Answer:
linear algebra, an n-by-n square matrix A is called invertible, if there exists an n-by-n square matrix B such that \mathbf {AB} =\mathbf {BA} =\mathbf {I} _{n}\ where Iₙ denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
Answer:
Brainliest pls
Step-by-step explanation:
The inverse of a square matrix A, denoted by A-1, is the matrix so that the product of A and A-1 is the Identity matrix.
Find a counterexample to show that the given conjecture is false.
If n is a real number, then n³>n.
Let [tex]n=0[/tex]. Then [tex]0^3 = 0[/tex] but 0 > 0 is a false statement.
StarWatch Camping Site Charge per person: £5 per night Tent pitch: (ground surface) < 10 m² at £12 per night > 10 m² at £15 per night Special offer: For every 5 nights you stay, only pay for 4. Lila and Wassim are planning a stay at the StarWatch camping site. They will: ● share a tent between them, both stay for a total of 10 nights, • use a tent with a rectangular base measuring 2.5 by 4.2 metres. The holiday is just 9 weeks away and they each plan to save £12 per week from now until their holiday. Will they save enough money to cover all their camping site charges? If the answer is 'yes' say how much extra money they will save. You must show all your working.
Yes, Lila and Wassim saved the extra money of £16.
What is defined as the total cost?A total is a complete or whole amount, or "to total" means to add numbers or destroy something. In mathematics, you total numbers by having to add them together; the result is indeed the total. Whenever you add 8 and 8, you get 16.For the given data in question;
Charge/person for Camping Site : £5 per night
Charges for Camping Site Tent = £15 per night for Tent pitch > 10m²
calculate the tent pitch;
Tent Pitch = 2.5 × 4.2 = 10.5 > 10
Total charges for tent = £15 per night
As, 2 Lila and Wassim sharing Tent
Total charges per night = Charge/person + Charges for Camping Tent
= 2× £5 + £15
= £25 per night
For every 5 nights of the stay, pay is 4.
Cost for 10 nights for two persons.
Lila and Wassim have to pay the cost for 8 Nights;
Total charges = £25 × 8 = £200
Lila and Wassim each plan to save £12 per week for 9 weeks.
Thus, the total Saving = 2 × 9 × 12 = £216
total Saving = 216 > 200
As, total savings of Lila and Wassim are £216 which are greater than the £200 cost of camping.
The extra money saved is;
= £260 - £200
= £16.
Therefore, Yes, Lila and Wassim will save sifficient money to cover all camping charges with extra saved money of £16.
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3 -1 ___ 1/4 = < >
which symbol is right?
Answer:
Greater than.
Step-by-step explanation:
3 - 1 = 2, 2 is greater than 1/4 which is equal to 0.25.
Find the inequality represented by the graph.
Answer: y<3x-4
Step-by-step explanation:
[tex](0,-4) \ \ \ \ \ \ (1,-1)[/tex]
The equation of the line
[tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
[tex]\displaystyle\\x_1=0\ \ \ \ x_2=1\ \ \ \ y_1=-4\ \ \ \ y_2=-1\\Hence,\\\frac{x-0}{1-0} =\frac{y-(-4)}{-1-(-4)} \\\\\frac{x}{1} =\frac{y+4}{-1+4} \\x=\frac{y+4}{3}[/tex]
Умножьте обе части уравнения на 3:
[tex]3x=y+4\\3x-4=y+4-4\\3x-4=y[/tex]
Thus, y<3x-4
if h(x)=4-6x, find each of the following
h(-1)
h(10)
h(5)
Answer:
(-1)=10
(10)= -54
(5)= -26
Step-by-step explanation:
h(-1)=4-6(-1)
h(-1)=4 (-6*-1)
h(-1)=4+6
h(-1)=10
h(10)=4-6(10)
h(10)=4 (-6*10)
h(10)=4-60
h(10)=-54
h(5)=4-6(5)
h(5)=4 (-6*5)
h(5)=4-30
h(5)=-26
Hope this helps.
find two possible lengths for CD if C, D, and E are collinear, CE 17.9 cm, and DE = 8.2 cm.
Two possible lengths for CD if C, D, and E are collinear, CE 17.9 cm, and DE = 8.2 cm is 12.3cm and 19.3cm.
In space, a point is a precise position or location. It is possible to depict it in relation to a coordinate system and its origin. It has no length and is a zero-dimensional entity.
A line is made up of an unlimited number of points that form a straight line. One-dimensional objects like lines lack both thickness and width. It stretches forever in both directions. An endpoint and a beginning point define a line segment, which is a component of a line. A linear equation can be used to depict a line.
D is between C and E
_ _ _
C D E
CD =CE-DE
CD=15.8-3.5cm
CD=12.3 cm
E is between D and C
_ _ _
D E C
CD=CE+DE
CD=15.8+3.5cm
=19.3cm
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Please help i will give out brainlist
Answer:
x = 16
Step-by-step explanation:
[tex]\frac{3x}{4}[/tex] + 3 = 15 (subtract 3 from both sides )
[tex]\frac{3x}{4}[/tex] = 12 ( multiply both sides by 4 to clear the fraction )
3x = 48 ( divide both sides by 3 )
x = 16
that is
subtraction / multiplication / division
Answer: ( not totally sure but I hope this helps)
Step-by-step explanation:
1. Given
2. Multiplication property of equality
3. Subtraction
4. Division property of equality
Given y = x² + 3x - 2, find y when x = -2
Answer: - 10
Step-by-step explanation: -2 to the 2nd power is - 4. And 3 * - 2 is -6. So -4 + -6 = - 10.
I hope I have helped and I hope you have a wonderful day!
Please explain all the steps you used to get the answer.
The complete compound inequality is 9 <= 1.5x <= 12
How to complete the compound inequality?From the given figure, we have'
Height = x
Base = 3
The area of a triangle is
Area = 0.5 * Base * Height
So, we have
A = 0.5 * 3 * x
Evaluate
A = 1.5x
The compound inequality is given as
9 <= A <= 12
Substitute A = 1.5x in 9 <= A <= 12
9 <= 1.5x <= 12
Hence, the complete compound inequality is 9 <= 1.5x <= 12
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find the direction cosines and direction angles of the vector. (give the direction angles correct to the nearest tenth of a degree.)
The direction cosines and direction angles will be - [tex]\frac{x}{r},\frac{y}{r},\frac{z}{r}[/tex] and
cos⁻¹([tex]\frac{x}{r}[/tex]), cos⁻¹([tex]\frac{y}{r}[/tex]),cos⁻¹([tex]\frac{z}{r}[/tex]) respectively.
The direction cosines of a specified vector, m = xi + yj + zk, are the cosines of the angles it makes well with x, y, and z axes.
The direction cosines of m are cos a, cos b, and cos c in the x, y, and z axes, respectively, if a forms the angles a,b and c (which are the direction angles) with the x, y, and z axes, respectively.
Let us consider equation as = [tex]xi + yj +zk[/tex]
vector of the equation will be - (x,y,z)
r = length of vector = [tex]\sqrt{x^{2} +y^{2} +z^{2} }[/tex]
The direction cosines will be -
[tex]\frac{x}{r},\frac{y}{r},\frac{z}{r}[/tex]
angles will be - cos⁻¹([tex]\frac{x}{r}[/tex]), cos⁻¹([tex]\frac{y}{r}[/tex]),cos⁻¹([tex]\frac{z}{r}[/tex])
Let us consider an example,
If we have vector as (1,2,3)
= i + 2j + 3k
= r = [tex]\sqrt{1^{2} +2^{2} +3^{2} }[/tex]
= [tex]\sqrt{14}[/tex]
Direction cosines will be -
[tex]\frac{1}{\sqrt{14} } , \frac{2}{\sqrt{14} }, \frac{3}{\sqrt{14} }[/tex]
Angles will be -
cos⁻¹([tex]\frac{1}{\sqrt{14} }[/tex]), cos⁻¹([tex]\frac{2}{\sqrt{14} }[/tex]),cos⁻¹([tex]\frac{3}{\sqrt{14} }[/tex])
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Jordan can ride her skateboard 75 meters in 30 seconds. How long will it take Jordan to ride her skateboard 1500 meters.
Step-by-step explanation:
1500÷75= 20
30×20= 600 seconds
600÷60= 10 minutes
A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (4, 5) and (3, 2), what is the equation for a parallel street that passes through (2, −3)?
y = 3x + 11
y = 3x − 9
y equals negative 1 third times x plus 1
y equals negative 1 third times x minus 7 thirds
The equation for the parallel street that passes through (2, -3) is: B. y = 3x - 9.
How to Find the Equation of Parallel Lines?Two lines that lie parallel to each other will have a slope (m) that is of the same value. The equation can be written as y = mx + b in slope-intercept form.
Find the slope of the line that passes through (4, 5) and (3, 2):
Slope (m) = change in y / change in x = (5 - 2)/(4 - 3)
Slope (m) = 3/1
Slope (m) = 3
The slope of a parallel line would also be 3.
Substitute (a, b) = (2, -3) and m = 3 into y - b = m(x - a):
y - (-3) = 3(x - 2)
y + 3 = 3x - 6
Subtract 3 to both sides of the equation
y + 3 - 3 = 3x - 6 - 3
y = 3x - 6 - 3
y = 3x - 9
Therefore, the equation for the parallel street that passes through (2, -3) is: B. y = 3x - 9.
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Which statement about this figure is true?
It has reflectional symmetry with one line of symmetry.
It has point symmetry.
It has no reflectional symmetry.
It has rotational symmetry with an angle of rotation of 180°.
You can earn 8 percent interest, compounded annually. how much must you deposit today to withdraw $10,000 in 6 years?
We must deposit (B) $6,301.70 today to withdraw $10,000 in 6 years.
What do we mean by compound interest?Compounding interest is an important concept in the financial sector that has a direct impact on the value of financial assets. According to this theory, received interest will be invested back in the initial investment. This will result in additional interest earnings on the initial interest.To find the amount:
Given -
Future account balance = $10,000N = 6I = 8%Estimate the initial deposit required to obtain $10,000 in 6 years:
Initial deposit = Balance/(1 + 1)ⁿInitial deposit = 10,000/(1 + 8%)⁶Initial deposit = 6,301.70Therefore, we must deposit (B) $6,301.70 today to withdraw $10,000 in 6 years.
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The correct question is given below;
You can earn 8 percent interest, compounded annually. How much must you deposit today to withdraw $10,000 in 6 years?
A. $5,402.69
B. $6,301.70
C. $6,756.76
D. $8,432.10
E. $9,259.26
Help me with this problem please I am begging you
Answer:
32/40
Step-by-step explanation:
First divide 40 by 15
to check denominator, calculate 15 * the ans and for numerator as well
Whenever he participates a race, he is the winner. either he participates the race or he is sick. he is not the winner. therefor he is sick write the argument form and test its validity.
A statement 'He is not the winner, then, he is sick.' is a valid argument.
To test the validity of a given argument, we need to see if we can find a counter-example that makes one of the statements non-valid. If after analyzing the statements we can't find a counter-argument, then we can conclude that the argument is valid.
Here we will find that the argument is valid.
We can write given statement as:
1) If he participates in a race then he is the winner.
2) Either he participates in the race, or he is sick.
3) He is not the winner, then, he is sick.
Now, from the first statement, we know that this person participates in a race, he wins.
From the second statement we know that he only participates if he is not sick, we can rewrite that one as:
"If he is sick, then he does not participate in the race".
Finally, from the third one, if he does not win, then he is sick.
This makes sense, he only does not participate when he is sick, then the only races where he is not the winner, are these races where he does not participate, and he does not participate only if he is sick, then this is a valid argument.
Concluding, the 3 statements are valid, as we can't find any counter-argument to any of these 3.
Therefore, a statement 'He is not the winner, then, he is sick.' is a valid argument.
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16 houses on 2 blocks = houses per block
Answer:
0.125
Step-by-step explanation:
15, 10, 20/3
Find the 9th term.
Answer:
15*2/3=10
10*2/3=20/3
20/3*2/3=40/9
40/9*2/3=80/27
80/27*2/3=160/81
160/81*2/3=480/243
480/243*2/3=960/729
960/729*2/3=1920/2187.
=1920/2187
The 9th term of the geometric sequence will be 1280 / 2187.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The sequence is given below.
15, 10, 20/3
The first term is 15. And the common ratio is given as,
r = 10 / 15
r = 2 / 3
The 9th term of the geometric sequence is given as,
a₉ = 15 · (2/3)⁹⁻¹
a₉ = 15 · (2/3)⁸
a₉ = 15 · 256/6561
a₉ = 1280 / 2187
The 9th term of the geometric sequence will be 1280 / 2187.
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PLS HELP
Ninety students auditioned for the school play. One-third of those who auditioned were cast, 6 in major roles. What fraction of those who were cast got major roles? Write your answer as a decimal.(1 point)
The fraction of those who were cast and got major roles is 1/5.
Number of the students who were cast
The number of the students who were cast out of the Ninety students auditioned for the school play is calculated as follows;
Total number of students = 90
Number of students who were cast = ¹/₃ x 90 = 30
Number of students who go major role = 6
The fraction of those who were cast and got major roles is calculated as follows;
fraction of students who got major role = 6/30
fraction of students who got major role = 1/5
Thus, the fraction of those who were cast and got major roles is 1/5.
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Answer:
Total number of students = 90
Number of students who were cast = ¹/₃ x 90 = 30
Number of students who go major role = 6
fraction of students who got major role = 6/30
fraction of students who got major role = 1/5
1/5 = 0.2
in a month, carlos can produce a maximum of either 60 bushels of pears or 30 bushels of apples, or any linear combination in between. similarly, diane can produce a maximum of either 20 bushels of pears or 5 bushels of apples, or any linear combination in between.
Thus 3 bushels of pears can be acceptable term of trade for bushels of pears.
Opportunity cost of 1bushel of apple for Carlos=2pears
Opp. Cost of 1 bushles of apple for Donna=4pears
Thus ,
Term of trade acceptable to both for one bushels of apple is 2-4 bushels of pears
Ryan bought 6 apples and 9 peaches for a total of $9.75. Madi bought 4 apples and 5 peaches for $5.75. How much are apples and peaches?Define the variables.▪ Write 2 equations that model the situation.▪ Solve the system by either graphing, substitution or linear combinations.▪ Answer the question that was asked.▪ Plug in both answers and check your worka. The required equations are 6a+9p = 9.75 and 4a+5p = 5.75 .
b. The solution is given in the attached picture.
c. Apples are 1/2 and Peaches are 0.75
d. Solving the equations by putting the values
Let's take equation 1
6a+9p = 9.75
6 (1/2) + 9 (0.75) = 9.75
So equation satisfies both sides
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1 Latisha and Maisha are twins. They have a brother who is eleven years younger than
them and an older sister who is four years older. The sum of the ages of all four siblings
is 73. Find Latisha's age.
The temperature was -6 f it rose to 0f what represents the change in temperature
5) At West High School, 362 students take
Spanish. This number has been increasing
at a rate of 20 per year. The number of
students taking French is 259 and has been
decreasing at a rate of 3 per year. At these
rates, when will there be two times as
many students taking Spanish as taking
French?
Please help
Answer:
Step-by-step explanation:
In 6 years, because I subtracted 3 from 259 6 times and added 20 to 362 6 times.
Freddy is 4 years older than 8 times his grandson's age. The sum of their ages is greater than 67.
What is the youngest age Freddy's grandson can be?
Answer:
eight is the answer
Step-by-step explanation:
........
I WILL GIVE 25 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer: The answer is b
Step-by-step explanation: Simplify and expand it to determine it
State the property that justifies the statement.
If 3(x- 2/3)=4 , then 3x-2=4.
The distributive property is the property that justifies the statement.
Properties of MultiplicationThe properties of multiplication are:
Distributive: a(b±c)= ab±ac Commutative: a . b = b. a Associative: a(b+c)= c(a+b) Identity: b.1=bFor the question, the number 3 was multiplied each term, then
3x - 3*2/3 = 4
3x - 6/3 = 4
3x - 2 = 4
Comparing the steps and results found, it is possible to note that the distributive property for multiplication was applied.
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Simplify this algebraic expression completely.
10y - 3(y + 5)
O A. 7y+2
O B. 7y+ 5
© C. 7y- 15
• D. 7y- 5
The answer for the following algebraic expression [tex]10y-3(y+5)[/tex] is Option C [tex]7y-15[/tex].
According to the given question statement, We are supposed to simplify the given algebraic expression [tex]10y - 3(y + 5)[/tex]
Solution is as follows:
[tex]10y - 3(y + 5)\\= 10y-3(y)-3(5)\\\[/tex]
[tex]=10y-3y-15[/tex]
[tex]=7y-15[/tex]
Hence [tex]7y-15[/tex] is our final answer.
Algebraic expression: The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We get to know how to express an unknown value using letters like x, y, and z in the basics of algebra. Here, we refer to these letters as variables. Variables and constants, both can be used in an algebraic expression. A coefficient is a value that is added before a variable and then multiplied by it. These letters are called as variables here. Both constants and variables may be employed in an algebraic expression. Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.To learn more about Algebraic expression, click on the link given below:
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For this exponential
function,
what is the output value (y),
when the input value (x) is O?
y = 10•5x
(0,[?])
The output value of (y) will be 1 .
In mathematics, an exponential function is a function of the form f(x) = ax. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. Exponential functions, as the name suggests, involve exponents. But note that the base of the exponential function has a constant and the exponent has a variable, not vice versa.We have given an exponential function [tex]y=10.5^x[/tex] ......(1)
It is given that input value is 0 which means that replace the x with the input value in the given function.
Putting x = 0 in the equation (1) , we get
[tex]y=10.5^0[/tex]
Value of any number raised to power zero is always one .
[tex]y=1[/tex]
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The coordinates of the midpoint of GH¯¯are M(8, 0) and the coordinates of one endpoint are H(−2, 9)
Using the midpoint concept, the other endpoint of the segment is: G(18,-9).
What is the missing information?The problem asks for the coordinates of the other endpoint, given by point G.
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
Hence the x-coordinate of G is found as follows:
8 = (x - 2)/2
x - 2 = 16
x = 18.
The y-coordinate of G is found as follows:
0 = (y + 9)/2
y + 9 = 0
y = -9.
The other endpoint of the segment is: G(18,-9).
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Round 2798.01 to 2 significant figure
The approximation of 2798.01 to 2 significant figures is 2800
How to round the expression to 2 significant figures?The expression is given as
2798.01
The approximation is given as
2 significant figures
The above means that we approximate the given expression such that only 2 significant figures are left
In this case, the 2 significant figures in the expression 2798.01 are 2 and 7
So, we start the approximation from 9
When 9 is approximated, the expression becomes
2798.01 = 2800
Hence, the approximation of 2798.01 to 2 significant figures is 2800
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