If it is multiplied by the identity matrix, what is the resulting matrix?
Answer:
D. [tex]\left[\begin{array}{cc}4&5\\-3&2\\\end{array}\right][/tex]
Step-by-step explanation:
The reason it is called an "identity matrix" is that it doesn't change anything. The result is what you started with.
When the matrix A = [ [2, 3], [4, 5] ] is multiplied by the 2x2 identity matrix, the resulting matrix is still A itself: [ [2, 3], [4, 5] ].
When you multiply a matrix by the identity matrix, the result is the original matrix itself. In this case, matrix A is given as A = [ [2, 3], [4, 5] ], and you want to find A * I, where I represents the identity matrix.
The identity matrix is a square matrix with ones on the main diagonal and zeros everywhere else. In this case, since A is a 2x2 matrix, you would use a 2x2 identity matrix, which looks like:
I = [ [1, 0], [0, 1] ]
Now, when you multiply A by I:
A * I = [ [2, 3], [4, 5] ] * [ [1, 0], [0, 1] ]
You can perform matrix multiplication as follows:
[ (2*1 + 3*0), (2*0 + 3*1) ]
[ (4*1 + 5*0), (4*0 + 5*1) ]
Simplifying the calculations:
[ 2, 3 ]
[ 4, 5 ]
The resulting matrix is exactly the same as matrix A. So, A * I equals the original matrix A: [ [2, 3], [4, 5] ].
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The probable question maybe:
Given the matrix A = [ [2, 3], [4, 5] ], what is the resulting matrix when it is multiplied by the identity matrix of the appropriate size?
The equation T^2 = A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?
A 2^1/3
B 2^1/2
C 2^2/3
D 2^3/2
If the orbital period of planet Y is twice the orbital period of Planet X, by then the factor is the mean distance increased by 4.
Given
The equation T^2 = A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU.
What is mean value?The mean is defined as the sum of all data set numbers and the total number in the data set.
If the orbital period of planet Y is twice the orbital period of Planet X,
Therefore,
If the orbital period of planet Y is twice the orbital period of Planet X, by then the factor is the mean distance increased is;
[tex]\rm Factor \of\ increase =\dfrac{2&^3}{2 }\\\\ Factor \of\ increase =4[/tex]
Hence, If the orbital period of planet Y is twice the orbital period of Planet X, by then the factor is the mean distance increased by 4.
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Answer:
D: 2^3/2
Step-by-step explanation:
Right on Edgenui test
Answer:
D: 2^3/2
Step-by-step explanation:
Right on Edgenui test
What are the two longest measurements below?
40,000 millimeters
3,500 centimeters
0.1 kilometers
30 meters
Below is the graph of y = g(x)
Translate it to make it the graph of y = g(x)^2
PLEASE SOMEONE HELP ME??
Instead of y = g(x)^2, it should be y = g(x)+2
What this means that every point on g(x) will be shifted up 2 units. A point like (2,-1) which is the saddle point shown on the graph, will move up to (2,1) after you shift up 2 units. Every other point will follow the same path. Another example: The point (0,-5) -- which is the y intercept -- will move up to (0,-3).
Check out the attached image below for a visual of what's going on.
The graph of the translation to make it y = g(x) + 2 is added as an attachment
Translating the graph to make it y = g(x) + 2From the question, we have the following parameters that can be used in our computation:
The graph of y = g(x)
Translating the graph to make it y = g(x) + 2, we simply move the given up by 2 units
This means that the curves are moved up by 2 units
The graph to make it y = g(x) + 2 is added as an attachment
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what is the value 4 in 12.47
It's in the tenths place.
Alleen can read 1.5 pages for every page her friend can read.Alleen's mom was very extcited and she said to alleen: "so,if your friend reads 20 pages, you can read 25 in tge same time period!" is alleen mom correct ?
Answer:
no. she can read 30
Question 1 A survey was sent to GCA students asking the question "Who is your favorite teacher?"
What type of data was collected?
Question 1 options:
Quantitative
Qualitative
Continuous
Discrete
Question 2
A survey was sent to GCA students asking the question "On a scale of 1 to 5, with 1 being the lowest and 5 being the highest, how would you rate your AMDM teacher?"
The data collected was
Question 2 options:
Quantitative
Qualitative
Continuous
redundant since every student rated their AMDM teacher as a 5.
Question 3
You decided to attend the GCA outing at Stone Mountain. Before you left for the park, you entered the park address into a GPS/Traffic app on your phone. The app told you that Stone Mountain was 47.6 miles from your house.
47.6 miles is an example of...
Question 3 options:
Qualitative, continuous data
Quantitative, discrete data
Qualitative, discrete data
Quantitative, continuous data
Question 4
While you were at the Stone Mountain outing, you played a game of corn hole. You counted the number times you tossed the beanbag into the hole.
The number of times you were able to sink the beanbag is an example of....
Question 4 options:
Qualitative, continuous data
Quantitative, discrete data
Qualitative, discrete data
Quantitative, continuous data
Question 5
You recorded the time you left Stone Mountain and the time you arrived home. You calculated time it took you get home was 57.28 minutes.
57.28 minutes is an example of....
Question 5 options:
Qualitative, continuous data
Quantitative, discrete data
Qualitative, discrete data
Quantitative, continuous data
okay the answers are
Question 1 A survey was sent to GCA students asking the question "Who is your favorite teacher?"
What type of data was collected?
Answer) Qualitative
Question 2 ) A survey was sent to GCA students asking the question "On a scale of 1 to 5, with 1 being the lowest and 5 being the highest, how would you rate your AMDM teacher?"
The data collected was
Answer) Quantitative
Question 3) You decided to attend the GCA outing at Stone Mountain. Before you left for the park, you entered the park address into a GPS/Traffic app on your phone. The app told you that Stone Mountain was 47.6 miles from your house.
47.6 miles is an example of...
Answer) Quantitative, continuous data
Question 4 ) While you were at the Stone Mountain outing, you played a game of corn hole. You counted the number times you tossed the beanbag into the hole.
The number of times you were able to sink the beanbag is an example of....
Answer) Quantitative, discrete data
Question 5) You recorded the time you left Stone Mountain and the time you arrived home. You calculated time it took you get home was 57.28 minutes.
57.28 minutes is an example of....
Answer) Quantitative, continuous data
To convert 4,450 m to cm, you would move the decimal point _____ places to the _____.
move the decimal point 2 places to the right
note 1m = 100 cm
4450m = 4450 × 100 cm
multiplying by 100 is equivalent to moving the decimal point 2 places to the right
Which of the following equations correctly describes the graphed line?
y = -x + 5
y =x + 5
y =x - 5
y = -x - 5
A(-3, -2) and B(3, -8)
slope m = (-2 + 8)/(-3 - 3) = 6/-6 = -1
b = y intercept = -5
Equation
y = -x - 5
Answer
y = -x - 5
The equation of the linear system will be y = - x - 5.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The graph is given below.
If the graph is decreasing, then the slope of the linear system will be negative.
And the y-intercept is negative 5.
Then the equation of the linear system will be y = - x - 5.
Thus, the correct option is D.
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Which of the following equations represents the line with a slope of negative 8/7 and a y-intercept of negative 3?
y = 8/7x - 3
y = 8/7x + 3
y = -8/7x - 3
y = -8/7x + 3
Solution
The general form of the equation is y = mx + b, where m is the slope and b is the y-intercept.
Given: m = 8/7 and b = -3
Plugin the given values into the formula.
y = 8/7x - 3
The answer is y = 8/7x - 3
Thank you :)
The correct equation representing the line with a slope of negative 8/7 and a y-intercept of negative 3 is y = -8/7x - 3. This was determined by substituting these values into the slope-intercept form of a line equation, y = mx + b.
Explanation:Line Equation with Given Slope and Y-interceptThe equation of a line in slope-intercept form is given as y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, we're looking for an equation with a slope (m) of -8/7 and a y-intercept (b) of -3.
Substituting these values into the slope-intercept form, we get: y = -8/7x - 3.
So, the correct answer is y = -8/7x - 3.
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Six students want to participate in the spelling bee, but there are only three spots. In how many ways can a group of three students be chosen?
The number of ways can a group of three students be chosen is 20 ways
What are Combinations?The number of ways of selecting r objects from n unlike objects is given by combinations
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the number of ways of selecting students be A
Now , the total number of students = 6
And , to choose 3 students out of 6 without regard to order. The formula for combinations is
n C r = n! / r!(n-r)!
where n is the total number of items, and r is the number of items to choose
6 C 3 = 6! / 3!(6-3)! = 20
Hence , there are 20 ways to choose a group of three students out of six
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The correct number of ways to choose a group of three students from six is [tex]\boxed{20}.[/tex]
To solve this problem, we can use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In our case, we have six students and we want to choose three of them to participate in the spelling bee. The order in which we choose the students does not matter since all three will participate equally.
The formula for calculating combinations is given by:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to that number.
For our problem:
[tex]- $n = 6$[/tex] (total number of students)
[tex]- $k = 3$[/tex] (number of students to choose)
Plugging these values into the formula, we get:
[tex]\[ C(6, 3) = \frac{6!}{3!(6-3)!} \][/tex]
Calculating the factorials, we have:
[tex]\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]
[tex]\[ 3! = 3 \times 2 \times 1 = 6 \][/tex]
[tex]\[ (6-3)! = 3! = 6 \][/tex]
Now, we substitute these values into the combination formula:
[tex]\[ C(6, 3) = \frac{720}{6 \times 6} \][/tex]
[tex]\[ C(6, 3) = \frac{720}{36} \][/tex]
[tex]\[ C(6, 3) = 20 \][/tex]
Therefore, there are 20 different ways to choose a group of three students from six for the spelling bee.
Gina bought 2.3 pounds of red apples and 2.42 pounds of green apples they were sold on sale for 0.75 a pound .How much did the apples cost all together
Mitchel are 45 hotdogs in 3 minutes at the annual hot for eating contes. What is mitchel’s unit rate
Mitchel Unit rate is 15 hotdogs per minute we know this because it show 45 hotdogs in 3 minutes and 45 divided by 3 is 15 so the unit rate is 15.
The temperature in a town increased 16 Fahrenheit in 5 hours. The temperature decreases 31 Fahrenheit in the next 8 hours. Which expressions shows the rate of the total change in temperature?
A. -15 hours
------------------
13 hours
B. 47 F
--------------
13 hours
C. 15 F
----------
10 min
D. 47 F
-----------
-13 hours
Correct answer is: A) [tex]\frac{-15F}{13hours}[/tex]
Solution:-
Given that temperature of town increased 16 Fahrenheit in 5 hours and decreases 31 Fahrenheit in the next 8 hours.
If we assume T as temperature, it became T+16 in 5 hours and (T+16-31) in next 8 hours.
That is change in temperature in (5+8) hours is 16-31 = -15 Fahrenheit.
Rate of total change in temperature = [tex]\frac{change in temperature}{time}[/tex]
= [tex]\frac{-15}{5+8}=\frac{-15}{13}[/tex]
Hence rate of total change in temperature is [tex]\frac{-15F}{13hours}[/tex]
The correct expression that shows the rate of the total change in temperature is -15 hours / 13 hours. The Option A.
What expression shows the rate of the total change in temperature?The rate of change in temperature refers to the speed at which the temperature is increasing or decreasing over a given period of time.
Given information:Temperature increase: 16°F in 5 hoursTemperature decrease: 31°F in 8 hoursTotal change in temperature is:
= Temperature increase - Temperature decrease
= 16°F - 31°F
= -15°F
Total time for the change:
= Time for increase + Time for decrease
= 5 hours + 8 hours
= 13 hours
Rate of total change in temperature:
= Total change in temperature / Total time for the change
= -15°F / 13 hours.
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Jamal filled his gas tank and then use 7/16 of the tank for traveling to visit his grandfather. He then used 1/3 of the remaining gas in the tank to run errands around town. What fraction of the tank is filled with gasoline
Answer:
The fraction of the tank is filled with gasoline is [tex]\frac{3}{8}[/tex].
Step-by-step explanation:
Consider the provided information.
Jamal filled his gas tank and then use 7/16 of the tank for traveling to visit his grandfather.
After his first traveling the amount of gas left can be calculated as:
[tex]1-\frac{7}{16}[/tex]
[tex]\frac{16-7}{16}[/tex]
[tex]\frac{9}{16}[/tex]
He then used 1/3 of the remaining gas in the tank to run around town.
That means he left with 2/3 of gas.
[tex]\frac{9}{16}\times \frac{2}{3}[/tex]
[tex]\frac{3}{8}[/tex]
Hence, the fraction of the tank is filled with gasoline is [tex]\frac{3}{8}[/tex].
Jose can read 7 pages of his book in 5 minutes at this rate how long will it take for him to read the full 175 page book
Answer:
125 minutes
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
1 and 4 are correct. 2 and 3 are not.
Step-by-step explanation:
1.
When x = 0 where does the horse start?
y = 1.5*sin(0 + 0.5)*2*pi + 1.5
y = 1.5*sin(0.5*2pi) + 1.5
y = 1.5*sin(pi) + 1.5 But sin pi = 0
y = 0 + 1.5 So the horse is starting at the midpoint of it's travel.
2.
This one is a trick question. You can reason it without exact answers. At some point the sin(x + 0.5)*2pi will equal 1. When it does 1.5 * 1 + 1.5 = 3.0 At some other point sin(x + 0.5)*2pi = -1. When that happens the whole thing goes to 0. So the total of the distance traveled is 6 not three.
3.
You can figure this one out by letting x = 0.01 When it does then the value of the function is
y = 1.5*sin [(0.01 + 0.5)*2pi] + 1.5
y = 1.5*sin(0.51*2*pi) + 1.5
y = 1.5*sin(3.204424) + 1.5
y = 1.5*(- .0623) + 1.5
y = -0.9418 + 1.5
y = 1.4058 so it is going downward The value is getting smaller.
4.
The horse starts out in the middle of the pole. What does x need to equal so that x + 0.5 = 1 ? And why 1. The answer to why 1 is that then the sine function will equal sin(2*pi)
That happens when x = 0.5 which is 1/2 a minute. If it takes 1/2 a minute to execute 1 complete cycle, then in 5 minutes the cycle will be executed 10 times. This one is correct.
Solve for x. 6x-10≤8 or 1/3 x+6>12
The solution is
[tex]x\le 3 \:or \:x>18[/tex]
[tex]<b><u>EXPLANATION</u></b>[/tex]
[tex]6x-10\le 8\: or \frac{1}{3}x+6>12[/tex]
We group like terms, to obtain;
[tex]6x\le 8+10\: or \frac{1}{3}x>12-6[/tex]
Simplify to get,
[tex]6x\le 18\: or \frac{1}{3}x>6[/tex]
We further simplify to get;
[tex]x\le 3\: or x>18[/tex]
This can also be rewritten as;
[tex]x\le 3, x>18[/tex]
Or
[tex](-\infty 3] \cup (18,+ \infty)[/tex]
This can be represented on the number line as shown in the diagram.
Answer: (-∞,3)∪(18,∞)
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You must solve for x, as following:
[tex]6x-10\leq8\\6x\leq18\\x\leq3[/tex]
[tex]\frac{1}{3}x+6>12\\x>3(6)\\x>18[/tex]
2. Therefore, you have that the result is:
(-∞,3]∪(18,∞)
Factor the expression over the complex numbers.
x^2+52
Here we are given the expression:
[tex]x^{2}+52[/tex]
Now let us equate it to zero to find x first,
[tex]x^{2}+52=0[/tex]
Now subtracting 52 from the other side,
[tex]x^{2}=-52[/tex]
taking square root on both sides,
So we will get two values of x as ,
[tex]x=+2\sqrt{-13}[/tex]
[tex]x=-2\sqrt{-13}[/tex]
Now we can write square root -1 as i,
So our factors become,
[tex]x=+2i\sqrt{13}[/tex]
[tex]x=-2i\sqrt{13}[/tex]
Answer:
The final factored form becomes,
[tex](x+2i\sqrt{13})(x-2i\sqrt{13})[/tex]
A cell phone company charges $45 a month for phone service and $0.25 for each text message. Which equation can be used to find the total number of text messages sent in a month? How many text messages were sent if the monthly bill was $75?
Only enter the capital letter of your choice into the blank (A, B, C, or D).
A) 45 + 0.25t = C; t = 480
B) 45t + 0.25 = C; t = 120
C) 45t + 0.25 = C; t = 480
D) 45 + 0.25t = C; t = 120
Hey!!
A cell phone company charges $45 a month and hence, this would be constant and would be same the same value. And the company charges $0.25 for every text message.
Let's take the number of text messages as ' t '
The question asks us to find the number of text messages needed to make it $75 for the first month.
We know, the constant is $45 and we know the number of text messages as ' t ' and we also know the cost of each text messages is $0.25. And with all this given, we can find the total cost which is denoted by ' c '.
The total cost would be the price of a month added to the cost of text messages.
The total cost = c
The price of for month = $45
The price of text messages = $0.25t
Now, let's form the equation :
... c = 45 + 0.25t ( this is the equation )
The total cost given is $75
Hence, the equation would be :
... 75 = 45 + 0.25t
Subtract 45 on both sides
... 30 = 0.25t
Divide 0.25 on both sides
... t = 120
Hence, the answer would be option ( D )
Hope my answer helps!!
Could 12.2 cm 6.0 cm and 4.2 cm be the side lengths of a triangle
Answer: No.
Step-by-step explanation: No, as two of sides need to be equal.
Answer:
we cannot form a triangle using the given lengths.
Step-by-step explanation:
There are three conditions that must be satisfied in order to form a triangle.
Let's take a, b and c are the sides of a triangle.
Conditions are:
i) a + b > c
ii) b + c > a
iii) c + a > b
Here let's take a = 12.2, b = 6.0 and c = 4.2
Let's check the conditions
i) 12.2 + 6 > 4.2
18.2 > 4.2
Which is true.
ii) 6 + 4.2 > 12.2
10.2 > 12.2
Which is not true.
The condition fails.
Therefore, we cannot form a triangle using the given lengths.
Hope this will helpful.
Thank you.
Parallelogram ESTA has vertices E (10, 0), S (14, 3), T (6, 9), and A (2, 6). To calculate its area, Jamal will first determine the equation of the line through point E and perpendicular to ST. What is the equation of this line in point intercept form?
Answer:
The vertices of parallelogram ESTA are E (10, 0), S (14, 3), T (6, 9), and A (2, 6).
As we know ,Area of parallelogram = Base × Height
As base can be determined by using distance formula because coordinates of the vertices are given.
Now to determine perpendicular, we will find the equation of line through E and perpendicular to ST.
Equation of line through S(14,3) and T(6,9) is
[tex]\frac{y-3}{x-14}=\frac{9-3}{6-14}\\\frac{y-3}{x-14} =\frac{6}{-8}[/tex]
[tex]\frac{y-3}{x-14}=\frac{-3}{4}\\4y -12=-3x+42[/tex]
⇒4y + 3x =12+42
⇒ 3 x + 4 y=54
Equation of line perpendicular to ST and passing through E(10,0) is
4 x-3 y + k=0
Put x=10, y=0 in above equation is
4×10 -3×0 +k=0
⇒ k= -40
The Equation of line through point E and perpendicular to ST is
4 x-3 y -40=0
A man walked steadily from 11 am to 2.30 pm at 5 kilometres per hour how far did he walk!
Answer:
Distance traveled 17.5 kilometers
Step-by-step explanation:
We can use the following equation to find the distance traveled,
Distance traveled = Speed * Time
First we need to find the total time he walked = 2.30 p.m. - 11.a.m.
=[tex]3.5[/tex] hours
Now we can substitute the values to the equation,
Distance traveled = [tex]5[/tex] kilometers per hour * [tex]3.5[/tex] hours
= [tex]5*3.5[/tex] kilometers
= 17.5 kilometers
please help asap 25 pts
Remark
This is much the same as the last inequality that you posted. When it tells you that you have 1 condition that is more than and one condition that is less than, then you need a compound statement. One of A and B is correct. C or D never will be.
At Least 4
This is the more than condition. You need 4 or more pennies to add to the collection. The rule is the same. The pointy end always points towards the smallest amount
4 ≤ x
No more than 2
That means that you can have 2 or under. The pointy end points to the x
2 ≥ x The biggest number (open end of the arrow) points at the 2.
Answer
2 ≥ x or 4 ≤ x That means the answer is A
16 1/5 yards of fabric divided by 5 2/5 yards of fabric
Easiest way for me is to convert those mixed fractions and then divide.
Sorry for some bad handwriting! Hope it helps
What is m∠M ? Enter your answer in the box. ° The figure shows what appears to be obtuse triangle M N O with obtuse angle M. The measure of angle M is left parentheses 3 times x minus 16 right parentheses degrees. The measure of angle N is x degrees. The measure of angle O is left parentheses x plus 6 right parentheses degrees.
We know:
The sum of the measures of the angles of a triangle is equal 180°.
Therefore we have the equation:
[tex](3x-16)+x+(x+6)=180\\\\3x-16+x+x+6=180\\\\(3x+x+x)+(-16+6)=180\\\\4x-10=180\ \ \ \ |+10\\\\4x=190\ \ \ \ |:4\\\\x=47.5[/tex]
m∠M = (3x-16)°
Substitute:
[tex]m\angle M=(3\cdot47.5-16)^o=(142.5-16)^o=126.5^o[/tex]
Answer: m∠M = 126.5°Answer:
98
Step-by-step explanation:
I got it wrong when I typed in 126.5, its actually 98
Go forth and Conquer
Ingrid types 3 pages in the same amount of time that tanya types 4.5 pages. If the grid and tanya start typing at the same time how many pages will tanya have typed when ingrid has typed 11 pages ?
A 4-cup carton of sour cream costs $5.68. What is the price per pint?
Answer: $2.84 per pint
Step-by-step explanation:
[tex]\frac{5.68 (dollars)}{4 (cups)} *\frac{2(cups)}{1(pint)} = \frac{5.68(2)dollars}{4 pints} = \frac{2.84 dollars}{1 pint}[/tex] = $2.84 per pint
Final answer:
To find the price per pint of sour cream from a 4-cup carton costing $5.68, divide the total cost by the number of pints, resulting in $2.84 per pint.
Explanation:
The question asks to find the price per pint for a 4-cup carton of sour cream that costs $5.68. Since there are 2 cups in a pint, a 4-cup carton is equivalent to 2 pints. To find the price per pint, we simply divide the total cost by the number of pints.
Calculation:
Determine the number of pints in the carton: 4 cups ÷ 2 cups/pint = 2 pints.Divide the total cost by the number of pints: $5.68 ÷ 2 pints = $2.84 per pint.Thus, the price per pint of sour cream is $2.84.
Simplify the expression.
x^5/x^9
a. 1/x^4
b.x^14
c. 1/x^14
d.x^4
which graph is represented by the table of values below?
Answer:
The graph B.
Step-by-step explanation:
1. As you can see in the table shown in the picture attached, the correct graph must have the following points (x,y): (-1,8); (0,6), (1,4); (2,2) and (3,0).
2. To draw the graph, you must plot each point. For example, the third point is (1,4). Then, you can draw an imaginay line vertically from 1 (x axis) and an imaginary line horizontally from 4 (y axis). The intersection of this lines is the point (1,4).
Answer:
B is the right answer
Step-by-step explanation:
I just did it and it was right