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
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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On the first day of an experiment, a scientist counts 31 bacteria. On the eighth day of the experiment, the count is 310,000 bacteria.
How many times greater is 310,000 than 31?
A. 310,000
B. 10,000
C. 1,000
D. 31
An elevator ascends at a rate of 29.6 feet per second. If a building is 1,450 feet tall, about how long would it take for the elevator to travel from the ground floor to the roof?
A. 0.49 minutes
B. 0.82 minutes
C. 4.9 minutes
D. 8.2 minutes
help me please please please triangle 111111
Answer:
144 cm²
Step-by-step explanation:
1.) Find the area of all of the faces
10*4=40 (Top Face)
4*8=32 (Bottom Face)
6*8*0.5=24 (One Triangle)
6*8*.5=24 (Other Triangle)
6*4=24 (Back Face)
2.) Add them all together to get the surface area
40+32+24+24+24= 144
***Don't forget the cm². Some teachers are really annoying about this
What is the direct variation equation for the line passing through the points A(4,−2) and B(10,−5)
The direct variation equation for the line passing through the points A(4,−2) and B(10,−5) as given in the task content is; y = -2x.
What is the direct equation of the points given?It follows from the task content that the direct variation of equation of the two points given be determined.
On this note, since the relation is said to be a direct variation.
It follows that the ratio of inputs to output in both ordered pairs, k is same and can be determined as;
10/-5 = 4/-2 = k = -2.
Therefore, the required direct variation equation is written as;
y = -2x.
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a data analyst creates a scatterplot with a lot of data points. the analyst wants to make some points on the plot more transparent than others. what aesthetic should the analyst use?
Analyzers should use the Alpha aesthetic.
Using the Alpha aesthetic, specific points on a scatterplot are more transparent than others to highlight specific data points.
What is a scatterplot?
A scatter plot is a set of points plotted along a horizontal and vertical axis. In statistics (also known as variables), scatter plots are crucial to demonstrating whether a correlation exists between observational quantities or phenomena.
A scatter plot plots data points on a horizontal and vertical axis to demonstrate one variable's influence on another. Each row in the data table is represented by a marker whose position is determined by the values of the columns on the X and Y axes.
Using a scatter plot, this line indicates the prevailing direction of a phenomenon. In a scatter plot, a trend line can be used to highlight the direction and speed of price changes.
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Question 5 of 10
Which of the following graphs represents a function that has a positive
leading coefficient? Check all that apply.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Which expression is the factored form of−4.5n+3?
Responses
A. −3(1.5n−1)
B. −1.5(3n+2)
C. −1.5(−3n+2)
D. −3(1.5n+1)
An expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)
The correct answer is an option (A)
In this question we have been given an expression -4.5n + 3
We need to identify an expression which is factored form of given expression.
If we simplify the factored form then it must be a give expression.
consider ,A. −3(1.5n−1)
= -4.5n + 3
consider an expression B. −1.5(3n+2)
= -4.5n - 3
consider C. −1.5(−3n+2)
= 4.5n - 3
consider D. −3(1.5n+1)
= -4.5n - 3
Therefore, an expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)
The correct answer is an option (A)
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Which ratio is equivalent to 1:6?
Answer:
2 : 12 and 3 : 24 are the two equivalent ratios
Please help will mark brainiest!!!
1.) Rowan graphs the function f (x) = 7x + 1 and then transforms the function by horizontally translating it 5 units to the right. What is the newly transformed function, g (x)?
The newly translated function of f(x) = 7x + 1 is; g(x) = 7(x - 1) + 1
How to carry out Translation of Functions?In transformation of functions, there are different operations such as translation, reflection, dilation, rotation.
Now, we are told that the function is given as;
f ( x ) = 7x + 1
We are told that it is translated by 5 units to the right.
It is pertinent to note that when talking about translation, it is as good as saying moving from one point to the other without changing the dimensions or shape.
Now, when we shift a function f(x) = x - 1 by a units to the left, it means the translated function is; f'(x) = (x + 1) - 1
However, when we shift a function f(x) = x - 1 by a units to the right, it means the translated function is; f'(x) = (x - 1) - 1
Now, applying that translation rule to our given function gives;
g(x) = 7(x - 1) + 1
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if an audit company picks a bank at random for audit what is the probability that a bank (a) is guilty of fraud? (b) is guilty of fraud given it is a private bank? probability problem
The probability of the randomly selected bank being a) guilty of fraud is 0.1 and b) guilty of fraud, it is given it is a private bank is 0.15
Here
let A be the event of the Bank being a fraud
Let B be the event of the bank being private
Here we see that 100 banks have been sampled.
a)
Probability = no. of favorable outcomes/total no. of outcomes
Here we see that under the row of Bank Fraud and Yes section there are
6 + 4
= 10 banks.
Hence,
n(A) = 10
n = 100
Therefore,
P(A) = 10/100
= 0.1
b)
The conditional Probability
P(X|Y) = P(X ∩ Y) / P(Y)
Here,
we need to find the bank is a fraud given that it is a private bank. Hence we need to find,
P(A|B)
= P(A ∩ B) / P(B)
Here we see that the private banks that are fraud are given to be 6.
Hence,
n(A ∩ B) = 6
Therefore,
P(A ∩ B) = 6/100
n(B) = 6 + 34 = 40
P(B) = 40/100
Hence P(A|B) = (6/100) / (40/100
= 6/40
= 3/20
= 0.15
Complete Question
(Information attached as an image)
if an audit company picks a bank at random for audit what is the probability that a bank
(a) is guilty of fraud?
(b) is guilty of fraud given it is a private bank?
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20 percent of all printers of a certain type are submitted for service under waranty. of these, 60 percent can be repaired and 40 percent must be replaced. if a company buys 10 such printers, what is the probability that exactly two will be replaced under warranty.
The probability that exactly two will be replaced under warrant is 0.1937.
Define probability.The possibility of an event occurring is determined by the probability formula. The ratio of positive outcomes to the total number of outcomes serves as the basis for calculating an event's probability. The probabilities are always between 0 and 1. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Given,
W = Warranty
V = Replaced
P(W) = 20/100
P(W) = 0.20
P(U/W) = 0.40
P(W ∩ U)
= P(U/W) × P(W)
= 0.40 × 0.20
0.-08
P( exactly two will be replaced under warranty)
Using binomial distribution:
= P(X = 2)
= 10/2 (0.0.8)² (0.9)⁸
= 0.1937
The probability that exactly two will be replaced under warrant is 0.1937.
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On Monday, a museum had 500 visitors. On Tuesday, it had 900 visitors. Estimate the percent change in the number of visitors to the museum. Use pencil and paper. Estimate how many people would have to visit the museum on Wednesday to have the same estimated percent change between Tuesday and Wednesday as between Monday and Tuesday. Explain your answer.
The percentage increase regarding the change in visitor is 80%.
How to calculate the percentage?From the information, the museum had 500 visitors and on Tuesday, it had 900 visitors.
It should be noted that the increase in numbers will be:
= 900 - 500
= 400
The percentage increase will be:
= Increase / initial value × 100
= 400/500 × 100
= 0.8 × 100
= 80%
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An isosceles right triangle has a hypotenuse length that can be modeled with the function . the combined length of the legs can be modeled with the function l(x) = 2x. which function, p(x), can be used to find the perimeter of the triangle?
The perimeter of the isosceles triangle will be P(x) = x√2 + 2x.
A polygon with three sides is known as a triangle. The angles of a triangle add up to form 180° and the sum of all sides of a triangle is known as the perimeter. In an isosceles triangle, the two sides are equal and their opposite angle too. In an isosceles triangle, the hypotenuse side of the triangle can be written as h(x) = x√2. The combined length comes out to be L(x) = 2x. Using this information the perimeter of the triangle comes out to be,
P(x) = h(x) + L(x).
P(x) = x√2 + 2x
Hence the perimeter of the triangle comes out to be P(x) = x√2 + 2x
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pls help me i’ll give brainliest
Answer:
25/0 aka infinity
Step-by-step explanation:
Equation used:
(y2-y1)/(x2-x1)
1. Plug in the values to get (27-2)/(9-9)
2. Simplify to get 25/0
3. This results in an infinity
please I am begging you, answer this TODAY and show your work.
Answer:
1) t = -2
2) t = 8
3) t = -2
4) t = 1
5)t = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
1)-22t+6 = 11t + 72
-33t = 66
t = -2
2) 3t + 4t - 20 = t + 28
6t = 48
t = 8
3) -8 -10t - 6t = 3t + 30
-19t = 38
t = -2
4) 12t - 6t + 24 = 12t + 12 +6
-6t = -6
t = 1
5) -12-21t-3t=48t-36
-24t - 48t = 12 - 36
-72t = -24
t = [tex]\frac{1}{3}[/tex]
Which factor most likely results in the loss of genetic variation from a small population?.
The factor most likely results in the loss of genetic variation from a small population is called genetic drift.
Small populations tend to lose genetic variation at a faster rate than large populations due to genetic drift (stochastic sampling error). Genetic drift refers to the change in an existing gene variant frequency in the population due to random chance. Genetic drift may result in the disappearance of gene variants completely and thus decreases genetic variation. Furthermore, it could initially cause rare alleles to become much more frequent, and even fixed. The loss of some versions of a gene due to random chance is more likely to happen when populations are small.
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determine if l=these points have a right angle
2,3 6,3 2,7
The points (2, 3) (6, 3), and (2, 7) sides corresponds to length of 4 : 4 : 5 and do not form Pythagorean triple hence they do not form a right angle
How to determine if the points (2, 3) (6, 3), and (2, 7) form a right angleThe distance between the points is calculated and Pythagoras theorem is used to determine if the triple forms a right angle
let the points be
A (2, 3) B (6, 3), and C (2, 7)
using the equation
d = √{(x₁ - x₂)² + (y₁ - y₂)²}
AB = √{(2 - 6)² + (3 - 3)²} = 4
BC = √{(6 - 2)² + (3 - 7)²} = 5
CA = √{(2 - 2)² + (3 - 7)²} = 4
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Angles RTG and GTU are adjacent angles. If m∠RTG=5.8° and m∠GTU=113.6°, what is m∠RTU in degrees?
If m∠RTG = 5.8° and m∠GTU = 113.6°. Then the measure of the angle ∠RTU will be 119.4°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
Angles RTG and GTU are adjacent angles. If m∠RTG = 5.8° and m∠GTU = 113.6°.
∠RTU = ∠RTG + ∠GTU
∠RTU = 5.8° + 113.6°
∠RTU = 119.4°
The measure of the angle ∠RTU will be 119.4°.
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Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5. Write the polynomial function for the graph. f(x) = (x – 2)(x – 3)(x – 5) Simplify the right side. What is the equation? f(x) = x3 + 31x – 30 f(x) = x3 – 10x2 + 31x – 30 f(x) = x3 – 10x2 + 19x – 30 f(x) = x3 + 19x – 30 graph
The equation which represents a cubic polynomial function with zeroes 2, 3 and 5 is; f(x) = x³ - 10x² + 31x - 30.
What is the equation of the polynomial with zeroes 2, 3 and 5?It follows that if a polynomial function has zeroes, a, b and c; The factors of such polynomial function are; (x - a), (x - b) and (x - c).
Therefore, since the given polynomial function has zeroes, 2, 3 and 5, the polynomial function is;
f(x) = (x - 2) (x - 3) (x - 5)
Therefore, by simplification; we have;
f(x) = (x² - 5x + 6) (x - 5)
f(x) = x³ - 5x² + 6x - 5x² + 25x - 30.
f(x) = x³ - 10x² + 31x - 30.
Therefore, the required cubic polynomial function is; f(x) = x³ - 10x² + 31x - 30.
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new york city is the most expensive city in the united states for lodging. the mean hotel room rate is $204 per night. assume that the room rates are normally distributed with a standard deviation of $55. answers to 3 decimals. what is the probability of more than $225?
The probability of more than $225 is 0.35197.
Here we need to find the probability of more than $225.
We need to calculate the z-score associated with x = $225
Z(score) = 225 - 204 / 55
= 0.381818
z(score) = 0.38
For z = 0.38 the corresponding probability is P(z < 0.38) = 0.64803.
Here we have to find the values greater than this value:
P(z > 0.38) = 1 - P (z < 0.38)
P( z > 0.38) = 0.35197
So the probability that a hotel room costs 225 or more per night is P (x > 225) = 0.35197 and the percentage is 35.197%.
Therefore the probability is 0.35197.
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when looking at the results of a 99% confidence interval, we can predict what the results of the two-sided significance test will be:
0.01 is the results of the two-sided significance test in confidence interval,
What is alpha in statistics?
A test statistic's statistical significance is determined by its alpha value. The researcher selects it. In a statistical test, the probability of a Type I error is represented by alpha. Considering that alpha is a probability, its range is 0 to 1.confidence level = 1 - alpha
so alpha = 1 - confidence level = 1 - 0.99 = 0.01
In statistics, alpha is the number that evaluates the test statistic to see if it is significant or not. In other words, alpha is the allowable type 1 error margin. The significance level, or alpha, is the antithesis of the confidence level. Confusion level + significance level = 1.
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suppose i randomly assign one group of angelenos to read a book about the history of the seattle supersonics, and the other to read a book about cheese. i then give them a quiz about basketball history (including recent events such as the los angeles lakers' twelfth championship). what is the independent variable in this experiment?
Using the concepts of probability, we got that book is independent variable in the experiment in which I randomly assign one group of angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese.
The independent variable is the condition that you actually change in an experiment. It is the variable you control. It is known as independent because its value does not depend on the value and is not affected by the state of any other variable in the experiment.
Hence, when i randomly assign one group of Angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese and then give them a quiz about basketball history (including recent events such as the Los Angeles Lakers then the independent variable in this experiment is the book given by me.
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if Richard correctly answered 52 questions on an exam that had 65 questions , what percent did he get
The percentage that Richard get is 8%
How to determine the percentage he got?The statement can be interpreted as:
He answered 52 correctly from a total of 65 questions
From the above statement, we have the following parameters
Dividend = 52
Divisor = 65
The percentage is then calculated as
Percentage = Dividend/Divisor x 100%
Substitute the known values in the above equation
So, we have
Percentage = 52/65 x 100%
Evaluate the quotient
Percentage = 0.8x 100%
Evaluate the product
Percentage = 8%
Hence, the percentage is 8%
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Length of a rectangle is 7 cm more than the width. The perimeter is 78 cm. Find the rectangles dimensions
Answer:
let the width be x
perimeter= 2(l+b)
78= 2(7 +x)
78-14= 2x
32= x
this must be the ans
the probability that a single radar station will detect an enemy plane is 0.65. (a) how many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station? stations (b) if four stations are in use, what is the expected number of stations that will detect an enemy plane? (round your answer to one decimal place.)
If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?The expected number of sucesses of a binomial variable is given by:If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.learn more about probability click here:
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Simplify the expression:
3(3+5g)
The value of the expression 3(3+5g) is 9 + 15g.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, we want to simplify 3(3 + 5g)
It's important to open the parentheses. This will be:
=3(3 + 5g)
= 9 + 15g
Therefore, the value is 9 + 15g.
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some answer?
4. Look at the functions that describe the profits of each business. Why do you think the a-value of the lawn care business is negative while the a-values of the dog walking and housesitting businesses are positive?
The a-values of the business are classified as follows:
Dog walking and house-sitting: positive because they are represented by increasing functions.Lawn care: negative because it is represented by a concave down parabola.How to obtain the a-value of a business?The a-value of a business depends on the behavior of the earning function for these business, as follows:
The a-value is positive if the function is increasing.The a-value is negative if the function has decreasing points.From the table given by the image at the end of the answer, for the lawn care business, a concave down parabola represents the situation, as the earnings start increasing but then during the 3rd month they start to decrease. Hence, the a-value of the business is negative.
For the dog walking and for the house-sitting business, the values are always increasing over the time interval of the table, hence the a-value of these two businesses is positive.
Missing InformationThe table is given by the image at the end of the answer.
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3* + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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If the line of best fit is y = 1.416x − 0.76, what is the residual value for the coordinate (10, 14)? −0.16 0.16 0.6 −0.6
The residual value is 0.6.
What is Residual?The estimated value of a fixed asset at the conclusion of its useful life or lease term is known as the residual value, also known as salvage value. In lease agreements, one of the lessor's main methods for figuring out how much the lessee must pay in periodic lease payments is the residual value.
Given:
y = 1.416x − 0.76
For (7, 8):
As, residual value = Measured value - Predicted value
or, residual value = (actual y-coordinate of the point) - (value of y from the
equation)
When x = 10:
So, the value of y from the equation,
[tex]y_1[/tex] = 1.416 x 10 - 0.76
[tex]y_1[/tex]= 14.16 - 0.76
[tex]y_1[/tex]= 13.4
and, actual y-coordinate of the point, [tex]y_2[/tex]= 14
Residual value = 14 - 13.4
Residual value = 14 - 13.4
Residual value = 0.6
Hence, the residual value is 0.6
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Answer:
0.6
Step-by-step explanation:
im taking the test rn