Choose an equation, multiply a row by a constant to make it equal to 1, use row operations to make all other elements in the same column equal to 0, repeat for all elements in the matrix, when all elements are equal to 1, the 3x3 matrix is solved
To solve a 3x3 matrix for beginners, start by writing the equation in the form of Ax = B. Then, choose a set of three equations from the matrix that are independent of each other and solve the first equation for one of the unknowns, substituting the known values for the other two unknowns. Substitute the value of the unknown from the first equation into the other two equations and solve for the remaining two unknowns. Finally, check the solution by substituting the values of all three unknowns into the original equation.
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a cone with a radius of 4.96 and a volume of 102
The volume of a cone is given by the formula:
V = (1/3) * π * r² * h
Where V is the volume, r is the radius, and h is the height.
In this case, we know the radius (4.96) and the volume (102), so we can use the formula to solve for the height.
Substituting the known values into the formula, we get:
102 = (1/3) * π * (4.96)² * h
Dividing both sides by (1/3) * π * (4.96)², we get:
h = 102 / [(1/3) * π * (4.96)²]
Substituting in the value for π, we get:
h = 102 / [(1/3) * 3.14 * (4.96)²]
Which simplifies to:
h = 102 / [(1/3) * 3.14 * 24.1952]
Which simplifies to:
h = 102 / (0.7853 * 24.1952)
Which simplifies to:
h = 102 / 19.1268
Which is approximately 5.33.
Therefore, the estimated height of the cone is approximately 5.33.
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Answer:
Step-by-step explanation:
The volume of a clone = 1/3 × π × r^2 × h
Volume, v = 102
Radius r = 4.96
r^2 = 4.96^2 = 24.6016
Approximately = 24.6
π = 3.142
v = 1/3 x π x r^2 x h
Cross multiply
3v = π x r^2 x h
h = (3 x 102) / 24.6 x 3.142
h = 3.959 cm
I hope this was helpful
(6x2 - 2x) + (5x-7)
A. 30x3 - 52x2 + 14x
B. 6x2 - 7x+7
c. 11x2 - 9x
D. 6x2 + 3x - 7
Answer:
D. 6x2 + 3x - 7
Step-by-step explanation:
help what is the answer to this picture?
WX is a segment bisector
WX is a perpendicular bisector
W is the midpoint of a segment in the diagram
What is the median of 50?
The median of the first 50 whole numbers is 24.5.
The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.
Non-negative numbers, which can be expressed without fractions, are known as whole numbers.
The first fifty whole numbers are 0,1,2,3,4,5................49
The number of terms in the data, n=50.
Let [tex]n^{th}[/tex] term be denoted by [tex]t_{n}[/tex]
As the number of terms is even, thus the median will be [tex]\frac{t_{\frac{n}{2} } +t_{\frac{n}{2} }+1}{2}[/tex]
Substitute n with 50.
Median = [tex]\frac{t_{\frac{50}{2} } +t_{\frac{50}{2} }+1}{2}= t_{25}+t_{26} /2[/tex]
The 25th term of the sequence is 24.
The 26th term of the sequence is 25.
Thus, median = 24+25/2 = 49/2 = 24.5
Complete question: What is the median of the first 50 whole numbers?
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You want to put $2,500 in a simple interest account. It has a 4% annual interest rate. How long must you invest that money to earn $500 in interest?
A) 1.25 years
B) 2.5 years
C) 5 years
D) 20 years
Answer:c
Step-by-step explanation:
Answer: C) 5 years
Step-by-step explanation:
Formula for the simple interest is: I = P * r * t, where: I = $500, P = $2,500, r = 0.04 and t stays for the number of the years. 500 = 2,500 * 0.04 * t; 500 = 100 * t; t = 500 : 100; t = 5.
A recipe that yields 30 servings calls for 3/4 cup flour. You want to prepare only 10 servings. After scaling the recipe to yield 10 servings, how much flour will you need?.
The number of servings that can be made from 3 / 4 cups, the number of cups of flour needed for 10 servings is 1/4 cups.
Given :
First the number of servings that can be made per cup :
= Number of servings / Number of cups
= 30 / 3/4
= 30 * 4 / 3
= 120 / 3
= 40 servings
To get 10 servings therefore, you would need:
= Number of servings needed / Number of servings per cup
= 10 / 40
= 1/4 cups
Hence the flour will be needed is 1/4 cup is needed.
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consider reordering the letters in the word tennessee. use the technique shown in example 9.5.11 to answer the following questions. (a) if the n's are placed first, how many ways are there to choose positions for them? if the e's are placed second, how many ways are there to choose positions for them? if the s's are placed third, how many ways are there to choose positions for them? if the t is placed fourth, how many ways are there to choose a position for it? so, the total number of ways to reorder the letters in the word tennessee is . (b) imagine placing the letters into positions in a different order. if the e's are placed first, how many ways are there to choose positions for them? if the t is placed second, how many ways are there to choose a position for it? if the s's are placed third, how many ways are there to choose positions for them? if the n's are placed fourth, how many ways are there to choose positions for them? (c) when the method suggested in part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is ---select--- when the method of part (a) is used.
Answer:
Step-by-step explanation:
(a) If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.
(b) If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.
(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.
What is permutation of rearranging letters?
A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .
The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.
Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.
Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.
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a) 36, 35, 3, 1 ways; b) 126, 5, 6, 1 ways; c) total number of ways to reorder the letters in the word tennessee is 3780 for both a) and b).
(a) If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.
(b) If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.
(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.
What is permutation of rearranging letters?
A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .
The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.
Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.
Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.
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What type of set is X?
A set X is a subset of set Y (Written as X ⊆ Y) if every element of X is an element of set Y.
What is a set ?A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.
A set has many types, such as;
Empty Set or Null set: It has no element present in it.Example: A = {} is a null set.
Finite Set: It has a limited number of elements.Example: A = {1,2,3,4}
Infinite Set: It has an infinite number of elements.Example: A = {x: x is the set of all whole numbers}
Equal Set: Two sets which have the same members.Example: A = {1,2,5} and B={2,5,1}: Set A = Set B
Subsets: A set ‘A’ is said to be a subset of B if each element of A is also an element of B.Example: A={1,2}, B={1,2,3,4}, then A ⊆ B
Universal Set: A set which consists of all elements of other sets present in a Venn diagram.Example: A={1,2}, B={2,3}, The universal set here will be, U = {1, 2,3}
A set X is a subset of set Y (Written as X ⊆ Y) if every element of X is an element of set Y.
Example : − Let, X = { 1, 2, 3, 4, 5, 6 } and Y = { 1, 2 }. Here set Y is a subset of set X as all the elements of set Y is in set X. Hence, we can write Y ⊆ X.
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Find the measure of angle MNQ
Answer:
∠MNO = 158°
Step-by-step explanation:
∠MNO = 1/2(91° + 225°) = 158°
You ask 50 of your classmates if they have any siblings. Complete the two-way frequency table to show the results of the survey.
Girls of 25 says Yes, 10 boys say No. 30 total Students say No, 45 girls total, with a total of 60 Students
What meant by mathematical expression ?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
An expression that uses numbers, variables, or both is a mathematical expression. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.
Given,
5 boys tell yes and total boys and girls tell yes is 30 by simplifying
no of girls tell yes =30 - 5= 25
no of girls tell no =20
overall total boys tell no = 15-5=10
The no of boys tell no =10
So total no of boys and girls tell no = 20+10=30
total no of girls tell yes and no =60-15=45
The complete question is : You ask 60 of your classmates if they have any siblings. Complete the two-way frequency table to show the results of the survey.
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Solve the system
x+2y=-11
3y=x+1
Answer:
x=-13, y=-4
Step-by-step explanation:
Answer: x=-7 y=-2
Step-by-step explanation:
x+2y=-11
3y=x+1
x=-2y-11 (1)
3y=x+1 (2)
Substitute the value of x of equation (1) into equation (2):
3y=-2y-11+1
3y=-2y-10
3y+2y=-2y-10+2y
5y=-10
Divide both parts of the equation by 5:
y=-2
Substitute the value of y=-2 into equation (1):
x=-2(-2)-11
x=4-11
x=-7
Thus, (-7,-2)
Why do we check up to the square root of a number to determine if the number is prime?
A number is said to be prime if the integers smaller than its square root cannot divide it, as numbers higher than its square root cannot possibly do so.
what is square root ?A mathematical concept known as a square root is a factor of a number that, when multiplied by itself, equals the original value. For instance, 3 and -3 are the square roots of 9. Starting in the second millennium BC, the Babylonians created effective methods for approximating square roots.
here ,
In other words, if we encounter a number when counting from 2 to sqrt(N), and that number is a factor of N .
then indicates that the number has more than two factors and is thus not a prime number.
Otherwise, if we are unable to locate any factors for N, it is likely that N only has two factors, one and itself, making it a prime number.
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How do you solve for x and y using substitution?
In substitution method we have to put the the value of one variable from one equation to the other equation. Then we solve the equation and can find the value of variable x and y.
In the given question we have to explain how we can solve for x and y using substitution.
In the Substitution method we find the value of one variable in term of other variable from the one equation then we put the value of that variable in other equation. After putting the value of that variable in other equation, equation converts into the similar variable. Then after solving we can easily find the value of one variable. After finding the value of one variable we put the value of that variable in first equation. By this we can find the value of both variable.
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neeed help with this thanks
Find x: a - bx = cx + d
Answer:
x= -(d-a)/(b+c)
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero
If$2500was invested 6 years ago, andtheinterestwascompoundedquar-terly,whatwastheinterestrateifthecurrentvalueis$3425?
Answer:
The interest rate was 5.24%.
Step-by-step explanation:
You can use the following formula to calculate the interest rate:
i=n*((A/P)^1/nt-1), where:
i= interest rate
n= number of times interest is compounded= 4
A=value of investment= 3425
P= principal= 2500
t=time= 6
Now, you can replace the values on the formula:
i=4*((3425/2500)^1/4*6-1)
i=4*(1.37^1/24-1)
i=4*0.0131
i=0.0524
According to this, the answer is that the interest rate was 5.24%.
How many more people in the world speak Chinese than speak English?
Answer:
The answer is 912 million
Step-by-step explanation:
912 million people speak Chinese in the world than they do English.
a number has three distinct digits, the sum of the digits equals the products of the digits. how many three digit numbers satisfy this condition?
Only one three digits number 111 would satisfy this condition.
Let the three digits be x, y and z. Since the sum of the digits is equal to the product of the digits, we can write x + y + z = xyz
Simplifying the equation, we get x + y + z - xyz = 0
This is a quadratic equation in the form ax2 + bx + c = 0 where a = 1, b = 1 and c = -xyz
To solve this equation, we use the quadratic formula: x = [-b ± √(b2 - 4ac)]/2a
In this case, x = [-1 ± √(1 - (-4 * 1 * (-xyz))]/2
Since xyz must be a positive integer, the only solution is when the square root of 1 - (-4 * -xyz) is 0
This means xyz must be 1, so x + y + z = 1 + y + z = 3
Since x, y and z are all distinct digits, the only possible solution is when x = 1, y = 1 and z = 1, giving the solution 111.
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Why is it called linear function?
A linear function is a type of function that can be expressed in the form of a linear equation with one or more variables.
The equation is written as y = mx + b, where m is the slope and b is the y-intercept. The slope is the rate at which the line rises or falls and the y-intercept is the point where the line crosses the y-axis. The slope and y-intercept of a linear function are constants, meaning that the line does not curve or change direction. This is why it is called a linear function.
When calculating linear functions, the equation is used to identify the slope and the y-intercept. The slope and y-intercept are then used to plot the points on a graph. A linear equation has the form y = mx + b, where m is the slope and b is the y-intercept. The slope indicates the rate of change of the function and the y-intercept indicates the point where the line crosses the y-axis. To find the slope of a linear function, the equation is solved for m, which is the rise over run. To find the y-intercept, the equation is solved for b, which is the y-value when x = 0. Once the slope and y-intercept are determined, the points can be plotted on a graph and the linear equation can be written.
In summary, a linear function is a type of function that can be expressed in the form of a linear equation. The equation of the linear function is used to identify the slope and y-intercept, which are then used to plot the points on a graph. Linear functions can be used to model many real-world situations and to solve for x and y values for any given point.
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Find the range of the following numbers: 10 78 22 354 75 81 8 6 A 8 C 27 B 81 D 78
Answer:
348
Step-by-step explanation:
6 8 10 22 75 78 81 354
subtract the highest number to the lowest number
Which is an example of a sequence?
3,7,11,15 is an example of sequence since we can see a pattern is previous and next term.
What are the name of four type of sequences?Arithmetic sequence
Geometric sequence
Harmonic sequence
Fibonnaci numbers.
Is sequence a set?In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important. A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions.
A sequence is a list of elements that has been arranged in a certain way. For instance, the sequence 3, 7, 11, 15,... is a sequence because it follows a pattern where each term is created by adding 4 to the term before it.
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Find the 87th term of the arithmetic sequence -19, -13, -7…
Answer:
497
Step-by-step explanation:
a(87) = -19+(87-1)6
a(87)=-19+(86)6
a(87)=-19+516
a(87)=497
I used the arithmetic formula which is an=a1+(n-1)d.....
1/4a + (-6) - 3/4a + 2.8, what is equivalent to this expression?
The equivalent for the expression 1/4a + (-6) - 3/4a + 2.8 is -(2+12.8a)
How do we find the equivalent of an expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
For example 2x+ y+5y+6x is an example of expression and it's equivalent is 8x+6y
simplifying the expression 1/4a + (-6) - 3/4a + 2.8,
multiply through by 4a
1-24a-3+11.2a
collect like terms
1-3-24a+11.2a
= -2-12.8a
= -(2+12.8a)
therefore 1/4a + (-6) - 3/4a + 2.8 = -(2+12.8a)
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For what values of x is the expression below defined?
A. 4> xs-1
B. 45xs1
C. 4 >x>1
D. -4sx< 1
Answer:
D.
Step-by-step explanation:
D.-4sx<1!I think is d
Can Someone Help Me Please
Answer:
63 with 3 left over
Step-by-step explanation:
381/6=63.5
63x6=378
378+3=381
5. Find the length of the side denoted b "y" to the nearest tenth.
Answer:
y = 24√3, or approximately 41.6
Step-by-step explanation: √3 36
Here the ratio 36/y = cosine of 30 degrees = ------- = ------
2 y
Cross-multiplying yields (√3)y = 72, so y = 72/√3, or 72√3/3, or y = 24√3
How do you complete the proof?
From the proof below, we have been able to prove that IK bisects ∠HIJ by CPCT postulate
How to complete the proof of congruent angles?Congruent angles are defined as angles that have equal measure.
Now, we are given that;
IK bisects ∠HKJ
HK ≅ JK
Thus, since IK bisects ∠HKJ, then it means that by definition of angle bisector that;
∠HKI = ∠JKI
Now, we are also told that HK ≅ JK.
Now, by reflexive property of congruence, we can say that IK is congruent to itself.
Thus, we now have 2 congruent sides and an include angle and as such both triangles are congruent by SAS Congruency postulate.
Thus, we can conclude that ∠HIK = ∠JIK by CPCT which states that Corresponding parts of Congruent Triangles are congruent.
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there are 549 coins in a bottle
one third of the coins are £1 coins
164 of the coins are 50p coins
the rest of the coins are 20p coins
work out the value of the 549 coins in pounds (£)
The value of the 549 coins in pounds (£) is 305.4 .
What is fraction multiply?
Multiplying fractions is defined as the product of a fraction with a fraction or with an integer or with the variables. The procedure to multiply the fractions are: Multiply the numerator with numerator. Multiply the denominator with the denominator. Simplify the fractions, if required.
Given:
Total coins : 549 coins
one third(1/3) of the coins are £1 coins
164 of the coins are 50p coins
rest of the coins are 20p coins
one third of 549 = 549/3 = 183
Thus ,
£1 coins = 183
50p coins = 164
20p coins = 549 - (183 + 164) = 202
value of the 549 coins in pounds (£) is given by
[tex]= 549 * \frac{1}{3} * 1 + 164* 0.5 + (549 *\frac{2}{3} - 164)*0.2\\\\= 183 + 82 +40.4\\\\= 305.4[/tex]
Hence , the value of the 549 coins in pounds (£) is 305.4 .
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How to compute 1sd 2sd 3sd?
The average degree of variability in the dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.
Explain the term standard deviation?Empirical principle
If your frequency distribution follows a normal distribution, the standard deviation and mean combined might help you determine where the majority of the values are located.
The 68-95-99.7 rule, often known as the empirical rule, reveals your values to you:
Nearly 68% of scores are within one deviation of the mean, nearly 95% are within two standard deviations, and nearly 99.7% are within three standard deviations.Thus, the standard deviation is a less trustworthy indicator of variability for non-normal distributions and should be combined with other metrics like range or interquartile range.
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What is the range of the function 4?
The range is 4.
The range is 4 because y=y can only take on 4 at any point.