIf a function f(x) is not continuous at a point 'a' in its domain D, it is said to be discontinuous at that location. A point of discontinuity of the function is thus referred to as point "a."
Any of the following scenarios might cause the discontinuity:
A function's right-hand limit, left-hand limit, or both limits might not exist.There may be a right-hand limit and a left-hand limit to function, but they are not equal.It is possible for a function to have both a right-hand limit and a left-hand limit, although neither limit necessarily has to equal f. (a).Two forms of Jump discontinuity exist:Discontinuity of the First Type: If the right hand of the function exists but is not equal to f, then the function f(x) is said to have a discontinuity of the first kind from the right at x = a. (a). The Left-Hand Limit and the Right-Hand Limit both exist in Jump Discontinuity and are finite, but they are not equivalent to one another.
Discontinuity of the Second Type: If a function f(x) at x = a has neither a left-hand limit nor a right-hand limit, it is said to have discontinuity of the second kind.
If the left-hand limit at x tends to point 'a' is equal to the right-hand limit at x tends to point 'a,' but their common value is not equal to f, then the function f(x) has a removable discontinuity at x = a. (a).One or both of the right hand and left hand limits are either infinite or nonexistent in infinite discontinuity. It also goes by the name of "Essential Discontinuity."To know more about discontinuity refer to:
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Discontinuity of the First Type: If the right hand of the function exists but is not equal to f, then the function f(x) is said to have a discontinuity of the first kind from the right at x = a. (a). The Left-Hand Limit and the Right-Hand Limit both exist in Jump Discontinuity and are finite, but they are not equivalent to one another.
Solve for x. Round to the nearest tenth.
X
21
27
Answers
The value of x for the given figure will be equal to √212.
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.
Apply the Pythagorean theorem for the first triangle,
H² = x² - 6²
Apply the Pythagorean theorem for the second triangle,
B² = 27² - x²
Apply the Pythagorean theorem to the third triangle,
H² = 27² - x² - 21²
H² = -x² + 288
x² - 6² = -x² + 288
2x² = 424
x² = 212
x=√212
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please help me this is my last chance.
Answers
Answer:9/5
Step-by-step explanation:
Answer:
A. 9/5
C. 1 4/5
Step-by-step explanation:
3 x 3/5 = (3 x 3)/5 = 9/5
9/5 = 5/5 + 4/5 = 1 4/5
Evaluate The Triple Integral ∭ExydV Where E Is The Solid Tetrahedon With Vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3)
Answers
The triple integration of ∭E xy dV and The Solid Tetrahedron With Vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3), is 8 / 5.
What is integration?
When infinitesimal data are combined, concepts like displacement, area, and volume can be described by assigning numerical values to the functions that make up an integral. Integration is the procedure for locating integrals.
Given:
∭E xy dV and The Solid Tetrahedron With Vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3),
Calculate the equation of plane passing through the vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3) as shown below,
x / 8 + y / 1 + z / 3 = 1
z = 24 - 3x -24y / 8
Put z = 0
y = 1 - 1 / 8x
Put y = o
x = 8
Calculate the integral as shown below,
[tex]\int \int\int_E xydV = \int _0^8 \int _0^{1-x/8} \int _0^{{24-3x-24y}/8} xy\ dz\ dy\ dx[/tex]
∫∫∫E = [tex]1/8 \int _0^8 [24xy^2 / 2 - 3x^2y^2 / 2 - 24xy^3 / 3]^{1-x /8}dx[/tex]
∫∫∫E = 1 / 8 × 64 / 5
∫∫∫E = 8 / 5
Thus, the triple integral is 8 / 5.
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What's the slope of 4y =- 4?
Answers
The slope of 4y =- 4 is zero.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
Given equation:
4y =- 4
To find the slope:
First, we simplify the equation.
Divide by 4.
(4/4)y = -4/4
y = -1
Now, we know the slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
Comparing, both the equation,
we get,
m = 0.
So, the slope is 0.
Therefore, the slope is 0. This produces a horizontal line.
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How do you explain comparing numbers?
Answers
Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.
What are comparing numbers?The number with more digits is the greater number. If two numbers are having the same number of digits, then compare the left-most digits of both numbers.Comparison of Numbers is the process that defines the similar properties between two numbers and identifies the number that is greater than, smaller than, or equal to another number. There are some basic signs or operators of comparison in Mathematics; they are greater than (>), less than (<), or equal sign (=).Comparison is the process that tells us the similar properties of different objects. This is the primary concept in Mathematics, which helps us describe whether the numbers are equal, or one is greater than or one is smaller than the other, in comparing two numbers. We can do fraction comparison, decimal comparison and also compare rational numbersIn Mathematics, there are three special symbols used in a comparison of numbers. The basic symbols used in the comparison of numbers are given below,Greater than (>)Less than (<)Equals to (=)Using the above symbols, we can compare two numbers of any type, such as natural numbers, whole numbers, integers, and decimal numbers, etc. Thus, the process of comparing and exploring the differences between the numbers is known as the Comparison of Numbers.To learn more about comparing numbers refers to:
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Is a hole considered an asymptote?
Answers
Yes, a hole is considered an asymptote.
There are "holes" in the graph called vertical asymptotes where the function cannot have a value. They represent areas where the x-value is not permitted.
In particular, a rational function's denominator can never equal zero. A vertical asymptote is any value of x that would result in the denominator being equal to zero.
We may determine which direction the graph will incline as its x-values rise by looking for a horizontal or slant asymptote. In contrast to the vertical asymptote, a horizontal or slant asymptote can be touched or crossed by the graph.
Yes, a hole is considered an asymptote.
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In example, the denominator of a rational function can never be 0. Any value of x that would cause the denominator to equal 0 is known as a vertical asymptote.
By searching for a horizontal or slant asymptote, we may determine which direction the graph will incline as its x-values increase. The graph can touch or cross a horizontal or slant asymptote as opposed to the vertical asymptote.
determine the average number of planes that will stack up, waiting to land. 2. (2) find the average time a plane must wait in line before it can land. 3. (2) calculate the average time it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land.
Answers
Average number of planes that will stack up waiting to land: This can vary greatly depending on the size of the airport, the number of flights per day, and the number of runways available.
What is average?
Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures.
To determine the average number of planes that will stack up waiting to land, we need to know the rate at which planes arrive at the airport and the rate at which they are able to land.
Generally, an airport can expect to experience a queue of up to 10 planes waiting to land at peak times.
Average time a plane must wait in line before it can land: This also varies significantly depending on the airport and the conditions. Generally, a plane must wait an average of 5-7 minutes before it is able to land.
Average time it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land: This time will depend on the size of the airport, the number of planes in the queue, and the amount of time it takes for the plane to taxi off the runway. Generally, a plane can expect to clear the runway in about 2-3 minutes.
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Select the correct answer from each drop-down menu. ∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. the measure of the longest side of ∆abc is units. ∆abc is triangle. if ∆abd is formed with the point d(1, 2) as its third vertex, then ∆abd is triangle. the length of side ad is units.
Answers
As per the distance formula, the longest side of triangle ABC is AB and the difference point is 9.1 units.
The formula to calculate the distance of two coordinates is written as
=> d = √(x2 - x1)² + (y2 - y1)²
where (x1, y1) and (x2, y2) are the coordinates.
Here we have given that ∆ABC has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices.
And we need to find the measure of the longest side of ∆ABC is units.
Here we have to take the points A and B and then we need to find the distance for the points AB,
AB = √(-2 - 7)² + (2 - 1)²
AB = √(-9)² + (1)²
AB = √81 + 1
AB = √82 = 9.1
Now, we have to take the next two points, and then we have to find the distance between the points,
BC = √(4 - (-2))² + (2 - 2)²
BC = √(6)² + (0)²
BC = √36 + 0
BC = √36 = 6
Finally, we have to calculate the distance between the point C and A then we get,
CA = √(7 - 4)² + (1 - 2)²
CA = √(3)² + (-1)²
CA = √9 + 1
CA = √10 = 3.2
While looking into the given distance we have identified the the point AB has the longest side.
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Can you use SSA to prove triangles congruent?
Answers
No, we can not use SSA to prove triangles are congruent.
The side-side-angle congruence rule also referred to as the SSA congruence rule, deals with the congruence of two triangles.
According to the SSA congruence rule, two sides and an angle that is not contained between them must be equal to two sides and an angle of the other triangle in order for the two triangles to be equal. Due to the possibility that the sides of the two triangles may not be on the same corresponding sides, this congruence rule does not consider two triangles to be congruent. It's possible that the two triangles will wind up being of different sizes and shapes. The SSA congruence rule is therefore invalid.
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How do you know if an image is congruent?
Answers
Answer:
One of them must be a mirror image of the other
Step-by-step explanation:
Two shapes are congruent if one is a mirror shape of the other or if both have the same size.
Austin went to the store to buy some chicken. The price per pound of the chicken is
$3.50 per pound and he has a coupon for $1.50 off the final amount. With the
coupon, how much would Austin have to pay to buy 3 pounds of chicken? Also, write
an expression for the cost to buy p pounds of chicken, assuming at least one pound is
purchased.
Answers
By using multiplication and subtraction, it can be calculated that-
Austin has to pay $9 for 3 pounds of chicken
Austin has to pay $(10.50 [tex]\times[/tex] p- 1.50) for p pounds of chicken
What is subtraction and multiplication?
To find how big or small one number is from the other, then the operation used is called subtraction of numbers
Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers
Here, subtraction and multiplication is used
Cost of one pound of chicken = $3.50
Cost of three pounds of chicken = $3.50 [tex]\times[/tex] 3 = $10.50
He has a coupon for $1.50 off the final amount.
Amount of money Austin has to pay for 3 pounds of chicken =
$(10.50 - 1.50) = $9
Amount of money Austin has to pay for p pounds of chicken =
$(10.50 [tex]\times[/tex] p- 1.50)
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The fraction simplifies to which of the following?
(32008)²-(32006)²/ (32007)²-(32005)²
(A) 1 (B) 9/4 (C) 3 (D) 9/2 (E) 9
Answers
The fraction simplifies to 1. Option A.
What is Difference of Squares?The difference of two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the difference of the square roots and the other shows the sum of the square roots, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. This identity is often used in algebra where it is useful in applications to integer factorization, the quadratic sieve, the algebraic factorization, etc.
One thing to note about this theorem is that it does not apply to the SUM of squares.
(32008)²-(32006)²/ (32007)²-(32005)²
(32008 - 32006)² / (32007 - 32005)²
(2)² / (2)²
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What graph is used in linear inequality?
Answers
The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The graph of an inequality is shown below:
What is an inequality equation?
The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.
Example -
Let us take an equation, 4x + 8y ≤ -24
Now, solve the above equation in the form of slope-intercept.
4x + 8y ≤ -24
or, 8y ≤ - 4x - 24
or, y ≤ -(1/2)x - 3
Now, the graph becomes according to the slope-intercept form is:
Here we noticed that,
This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.
Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.
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This has 2 parts - The first one is the easy part, the
second parts presents a challenge. You must show
your strategy and calculations to receive full credit.
Write your answer as whole numbers in hours and
in minutes. (Example: 35.25 = 35 hours and 15
minutes (NOTE: every 0.1 hour = 6 minutes))
Part 1: 2 airplanes left the same airport at the same
time. One is traveling at 422 mph straight east, the
other is traveling 384 mph straight west.
How long will it take before they are 6045 miles
apart?
Part 2: 2 airplanes left the same airport at the same
time. One is traveling at 422 mph straight NORTH,
the other is traveling 384 mph straight WEST.
How long will it take before they are 1997 miles
apart?
Answers
Answer:
Step-by-step explanation:
Part 1)
add their velocities
422+384= 806
now divide 6045 by 806 = 7.5 or 7 hours 30 minutes
7:30 = t hours:minutes
Part 2)
For this part we will need to employ Pythagoras theorem. we need the hypotenuse to be 1,997
so, when will plane traveling N , and plane traveling W be that far (1997)?
or
when does [tex]1997^{2}[/tex] = [tex]N^{2}[/tex] + [tex]W^{2}[/tex]
then we're also given that N = 422*t
and that W = 384 * t
so now our formula looks like
[tex]1997^{2}[/tex] = [tex](422*t)^{2}[/tex] + [tex](384*t)^{2}[/tex]
rewrite this so it's making clear math sense
[tex]1997^{2}[/tex] = [tex]422^{2}[/tex] * [tex]t^{2}[/tex] + [tex]384^{2}[/tex] * [tex]t^{2}[/tex]
now pull out the [tex]t^{2}[/tex]
[tex]1997^{2}[/tex] = ( [tex]422^{2}[/tex] + [tex]384^{2}[/tex] ) * [tex]t^{2}[/tex]
now simplify some
3988009 = (178084 + 147456 ) * [tex]t^{2}[/tex]
now divide the left side by the numbers on the right
3988009 / (178084 + 147456 ) = [tex]t^{2}[/tex]
12.12044234 = [tex]t^{2}[/tex]
[tex]\sqrt{12.25044234}[/tex] = t
3.500063191 = t
so at 3 and a half hours, the planes will be 1997 miles apart
3:30 = t