![2. What Is The Solution Of Matrix Equation [2 7 1 4] X=[2 5]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/Va8Gxnhu7yFQND7DYzEePR5GY723jFbm.png)
Answers
Answer:
(d) X = [-27, 8]
Step-by-step explanation:
The solution to the matrix equation can be found by left-multiplying both sides of the equation by the inverse of the coefficient matrix.
AX = B . . . . given
X = A⁻¹B
__
[tex]X=\left[\begin{array}{cc}2&7\\1&4\end{array}\right]^{-1}\left[\begin{array}{c}2\\5\end{array}\right] =\left[\begin{array}{cc}4&-7\\-1&2\end{array}\right]\left[\begin{array}{c}2\\5\end{array}\right] \\\\X=\left[\begin{array}{c}-27\\8\end{array}\right][/tex]
_____
Additional comment
A calculator or spreadsheet can help with this. The solution can also be found by row-reducing the augmented matrix.
![2. What Is The Solution Of Matrix Equation [2 7 1 4] X=[2 5]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/wT2EiviQsmkaR0AcxVUrBoAgrK4NukbC.png)
Related Questions
Simplify each expression, and classify the result as rational or irrational.
Answers
The number 2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
= 2√5×3√6
= 6√30
= √1080 = 32.863353450309965
The number is irrational.
= √42/√168
= 1/2
The number is rational.
= 5(4√5 - 3√5)
= 5√5
= √125 = 11.180339887498949
The above number is irrational.
= √64/32
= 1/4
The above number is rational.
= (5√3—√3)/2√3
= 2
The above number is rational.
Similarly, we can find whether a number is irrational or rational
Thus, the number 2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.
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findin the measure of each angle (3x-13)° 5x -47
Answers
The measure of each angle is 43.25 and 46.75
How to determine the measure of each angle?The attached image represents the missing piece in the question.
From the image, we can see that:
3x - 13 + 5x - 47 = 90 ---- complementary angles
Evaluate the like terms
8x = 150
Divide by 8
x = 18.75
Substitute x = 18.75 in the given angles
3x-13 = 3 * 18,75 - 13 = 43.25
5x -47 = 5 * 18.75 - 47 = 46.75
Hence, the measure of each angle is 43.25 and 46.75
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How do I look at the recently posted questions? i'm lost and I want to answer some questions but I forgot how to go to the section. Send help please.
Answers
Tap it and all the recently posted questions appear.
There should be q icon that says give answer, to find new questions in that section refresh the page
The radius of the surface of the water in the tank is increasing at a rate of 0.25m/min. at what rate is the area of the surface changing when the radius is 1.2m?
Answers
Answer:
1.88 m^2/min to the nearest hundredth.
Step-by-step explanation:
Area = π r^2
Using Calculus notation:
dA/dr = 2π r
dr/dt = 0.25 (given)
So the rate of change of area
dA/dt = dA/dr * dr/dt
So when r = 1.2
dA/dt = 2 π * 1.2 * 0.25
= 0.6π m^2/min.
= 1.88 m^2/min to the nearest hundredth.
Solve for X. Round to the nearest tenth, if necessary.
Answers
Answer:
still don't get it
Step-by-step explanation:
but please write it in an understanding meaning
what is the equation of the line that contains the point (6-1) and is perpendicular to line whose equation is y=2x+1
A(9,5)
B(-3,1)
C(6,3)
D(-9,7)
Answers
Answer:
y = -x/2 + 2
what are those mutli choice answers?
if that point is (6,1)
y = -x/2 + 4
Step-by-step explanation:
the perpendicular line has a gradient which is the negative inverse, that is -1/m
so the equation will be of the form y = -x/2 + c
substituting in the point (6, -1)
-1 = -6/2 + c
c = 2
so y = -x/2 + 2
Using the net below, find the surface area of the triangular prism 5 cm 5 cm 4 cm 4 cm 3 cm 3 cm 3 cm 5 cm
Answers
Answer:
54000
Step-by-step explanation:
use multiplication
do ur own work if you want to see if I'm wrong
Each edge of this cube is 6.7 cm long.
Work out
a) volume
b) surface area
Answers
Answer:
Hii.. The answer of the volume is 300.74 cm
And the surface area is 269.34 cm
Answer:
V=6.7×6.7×6.7
=300.763 cm^3
SA=6×6.7×6.7
=269.34 cm^2
This makes zero sense give answer
Answers
Answer:
IQR for males: 3
IQR for females: 2
Q1 for males: 5
Q1 for females: 6
the number of females who spend over 6 hours exercising is greater(?) than the number of males who spent 6 hours exercising
Step-by-step explanation:
An equal amount of men and women were randomly selected and asked how many hours per week they spend excercising
How to find IQR?to find IQR you have to identify your median(middle value) of the lower and upper half of the data. These are called quartile 1(Q1) and quartile 3(Q3). You subtract these two (Q3 and Q1) and the IQR is the difference.
Males box plot:
Minimum: 1
Maximum: 10
Q1: 5
Q2: 7
Q3: 8
Subtract Q3 and Q1
8 - 5 = 3
This is the IQR
Females box plot:
Minimum: 4
Maximum: 10
Q1: 6
Q2: 7
Q3: 8
Subtract Q3 and Q1
8 - 6 = 2
IQR =2
the number of females who spend over 6 hours exercising is greater than the number of males who spent 6 hours exercising
What is 3,740,231,580 rounded to the nearest million
Answers
Step-by-step explanation:
3,740,231,580
we normally start rounding from the end so the last number should be checked. If it's not more than 5, then make it a zero and move on to the next. if it's more than five, make the number zero and add 1 to the the next number. So this is how it will look.
3,740,231,580
3,740,231,580
3,740,231,590
3,740,231,600
3,740,232,000
3,740,230,000
3,740,200,000
3,740,000,000
And I think that's it
I need help answering this question please!
Answers
Answer:
p(x) = x⁴ -7x³ +59x² -343x +490
Step-by-step explanation:
Each root is the zero of a binomial factor. That is, for root x = a, the polynomial has a factor (x -a). Complex roots come in conjugate pairs, so if there is a root 7i, there is also a root -7i.
__
The given roots mean the polynomial can be written in factored form as ...
p(x) = (x -2)(x -5)(x -7i)(x -(-7i))
We can combine multiply these factors together to simplify the polynomial.
p(x) = (x² -7x +10)(x² +49)
p(x) = x⁴ -7x³ +59x² -343x +490
_____
Additional comment
Combining the conjugate complex roots uses the special form for the factoring of the difference of squares.
a² -b² = (a -b)(a +b)
(x -7i)(x +7i) = x² -(7i)² = x² -49i² = x² +49 . . . . . where i = √(-1)
Need help with geometry circles problem
Answers
Answer:
Step-by-step explanation:
What is the area of this figure? PLS ANSWER
Answers
Answer:
42 units ^2
Step-by-step explanation:
Break in to a top triangle a middle rectangle and a bottom triangle
area = 1/2 7 *2 + 4 * 7 1/2 * 2 * 7 = 42 units ^2
Consider the line shown on the graph. Enter the
equation of the line in the form y = mx + b where m is
the slope and b is the y-intercept.
y=
Answers
From the graph, we concluded that line passes through the points (0, 3) and (1, 4) respectively.
So, slope of the line (m) passing through the points (a, b) and (c, d) is
m = d - b/ c - a
So, on substituting the values, we getm = 4 - 3 / 1 - 0 = 1/1 = 1
Also, line makes an intercept of 3 units in positive direction of y - axis.
So, c = 3
So, Equation of line is given byy = mx + c
y = 1 × x + 3
y = x + 3Alternative Method :-We know, Equation of line passing through the points (a,b) and (c, d) is given by
y - b = d - b / c - a (x - a)
Here,a = 0
b = 3
c = 1
d = 4
So, on substituting these values in above result, we get :-y - 3 = 4 - 3 /1 - 0 ( x - 0 )
y - 3 = 1/1 ( x - 0 )
y - 3 = x
y = x + 3Different forms of equations of a straight line :-1. Equations of horizontal and vertical lines
Equation of line parallel to x - axis passes through the point (a, b) is y = b.
Equation of line parallel to y - axis passes through the point (a, b) is x = a.
2. Point-slope form equation of lineEquation of line passing through the point (a, b) having slope m isy - b = m(x - a)
3. Slope-intercept form equation of lineEquation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.
4. Intercept Form of LineEquation of line which makes an intercept of a and b units on x - axis and y axis respectively is x/a + y/b = 1.
5. Normal form of LineEquation of line which is at a distance of p units from the origin and perpendicular makes an angle B with the positive X-axis is x cosB + y sinB = p.
Part B: Your cell phone and tablet use the same account. The cell phone costs $0.10 for
each minute of use and the tablet costs $0.15 for every minute of use. Each month, you
want to only spend up to $450 and use Tess than 5,000 minutes on both of the devices.
Now, create a system of inequalities using the above information (use x and y as the
variables).
pls help for brainliest
Answers
The inequalities are x + y < 5000 and 0.10x + 0.15y ≤ $450 which shows each month, you want to only spend up to $450 and use less than 5,000 minutes on both of the devices.
What is inequality?Inequality is defined as a mathematical expression in which both sides are not equal and have mathematical signs that are either less than or greater than.
Let's suppose the total minutes of uses for cell phone is x
and total minutes of uses of for tablet is y
Cell phone cost $0.10 each minute and tablet cost $0.15 each minute.
Then total minutes will be:
x + y < 5000 (as it is given that the time will be less than 5,000 minutes on both of the devices)
And total cost = $450
0.10x + 0.15y ≤ $450
Thus, the inequalities are x + y < 5000 and 0.10x + 0.15y ≤ $450 which shows each month, you want to only spend up to $450 and use less than 5,000 minutes on both of the devices.
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A right rectangular prism has a base area of 20 cm? and a height of 9. 2 cm.
Answers
Answer:
the answer to this question is 184cm^2 because the formula to find the area for a rectangular prism is A= BH so we need to multiply 20 which is the base times 9.2 which is the height and when we do those steps of multiplying we get an answer of 184cm^2 so 184 cm^2 is hopefully the correct answer for this problem.
Step-by-step explanation: hopefully that is the correct and have a great day.
How many yards is 6 inches
Answers
Answer: 6 inches equals 0.16666667 yards, or about 0.2 yards.
Step-by-step explanation: 1 yard equals 36 inches. By that reasoning, we can divide 6 by 36, since we are trying to find out how many yards are in 6 inches.
6/36 = 0.16666667
The answer is 0.16666667 yards, or about 0.2 yards.
PLS HELP! The figure is a triangle that is divided into two parts. Angle A and angle E are right angles, and the measure of angle F is 30°. What is the measure of angle C?
Complete the steps below to solve the problem using equations.
Answers
=60 degrees
Then angle C =180 - 60 (Linear pair)
Angle C = 120 degrees
What is the area of a triangle if the height is 9 and base is 11?
Answers
Answer:
49.5
Step-by-step explanation:
you multiply the height and base then divide that awnser by 2
The numbers in this sequence increase by 12 each time
24
36
48
60
The sequence is continued with the same rule.
Which number in the sequence will be closest to 100?
Answers
6 Mateo and Katia each walked into a
video arcade with $9.50 in quarters. After
they played video games for an hour, Katia
had $1.75 more than Mateo. Which could
be the amounts of money they had then?
Answers
Answer:
(amounts could be:)
Katia: $3.50
Mateo: $1.75
Step-by-step explanation:
Remember that a quarter = $0.25, 4 quarters = $1.00
We know that they both have 38 quarters ($9.50)after an hour of playing games in the arcade, Katia has $1.75 more than Mateo
lets say that Katia has (random amount)$3.50(14 quarters) and Mateo has $1.75 less than that.
$3.50 - $1.75 = $1.75
Katia has $3.50 and Mateo has $1.75.What is the area of a rectangle with a length of 9
centimeters and a width of 4 centimeters?
Sketch: ?
Area: ?
Answers
Answer:
We are given a length of 9 cm and a width of 4 cm and we are also told that it our shape is a rectangle. This means that we are able to use the rectangle formula which is [tex]A=l*w[/tex].
Therefore, we can just multiply 9 cm by 4 cm and we get [tex]A = 36\ cm^2[/tex]
Hope this helps! Let me know if you have any questions
The scatterplot that represents the monthly values of stock QRS has an r-
value of -0.993. Which best describes the correlation of the graph?
OA. Weak correlation
B. Strong positive correlation
C. Strong negative correlation
OD. No correlation
Answers
Answer:
C
Step-by-step explanation:
Because it's a negative, then we could assume that it is a negative correlation. And because it's closer to -1, it is a strong negative correlation.
The value -0.993 is Strong Negative correlation.
What is Coefficient Correlation?The strength and direction of two variables in a scatterplot are quantified by the correlation coefficient, or r value. It goes from one to one.
A perfect positive correlation is denoted by +1.A perfect negative correlation is denoted by -1.0 indicates a lack of associationSo, the value close to 1 is Strong positive correlation and close to -1 is Strong Negative correlation.
Thus, -0.993 close to -1 is Strong Negative correlation.
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Does anybody know this? I got told it was 828.8 by someone and it was wrong.Find the surface area of the square pyranid
Answers
Answer:
800 ft²
Step-by-step explanation:
The total surface area of a square-base pyramid is given by the formula ...
A = s(s +2h) . . . . . . where s is the side length, h is the face slant height
In this problem, we need to find the slant height of a face in order to use this formula.
__
slant heightThe distance from the middle of one edge of the base to the peak of the pyramid is the slant height of a face of the pyramid. It is the hypotenuse of a right triangle whose legs are the pyramid height, and half the width of the base. For this pyramid, that is a right triangle with legs 15 and 8.
The Pythagorean theorem is used to find the hypotenuse of that triangle:
c² = a² +b² . . . . square of hypotenuse = sum of squares of legs
c² = 15² +8² = 225 +64 = 289
c = √289 = 17
The slant height of a face of the pyramid is 17 ft.
total areaThe area formula tells us the total surface area is ...
A = s(s +2h)
A = (16 ft)(16 ft + 2×17 ft) = (16 ft)(50 ft)
A = 800 ft²
The total surface area is 800 square feet.
Which symbol in a chemical equation separates the reactants from the products? = → >
Answers
The symbol in a chemical equation that separates the reactants from the products is →
How to determine the symbol?A chemical equation is represented as:
A + B → C + D
Where A and B are the reactants, and C and D are the products.
The symbol → links the reactants with the products
Hence, the symbol that separates the reactants from the products is →
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Answer:
→
Step-by-step explanation:
edge 2022
Hi pls how do I find the volume of a short cylinder
Answers
Answer:
You find the volume of a cylinder with the formula of π × r² × h
Jim works as a manager at a local supermarket in dallas. jim worked 36 hours and his paycheck for this week was $1,620.51. how much does jim make per hour? round your answer to the nearest cent.
Answers
324
Step-by-step explanation:
roughly about that much
PLEASE HELP ILL MARK BRAINEST!!!
Answers
Answer:
0,5
Step-by-step explanation:
Find the area of this circle. Use 3 for pi
Answers
Answer:
243 in²
Step-by-step explanation:
Diameter = 18 in
Radius ( r ) = Diameter / 2 = 18 / 2
r = 9 in
π = 3
To find : Area of circle ( A )
Formula : -
A = πr²
A = 3 x 9²
= 3 x 9 x 9
A = 243 in²
P+d= 19 9p+ 5.50d= 150 solve the system of equations , step by step
Answers
Answer:
d=6 & p=13
Step-by-step explanation:
1. P+d=19
×9
2. 9p +5.50d=150
×1
9p+9d=171
-
9p +5.50d=150
3.5d=21
d=6
Substituting d=6 in 1.
P+6=19
P=13
