Using Cramer's rule the values are:
a) b12 = -15/22
b) b22 = 1/22
c) bs2 = 5/22
d) b23 = -3/22
To find the entries of A-1, we can use Cramer's rule and the formula for computing inverse matrices. First, we need to compute the determinant of A using row reduction:
|1 0 5 3|
|0 1 3 2| = det(A)
|1 0 1 1|
|1 0 0 1|
We can reduce the matrix to upper triangular form by subtracting the first row from the third and fourth rows:
|1 0 5 3|
|0 1 3 2|
|0 0 -4 -2|
|0 0 -5 -2|
Now, the determinant of A is the product of the diagonal entries, which is (-4)(-2)(1)(1) = 8.
To find b12, we replace the second column of A with the column vector [0 1 0 0] and compute the determinant of the resulting matrix. We get:
|-15 0 5 3|
| 8 1 3 2| = b12 det(A)
|-11 0 1 1|
| 4 0 0 1|
Using the formula for 4x4 determinants, we can expand along the first column to get:
b12 = (-15)(-2)(1) + (8)(1)(1) + (-11)(0)(-2) + (4)(0)(5) = -15/22
Similarly, we can find b22, bs2, and b23 by replacing the corresponding columns of A with [0 1 0 0], [0 0 1 0], and [0 0 0 1], respectively, and computing the determinants of the resulting matrices using Cramer's rule. We get:
b22 = 1/22
bs2 = 5/22
b23 = -3/22
Therefore, the entries of A-1 are:
| -15/22 1/22 5/22 |
| 7/22 1/22 -3/22 |
| 1/22 -2/22 1/22 |
Note that we can also find A-1 directly using the formula A-1 = (1/det(A)) adj(A), where adj(A) is the adjugate matrix of A. The adjugate matrix is obtained by taking the transpose of the matrix of cofactors of A, where the (i,j)-cofactor of A is (-1)^(i+j) times the determinant of the submatrix obtained by deleting the i-th row and j-th column of A.
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Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0
The general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41
How to determine the general form of the equation for the given circle centered at O(0, 0)?The given parameters are
Center = (0, 0)
Point = (4, 5)
Rewrite the given parameters are
(a, b)= (0, 0)
(x, y) = (4, 5)
The general form of the equation for the given circle is represented as:
(x - a)^2 + (y - b)^2 = r^2
Substitute the known values in the above equation to calculate the radius r
(4 - 0)^2 + (5 - 0)^2 = r^2
Evaluate the difference
4^2 + 5^2 = r^2
Evaluate the exponent
16 + 25 = r^2
Evaluate the sum
41= r^2
Rewrite as
r^2 = 41
Substitute r^2 = 41 in (x - a)^2 + (y - b)^2 = r^2
(x - a)^2 + (y - b)^2 = 41
Substitute (a, b)= (0, 0) in (x - a)^2 + (y - b)^2 = 41
(x - 0)^2 + (y - 0)^2 = 41
Evaluate the difference
x^2 + y^2 = 41
Hence, the general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41
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A motorcycle travels 20 miles west and then turns and goes 52° north of west another 38 miles. How far is the motorcycle from its starting point?? Round your answer to the nearest tenth
__ miles
Answer:
52.7 miles
Step-by-step explanation:
Please refer to attached photo. (Apologies for the terrible drawing).
We can deduce from A to B the distance is 20 miles, therefore no calculations is required.
However, from B to C, we will have to find the horizontal and vertical distances.
Horizontal Distance B > C = = hBC = [tex]BCcos(52)[/tex] = [tex]38cos(52) miles[/tex]
Vertical Distance B > C = vBC = [tex]BCsin(52)[/tex] = [tex]38sin(52)miles[/tex]
Here you can see the whole diagram is a right angle triangle. Which means, we can use Pythagoras' Theorem to find AC.
By Pythagoras Theorem,
[tex]c^{2} =a^{2}+b^{2}[/tex]
[tex]AC^{2} = (AB + hBC)^{2} + vBC^{2} \\AC^{2} = (20+38cos(52))^{2} +(38sin(52))^{2} \\AC = \sqrt{(20+38cos(52))^{2} +(38sin(52))^{2} } \\AC = 52.7 miles[/tex](nearest tenth)
How are the coordinates of the extreme value and the equation from part B in the form y=(x-h)^2-c related.
The extreme value of y = (x - h)² - c is the vertex of the equation.
What are extreme values of a function?The extreme values of a function are either the maximum or minimum values of the function.
The equation of a parabola in vertex formThe equation of a parabola in vertex form with vertex (h', k) is given by
y = a(x - h')² + k and its extreme values are
if a > 0 (h', k) is a minimum point and if a < 0 (h', k) is a maximum point.Since y = (x - h)² - c is the equation of a parabola in vertex form, comparing with y = a(x - h')² + k,
h = h' -c = k and a = 1.So, the cooordinates of the vertex of y = (x - h)² - c is (h, -c).
Now, since a = 1 > 0, (h, -c) is a minimum point.
So, the extreme value of y = (x - h)² - c is the vertex of the equation.
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Answer:
The lowest value is at (1, -8). H and C are equal to 1 and 8 in the equation y = (x - 1)2 - 8. Therefore, the minimum's x-coordinate corresponds to the equation's h-value, and its y-value is the opposite of the c-value.
Step-by-step explanation:
i re wrote it
What is the x-intercept of p(x) = -x + 8?
Answer:
x-intercept = 8
Step-by-step explanation:
Hello!
An x-intercept is when the y-value is 0, or when the graph intersects the x-axis.
We can replace p(x) with 0 and solve for x.
Solve for x[tex]p(x) = -x + 8[/tex][tex]0 = -x + 8[/tex][tex]-8 = -x[/tex][tex]8 = x[/tex]The x-intercept is 8.
A summer camp has 32 campers. 22 of them swim, 20 play softball, and 5 do not play softball or swim. which values correctly complete the table? a) a = 15, b = 10, c = 7, d = 5, e = 12 b) a = 15, b = 7, c = 5, d = 10, e = 12 c) a = 14, b = 7, c = 5, d = 12, e = 10 d) a = 14, b = 12, c = 7, d = 5, e = 10
The values which completes the table regarding summer camp is option b which is a=15,b=7, c=5, d=10, e=12.
Given that there are 32 campers, 22 of them can swim, 20 play softball and 5 do not play softball or swim.
We have to find the values of a,b,c,d,e so that we can complete the table.
Table is a combination of rows and columns. In our case the third row and third column shows the total.
from the table we can write that 22+d=32-----------1
so d=32-22
=10
d=10
c+5=d-----------2
c=10-5=5
c=5
a+c=20------------------3
a+5=20
a=20-5
a=15
a+b=22--------------3
15+b=22
b=7
20+e=32----------4
e=32-22
e=10.
Hence the values which completes the table is a=15,b=7, c=5, d=10, e=12.
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Question is incomplete as it should include figure showing table of values.
Cruz and erica were both getting ready for soccer. cruz ran 1 lap around the school. erica ran 3 laps around the playground. erica said, i ran more laps, so i ran farther. cruz said, 4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. my laps are much longer, so i ran farther. 1. who is right?
Both ran equal and both covered equal distance.
As cruz ran 1 lap out of 4 to cover one mile.
and erica ran 3 lap out of 12 to cover one mile:
3/12 = 1/4
So Cruz = Erica = 1/4.
Hence Both ran equal.
Fraction:
Fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
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: Nicole and Ian generate two patterns. Nicole uses the rule multiply by 3 then add 2 starting with 1.
Ian uses the rule add 1/2 then multiply by 2 starting from 0. Complete the table to show the
numbers in each pattern. Then create the ordered pairs.
help
The ordered pairs of Nicole and Ian's sequence pattern are:(5,1),(17,3),(53,5),(161,10),(485,20).
Given that Nicole uses the rule multiply by 3 then add 2 starting with it and Ian uses the rule add 1/2 then multiply by 2 starting from 0,
We ar rquired to find the ordered pairs of Nicole's and Ian's rules.
We are told that Nicole's pattern is multiply by 3 then add 2 starting with 1.
Thus Nicole's pattern is :5,17,53,161,485.
Ian's pattern is add 1/2 then multiply by 2 and starting with 0.Thus the numbers are :1,3,5,10,20.
If we combine the numbers of both the person'rule then we will get the ordered pairs which can be written as under:
The ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).
Hence the ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).
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Write an equation of the line that passes through $\left(-1,\ 7\right)$ and is perpendicular to the line $y=-\frac{1}{8}x-1$ .
Equation of the line which is passing through the points [tex](-1,7)[/tex] and perpendicular to the line [tex]$y=-\frac{1}{8}x-1$[/tex]
is [tex]y=8x+15[/tex]
How to find the equation which passing through one point [tex](-1,7)[/tex]and perpendicular to the equation [tex]$y=-\frac{1}{8}x-1$[/tex] ?
We know that the equation of line in form of slope and point is
[tex]y-y_{1} =m(x-x_{1} )[/tex]
So first equation of line which is passing through point [tex](-1,7)[/tex] is
[tex]y-7=m_{1} (x-(-1))\\y-7=m_{1}(x+1)[/tex].....(a)
Line [tex]$y=-\frac{1}{8}x-1$[/tex] perpendicular to the line (a)
And we know when two lines are perpendicular then
[tex]m_{1} m_{2} =-1[/tex]
So [tex]m_{1} =-1/m_{2}[/tex]
and we know [tex]m_{2} =-1/8[/tex]
So
[tex]m_{1} =-1/\frac{-1}{8} \\=-1*8/-1\\=8[/tex]
The equation of the line is
[tex]y-7=8(x+1)\\y-7=8x+8\\y=8x+8+7\\y=8x+15[/tex]
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2 parallelograms. The pre-image is smaller than the image.
How can you tell that this transformation is a dilation?
The figure flipped upside down.
The figure changed size.
The figure completed a half turn.
The figure did not change.
Answer: The figure changed size.
Step-by-step explanation: Dilations change the sizes of shapes. They can either make them bigger or make them smaller.
Find the original price if the price was:
$520 after a 30% increase
(Please Help with explanation that makes sense...will mark brainliest)
Given that price was $520 after a 30% increase, the original price was $400.
What is the the original price?Given that;
Percentage increase = 30%Price after the increase = $520Original price = x
To determine the original price, we say;
x × ( 100% + 30% ) = $520
x × ( 130% ) = $520
x × (130/100) = $520
130x / 100 = $520
130x = $52000
x = $52000 / 130
x = $400
Given that price was $520 after a 30% increase, the original price was $400.
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Help fast!!!
each shelf holds a total of 64 deciliters of apple juice. the bottles have three different sizes: large medium, and small. how many deciliters of apple juice does a medium bottle contain?
do a quick explanation!
dont just take the points or i will report you!
less than a minute!!!
The quantity of deciliters of apple juice a medium bottle contain is 10 deciliters
EquationLarge bottles = lMedium bottles = mSmall bottles = sTotal bottles in each shelf = 644s + 3l = 64
3s + 2l + 2m = 64
6s + 4m = 64
If
m = 10
s = 4
l = 16
Check:
3s + 2l + 2m = 64
3(4) + 2(16) + 2(10)
= 12 + 32 + 20
= 64
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14 m
10 m
what is the volume of the following cylinder?
The volume of the cylinder is approximately, 1,539.4 cubic meters.
What is the Volume of a Cylinder?Volume of a cylinder = πr²h
Given the following:
Diameter of cylinder = 14 m
Radius (r) = 14/2 = 7 m
Height of cylinder = 10 m
Volume of cylinder = πr²h = π(7²)(10)
Volume of cylinder ≈ 1,539.4 cubic meters.
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how much more did lan deposit each week than Jeremy?
Find the term that must be added to the equation x2−6x=7 to make it into a perfect square.
answer:
+16
steps:
number without the x should be 9
number without the x should be 9c to be 9 needs +16
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divide the number next to the x by 2
-6 divided by 2 is -3
find the square
-3 squared is 9
number without the x should be 9
x²-6x=7
make the equation = 0
x²-6x-7=0
a is the number next x²
b is the number next to x
c is the number without the x
c has to be 9
c is -7
c to be 9 needs +16
x²-6x+9 =0
x²-6x+(-3)² =0
(x-3)²
Answer:
9
Step-by-step explanation:
Completing the square is a method used to solve the quadratic equation.
Divide the co efficient of 'x' by 2.Coefficient of x is '6'. 6 ÷ 2 = 3
Square the quotient of (x ÷ 2) and add to the both side of the equation.3² = 9
x² - 6x + 9 = 7 + 9
Answer: To make into a perfect square, 9 must be added.
SELECT ALL THAT APPLY. The probability of rolling an even number with a six-sided, equally weighted die is ______.
The probability of rolling an even number with six sided equally weighted die is 0.5.
Given a six sided equally weighted die.
We are required to find the probability of rolling an even number.
Probability is the calculation of likeliness of happening an event among all the events possible. It lies between 0 and 1. It can be calculated through simple values and with the formula of combination also. The formula of calculating probability is as under:
Probability= number of items/ total number of items.
Total sides in die=6
Total numbers=1,2,3,4,5,6, therefore 6.
Even numbers=2,4,6. Therefore 3.
Probability = even numbers/total numbers.
=3/6
=1/2
=0.5
Hence the probabilty of receiving an even number from a six sided equally weighted die is 0.5.
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please help me im in a rush
(a) The city with a larger median room temperature is city B.
(b) The city having the highest noon temperature is city B.
(c) The city having the noon temperatures with a higher interquartile range is city A.
(d) The city having more noon temperatures that 81°F is city B.
In the given question, the noon temperatures for two cities, A and B, recorded over a month are shown via the box-and-whisker plots.
We are asked to use it and answer the questions:
(a) The median of data is represented by the line in the box of the box-and-whisker plot. Thus,
The median noon temperature for city A is 73°F.
The median noon temperature for city B is 76°F.
Thus, the city with a larger median room temperature is city B.
(b) The highest temperature is seen as the end point of the whiskers. Thus,
The highest temperature for city A is 85°F.
The highest temperature for city B is 92°F.
Thus, the city having the highest noon temperature is city B.
(c) The interquartile range is the difference between the end line of the box and its start line. Thus,
The interquartile range for city A is (81 - 64)°F or 17°F.
The interquartile range for city B is (81 - 68)°F or 13°F.
Thus, the city having the noon temperatures with a higher interquartile range is city A.
(d) From the given box-and-whisker plots, we can see that after 81°F, city B has a long whisker, showing more outliers.
Thus, the city having more noon temperatures that 81°F is city B.
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Find the missing segment in the image below.
What is the slope of the line through (-3, 3) and (-1, -1)?
(-3, 3)
-3 -2 -1
(-1,-1)
4
3
2
You
1
-1
2.
y
1 2
3
4
X
Answer:
The slope is -2
Step-by-step explanation:
To find the slope, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= (-1 -3)/(-1 - -3)
= ( -1-3)/(-1+3)
= -4/2
= -2
The slope is -2
The solution to the system of equations shown is (2, 0).
3x − 2y = 6
x + 4y = 2
When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14
.
Which system of equations will also have a solution of (2, 0)?
Answer:
7x = 14
x + 4y = 2
Step-by-step explanation:
3x − 2y = 6
x + 4y = 2
6x - 4y = 12
x + 4y = 2
-----------------------
7x = 14 Replace the first equation with this one.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. On a number line, point D is at -3, and point E is at 6. The point F lies on . The ratio of to is 2 : 3. Where does point F lie on the number line
On the number line the position of point F is at point 4.
According to the statement
We have a given that the on a number line , point D is at -3, and point E is at 6. The point F lies on the ratio of to is 2 : 3.
and we have to find the F point on the number line.
Firstly,
Number line is a line on which numbers are marked at intervals, used to illustrate simple numerical operations.
So, According to given information,
Point D is at -3, and point E is at 6.
Ratio of point E to F = 6*2/3
Then
Ratio of point E to F = 6*2/3
After solving it
The point F = 2*2
The point F = 4.
So, On the number line the position of point F is at point 4.
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The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the form
g(x) = (x – h)3 + k.
What are the values of h and k?
h = 4
k = –2
h = –4
k = –2
h = 4
k = 2
h = –4
k = 2
Using translation concepts, the correct values are given as follows:
h = 4.k = -2.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, we have that:
The function was shifted 4 units right, hence x -> x - 4, that is, h = 4.The function was shifted 2 units down, hence y -> y - 2, that is, k = -2.More can be learned about translation concepts at https://brainly.com/question/4521517
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Which function is negative for the interval [-1, 1]?
ty
3
2
-3-2-11
-3
ty
O
Intro
123
x
3
2
1
-3-2-1₁
-3
O
x
23
2,
-3-2-1
2 of 11
O
x
123
321
-3-2-11
-2
MAR
-3
ty
x
23
Done
O
Answer:
Graph number 2
Step-by-step explanation:
See attached image.
A cylinder with a base diameter of x units has a volume of πx3 cubic units. a cylinder with a base diameter of x units has a volume of pi x cubed cubic units. which statements about the cylinder are true? select two options.
The height of the cylinder is 4 x units.
The area of the cylinder’s base is One-fourthπx2 square units .
What is the volume of cylinder?
We know the volume of a cylinder is given by the formula π r2 h, where r is the radius of the cylinder and h is the height.
Formula for volume of the cylinder
V = r² π h
Volume of the cylinder= πx³
Diameter=x
Radius (r)=diameter/2
r = x/2
V = r² π h
πx³=(x/2)² πh
πx³= (x²/4)πh
Divide both sides by π
x³ =(x²/4)h
Make h the subject of the formula
h = x³ ÷ x²/4
=x³ ×4 / x²
=4x³ / x²
=4 * x * x * x / x * x
h=4x
Area of the base:
B = r² π
r=x/2
B=(x/2)² * π
=(x²/4)π
=πx²/4
=1/4(πx²)
Therefore, The area of the cylinder’s base is One-fourthπx2 square units.
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The complete question is -
A cylinder with a base diameter of x units has a volume of πx3 cubic units. A cylinder with a base diameter of x units has a volume of pi x cubed cubic units. Which statements about the cylinder are true? Select two options. The radius of the cylinder is 2x units. The area of the cylinder’s base is One-fourthπx2 square units. The area of the cylinder’s base is One-halfπx2 square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations which gave the same solution as; 2.3p – 10.1 = 6.5p – 4 – 0.01p are;
2.3p – 10.1 = 6.49p – 4 and230p – 1010 = 650p – 400 – pWhich equations have the same solution as the given equation?It follows from the answer choices that the equation; 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation as the algebraic sum of p variables is evaluated on the right hand side.
The second equation; 230p – 1010 = 650p – 400 – p also is equivalent to the given equation, when multiplied through by 100.
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What is the equation in vertex form of a
parabola with vertex (2, 4) that opens
downward and is stretched by a factor of
3?
Answer:
B.
Step-by-step explanation:
Vertex with (2,4) means that the equation will have:
y=a(x-2)^2 + 4
Open downwards means that the a will be negative:
so: y = -a (x-2)^2 + 4
Stretched by a factor of 3 means that the a=3
So if we combine all of these, we will get the equation:
y = -3 (x-2)^2 + 4
Concrete blocks are 8in. high. if a 3/8-in. mortar joint is used, how high will a wal of 12 courses of concrete blocks be?
Answer:
100.5 inches
Step-by-step explanation:
If each course has 3/8 inch of concrete below it (including the bottom one)
8 in * 12 + 3/8 in * 12 = 100 1/2 inches
A right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid m. what is the shape of the cross section?
The cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.
If the peak of the rectangular pyramid is directly above the center of the base, it creates a perpendicular to the base, indicating the height of the pyramid. This type of rectangular pyramid is known as the right rectangular pyramid.
A rectangle is a quadrilateral, that is a closed figure with 4 line segments, with all four interior angles at 90°.
When we slice a right rectangular pyramid vertically down at the red line by a plane, not passing through the vertex, of the pyramid will be a dilated image of its base.
A dilated image is an enlarged or diminished image of the preimage, similar with all angles.
Thus, the cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.
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For complete question, refer to the attachment.
Answer:trapozoid
Step-by-step explanation:
Which function is undefined for x=0
Answer:
of course 0
Step-by-step explanation:
because it doesn't have any value in its first equation
PLEASE HELP IM STUCK PLEASE HELP
Answer:
y = 3x + 5
Step-by-step explanation:
x = number of years
• bush grows 3cm per year
• the initial height is 5cm
3cm per year times x number of years: y = 3x
Add the initial height of 5cm: y = 3x + 5
Drag each number to the correct location on the table. classify the real numbers as rational or irrational numbers.
The rational numbers are -5/250, [tex]\sqrt{400}[/tex] ,and irrational numbers are 5.012121212......., [tex]\sqrt[3]{30}[/tex] , 0.01562138411........,[tex]\sqrt{1000}[/tex]
Given six numbers:5.012121212..,[tex]\sqrt{1000}[/tex],[tex]\sqrt[3]{30}[/tex], -5/250, 0.01562138411.....,[tex]\sqrt{400}[/tex].
We have to identify which numbers are rational and which are irrational numbers.
Rational numbers are those numbers which can be written in p/q form where q cannot be equal to zero because if q is zeo then the value of p/q will be infinity.
Irrational numbers are those numbers which cannot be written in p/q form.
First number :5.0121212121....
In the above numbers 12 is repeating next to the decimals. So it is a irrational numbers.
Second number:[tex]\sqrt{1000}[/tex]
If we solve the above number we will find it 31.6227766017 . It is cannot be expressed in p/q form, so it is irrational number.
Third number:[tex]\sqrt[3]{30}[/tex]
The abov number is irrational number as we cannot express it in p/q form.
Fourth number:-5/250
The value of above number is -0.02.It can be in the form of -2/100. so it is rational number.
Fifth number:0.01562138411........
Because the digits are repeating after decimals so it is irrational number.
Sixth number:[tex]\sqrt{400}[/tex]
The value of above number is 20, so it is rational number.
Learn more about rational numbers at https://brainly.com/question/12088221
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Question is incomplete as it should include figure.