Which statements are true about the ordered pair (5, -6) and the sys
[x+y=−1
3x - y = 21
Select each correct answer.
Select 3 correct answer(s)
The ordered pair (5, -6) is a solution to the first e
because it makes the first equation true.
The ordered pair (5, -6) is a solution to the secon
equation because it makes the second equation
Answers
The ordered pair (5, −6) is a solution to the first and second equations because it makes both equations true.
What are linear equations?In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
The given system of equations is
x + y = -1 ......(1)
3x - y = 21 ......(2)
Rewrite equation (1)
y = - x - 1 ......(3)
Put equation (4) in equation (3)
3x -(-x -1) = 21
3x + x + 1 = 21
4x = 20
x = 20/4
x = 5
Put x= 5 in equation (3)
y = - 5 - 1
y = - 6
So, both the options are correct, (5, -6) is the solution of both equations.
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Related Questions
A motorcycle travels at a rate of 55 miles per hour for 4 hours. Let y be the distance, in miles, the motorcycle travels for a given amount of time, x, in hours. This situation can be modeled by a linear function. What is the domain of the function?
Answers
Answer:divide 55 by 4
Step-by-step explanation:
A gym charges members for a registration fee, and then per month. You became a member some time ago, and now you have paid a total of to the gym. How many months have passed since you joined the gym?
Answers
The number of months that have passed since joining the gym can be calculated by subtracting the registration fee from the total amount paid and dividing the result by the monthly fee. This will give the number of months as the solution to the problem.
The problem provides information about a gym membership fee structure, where members pay a registration fee and a monthly fee. Given the total amount paid to the gym, we need to determine the number of months that have passed since joining.
To solve the problem, we can set up an equation using the given information. Let's denote the registration fee as 'R' and the monthly fee as 'M'. We know that the total amount paid to the gym is the sum of the registration fee and the product of the monthly fee and the number of months.
In the equation, we have the total amount paid, and we need to find the number of months. Rearranging the equation, we can isolate the number of months by subtracting the registration fee from the total amount paid and then dividing by the monthly fee.
By plugging in the given values of the total amount paid and the registration fee and monthly fee, we can calculate the number of months that have passed since joining the gym.
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A nursery owner buys 7 panes of glass to fix some damage to greenhouse. The 7 panes cost $20.65. Unfortunately, breaks 3 more panes while repairing the damage. What is the cost of another panes of glass?
Answers
Cost of 3 panes= 3.09 multiplied by 3 = $9.27
Find the value of x and the measure of the angle labeled 3x°.
A. X= 14; angle measure is 30°.
B. X = 10; angle measure is 42°.
C. X= 14; angle measure is 42°.
D. x = 10; angle measure is 30°.
Answers
Answer:
answer is B............
Step-by-step explanation:
72-42...30
angle is 3x so divide it by 3
30 divided by 3 gives you 10
Answer:
D. x = 10; angle measure is 30°.
Step-by-step explanation:
I did this exact question on A P E X and it correct. I hope this helped. Have a good day!
Proof:
Which description best fits the graph?
A. always increasing
B. increasing, then decreasing
C. always decreasing
D. decreasing, then increasing
Answers
Answer:
always increasing
Step-by-step explanation:
When you look at the graph from left to right on the x-axis the y-axis is always increasing in value.
show that the congruence x^2 =1(mod 2^k) has exactly four incongruent solutions, namely x = -1 or -(1 2^k-1) (mod2^k), when k>2
Answers
To show that the congruence x^2 =1(mod 2^k) has exactly four incongruent solutions, namely x = -1 or -(1 2^k-1) (mod2^k), when k>2, we can use the following steps:
1. First, let's write the congruence x^2 =1(mod 2^k) in the form x^2 - 1 = 0(mod 2^k).
2. Next, we can factor the left-hand side of the congruence as (x-1)(x+1) = 0(mod 2^k).
3. Now, we can see that there are two possible solutions for x: x = 1(mod 2^k) and x = -1(mod 2^k).
4. However, since k>2, we know that 2^k > 4, so there are also two more solutions for x: x = 1 + 2^k-1(mod 2^k) and x = -1 - 2^k-1(mod 2^k).
5. These four solutions are all incongruent because they differ by multiples of 2^k-1, which is greater than 1.
6. Therefore, the congruence x^2 =1(mod 2^k) has exactly four incongruent solutions, namely x = -1 or -(1 2^k-1) (mod2^k), when k>2.
In conclusion, the congruence x^2 =1(mod 2^k) has exactly four incongruent solutions, namely x = -1 or -(1 2^k-1) (mod2^k), when k>2.
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please helpppppp :((
Answers
Answer:
\(4^{21}\)
Step-by-step explanation:
\(\frac{4^{12}}{4^{-9}}\\\)
Given 4 = a
From the properties of exponents for the example...
\(\frac{a^4}{a^{-2}} = \frac{a*a*a*a}{\frac{1}{a^2} } = (a*a*a*a)*a^2 = a^4 * a^2 = a^{4+2} = a^6\)
Therefore, the answer is....
\(4^{12}*4^{9} = 4^{12+9} = 4^{21}\)
5^3 x 7^5+9^8+0+0+0+0+0+0+(9^7x5^6)
Answers
Answer:
74,779,038,221
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given
\(5^3*7^5+9^8+0+0+0+0+0+0+9^7*5^6\)
We can eliminate all the zeroes.
\(5^3*7^5+9^8+9^7*5^6\)
Evaluate each term.
Raise 5 to the power of 3.
\(125*7^5+9^8+9^7*5^6\)
Raise 7 to the power of 5.
\(125*16807+9^8+9^7*5^6\)
Raise 9 to the power of 8.
\(125*16807+43046721+9^7*5^6\)
Raise 9 to the power of 7.
\(125*16807+43046721+4782969*5^6\)
Raise 5 to the power of 6.
\(125*16807+43046721+4782969*15625\)
Multiply 125 by 16807.
\(2100875+43046721+4782969*15625\)
Multiply 4782969 by 15625.
\(2100875+43046721+74733890625\)
Add 2100875 and 43046721.
\(45147596+74733890625\)
Add 45147596 and 74733890625.
\(74779038221\)
A calculator would help but here you go.
A baseball player made 9 errors in 60 games. How many errors would we expect the player to make in 100 games
Answers
The basketball player made 15 errors in 100 games as of the given condition.
Given that,
A baseball player made 9 errors in 60 games, how many errors would we expect the player to make in 100 games is to be determined.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Let the error be x, for 100 games,
Now, according to ot the question,
9/60= x / 100
x = 15
Thus, the basketball player made 15 errors in 100 games.
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1.Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.
How many miles does the first cyclist bike in 45 minutes?
Answers
Answer:
9 miles
Step-by-step explanation:
If 1 hour is 12 miles, then 30 mins is 6 miles, then 15 minutes is 3 miles.
30+15=45
6+3=9
The first cyclist bikes 9 miles in 45 minutes.
Since two cyclists are 7 miles apart when they begin biking away from each other in opposite directions, and the speed of the first cyclist is 12 miles per hour, to determine how many miles does the first cyclist bike in 45 minutes the following calculation must be done:
60 = 12 45 = X 45 x 12/60 = X 540/60 = X 9 = X
Therefore, the first cyclist bikes 9 miles in 45 minutes.
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The perimeter of a rectangle is 172 feet. Find the length and width if the length is an integer and the width is 2 times the next consecutive integer.
Answers
The length of the rectangle is 28 feet, and the width is 58 feet.
How to find the length and width of the rectangle?We know that for a rectangle of length L and width W, the perimeter can be written as:
P = 2*(L + W)
Here we know that the perimeter is 172 ft, then we can write:
172 ft = 2*(L + W)
And we know that the length is an integer:
L = x
And the width is two times the next integer:
W = 2*(x + 1)
Then we can replace these two in the perimeter equation so we get:
172 = 2*(x + 2*(x + 1))
172 = 2*(x + 2x + 2)
172 = 6x + 4
172 - 4 = 6x
168 = 6x
168/6 = x
28 = x
So we have:
Length = x = 28 ft
Width = 2*(x + 1) = 2*(29) ft = 58ft
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The the length and width of the rectangle are 43 feet and 129 feet
What is a perimeter?Perimeter is the distance round an object, The rectangle is a polygon that has four sides and some of its angles is equal to 360 degrees
The given parameters that will help us to find the values of the length and width of the rectangle are
Perimeter = 172
The length is an integer = 2
The width is 2 times the next consecutive integer = 2(3) = 6
The ratio of the sides of the rectangle is
W = 2/8 *172 = 43
Length = 6/8*172 = 129
Therefore length and the width of the rectangle are 43 feet and 129 feet
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Status
Exam
Find the missing length.
10
4
C=
✓ [?]
Pythagorean Theorem: a? + b2 = ?
Enter
![StatusExamFind the missing length.104C= [?]Pythagorean Theorem: a? + b2 = ?Enter](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/070z5amBHeIaHpP5TzyOmxhOZyDqkdJo.png)
Answers
Answer:
116
Step-by-step explanation:
A student states that −x is always equal to a negative integer. Complete the following statement to determine if the student is correct.
Answers
Answer:
iF X IS POSITIVE THEN -X IS ALWAYS NEGATIVE
IF X IS NEGATIVE, THEN -X IS ALWAYS POSITIVE
THE NEGATIVE OF A POSITIVE IS ALWAYS POSITIV
THE NEGATIVE OF A NEGATIVE IS ALWAYS POSITIVE
Step-by-step explanation:YS
−x is always equal to a negative integer is an incorrect statement.
The student is not correct.
What is Number system?A number system is defined as a system of writing to express numbers.
−x is always equal to a negative integer when x is positive integer
−x is always equal to a positive integer when x is negative integer
Which means the value of -x changes on the integer of x.
If x is positive then -x will be always negative, If x is negative then -x is positive.
The negative of a negative integer is positive and the negative of positive integer is negative.
Hence −x is always equal to a negative integer is an incorrect statement.
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how many independent variables are in a 2x3x2 factorial design
Answers
A 2x3x2 factorial design has three independent variables. What is a factorial design? A factorial design is an experimental design that studies the impact of two or more independent variables on a dependent variable.
The notation of a factorial design specifies how many independent variables are used and how many levels each independent variable has. In a 2x3x2 factorial design, there are three independent variables, with the first variable having two levels, the second variable having three levels, and the third variable having two levels.
The number of treatments or conditions required to create all feasible combinations of the independent variables is equal to the total number of cells in the design matrix, which can be computed as the product of the levels for each factor.
In this case, the number of cells would be 2x3x2=12.Therefore, a 2x3x2 factorial design has three independent variables and 12 treatment groups..
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5
Which of those points does not lie on the line y = 3x + 5*
(1 Point)
O (1,8)
O (4, 17)
O (-2, 11)
0 (0,5)
Answers
Answer:
point (-2,11) does not lie on the given line
Step-by-step explanation:
To find : Which of the following points does not lie on the line ?
Solution :
To determine the point lie on line or not we have to put points in equation if it satisfy then it lie otherwise not.
a) Point (1,8)
Line y=3x+5
Substitute x=1 and y=8
8=3(1)+5
8=8
(1,8) point lie on the line.
b) Point (4,12)
Line y=3x+5
Substitute x=4 and y=17,
17=3(4)+5
17=12+5
17=17
(4,17) point does not lie on the line.
c) point (-2,11)
Line y=3x+5
substitute x=-2 and y=11
11=3(-2)+5
11=-6+5
11 is not equal to -1
d) Point(0.5)
Line y=3x+5
Substitute x=0 and y=5
5=3(0)+5
5=5
Whyy, do vou think, banks and other financial institutions offer cash loans to people that did not apply for it?
Answers
Answer:
because there are in need of it
Step-by-step explanation:
yes
Once we have categorized an object, our memory of the object increasingly resembles thecategoryA) algorithm.B) prototype.C) heuristic.D) mental set
Answers
Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.
This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.
our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.
A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.
Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.
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what does it mean to be 90% confident in this problem? use the definition of confidence level. there is a 90% chance that the confidence interval contains the population mean 90% of all simple random samples of size 8 from this population will result in confidence intervals that contain the population mean the confidence interval contains 90% of all samples
Answers
Being 90% confident in a problem means that there is a 90% chance that the confidence interval calculated from a sample contains the true population mean.
In other words, if we take 100 different samples of the same size from the population and calculate a confidence interval for each sample, then we can expect that 90 of those intervals will contain the true population mean.
This is the definition of a confidence level. Therefore, we can say that there is a 90% chance that the confidence interval we have calculated includes the true population mean.
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87.0 x 1.6 =
I don’t get multiplication with decimal I do right and somehow it’s wrong so if anybody can help me solve it step by step would be a big help
Answers
Answer: The answer is 139.2
Step-by-step explanation:
All that you have to do is multiply them normally, but making sure you keep the decimal in the correct spot!
87.0 can be simplified into 87.
87 x 1.6 = 139.2.
================================================================= Hope this helped!
- bucketsarecool
What expression represents the verbal phrase?
The sum of 15 and 15% of a number m
15 + 15m
15 + 0.15m
0.15 + 15m
0.15 + 0.15m
Answers
The expression of the verbal statement is 15 + 0.15m
How to determine the expressionFrom the question, we have the following parameters that can be used in our computation:
The sum of 15 and 15% of a number m
15% of a number m means 0.15m
So, we have the following representation
The sum of 15 and 0.15m
Sum mean plus
So, we have
15 + 0.15m
We can get the equivalent expression
So, we have the following representation
(30 + 0.3m)/2
Hence, the expression is 15 + 0.15m
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Which formulas are tautologies? Select all that apply. p∧¬(p∨q)
p∧(p∨q)↔p
p∧T
(p∧(p→q))→q
Answers
The formulas that are tautologies are p ∧ T and (p ∧ (p → q)) → q. These formulas are always true regardless of the truth values of p and q. However, the formula p ∧ ¬(p ∨ q) is not a tautology as it can be false in certain cases.
The formula p ∧ ¬(p ∨ q) is not a tautology because it is not always true regardless of the truth values of p and q. For example, if p is true and q is false, the formula becomes false.
The formula p ∧ (p ∨ q) ↔ p is a tautology. This can be proven by constructing a truth table where all possible combinations of truth values for p and q are evaluated, and the formula is found to be true in every row of the truth table.
The formula p ∧ T is a tautology. Since T represents true, the conjunction of any proposition p with true will always be p itself, making the formula true for all possible truth values of p.
The formula (p ∧ (p → q)) → q is also a tautology. This can be shown through logical equivalence transformations or by constructing a truth table where the formula is found to be true in every row.
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The radius of a circle is 1 centimeter What is the circle's area?
Answers
Answer: It would be A= 3.14cm²
Step-by-step explanation:
Which statement is true about 1?
A. It is a prime number.
B. It is a composite number.
C. It is a whole number that is neither prime nor composite.
D. It is not a whole number.
Please dont be greedy and answer the question saying something like "i have no idea" Thanks
Answers
Answer:
C. It is a whole number that is neither prime nor composite.
Step-by-step explanation:
A prime number is a number that has two factors: one and another number. Thus, since 1 only has one factor (itself), it cannot be a prime number.
However, a composite number must have more than two factors, which 1 doesn't have either.
Since 1 is a whole number (not a decimal or fraction), and it is neither prime nor composite, the answer would be C.
Have a nice day!
Answer:
C!
Step-by-step explanation:
hope it helped
. A large cake is in a room. The first person who comes in takes 1/3 of the cake. Then a second person takes 1/3 of what is left. Then a third person takes 1/3 of what is left. And so on.
a) Is there still cake left after three people each take some cake? Why or why not?
b) Complete the table for C(n), the fraction of the original cake left after n people take some.
n C(n)
0
1 2/3
2
3
4
Answers
Answer:
Hiya
Step-by-step explanation:
1) No because they took a 3rd of the cake meaning they took all the cake depending on the size that’s a lotta cake so lets say this
I have a whole pizza I take 1/3 of it and so do two other people therefore no pizza is left.
A fraction is a way to describe a part of a whole. Yes, there is still cake left after three people each take some cake.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
Let the total amount of cake be represented by x.
Now, if the first person who comes in takes 1/3 of the cake. Then the amount of cake that will be left is,
Amount of cake left after the first person = x - (1/3)x
= (2/3)x
Then a second person takes 1/3 of what is left. Therefore, we will take 1/3rd of what is left, which means he will take 1/3 of (2/3)x.
Amount of cake left after the second person = (2/3)x - (1/3)(2/3)x
= 4x/9
=(2/3)²x
Then a third person takes 1/3 of what is left. Therefore, we will take 1/3rd of what is left, which means he will take 1/3 of 4x/9.
Amount of cake left after the third person = (4x/9) - (1/3)(4x/9)
= 8x/27
=(2/3)³x
A.) Yes, there is still cake left after three people each take some cake. This is because each person takes 1/3 of what is left, which means they will take a portion of "what is left" and leave the rest.
B.) The given table can be completed as shown below.
n C(n)
0 0
1 2/3
2 (2/3)²
3 (2/3)³
4 (2/3)⁴
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James bought a car and paid for it in equal payments of $854. After making 41 payments, he still had to pay $16,331.
Answers
Oh 19.122 payments left
Solve the following please:
Answers
Answer:21
Step-by-step explanation: solve whats in the numerator then solve whats in the denominator then you divide
Can someone help me find the mistake!!!!!
Answers
Answer:
She supposedly multiplies 4*4*16*-3y but distributes it correctly as if she put (16*4)+(4*-3y) which equals 64-12y.
The work shown is a mistake, the answer of y=5 isn't.
If X and Y varies inversely, what would the value of X be? (-9,4) (x,-12)
Answers
Answer:
Use papa math
Step-by-step explanation:
Use papa math
which of the points shown below are on the line given by the equation y=3x?
check all that apply
a. point a (1,3)
b. point b (3,1)
c. point c (3,-1)
d. point d (-1,-3)
Answers
The points (1,3) and (-1,-3) are on the line given by the given equation.
Linear Equation
An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=6x+7. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=6 and b=7.
The question gives the equation y=3x from the standard form equation, you can identify that: m=3 and b=0.
For solving the question, you should check if the given coordinates comply with the equation y=3x. See below.
Coordinate (1,3) - Here x=1 and y=3, then you should replace x with 1. After that, check that the result for y is equal to the given y-coordinate.y=3*1
y=3
Therefore, the coordinate (1,3) is on the line given by the equation y=3x.
Coordinate (3,1) - Here x=3 and y=1, then you should replace x with 3. After that, check that the result for y is equal to the given y-coordinate. y=3*3 y=9Therefore, the coordinate (3,1) is not on the line given by the equation y=3x.Coordinate (3,-1) - Here x=3 and y=-1, then you should replace x with 3. After that, check that the result for y is equal to the given y-coordinate. y=3*3 y=9Therefore, the coordinate (3,-1) is not on the line given by the equation y=3x.Coordinate (-1,-3) - Here x= -1 and y=-3, then you should replace x with 3. After that, check that the result for y is equal to the given y-coordinate. y=3*(-1) y=-3Therefore, the coordinate (3,-1) is on the line given by the equation y=3x.
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Use the Left and Right Riemann Sums with 3 rectangles to estimate the area under the curve of y=lnx on the interval of [2,9]. Round your answers to the second decimal place.
Answers
Rieman sums are used to calculate the approximate value of the area under the curve of real functions.
A left Riemann sum uses rectangles whose top-left vertices are on the curve while the right Riemann sum uses rectangles whose top-right vertices are on the curve.
The width of each rectangle is given by:
\(w=\frac{b-a}{n}\)Where a and b are the endpoints of the interval and n is the number of rectangles.
We are given the function:
y = ln x on the interval [2, 9]
And it's required to use n = 3 rectangles, thus:
\(w=\frac{9-2}{3}=2.333\)For the left Riemann sum, we need to calculate the values of y for:
x = 2
x = 2 + w = 4.333
x = 2 + 2w = 6.667
f(2) = ln 2 = 0.6931
f(4.333) = 1.4662
f(6.667) = 1.8972
The area of the rectangles is the height by the base:
A = 0.6931 x 2.333 + 1.4662 x 2.333 + 1.8972 x 2.333
A = 9.4640
For the right Rieman sum, we need to calculate the values of y for:
x = 2 + w = 4.333
x = 2 + 2w = 6.667
x = 2 + 3w = 9
f(4.333) = 1.4662
f(6.667) = 1.8972
f(9)= 2.1972
Calculate the area of the rectangles:
A = 1.4662 x 2.333 + 1.8972 x 2.333 + 2.1972 x 2.333
A = 12.973
Note: The real value for the area (using integration) is 11.39