Answer:
Step-by-step explanation:
To determine if they can use 26 of one type and 14 of the other, we need to calculate the cost for each scenario and compare it to their budget of $400.
If they use 26 round tables, it would cost 26 * $10 = $260.
And if they use 14 square tables, it would cost 14 * $10 = $140.
The total cost would be $260 + $140 = $400, which is equal to their budget.
Now, we need to make sure that they can seat all the guests with the tables they plan to rent.
If they use 26 round tables, they can seat 26 * 6 = 156 guests.
And if they use 14 square tables, they can seat 14 * 8 = 112 guests.
The total number of guests they can seat would be 156 + 112 = 268.
since they expect at least 260 guests to attend and they can seat 268 guests, the table rental plan of 26 round tables and 14 square tables is feasible both financially and in terms of seating capacity.
let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 4, h'(1) = 4, g'(2) = 4, and f '(4) = 7. find r'(1). r'(1)
The value of r'(1) is 112.
To find the derivative of r(x) at x = 1, we'll use the chain rule. The chain rule states that if r(x) = f(g(h(x))), then the derivative of r(x) with respect to x is given by r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x).
When r(x) = f(g(h(x))) by chain rule
r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)
So r'(1) = f'(g(h(1))) * g'(h(1)) * h'(x)
As h(1) = 2 and h'(1) = 4
r'(1) = f'(g(2)) * g'(2) * 4
As g(2) = 4 and g'(2) = 4
r'(1) = f'(4) * 4 * 4
As f'(4) = 7
r'(1) = 7 * 4 * 4
r'(1) = 112
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5 times the sum of two numbers is 250 and the difference of the numbers is 18
54 kilometers in 4 hours = 81 kilometers in __ hours
Answer:
6 hours
Step-by-step explanation:
create a proportion:
54 km/4 hrs equals 81km/? hours
[tex]\frac{54}{4}[/tex] = [tex]\frac{81}{?}[/tex]
solve a proportion by cross-multiplying:
54? = 324
? = 324/54
? = 6
Answer:
6 hr
Step-by-step explanation:
If 54 km --> 4 hr then,
81 km --> ? hr
You can make a rule of three:
? hr = (81*4)/54
? hr = 6
So 81 km in 6 hours
Find the length of AE if BD is a midsegment. PLEASE HELP
The length of AE is given as follows:
AE = 7 units.
What is the midsegment theorem?The midsegment of a triangle states that the segment connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.
The midsegment of the triangle in this problem is given by the following segment:
BD.
The length of BD is given as follows:
BD = 2 - (-1.5)
BD = 3.5 units.
Hence the length of AE is obtained as follows:
AE = 2BD
AE = 2 x 3.5
AE = 7 units.
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Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) a_n = sin (4n)/2n + squareroot n lim n rightarrow a_n = DNE
The sequence aₙ = sin (4n)/2n + √n diverges because it does not have a limit that can be expressed in a finite manner.
A sequence is a set of numbers that follow a certain pattern. The behavior of the sequence as n approaches infinity determines whether the sequence converges or diverges.
In this case, the sequence
=> aₙ = sin (4n)/2n + √n.
To determine whether the sequence converges or diverges, we need to find the limit as n approaches infinity.
However, in this case, the limit as n approaches infinity is DNE, meaning it does not exist. This means that the sequence diverges, as it does not approach a limit as n approaches infinity.
In this case, the sequence
=> aₙ = sin (4n)/2n + √n
converges to DNE, meaning that it does not have a limit that can be expressed in a finite manner.
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a triangular fence is being built to surround a garden. if two of the side lengths must be 4 feet and 12 feet, which inequality could be solved to determine the minimum length of the third side?
The minimum length of the third side must be greater than 16 feet.
The minimum length of the third side can be determined using the Triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. The Triangle Inequality Theorem can be expressed by the following inequality: a + b > c, where a, b, and c are the lengths of the three sides of the triangle. In this case, we have two sides of 4 feet and 12 feet, so the inequality can be written as 4 + 12 > c, which simplifies to 16 > c. Solving for c yields c > 16, which means that the minimum length of the third side must be greater than 16 feet.
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Seasons entire family took the train to watch the baseball game. The admission to the game is eight dollars per person. The round-trip price for the train cost $4.50 per person. There are six people and seasons family. Write an expression for the total cost of the outing using parentheses. Use the distributive property to find the cost.
Answer: $75
Step-by-step explanation:
Price for one person: $4.50+$8
Price for six people: 6($4.50+$8)=$75
Given EFG = XYZ, find m
A. 45 degrees
B. 60 degrees
C. 90 degrees
D. 30 degrees
Based on the definition of congruent triangles, m<X = 45 degrees.
What are Congruent Triangles?Congruent triangles are two triangles that have exactly the same size and shape, which connotes that every corresponding parts of the triangles are equal.
Given EFG = XYZ, therefore, the measure of angle E will be congruent to the measure of angle X.
m<E = m<X
m<E = 180 - 90 - 60
m<E = 30°
Therefore, m<X = 30°.
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You have a biased coin, where each toss has a 3 / 5 3/5 chance of landing heads. But each toss is independent of the others. Suppose you’re going to flip the coin 1 , 000 1,000 times. The first 998 tosses all land tails. What is the probability at least one of the last two flips will be tails?
The probability of getting at least one tails on the last two flips is 8/25.
The probability of getting a tails on a single toss of the coin is 3/5. Therefore the probability of getting tails on the last two flips is (3/5)^2. This is because the coin tosses are independent of one another.
Therefore the probability of getting at least one tails on the last two flips is 1 - (3/5)^2 = 8/25.
This is because the probability of getting two tails is (3/5)^2, and the probability of getting at least one tails is the complement of that. Therefore the probability of getting at least one tails on the last two flips is 8/25.
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A scatter plot is shown on the coordinate plane.
Which two points would a line of fit go through to best fit the data?
(1, 10) and (10, 1)
(1, 7) and (2, 6)
(3, 7) and (7, 4)
(3, 8) and (6, 6)
Line of fit go through (1, 10) and (10, 1) to best fit the data.
What is Scatterplots?Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.
Line of best fit of the scatterplot should go through as many points as possible of the graph.
If we draw a line passing through the pair of points given in the options, the line passing through (1, 10) and (10, 1) passes through (9, 2), (7, 4) and (3, 8).
No other line drawn through points in the options passes through 5 points.
Hence the line of best fit is the line passing through (1, 10) and (10, 1).
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5. Angela earns £35 240 a year.
She has to pay income tax.
She is allowed to earn £6475 before paying tax.
She pays 20% tax on the rest.
Her employer deducts the income tax each month.
Work out how much income tax Angela gets deducted each month
£479.42 is the income tax Angela gets deducted each month.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, Angela earns £35 240 a year. She has to pay income tax. She is allowed to earn £6475 before paying tax. She pays 20% tax on the rest.
So,
taxable income = 35,240-6,475
taxable income = 28,765
Since She pays 20% tax
Thus,
The Total tax = 28,765 * 20%
the total tax = 5,753
Since Her employer deducts the income tax each month.
so,
Income tax deducted each month = 5,753/12
Income tax deducted each month = 479.417
Therefore, the income tax Angela gets deducted each month is £479.42.
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(1 point) select all statements that are correct. there may be more than one correct answer. the statements may appear in what seems to be a random order. a. if a system has three unknowns and the reduced row echelon form of the augmented matrix has two nonzero rows, then the system can have an infinite number of solutions. b. a system of linear equations with more unknowns than equations will have an infinite number of solutions. c. every matrix a is row equivalent to a matrix in (row) echelon form. d. every matrix has a unique reduced row echelon form. e. adding one row to a multiple of another row is one type of elementary row operation. f. if a system has three unknowns and its reduced row echelon form of the augmented matrix has three nonzero rows, then the system has at least one solution. g. adding a multiple of one row to another row is one type of elementary row operation. h. none of the above
The answer to all the following options is given below along with the suitable reasoning.
a. Incorrect. If a system of linear equations has more unknowns than equations and the reduced row echelon form of the augmented matrix has two nonzero rows, the system is inconsistent and has no solutions.
b. Incorrect. A system of linear equations with more unknowns than equations is underdetermined and can have either no solutions or an infinite number of solutions.
c. Correct. A matrix can be row-reduced to an echelon form, which is a simpler form that makes it easier to find the solution to the system of linear equations represented by the matrix.
d. Correct. Every matrix can be row-reduced to a unique reduced row echelon form by performing a sequence of elementary row operations, which are reversible and preserve the solutions of the system of linear equations.
e. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.
f. Correct. If a system of linear equations has three unknowns and the reduced row echelon form of the augmented matrix has three nonzero rows, then the system is consistent and has a unique solution.
g. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.
h. Incorrect. Some of the statements are correct.
Therefore, The answer to all the following options is given above along with the suitable reasoning.
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The answer to all the following options is given below along with the suitable reasoning.
a. Incorrect. If a system of linear equations has more unknowns than equations and the reduced row echelon form of the augmented matrix has two nonzero rows, the system is inconsistent and has no solutions.
b. Incorrect. A system of linear equations with more unknowns than equations is underdetermined and can have either no solutions or an infinite number of solutions.
c. Correct. A matrix can be row-reduced to an echelon form, which is a simpler form that makes it easier to find the solution to the system of linear equations represented by the matrix.
d. Correct. Every matrix can be row-reduced to a unique reduced row echelon form by performing a sequence of elementary row operations, which are reversible and preserve the solutions of the system of linear equations.
e. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.
f. Correct. If a system of linear equations has three unknowns and the reduced row echelon form of the augmented matrix has three nonzero rows, then the system is consistent and has a unique solution.
g. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.
h. Incorrect. Some of the statements are correct.
Therefore, The answer to all the following options is given above along with the suitable reasoning.
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1
• En una plaza comercial se desea construir un
domo que permita dar sombra a un espacio de
forma triangular. ¿En qué punto se recomienda
poner el pilar de apoyo que sostenga el domo?
¿A qué se debe esto?
PLEASE HELP ME. THE ASSIGNMENT IS ON THE SCREEN
Answer:
D.) the ovens temperature after 1 minute.
Step-by-step explanation:
if "x" is the number of minutes that have passed then the output is the temp after the oven was preheating for 'x" amount of minutes
one point is in quadrant lll. The points are reflections of each other across the y-axis
The points are reflections of each other across the y-axis is,
⇒ ( x, - y)
What is Refection?Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.
We have to given that;
One point is in quadrant lll.
And, The points are reflections of each other across the y-axis.
Now, Let a point is in quadrant III = (-x, - y)
Where, x > 0, y > 0
We know that;
The rule of the reflection across the y - axis is,
⇒ (x, y) → (- x, y)
Thus, We get;
The points are reflections of each other across the y-axis is,
⇒ (- x, - y) → (- (-x), - y)
→ (x, - y)
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Jack Pott is paid a straight commission of 6% on his sales. During
February, his sales were $38,000. What was his commission?
Answer:
$2280
Step-by-step explanation:
38000*6% =2280
Find the missing number.
Increased
by 25
Decreased
by. %
The percentage by which the number has to be decreased is 20%.
What do you mean by algebraic expression?It represents a mathematical relationship or calculation. For example, the expression "2x + 3" is an algebraic expression that represents a linear equation with a variable x and constants 2 and 3. Algebraic expressions can be simplified, evaluated for specific values of the variables, and used to solve equations.
Given:
A number is increased by 25%
To find:
The percentage by which it has decreased
Solution:
The percentage by which the number has to be decreased is 20%.
We can find the percentage by following the given steps-
We know that a number increased by a percentage decreases by a different percentage.
Let us assume that the number is 100.
We know that this number has been increased by 25%.
So, the new number=100+25% of 100
=100+25/100×100
=100+25
=125
Now, the new number is 125.
Let us assume that this number has to be decreased by X% to obtain 100.
So, 125-X% of 125=100
125-X/100×125=100
125-1.25X=100
125-100=1.25X
25=1.25X
25×100/125=X
2500/125=X
X=20%
Therefore, the percentage by which the number has to be decreased is 20%.
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Solve the initial value problem. dt/ds = 8 sin2 +[t=π/12] s(0)=2 (Type an exact answer, using à as needed
After integration, the expression will be[tex]S=8(sin^{3}(t+\frac{\pi}{3} )(-cos(t+\frac{\pi}{3}+t^{2}+\frac{\pi}{12t})-8tsin^{2}(t+\frac{\pi}{3})[/tex]
Indicate integrationIntegration is the process of calculating an integral. Integrals are used by mathematicians to compute a range of useful quantities, such as areas, volumes, displacement, etc. Usually, when we talk about integrals, we mean definite integrals. Indefinite integrals are used for antiderivatives. Integration is one of the two primary calculus topics in mathematics, along with differentiation (which measure the rate of change of any function with respect to its variables).
Fundamental IntegralAn integral that has both the upper and lower boundaries is said to be definite. Only a real line may be used for X to lay. A Riemann Integral is another name for the Definite Integral.
∫f(x)dx from a to b.
Indefinite integralThe definition of integrals without upper and lower bounds. It appears as follows:
A definite Integral is represented as:
∫f(x)dx = F(x) + C
Where C is any constant and the function f(x) is called the integrand.
Now,
Right expression is
[tex]\frac{dS}{dt} = 8sin^{2}(t+\frac{\pi}{12} )[/tex]
After integration
[tex]S = 8sin^{2} (t+\frac{\pi}{12} ).dt[/tex]
[tex]S=8(sin^{3}(t+\frac{\pi}{3} )(-cos(t+\frac{\pi}{3}+t^{2}+\frac{\pi}{12t})-8tsin^{2}(t+\frac{\pi}{3})[/tex]
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How ti calculate loan interest?
Divide your interest rate by the number of payments you’ll make that year
How to calculate simple interest
By utilizing the following calculation, you may get your total interest:
Interest is calculated as follows: principal loan amount x interest rate x duration
The simple interest formula is $20,000 x.05 x 5 = $5,000 in interest, for instance, if you take out a $20,000 loan with a five-year term and a 5% interest rate.
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"Simple Interest is Principal x Interest Rate x Time" is the written formula.The simplest method for computing interest is using this equation.
What is the simplest interest formula?The easy interest calculation is as follows:Interest is equal to P x R x T.principal amount (the beginning balance). The interest rate, R (usually per year, expressed as a decimal).T is the quantity of time periods (generally one-year time periods).If, for instance, your current APR is 17.99% and you currently owe $500 on your credit card over the course of the month, you can get your monthly interest rate by dividing 17.99% by 12, which is roughly 1.49%.To get a monthly payment of $7.45 from $500, multiply the sum by 0.0149.Divide the principal by the time, interest rate, and time period to calculate simple interest.The equation is expressed as "Simple Interest = Principal x Interest Rate x Time."It is easiest to calculate interest using this equation.To learn more about Interest refer
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27. write the following mask in slash notation (/n): a. 255.255.255.0
255.255.255.0 is written as /24 in slash notation (/n).
Slash notation is a compact way to show or write an IPv4 subnet mask. When you use slash notation, you write the IP address, a forward slash (/), and the subnet mask number.
1- To find the subnet mask number:
2- Convert the decimal representation of the subnet mask to a binary representation.
Count each “1” in the subnet mask. The total is the subnet mask number.
In IPv6, slash notation is used to represent the network identifier prefix for an IPv6 network. The prefix is expressed as a slash (/) followed by the prefix size, which is a decimal number between 1 and 128.
Thus, 255.255.255.0 is written as /24 in slash notation (/n).
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ABCD is a trapezoid with shorter base DC = 3 cm and altitude PQ going through the point of intersection of the diagonals O, such that PO = 1 cm and 0Q = 3 cm. Find AB, the ratio CO: AO, and the ratio between the areas of ADOC and ABOA.
The ratio of Areas is 1:1.
What is Trapezium?A quadrilateral with one set of parallel opposite sides is a trapezium. The bases and legs of a trapezium are referred to as parallel and non-parallel, respectively. It also goes by the name trapezoid.
As, The diagonals of a trapezium divide each other proportionally.
AO / OC = OB/ OD
Also, OA= OB and OC= OD
So, OA/ OC = 1: 1
In Triangle DOC and BOA
<AOB = <COD (Vertical Opposite angle)
<BAO = <OCD ( Alternate Interior angle)
By AA similarity Criteria Triangle DOC and BOA are similar.
So, ar (Δ DOC)/ ar (ΔBOA)
= DO / OB = OC / OA = DC / BA
As, the ratio of corresponding length is equal.
So, the ratio of Triangle is 1:1
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2/9 of the students in a school are in sixth grade.
Type the answers to each question in the boxes below.
a. How many sixth graders are there if the school has 90 students?
b. How many sixth graders are there if the school has 27 students?
c. If the school has a students, write an expression for the number of sixth graders in terms of x.
If 2/9 of the students in a school are in sixth grade.
then 20 students sixth graders are there if the school has 90 students.
6 students sixth graders are there if the school has 90 students
If the school has a students then 2x/9 the number of sixth graders in terms of x.
what are fractions?Part of a full number and a means of dividing a numbers into equal pieces are represented by fractions. The denominator is the total number of components in the whole, while the numerator is the fraction of equal portions being counted.
a. From the details of the question, we have 2/9 of the students in the school in sixth grade. Hence;
Number of students in sixth grade = 2/9 × 90 = 20 sixth grade students
b. If the school has 27 students, number of sixth graders = 2/9 × 27 = 6 sixth grade students
c. If we have x students in the school, the number of sixth graders = 2/9 × x = 2/9x students
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When we say ‘the limit does not exist’, do we mean it is actually in a determinate form or it is defined (like it's not something divided by zero)? If not, what is the basic meaning of ‘the limit does not exist’?
The limit does not exist if the graph features a vertical asymptote with one side going toward infinity and the other toward negative infinity.
What is meant by negative infinity?Since the graph is infinitely negative as one approaches zero from either side, the limit as x approaches zero would be negative infinity: In general, the limit will reach infinity or negative infinity when you take a limit and the denominator is equal to zero (depending on the sign of the function). The set of real numbers does not include infinity. The real number set is closed under addition and multiplication, which is one of its axioms. That is, you will always obtain a real number if you add two real numbers together. However, the closure rule is broken by the expressions ∞+(−∞) And ∞×0 for which there is no valid definition.To learn more about negative infinity, refer to:
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write negations for each of the following statements: a) john is 200 pounds, and he is at least 6 feet. b) tom’s watch was slow or the bus was late
The neg-ations of the given statements are: a) John is not 200 pounds or he is less than 6 feet and b) Neither Tom's watch was slow nor was the bus late.
To answer this question first let's understand what negation is.
Neg-ation is a concept in mathematical reasoning which is represented by the symbol "∼" and represents the opposite of the given mathematical statement. For example negation of “A and B” is “not(A) or not(B).
a) The neg-ation of the statement "john is 200 pounds, and he is at least 6 feet" is "John is not 200 pounds or he is less than 6 feet"
b) The neg-ation of the statement "tom’s watch was slow or the bus was late" is "Neither Tom's watch was slow nor was the bus late."
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What are Corresponding Angles in Geometry?
The corresponding angles must be equal for the transversal to join two parallel lines.
What is meant by Corresponding Angles?In the intersection of two parallel lines and a transversal, corresponding angles are created. The opening and closing of a lunchbox, completing a Rubik's cube, and endless parallel railroad tracks are a few examples of matching angles in daily life.
The angles in the same corners of two lines, which are typically parallel, are referred to as corresponding angles when they cross each other across a plane (a transversal). In two separate shapes, corresponding sides and angles refer to a pair of matching sides or angles that are in the same location.
Every matching angle is not created equally. The transversal must connect two parallel lines in order for the corresponding angles to be equal. The equivalent angles that are created when a transversal encounters a line that is not parallel are not congruent and have no connection to one another.
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I need help my homework is due in 15 mins
Answer:
1st box = 200
2nd box = 7
3rd box = 237
4th box = 270
5th box = 333
Step-by-step explanation:
1st box:
find a basis for the nullspace of the matrix. (if there is no basis, enter none in any single cell.) a = 1 2 −4 5 0 1 −1 3 −2 −4 8 −10
The basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.
The basis for the nullspace of the matrix can be found by reducing the augmented matrix to row echelon form and finding the free variables. The free variables correspond to the columns that have a leading entry of 0 and non-zero entries below it, which are the basis vectors for the nullspace.
Using row operations, the augmented matrix can be reduced to:
1 2 -4 5 | 0
0 1 -3 2 | 0
0 0 0 0 | 0
From this, we can see that the free variables are x2 and x4, so the basis for the nullspace is:
-3 x2 + x4
x2
So the basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.
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Three side lengths of
23, 32, and 45 units will
form exactly one
unique triangle.
No, the length of any pair of sides added together is not necessarily longer than the length of the third side.
Can a triangle be built with the provided side lengths of 23 32 45? No, the length of any pair of sides added together is not necessarily longer than the length of the third side.Triangle Unevenness Theorem.According to the Triangle Inequality Theorem, a triangle can only be formed if its two sides are greater than its third side when added together.If and only if the side lengths a, b, and c fulfill the formula a2 + b2 = c2, a right triangle is formed.We state that a Pythagorean triple exists between these integers.Triangles are singular because you can only ever draw one.There may be more than one triangle obtained if a triangle can be formed by using the two side lengths provided and the angle measure of an omitted angle.
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It is true three side lengths of 23, 32, and 45 units will form exactly one unique triangle.
How many triangles are possible with three different side lengths?One unique triangle, You create the same triangle again and over again. Therefore, if a triangle can be formed by your three side lengths, it can only be one specific triangle.If you are provided all three sides (Side-Side-Side), two sides and the included angle (Side-Angle-Side), two angles, and the included side, a unique triangle will be created (Angle-Side-Angle)Any two triangles that have the same side dimensions will be congruent, or identical, according to the SSS rule. You may so create a distinctive triangle. But only if the lengths of any two of those sides added together exceed the length of the third side can this occur.The complete question is
Three side lengths of 23, 32, and 45 units will form exactly one unique triangle. true /false.
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how many cards in the deck are either a jack or a heart?
The number of cards in the deck that are either a jack or a heart = 16
We know that a standard deck of cards has four suites.
These four suits are:
a) Hearts,
b) Clubs,
c) Spades,
d) Diamonds.
Each suite has thirteen cards.
These thirteen cards are:
Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and king.
This means, the entire deck of cards has 52 cards total.
The number of Jack cards in a standard deck of cards = 4
The number of Hearts in a standard deck of cards = 13
This means, there are 13 + 3 = 16 cards in the deck are either a jack or a heart.
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Given the relation, find its inverse and determine whether or not the function and its inverse are functions.
((-5,0), (-1, -2). (-2, 1), (0,4), (1, 2), (2, -1)}
A. The relation is a function, but the inverse is not.
B. The relation is not a function, but the inverse is.
C. Both the relation and inverse are functions.
D. Neither the relation nor the inverse are functions.
Answer:
C; both the relation and inverse are functions
Step-by-step explanation:
A function has no more than one output for a specific input, therefore, the original set of points is a function.
To find the inverse, you swap the x and y, so you would get:
(0, -5), (-2, -1), (1, -2), (4, 0), (2, 1), (-1, 2)
The inverse is also a function, because each input has only one output.