The value of k is 7
Consider the given equations are:
2x+3y=7
(k−1)x+(k+2)y=3k
The general equations
[tex]a_{1} x+b_{1} y =c_{1}[/tex]
[tex]a_{2} x+b_{2} y =c_{2}[/tex]
substituting the values,
[tex]a_{1} = 2, b_{1} y=3,c_{1}=7[/tex]
[tex]a_{2}=(k-1) ,b_{2} =( k+2), c_{2}= 3k[/tex]
An equation can have infinitely many solutions when it should assure some conditions. The system of an equation has infinitely numerous solutions when the lines are coincident, and they have the same y-intercept.
We know, the condition of infinite solutions
[tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]
Therefore,
[tex]\frac{2}{k-1} = \frac{3}{k+2} =\frac{7}{3k}[/tex]
⇒[tex]\frac{2}{k-1} =\frac{3}{k-2}[/tex]
⇒ 2k -4 = 3k-3
⇒ k = 7
Hence, the value of k is 7.
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The complete question is:
Find the value of k, infinitely many solutions
2x+3y=7,(k−1)x+(k+2)y=3k
+12 Coins Earned
Will the quotient of the division problem shown below be positive or negative?
(-8) ÷ (-4)
Answer: Positive
Hope this helps :)
Step-by-step explanation:
When multiplying or dividing with two negative numbers, the product/quotient will always be positive.
-8/-4 = 2
Answer: Positive
Step-by-step explanation:
Example for multiplication:
Imagine 4 friends that owe you $8 each.
Each friend that pays you back represents their payback as -$8.
-$8 * 4 friends = -$32 that they owe you.
The moment they give it back, you now have +$32. The Debt was taken away.
Example for Division:
Imagine splitting 8 dollars in debt with 4 friends, each friend then has $2 in debt. Each payback means you have +$2.
Another visual way to think of this is with Number Lines.
On a number line, when you multiply by a larger absolute value the numbers get bigger and go farther away from 0. So, taking a negative and multiplying it by a positive makes it MORE negative, as opposed to multiplying it by negative and then it reflects the number line,
Can someone help me on these? I'd really appreciate it.
Answer: view below
Step-by-step explanation:
a. [tex]-\frac{2}{3}x \geq 7[/tex]
[tex]x\leq -\frac{21}{2}[/tex]
b. 32>23-x
x>-9
c. 2(x+6)<10
x+6<5
x<-1
d. 15-4x[tex]\leq 3x-6[/tex]
21[tex]\leq[/tex]7x
3[tex]\leq[/tex]x
x[tex]\geq[/tex]3
What is a solution set called?.
The solution sets are called algebraic sets.
An algebraic set is the locus of zeros of a collection of polynomials, and it is the set of solutions.
A solution set is a set of values that satisfy a given set of equations or inequalities.
The set containing all the solutions of an equation is called the solution set for that equation. If an equation has no solutions, we write ∅ for the solution set. ∅ means the null set.
A linear system with a unique solution has a solution set with one element. Solution sets are a challenge to describe only when they contain many elements.
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explicit formula 9,15,21,27
Answer:
n_(n-1)+6
Step-by-step explanation:
n_(n-1)+6
im pretty sure?
21=3(y+3)
Responses
y = 3
y, = 3
y = 4
y, = 4
y = 5
y, = 5
y = 6
y , = 6
Answer:
y = 4
Step-by-step explanation:
21/3 = 7
7 - 3 = 4
What angle has 120 degrees?.
An obtuse angle has 120 degrees in them.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Any angle more than 90 degrees is called obtuse: A straight angle is one with a 180° measurement: A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.
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What is your research plan? Write a short paragraph about how you plan to conduct you research. Where will you gather your notes? What keys words will you use to find information on your topic? Where will you record your notes and bibliographic information?
Research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.
What is Research Plan?A research plan is the main part of a grant application and describes a principal investigator's proposed research.
A research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.
We write a research plan by given steps.
Define the project purpose.
Identify individual objectives.
Select a research method.
Recruit participants and allocate tasks.
Prepare a project summary.
Create a realistic timeline.
Determine how to present your results.
The bibliographic information has Author name, Title of publication., Article title (if using a journal), Date of publication, Place of publication., Publisher, Volume number of a journal, magazine or encyclopedia and
Page number(s)
Hence, research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.
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What are the factors of x2 XY − 2xz − 2yz?.
Since a square is either positive or zero, negative numbers don't have real square roots.
No, we are unable to compute the negative number's square root. Positive is always the result of adding two numbers with the same sign.
How is a negative square root treated?Theorem: Square Roots of a Negative Number Simplifying an expression involving the square root of a negative number by simplifying the number as if it were a positive number and putting an i in front of it as a coefficient is one method. To put it another way, x=ix x = i x for every x where x is a positive number and where x is a negative number.
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PLEASE HELP ASAP
which expression can be used to find the sum of the polynomials?
The correct expression to solve te sum of polynomials is [(-3x)+(-8x)]+4x+[9+5] (D).
To solve any polynomials problems, it is important for us to take a close look on the orders of each number. For the sum and substraction operation, we need to categorize each number based on its orders.
From the case, we have a problem as:
(9 - 3x²) + (-8x² + 4x + 5)
We can categorize each order:
Order 2 = (-3x²) and (-8x²)
Order 1 = 4x
Order 0 = 9 and 5
Hence, we can solve the problem as:
(9 - 3x²) + (-8x² + 4x + 5)
= [(-3x²) + (-8x²)] + 4x + (9 + 5)
= -11x² + 4x + 14
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a total of 516 tickets were sold for the school play. they were either adult tickets or student tickets. there were 66 more student tickets sold than adult tickets. How many adult tickets were sold
In the word problem the number of the adult ticket is 225.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here total number of tickets = 516.
Which is contains adult and students tickets. Then let us take x is number of adult ticket and y is number of student tickets then,
=> x + y = 516 ------> 1
Now there were 66 more student tickets sold than adult tickets then
=> y = x+66 -----> 2
Now put 2 into 1 then
=> x+66+x = 516
=> 2x = 516-66 = 450
=> x = 225.
Now put x = 225 into then
=> y = 225+66 = 291.
Hence the number of adult tickets is 291.
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Make a box-and-whisker plot of the data. Find the interquartile range.
7,9, 11, 12, 13, 15, 12, 17, 18, 12, 9, 7, 12, 15, 18, 10
O
++
6 7 8 9 10 11 12 13 14 15 16 17 18 19
Interquartile range: 5.5
←+++
++
6 7 8 9 10 11 12 13 14 15 16 17 18 19
Interquartile range: 5
++
6 7 8 9 10 11 12 13 14 15 16 17 18 19
Interquartile range: 5.5
++
6 7 8 9 10 11 12 13 14 15 16 17 18 19
Interquartile range: 5
From the box-and-whisker plot of the data, the Interquartile range is 6.
What is the Interquartile range?
An interquartile range is finding the median of the first half of the data set, and the second half, then subtracting the first median from the second one.
Steps to create a box-and-whisker plot and find the interquartile range.
Step 1: Sort the data in ascending order: 7, 7, 9, 10, 11, 12, 12, 12, 12, 13, 15, 15, 17, 18, 18
Step 2: Find the median (middle value) of the data: 12
Step 3: Divide the data into two halves:
Lower half: 7, 7, 9, 10, 11, 12, 12
Upper half: 12, 12, 13, 15, 15, 17, 18, 18
Step 4: Find the median of the lower half (Q1) and the median of the upper half (Q3).
Q1: 9
Q3: 15
Step 5: Draw a box-and-whisker plot:
Draw a number line and mark the minimum, Q1, median, Q3, and maximum values.
Draw a box between Q1 and Q3 and a vertical line inside the box to represent the median.
Draw lines (whiskers) from the box to the minimum and maximum values.
Step 6: Find the interquartile range (IQR) by subtracting Q1 from Q3: 15 - 9 = 6.
Hence, the Interquartile range is 6.
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What does ∑ ∑ mean?.
The mathematical symbol ∑∑ is used to represent a double summation. It is a way of expressing the sum of two series of numbers.
Double summation is a way of expressing the sum of two series of numbers, written as ∑∑. The upper sigma symbol represents the outer summation, while the lower sigma symbol represents the inner summation. The two series of numbers that form the double summation can be related or unrelated.
The double summation is written in the following form: ∑∑ aij, where aij is an element from the two series of numbers, i and j are the upper and lower limits of the double summation, respectively.
This type of expression is used to find the sum of a set of numbers that are related to each other in some way, such as the sum of the elements in a matrix or a table, or the sum of two series of numbers that are not related. The double summation is a useful tool for expressing the sum of two series of numbers and is widely used in mathematics and science.
Complete answer:
What does ∑∑ mean?
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Write y = 2x + 5 in standard form
The equation y = 2x + 5 is already in standard form.
Standard form of a linear equation is Ax + By = C, where A, B, and C are constants and A and B cannot be both zero. In this case, A=2, B=1 and C=5, which meets the standard form equation, y = 2x + 5 is already in standard form.
Answer: y = 2x + 5 in standard form is 2x - y = -5
Step-by-step explanation: I hope this helps!
Does 6 8 15 form a triangle?.
No, it is not possible to draw a triangle.
This will be done by the property: the sum of two sides of a triangle should be more than the third side.
(6cm + 8cm) =15cm
14cm = 15cm
LHS<RHS
A triangle is not possible.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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What is the inverse of 7 *?.
The inverse of 7 is 1/7.
A reciprocal is one of a pair of numbers that when multiplied with another number equals the number 1.
The reciprocal of a and 1/a.
For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1.
Multiplicative inverse:
The multiplicative inverse of a number can either be expressed as a fraction or as a number raised to the power of a negative one. A number multiplied by its multiplicative inverse is one.
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A large concrete block is used for the cornerstone of a building. The block is 18 yd deep, 23 yd wide, and 16 yd long. What volume of concrete is needed to make this block?
Answer:
Step-by-step explanation:
To find the volume of concrete needed to make this block, you need to calculate the volume of the block using the formula:
Volume = Length x Width x Height
In this case:
Volume = 18 yd x 23 yd x 16 yd = 7,648 cubic yards
So, 7,648 cubic yards of concrete are needed to make this block.
Alternatively, you can use the formula:
V=LWH, where V is the volume, L is the length, W is the width and H is the height.
(Need it urgently, thank you!)
Write a two-column proof.
Given: AC bisects ZBAD, ZBCA ZDCA
Prove: BC= DC
Left Column: AC bisects ZBCA ZDCA. Right Column: Angle ZBAC = Angle ZDCA (Angle Bisector Theorem).
What is an angle bisector theorem?Angle bisector theorem states that in any triangle, the line that bisects an angle also divides the opposite side into two segments that are proportional to the other two sides of the triangle. This theorem can be used to prove that the angle bisector of any triangle is the perpendicular bisector of the opposite side. In other words, the line that bisects the angle of a triangle will also divide the opposite side into two segments with lengths that are equal to the ratio of the other two sides of the triangle.
Left Column Right Column
1. AC bisects ZBAD 1. AC bisects ZBCA ZDCA
2. ZBAD = ZBCA + ZDCA 2. Angle ZBAC = Angle ZDCA (Angle Bisector Theorem)
3. Angle ZBAC = Angle ZBCA + Angle ZDCA 3. BC = DC (Congruent Sides of Congruent Triangles)
4. Angle ZBCA = Angle ZDCA
5. BC = DC (Congruent Sides of Congruent Triangles)
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What is the range of the function f x − x 3 2 7?.
Answer:
Step-by-step explanation:
nhbjbjhbnjbjnjnjny6778899
You are trying to save $540 for your trip to New York. You started with $54 that you saved up and you earn $9 per hour of babysitting. How many hours will you have to babysit in order to have the money you need?
Answer:
54 Hours
Step-by-step explanation:
first of all 540-54 he started with is 486 and 486/9 is 54 since you get 9 per hour
Answer: 54 Hours of babysitting
Step-by-step explanation: 540-54=486 Then you take 486 and you divide it by 9 to see how many hours you have to work and that would be 54 hours.
Max puts a stopper in the bathtub and turns on the faucet at t = 0.
After 5 minutes, there are 11 gallons of water in the tub and after 10 minutes, there are 22 gallons in the tub.
Write an equation that relates the number of gallons, g, to the time, t.
Does the relationship represent a linear function? Justify your response.
The equation is y = 2.2x. Yes, it represents a linear function.
What is a linear function?
A linear function is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear function with exponents greater than 1. Such an equation on the graph, forms a straight line.
We are given that
Stopper is applied at t = 0
At t = 5 minutes ; water in tub = 11 gallons
At t = 10 minutes ; water in tub = 22 gallons
We know that a general form of a linear function is y = mx + c.
Where c is the intercept ; m is the Slope ; y and x are dependent and independent variables respectively
Here, the intercept is gallon of water at t = 0 ;
Since, it is not mentioned, therefore it will be taken as 0.
Slope = change in y / change in x
Slope = (22 - 11) / (10 - 5)
Slope = 11 / 5
Slope = 2.2
Therefore, the equation becomes
y = 2.2x + 0
y = 2.2x
Yes, it represents a linear function because the highest degree is 1.
Hence, the equation is y = 2.2x. and it represents a linear function.
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Attendance i decreaing at a rate of 0. 5% per year. If there are 1200 people attending now how many will be attending in 4 year?
So, in 4 years, there will be 1176 people attending.
To find out how many people will be attending in 4 years, you need to determine the total decrease in attendance over that time period. The attendance is decreasing at a rate of 0.5% per year, so over 4 years, the decrease in attendance will be 4 years x 0.5% = 2%
To find out how many people will be attending in 4 years, you can then subtract the 2% decrease from the current attendance of 1200 people:
1200 x (1 - 0.02) = 1176 people
So, in 4 years, there will be 1176 people attending.
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You must ascertain the overall drop in attendance over that time span in order to calculate the number of attendees in 4 years. If enrollment drops by 0.5% annually, it will drop by 2% over the course of four years (4 years x 0.5%).
Then, from the present attendance of 1200 people, subtract the 2% decline to determine how many attendees there will be in 4 years:
1200 times (1-0.02) ≈ 1176 individuals
Therefore, there will be 1176 attendees in 4 years.
Which techniques can be used to evaluate the expression 12.75 = 1.5? Select all that apply.
The evaluation of the expression 12.75 ÷ 1.5 is 51 / 6.
How to evaluate expression?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
Therefore, let's evaluate the expression as follows:
Hence,
12.75 ÷ 1.5
Let's convert each decimal to fractions for easy evaluation
Therefore,
12.75 = 1275 / 100
1.5 = 15 / 10
Therefore,
1275 / 100 ÷ 15 / 10
Let's change the division sign to multiplication sign.
1275 / 100 × 10 / 15
1275 / 150
Therefore,
255 / 30 = 51 / 6
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What is the formula for the sum of a sequence?.
The formula for the sum of an arithmetic sequence is [tex]S_n[/tex]=[tex]n/2[/tex][2a+(n−1)d], [tex]S_n[/tex] = [tex]n/2[/tex] [2a +( n − 1 )d ], where: n = the number of terms to be added. a = the first term in the sequence. d = the constant value between terms.
In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.
Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.
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Mateo is making bookmarks with different colored ribbon.The amount of color he has is shown in the table.Each bookmark will be 1/6 yard long.How many more orange bookmarks can he make than aqua bookmarks.
color length(yd)
Aqua 3/4
orange 9/10
yellow 15/16
use reciprocals pls
The orange bookmarks that Mateo can make than aqua bookmarks is 1.
How to calculate the number of bookmark?Based on the information given, let x = number of aqua bookmarks
(1/6) × x = 3/4
x = (3/4) × (6/1)
x = 18/4
x = 4.5
Rounding down shows that we can make 4 aqua bookmarks.
y = number of orange bookmarks
(1/6)y = 9/10
y = (9/10)*(6/1)
y = 54/10
y = 5.4
This rounds down to 5 orange bookmarks.
Therefore, Mateo can make 5-4 = 1 extra orange bookmark compared to aqua.
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Mateo is making bookmarks with different colored ribbon. The
amount of each color he has is shown in the table. Each bookmark
will be yard long. How many more orange bookmarks can he make
than aqua bookmarks?
Table:
Color: Length (yd):
———————————-
Aqua. 3/4
Orange. 9/10
Yellow. 15/16
Which inequality represents all values of x for which the product below is defined? square root 5x times square root x + 3
The values of x for which the product:
√(5x)*√(x + 3)
Is defined are:
x ≥ 0
For which values of x is the product not defined?Here we want to see for which values of x is the following product not defined.
√(5x)*√(x + 3)
Ok, remember that the argument of the square root must be zero or larger, then we have two inequalities here:
5*x ≥ 0
x + 3≥ 0
We can simplify both of these inequalities to get:
x ≥0
x≥ -3
We take the first one, which is more restrictive, the values of x for which the product is defined are:
x ≥0
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Mybankaccount pay 4% interet at the end of each year. Suppoe that I have $x in my bank account at the tart of thi year, and that I never add money to the account or take money out of the account. (a) Howmuchwill be in the account at the end thi year (after the interet i paid)? (b) Howmuchwill be in the account at the end of next year (again, after the interet)? (c) Find an expreion for the amount in the account after N year
a) The amount in the account at the end of this year after the interest is paid will be 1.04x.
b) The amount in the account at the end of this year after the interest is paid will be 1.08x.
c) The expression for the amount in the account after N years will be x + 0.04xn.
a) From the information, Mybankaccount pays 4% interest at the end of each year. The person has $x in the bank account at the start of this year. The amount in the account at the end of this year after the interest is paid will be:
= x + (x*0.04*1)
= x + 0.04x
= 1.04x
b) The amount in the account at the end of 2 years after the interest is paid will be:
= x + (x*0.04*2)
= x + 0.08x
= 1.08x
c) The expression for the amount in the account after N years will:
= x + (x*0.04*n)
= x + 0.04xn
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What is improper fraction in Maths for Class 5?.
When the numerator of the fraction is greater than the denominator, the the fraction is an improper fraction.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
consider a fraction 1/6.
Here, numerator is 1, denominator is 6
When certain thing is divided into 6 equal parts then each part of is represented by fraction1/6
As we the types of fractions are: Proper fraction, Unit Fraction ,Improper fraction, Mixed fraction, Like fractions, Unlike fractions and Equivalent fractions
An improper fraction is a fracton in which the numerator of the fraction is greater than the denominator.
For example, 8/7 is an improper fraction.
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in the figure angle APC is equal to angle BQD prove that AB is parallel to CD
From the given proof below, we have shown that AB is parallel to CD.
How to prove parallel lines?From the attached diagram showing the triangles inside the circle, we are given that;
<APC = <DQB [ Given]
Now, we know that in cyclic quadrilaterals that Equal angles subtend equal arcs and therefore; Arc(AC = BD)
From the statement above showing that Equal angles subtend equal arcs. we can conclude that AB is parallel to CD
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Please helppppp meeeeee !!!!!!
Answer:
72.5 / 2.5 = 29
29 - 8 = 21
21 / 3 = 7
7
Step-by-step explanation:
How is the intensity of an earthquake decided on the Richter scale?.
The intensity of an earthquake decided on the Richter scale by the following formula,
10ᴬ⁻ᴮ , where A and B are magnitude of earthquake recorded by Richter Scale.
The Richter magnitude scale was developed in 1935 by Charles F. Richter of the California Institute of Technology as a mathematical device for comparing the magnitude of earthquakes. The size of an earthquake is determined from the logarithm of the amplitude of the waves recorded by seismographs. Adjustments are included for the change in distance between different seismographs and the epicenter of the earthquake. The Richter scale is a logarithmic scale with a base of 10, meaning that each order is 10 times more intense than the previous one. In other words, a two is 10 times more intense than a one, and a three is 100 times greater. In the case of the Richter scale, there is an increase in the amplitude of the wave.The Formula used to measured the intensity of an earthquake is A is x times intense than B, x = 10ᴬ⁻ᴮ.
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