We found a counterexample, so the statement is false.
Is the statement true?
Let's use the matrix:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
This is a 4x4 matrix with determinant equal to -2.
The inverse matrix is:
[tex]\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right][/tex]
If we multiply it by 2, we get:
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right][/tex]
The adjoint of that is the original matrix, actually:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
Which we already know, has a determinant of -2.
So the statement is false, as we found a counterexample.
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Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:
A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1.
Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
The sequence of transformations used to obtain figure A'B'C'D'from figure ABCD are a reflection across the y-axis followed by a horizontal translation 1 unit right
Complete questionFigure ABCD is transformed to figure A'B'C'D', as shown below: (see attachment)
Which of the following sequences of transformations is used to obtain figure A'B'C'D'from figure ABCD?
How to determine the transformation?From the attached figure, we can see that:
ABCD and A'B'C'D' are on either sides of the y-axis.
This means that ABCD is first reflected across the y-axis.
ABCD is 2 units from the y-axis, while A'B'C'D' is 1 unit from the y-axis.
This means that the reflection is followed by a translation.
The unit of translation is:
Unit = 2 - 1
Evaluate
Unit = 1
1 represents a right translation
Hence, the sequence of transformations are a reflection across the y-axis followed by a horizontal translation 1 unit right
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What is the domain of the given function?
{x|x = -6, -1, 0, 3}
{y ly=-7, -2, 1, 9}
{x|x=-7, -6, -2, -1, 0, 1, 3, 9}
y ly=-7, -6, -2, -1, 0, 1, 3, 9}
Step-by-step explanation:
Easy buddy....
_________________________________
Remember, from now on, wherever the function domain is asked
They mean the same inputs or xs of the function.
Now you can answer them yourself but I like to help you to do it buddy.
_________________________________
The first function's domain is :
D = { -6 , -1 , 0 , 3 }
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
The second function's domain is :
D = { -7 , -6 , -2 , -1 , 0 , 1 , 3 , 9 }
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
The domain of the function in the table given is:
A. {x|x = -6, -1, 0, 3}.
In any given function, all x-values (input) make up the domain of the function, while corresponding y-values (output) make up the range of the function.
In the table given, the x-values (input) are -6, -1, 0, and 3.
Therefore, the domain of the function in the table given is:
A. {x|x = -6, -1, 0, 3}.
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four times a number is 48 less than 6 times the number
Answer:
the answer is 24
Step-by-step explanation:
6x - 48 = 4x
6x - 4x - 48 = 0
2x - 48 = 0
2x = 0 + 48
2x = 48
x = 24
Find a solution to the linear equation 11x−y=−11.Find a solution to the linear equation 11x−y=−11.
Answer:
(0,11)
Step-by-step explanation:
If we let x=0, then -y = -11, and so y=11.
Thus, (0,11) is a solution to the linear equation.
In(2e^9) in logarithmic expression
I’m having trouble with all of the “In” section and very confused
In logarithmic form, we get In(2e^9)= ln(2)+9.
LogarithmsWe define the logarithm as the power to which any number must be raised to get few other values.Exponentiation is the reverse process of logarithm.We are given,
ln(2[tex]e^{9}[/tex])
We know that, ln(ab) = ln(a) + ln(b)
So we get,
ln(2[tex]e^{9}[/tex]) = ln(2)+ln([tex]e^{9}[/tex])
Since ln(m^n)=n ln(m)
And ln(e)= 1, we will get,
ln(2[tex]e^{9}[/tex]) = ln(2) +9 ln(e)
= ln(2) +9
Hence, the logarithmic form, we get In(2e^9)= ln(2)+9.
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simplify. evaluate.
Answer:
[tex]\frac{1}{18}[/tex]
Step-by-step explanation:
The best way to solve this problem is to simplify each factorial one by one!
Starting at the numerator, the factorial for 2! is just 2, while the factorial for 5 is 120.
At the denominator, the factorial of 6! is 720, while the factorial for 3 is 6.
To write this out, we're given: [tex]\frac{(2) (120)}{(720) (6)}[/tex]
Just simply multiply and then divide, and we are given 1/18
Advise the committee of the minimum number of shade tents that must be set up to hold all the balloons so that they don’t fly away ?
The maximum number of spherical balloons that can be held in the canopy will be 30.
What is a canopy?The canopy is the fabric cover that hangs above a bed. It is a covering that is fastened to or carried over a dignitary or a holy item.
The base layer of spheres in a square pyramidal arrangement has n2 balls, where n is the number of balls that make up a square's side.
n=4 inch
The total number of spheres in the pyramid is;
⇒n(n+1)(2n+1)/6
⇒4(4+1)(2×4+1)/6
⇒(4×5×9)/6
⇒30
Hence, in the canopy, 30 spherical balloons are the most that may be accommodated.
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For the first 8 months at his new job, James gets
an increase in pay. What is the rate at which
James receives a pay increase? Approximately
what was his starting pay? Write an equation to
model the relationship.
James receives a pay increase of 100% per month and has a starting salary of $500.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let b represent the rate of pay increase and a represent the initial pay.
Let us assume that he had received 128000 after the 8 months. hence:
128000 = ab⁸ (1)
Also in the 10th month, he had received 512000, hence:
512000 = ab¹⁰ (2)
From the both equations:
a = 500, b = 2
rate of increase = 200% - 100% = 100%
James receives a pay increase of 100% per month and has a starting salary of $500.
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A clock was reading the time accurately on Friday at noon. On Monday at 6pm the clock was running late by 468 seconds. On average, how many seconds did the clock skip every 30 minutes?
The clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.
The clock was still accurate by Friday noon. The clock was late by 468 seconds by Monday, 6 pm.
To solve the problem, we must:
Know how many 30-minutes have passed during the time period.
1 day = 24 hours
1 hour = 60 minutes = 2 × (30 minutes)
1 day = 24 hours × 2 × (30 minutes)
1 day = 48 × (30 minutes)
Thus, there are 48, 30-minutes in a day. On Friday, however, we start counting at noon, which is half of the day. Moreover, on Monday, the mark is only up to 6 pm, which is three-fourths of the day.
Friday = 48 × [tex]\frac{1}{2}[/tex] = 24
Saturday = 48
Sunday = 48
Monday = 48 × [tex]\frac{3}{4}[/tex] = 36
TOTAL = 24 + 48 + 48 + 36 = 156
Therefore, the total number of 30-minutes that have passed is 156. There were 156, 30-minutes that passed during the time period.
Divide the number of total seconds late by the number of 30-minutes passed.
That is, the number of total seconds late= 468 seconds ÷ 156
= 3 seconds
Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.
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Line l has a slope of 2/3 The line through which of the following pair of points is perpendicular to l?
We conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.
The line through which of the following pair of points is perpendicular to l?Remember that two lines are perpendicular only if the slope of one of the lines is equal to the opposite of the inverse of the slope of the other line.
So, if line l has the slope 2/3.
Then the perpendicular lines have a slope equal to -3/2.
Now, remember that if a line goes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So here we just need to find two points (x₁, y₁) and (x₂, y₂) such that the slope is equal to -3/2.
If we define (x₁, y₁) = (0, 0), then the other point must be:
[tex]a = \frac{y_2 - 0}{x_2 - 0} = -3/2\\\\y_2/x_2 = -3/2[/tex]
Then we can write the other point as (2, -3).
So we conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.
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find the measure of angle S and angle TRS pls help
Answer:
60°
Step-by-step explanation:
since angle on straight line is 180° you take the sum of the exterior angle of R and its interior angle then divide both sides by the coefficient of y to find y then things get easier from there
Answer:
Step-by-step explanation:
Plan
7y and 5y are made on the same straight line. Therefore they are supplementary and add to 180 degrees. <s has to be found by finding 3x and 5y first. Find <s by solving 3y + 5y + x = 180 degrees.
Solution
7y + 5y = 180 degrees Combine the left
12y = 180 degrees Divide by 12
12y/12 = 180/12
y = 15
3y + 5y + x = 180 Combine the left side
8y + x = 180 Substitute 15 for y
8*15 + x = 180 Combine
120 + x = 180 Subtract 120 from both sides
120 -120 +x =180 - 120 Combine
x = 60
Answer
s = 60 degrees
<TRS = 5y = 75
1. (y + x) = 4; use x = 2 and y = 2
2. x + y = 6; use x = 5 and y = 6
3. y(x + 5); use x = 1 and y = 4
4. q-m+q; use m = 3 and q = 6
Simplify each expression.
10x³y²
5x³y
x = 0, y = 0
Step-by-step explanation:
Very easy the value are given apply the value for X and y
How many degrees does Earth turn in one hour?
Answer:
15 degrees
Step-by-step explanation:
Answer:
The earth turns 15 degrees in one hour. Hope this helps!
Step-by-step explanation:
Which of the following equations is equivalent to the formula for velocity
A company decides to offer a monetary incentive for employees who log a specified number of hours spent exercising in an attempt to improve employee health. The average health score (higher = better) of the 75 employees who logged enough hours was 87. The mean health score for all employees (population) was 85, with a population standard deviation of 6.5. Calculate the standard error of the mean
The standard error will be equal to 0.75.
What is the standard error?The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean.
The standard error will be calculated by using the formula:-
SE = [tex]\sigma[/tex] / √n
Here [tex]\sigma[/tex] is the standard deviation and n is the sample number.
SE = 6.5 / √75
SE = 0.75
Therefore the standard error will be equal to 0.75.
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3x² - 2x + 1 = [?]
x=4
Answer:
3x²-2x+1=?
3(4²)-2(4)+1=?
3(16)-8+1=?
48-8+1=?
40+1=41
which of the following are characteristics of the graph of the square root parent function
Answer:
C
Step-by-step explanation:
Expression Math problem...help and get 15 pts!
When h = 0 , [f(x + h) - f(x)]/h = 2x +2 for the given expression.
The missing expression is f(x) = x² + 2x.
What is formula of difference quotient ?f(x+h)-f(x)/h is called the formula of difference quotient.
When h---> 0 ,
the expression f'(x) = (f(x-h) - f(x)) / h is the equation for tangent to the line
Here the the expression is
f(x) = x² + 2x
Determining f(x + h) by substituting x = x + h on both sides of the given f(x).
Then f(x + h) = (x + h)² + 2(x + h)
= x² + 2xh + h² + 2x + 2h
the difference f(x + h) - f(x).
f(x + h) - f(x) = [x² + 2xh + h² + 2x + 2h] - [x² + 2x]
= 2xh + h² + 2h
Divide the difference from h as in the formula of difference coefficient
[f(x + h) - f(x)]/h = (2xh + h² + 2h) / h
= 2x + h + 2
So, when h = 0 , [f(x + h) - f(x)]/h = 2x +2
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From this diagram, select the
pair of lines that must be
parallel if 27 and 25 are
supplementary. If there is no
pair of lines, select "none."
Answer:
l
Step-by-step explanation:
Answer:
Lines L and n are parallel
Explanation -
In the question it is given that angle 7 and angle 5 are supplementary.
which means that sum of this angle is 180°
so line L and n are parallel
The tables represent the functions f(x) and g(x).
Which input value produces the same output value for the two functions?
x = –12
x = –9
x = –6
x = –3
A function assigns the values. The correct option is C, x=-6.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) When the value of x is -12,
f(-12) = 2/3(-12) + 7 = -1
g(-12) = 2(-12) + 15 = -9
B.) When the value of x is -9,
f(-9) = 2/3(-9) + 7 = 1
g(-9) = 2(-9) + 15 = -3
C.) When the value of x is -6,
f(-6) = 2/3(-6) + 7 = 3
g(-6) = 2(-6) + 15 = 3
D.) When the value of x is -3,
f(-9) = 2/3(-3) + 7 = 5
g(-9) = 2(-2) + 15 = 11
Hence, the correct option is C, x=-6.
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X= ABC+ AB+ ABC Simplify followings
Answer:
X = ABC+ AB+ ABC
X = AB(C+1+C)
X = AB(2C+1)
Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?
The true option about the system of linear equation is that the system can only be independent and consistent.
How to illustrate the equation?It should be noted that the system is consistent as it can illustrate more than a solution.
Also, it can't be independent and dependent at the same time as depicted in some of the option given.
In this case, true option about the system is that the system can only be independent and consistent.
The complete question is:
Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?
The system can be either inconsistent or consistent.
The system can be either independent or dependent.
The system can only be independent and consistent.
The system can only be dependent and inconsistent.
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Find the equation of a line that contains the points (−2,−4) and (−5,4). Write the equation in slope-intercept form, using fractions when required.
The equation would be y+ 3/8x+9/4.
Lets try to explain in the further steps to calculate the equation,
Slope formula: (y₂ - y₁) / (x₂ - x₁)
First, plug in these values of the two given points.
[tex]= > (-5+2) / (4+4)\\= > -3/8[/tex]
Slope = -3/8
To find the equation of the line, (y- y1) = m* (x-x1)
So by putting the values into the above equation we get,
[tex]= > (y-4) = -3/8(x+5)\\= > y-4 = -3/8x - 15/8\\= > y + 3/8x + 4 - 15/8\\= > y + 3/8x + 9/4[/tex]
Hence the equation is [tex]y+ 3/8x+9/4.[/tex]
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Find the area of the rectangle.
A rectangle is shown. The left side is labeled with the expression 8 x. The top side is labeled with the expression 7 x plus 1. (1 point)
15x + 1
56x2 + 8x
56x + 8
15x2 + 9x
Answer:
56x² + 8x
(second option listed)
Step-by-step explanation:
area: length × width
length: 7x + 1
width: 8x
(8x)(7x + 1)
{distribute 8x}:
(8x)(7x): 8x × 7x = 8 · 7 · x · x = 56 · x · x = 56x²
(8x)(1) = 8x
area = 56x² + 8x
so, the area of this rectangle is 56x² + 8x
Answer:
56x² + 8x
[answer B]
Evaluate the expression.
Answer:
18
Step-by-step explanation:
Using order of operations:
[tex] \frac{15 - 9}{3} (19 - 10)[/tex]
[tex] \frac{6}{3} (9)[/tex]
[tex]2(9) = 18[/tex]
Which line is perpendicular to a line that has a slope of -5/6?
Answer:
Line LM
Step-by-step explanation:
First, we need to know what the slope is of a line that would be perpendicular to a line with a slope of -5/6. To find this, we take the reciprocal and multiply it by -1. Therefore, the line we are looking for needs to have a slope of 6/5.
Based on the fact that the slope is positive, we can eliminate lines PQ and JK as they have a negative slope. This leaves us with lines LM and NO.
To find out whether or not it is between LM and NO, you could eyeball it by looking at the graph and simply counting which might be faster if you understand how to do that (rise/run), or you can use the pair of coordinates given to you on each line to calculate for slope.
Line LM - [tex]\frac{-3-3}{-5-0}=\frac{-6}{-5}=\frac{6}{5}[/tex]
Line NO - [tex]\frac{-5-0}{-6-0}=\frac{-5}{-6}=\frac{5}{6}[/tex]
Based on this, we know that line LM is perpendicular to a line that has a slope of -5/6.
If you need help on calculating slope from two points, I'd suggest watching this video: https://www.brightstorm.com/math/algebra/linear-equations-and-their-graphs/finding-the-slope-of-a-line-from-2-points-problem-1/#:~:text=Use%20the%20slope%20formula%20to,second%20points%20are%20x2%2C%20y2.
what is the slope of the line through the points (-2,-1) and (8,-3)
Answer:
Step-by-step explanation:
Using slope m = y_2-y_1/x_2-x_1 to find the solution slope that passes through those two-point.
Point-slope form into y-intercept form.
Answer:
For finding slope
we have the formula
m = y2 - y1/ x2 - x1
x1 = (-2)
x2. = ( 8)
y1. = (-1)
y2 =(-3)
putting the value of this in the formula we get,
m = (-3)-(-1)/8-(-2)
m = (-3+1)/8 + 2.
m = (-2)/10
m = (-1)/5.
m = (-1)/5
Brainliest to whoever answers :) Highly appreciated
Answer:
the answer is L
Step-by-step explanation:
rounding up to any number/decimal requires the digit before the specified digit to be 5 or greater.
rounding down requires the digit to be 4 or less.
if the estimated time to the nearest 0.01 of a second is 35.20 then the actual race time could be from 35.195 to 35.205 since any number between could be rounded to 35.20
What are some limitations in using a line of best fit drawn on a scatter plot to make predictions?
a.
There may be too much information given on the scatter plot.
b.
The line may represent a negative or positive correlation.
c.
It is possible to draw different lines to approximate the same data. The line of best fit is only an estimate.
d.
The axes of the scatter plot may be labeled incorrectly.
Please select the best answer from the choices provided
A
B
C
D
Mark this and return
Answer: It is possible to draw different lines to approximate the same data. The line of best fit is only an estimate.
