The echelon form of the given augmented matrix with 1's on the diagonal is:
1 -1 0 1000
0 1 0 1100
0 0 1 300
What is the echelon form of this matrixTo find the echelon form of the given augmented matrix with 1's on the diagonal, we perform row operations to eliminate the entries below the diagonal. The goal is to get the matrix in row echelon form. Here are the steps:
Step 1: Subtract the first row from the second and third rows to eliminate the 1's in the first column below the diagonal:
1 -1 2 400
0 1 -2 500
0 -2 5 -700
Step 2: Add twice the second row to the third row to eliminate the -2 below the diagonal:
1 -1 2 400
0 1 -2 500
0 0 1 300
Step 3: Add 2 times the third row to the first row and add 2 times the third row to the second row to eliminate the entries above the diagonal:
1 -1 0 1000
0 1 0 1100
0 0 1 300
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If f(x) = 2x² - x - 6 and g(x) = x² - 4, find f(x) = g(x).
OA.
B.
C.
2x+3
2
2x-3
#+2
2x+3
#+2
O D. 22-2
Jhayq
Answer:
Step-by-step explanation:
To find the value of x such that f(x) = g(x), we need to set the two functions equal to each other and solve for x.
First, let's define the variables:
f(x) = 2x² - x - 6 is a quadratic function with x as the variable.
g(x) = x² - 4 is also a quadratic function with x as the variable.
Now, to find the value of x such that f(x) = g(x), we set the two functions equal to each other:
2x² - x - 6 = x² - 4
Next, we simplify this equation by subtracting x² from both sides:
x² + x - 10 = 0
This is a quadratic equation, which we can solve for x using either the quadratic formula or by factoring.
Let's try factoring:
x² + x - 10 = (x + 5)(x - 2) = 0
So either x + 5 = 0 or x - 2 = 0. Solving for x, we find that:
x = -5 or x = 2
These are the two values of x such that f(x) = g(x).
Find the dimensions for which the enclosed area is 1600 square feet. (View image)
Answer:
perimeter of rectangle = 2(length +breadth)
=2(20+80) m
=200 m
∴perimeter of rectangle is 200 m
-10 -8 -6 -4 -2 0 2 4 6 8 10
Plot the integer -7 on the number line.
The distance between 0 and -7 is
The absolute value of -7 is
The magnitude of -7 is
Step-by-step explanation:
To plot the integer -7 on the number line, we can place it to the left of 0. The number line would look like this:
-10 -8 -7 -6 -4 -2 0 2 4 6 8 10
The distance between 0 and -7 is 7 units, since 0 is 7 units to the right of -7.
The absolute value of -7 is 7, since the absolute value of a number is its distance from 0 on the number line.
The magnitude of -7 is also 7, which is the same as its absolute value. The magnitude of a number refers to its size or absolute value, regardless of its sign. In this case, the magnitude of -7 is 7.
How do I find the answer to this question?
Answer:
you see
Step-by-step explanation:
A woman has a total of $7,000 to invest. She invests part of the money in an account that pays 10% per year and the rest in an account that pays 11 per year. If the interest earned in the first year is $730 , how much did she invest in each account
The investments are $ 4000 and $ 3000 in the respective accounts
What is Algebra ?The mathematical field of algebra assists in the depiction of problems or conditions as mathematical statements. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
In the given question,
x = amount invested at 10 %
( 7000 - x ) = amount invested at 11 %
The total interest was $730 :
.10 (x) + .11 (7000-x) = 730
0.1 x + 770 - 0.11 x = 730
0.01 x = 40
x = 4000
Therefore, the amount invested in an account that pays 10 % per year is $ 4000.
Hence , the amount invested in an account that pays 11 % per year is
= ( 7000 - x ) = 7000 - 4000 = $ 3000.
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For each value of y , determine whether it is a solution to 10 < y
If a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.
What is inequality?
In mathematics, an inequality is a statement that describes a relationship between two values, expressing that one value is greater than, less than, or equal to the other value. Inequalities are denoted by symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).
The inequality 10 < y means that "y" is greater than 10. To determine whether a given value of "y" is a solution to this inequality, we simply need to check whether that value is indeed greater than 10.
For example:
If y = 11, then 10 < y is true, because 11 is greater than 10.
If y = 10, then 10 < y is false, because 10 is not greater than 10 (they are equal).
If y = 9, then 10 < y is false, because 9 is not greater than 10.
Hence, if a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.
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128 Sa se afle suma dintre produsul numerelor 45 250 şi 98 numer 100 000 şi 89 756.
graph the function f (x) = 3 cos (x) -4
Answer: DESMOS
Step-by-step explanation:
Your OHVA teacher reminded you in class to use DESMOS to see the graph and then sketch it on your test...
What is 7/8 of sixteen times a half of 30
7/8 of sixteen times a half of 30 is 210.
What is a PEMDAS rule?
PEMDAS is an acronym that stands for the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
To calculate this, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
Start with the expression inside the parentheses: half of 30 is 15.
Multiply 16 by 15: 16 times 15 is 240.
Find 7/8 of 240:
7/8 of 240 = (7/8) x 240
= 210
Hence, 7/8 of sixteen times a half of 30 is 210.
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Select the correct answer.
A fantasy board game makes use of four dice. The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each. If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?
A.
30
B.
240
C.
2,400
D.
3,000
Answer:
The total possible outcomes that exist are:
2400
Step-by-step explanation:
We are given four dices:
first is a standard 6-faced die.
The second die has 4 faces.
Third dice has 10 faces.
Fourth dice has 10 faces.
Now when all the dice are thrown together then the total number of possible outcomes are:
( Since there are 4 numbers possible for the first die, 6 for second and 10 each for third and fourth)
The answer is:
2400
How much time will it take to earn $760.00 in interest if you deposit $3,200.00 into a simple interest account earning 4.5% annum Simple interest
Using the formula of simple interest, the time it will take to accumulate to $3200 at a rate of 4.5% is 71.35 years
What is Simple InterestSimple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.
The formula for simple interest is:
I = P * r * t
where:
I is the interest amount
P is the principal amount
r is the interest rate (expressed as a decimal)
t is the time period (in years)
Substituting the values into the formula;
A = P(1 + rt)
3200 = 760(1 + 0.045(t))
3200 = 760 + 34.2t
34.2t = 3200 - 760
34.2t = 2440
t = 2440 / 34.2
t = 72.35 years
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Identify the y- intercept of the graph below
b= -4
b=6
b=4
b= -10
Select all the expressions that have a value of 13.5 when s = 1.5
Answer:
Given that s = 1.5, the expressions that have a value of 13.5 are:
(1) 5s + 8 = 5 × 1.5 + 8 = 13.5
(2) 2s^2 + 9 = 2 × 1.5^2 + 9 = 13.5
Note: The value of any other expression will depend on the specific formula and the value of other variables used in the expression.
Need assistance with this problem
We can see that the exponential model is better
What is the difference between a linear and an exponential function?The main difference between a linear and an exponential function is the way they change as their input variable (usually denoted as x) increases.
In summary, linear functions have a constant rate of change, while exponential functions have an increasing rate of change.
For the linear function;
f(x) = 946(6) + 3349
= 9025
For the exponential function;
g(x) = 3866e^0.138(6)
g(x) = 8848
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Rylon Corporation manufactures Brute and Chanelle perfumes. The raw materials needed to manufacture each type of perfume can be purchased for $3 per pound. Processing 1 lb of raw material requires 1 hour of laboratory time. Each pound of processed raw material yields 3 oz of Regular Brute Perfume and 4 oz of Chanelle perfume. Regular Brute can be sold for $7/oz and Regular Chanelle for $6/oz. Rylon also has the option of further processing Regular Brute and Regular Chanelle to produce Luxury Brute, sold at $18/oz, and Luxury Chanelle, sold at $14/oz. Each ounce of Regular Brute processed further requires an additional 3 hours of laboratory time and $4 processing cost and yields 1 oz of Luxury Brute. Each ounce of Regular Chanelle processed further requires an additional 2 hours of laboratory time and $4 processing cost and yields 1 oz of Luxury Chanelle. Each year, Rylon has 6,000 hours of laboratory time available and can purchase up to 4,000 lb of raw material. Question : what is the simplex algorithm (manual table ) to find a solution to the linear programming problem given above
Convert the problem to standard form and write the initial tableau with slack variables:
Maximize
[tex]Z = 7*3 + 6*4 + 18*5 + 14*6 - 3*1 - 3*2 - 4*5 - 4*6[/tex]
Subject to:
[tex]x1 + x2 + s1 = 4000\\x3 - (1/3)*1 + (1/3)*5 = 0\\x4 - (1/3)*2 + (1/2)*6 = 0\\x3*1 + 3*2 + 3*3 + 3*4 + 3*5 + 2*6 + s2 = 6000[/tex]
All variables are non-negative.
Tableau
x1 x2 x3 x4 x5 x6 s1 s2 b
Z -3 -3 7 6 18 14 0 0 0
s1 1 1 0 0 0 0 1 0 4000
s2 3 3 3 3 3 2 0 1 6000
x5 0 0 1 0 1/3 0 0 0 0
x6 0 0 0 1 0 1/2 0 0 0
The basic variables are s1, s2, x5, and x6.
Step 1: Choose entering variable. The most positive coefficient in objective row is 18, corresponding to x5. x5 enters the basis.
Step 2: Choose the leaving variable. The minimum ratio of right-hand side to coefficient of x5 is 12000/(1/3) = 36000,
corresponding to s1. s1 leaves the basis.
Step 3: Perform, pivot operation to make x5 the basic variable for s1. Divide, pivot row by 1/3 and subtract appropriate multiples of the pivot row from other rows to make other entries in column 5 zero.
x1 x2 x3 x4 x5 x6 s1 s2 b
Z -3 -3 7 6 18 14 0 0 0
x5 0 0 1 0 1/3 0 0 0 0
s2 3 3 3 3 2 2/3 2/3 0 1/3 24000
x3 1 0 1/3 0 1/3 0 -1/3 0 0
x4 0 1 0 1/3 0 1/2 -1/6 0 0
The basic variables are x5, x3, x4, and s2.
Step 4: Choose the entering variable. The most positive coefficient in the objective row is 7, corresponding to x3. x3 enters the basis.
Step 5: Determine the leaving variable. The right-hand side's minimum ratio to the coefficient of x3 is 0, indicating that x3 can be increased without bound. This implies that the optimal solution is unbounded and that there is no finite optimal value for the problem.
As a result, the simplex algorithm demonstrates that the given linear programming problem lacks a feasible solution. This means that it is not possible to meet all of the constraints at the same time.
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What is the x-coordinate of the image when M(4, −1) is reflected in y=3.
The image of the point M(4, -1) after reflection in the line y = 3 would have the x-coordinate of 4.
What is another way to say reflecting?When you reflect, you are giving something serious thought. [written] I continued my thoughtful stroll to the car while contemplating the unfortunate honeymooners. Synonyms: thoughtful, ponderous, contemplative, and pensive More reflective's opposites.
What other word for reflecting is there?Cogitate, deliberate, reason, conjecture, and think are a few words that frequently replace the word reflect. All of these terms indicate "to utilise one's faculties of imagination, reasoning, or inference," but reflect denotes thoughtful deliberation over a memory that has just come to mind.
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What is the measure of each angle in a regular polygon with 14 sides? If necessary, round your answer to the nearest tenth.
The measure of each angle in the regular polygon is 154.3 degrees
How to determine the measure of each angle in a regular polygonFrom the question, we have the following parameters that can be used in our computation:
Number of sides, n = 14
The measure of each angle is calculated as
Angle = ( n − 2 ) × 180/n
substitute the known values in the above equation, so, we have the following representation
Angle = (14 − 2) × 180/14
Evaluate
Angle = 154.3
Hence, the angle is 154.3
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Allen’s hummingbird has been studied by zoologist Bill Alther (Reference: Hummingbirds, K. Long and W. Alther). A small group of 15 of Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is = 3.15 grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds have a normal distribution, with = 0.33 gram.
Find an 80% confidence interval for the average weights of Allen’s hummingbirds in the
study region. What is the margin of error?3.02, 3.28).
Sample mean of :
Population standard deviation of:σ=0.32
Sample size of : n=10
The confidence interval is:
80% confidence level, hence, z is the value of Z that has a p-value of , so .
The margin of error is:Then
The 80% confidence interval for the average weights of Allen's hummingbirds in the study region is (3.02, 3.28).
The margin of error is of 0.13.
The lower limit is of 3.02.
The upper limit is of 3.28.
Give a brief interpretation of your results in the context of this problem The standard deviation σ is known.
•the standard deviation σis known
•normal distribution of weight
•n is large
Find the sample size necessary for an 80 % confidence level with a maximal error of estimate = 0.08 for the mean weights of the hummingbirds.
a) The required margin of error and lower and upper limits are:-
E =0.124
Lower limit =3.026
Upper limit = 3.274
b) sample size is n = 27.
What is a confidence interval?An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
The margin of error will be calculated as:-
a) Margin of error (E) :
[tex]E = Z_c\times \dfrac{\sigma}{\sqrt{n}}[/tex]
E =0.124
Margin of error = E =0.124
The lower and upper limits are calculated as:-
Lower limit = x-E
L= 3.15 - 0.124
L= 3.026
Lower limit =3.026
Upper limit = x + E
U= 3.15 + 0.124
U= 3.274
Upper limit = 3.274
b) The following equation may be used to calculate the right number of samples, n when is already known:
Margin of error = 0.13
Sample size (n):
[tex]n = (\dfrac{Z_c\sigma}{E})^2[/tex]
[tex]n = (\dfrac{1.28\times 0.36}{0.09})^2[/tex]
n = 26.21
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A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the (((volume of 15 bags in cubic yards.)))
Answer:
he weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Step-by-step explanation:
To find the weight of 15 bags in kilograms, we can first convert the weight of one bag from pounds to kilograms and then multiply by the number of bags:
1 pound = 0.453592 kilograms
So the weight of one bag in kilograms is:
42 pounds * 0.453592 kilograms/pound = 19.05 kilograms
The weight of 15 bags in kilograms is:
15 bags * 19.05 kilograms/bag = 285.75 kilograms
To find the volume of 15 bags in cubic yards, we can first convert the volume of one bag from cubic feet to cubic yards and then multiply by the number of bags:
1 cubic yard = 27 cubic feet
So the volume of one bag in cubic yards is:
2 cubic feet / 27 cubic feet/cubic yard = 2 / 27 = 0.07407 cubic yards
The volume of 15 bags in cubic yards is:
15 bags * 0.07407 cubic yards/bag = 1.111 cubic yards
Therefore, the weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Here are the first four terms of a number sequence.
2 7 12 17
Here are the first five terms of another number sequence.
-4 -1 2 5 8
Find two numbers that are in both number sequences.
Two numbers that are in both sequences are the numbers 17 and 32.
What is a sequence?A sequence can be described as a set of numbers each with a defined interval between one another. For example, in the sequence 2, 4, 6, 8, 10, the interval is 2.
What numbers do these sequences have in common?To find two common numbers, let's expand the sequences as it is shown below:
First sequence: In this sequence, the interval is 5.
2 7 12 17 22 27 32
Second sequence: In this sequence, the interval is 3.
-4 -1 2 5 8 11 14 17 20 23 26 29 32
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Convert the following quantities to the indicated units. 34 liters=to how many quarts
Answer:
Step-by-step explanation: 34 quarts
1 Liter = approximately 1.06 quarts
so 34 x 1.06 is about 36.04 quarts
Qué fracción restada a 1/2 da como resultado 4/10?
-1/10 should be subtracted from 1/2 to get 4/10.
How can you represent a fraction? Are fractions and ratios same?A fraction is of the form → (x/y).
For example, we can write fractions as → 2/3.
Fractions and ratios represent the same aspect. We can write -
2 : 3 = 2/3
4 : 7 = 4/7
Given is to solve the expression -
(1/2) - ? = 4/10
We can write the expression as -
(1/2) - (x) = (4/10)
(x) = 4/10 - 1/2
(x) = 4/10 - 5/10
(x) = -1/10
Therefore, -1/10 should be subtracted from 1/2 to get 4/10.
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{Question in English -
What fraction subtracted from 1/2 equals 4/10?}
I need help answering this
The domain of the function for this situation is given as follows:
B. All whole numbers greater than or equal to 0 and less than or equal to 7.
How to obtain the domain of a function?The domain of a function is the set that contains all the values assumed by the input of the function.
Hence, on a graph, the domain is given by the values assumes on the horizontal axis of the graph.
The values that compose the domain of the graph are given as follows:
0, 1, 2, 3, 4, 5, 6 and 7.
Which is best described by option B.
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Select the correct answer. What is the simplified form of this expression? (-3x2 + x + 5) − (4x2 − 2x)
Answer:
-9+3x
Step-by-step explanation:
(-3x2 + x + 5) − (4x2 − 2x)
(-6+x+5)-(8-2x)
(-1+x)-8+2x
-1+x-8+2x
-9+3x
The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 2 and roots of multiplicity 1 at x = 0 and x = -2 . It goes through the point (5,189).
If "a" is a root of a polynomial, then (x-a) is a factor of the polynomial.
If the multiplicity of a root a is "p", then (x-a)^p is a factor of the polynomial.
Based on the roots and multiplicity, we have:
P(x) = k · (x-2)^2 · (x-0) · (x - (-2))
P(x) = k · (x-2)^2 · (x-0) · (x+2)
We need that "k" up front to account for any vertical stretch or compression to hit the exact point (5,189).
To find "k", we plug in that point and solve for "k":
189 = k · (5-2)^2 · (5-0) · (5+2)
189 = k · (3)^2 · (5) · (7)
189 = k · 315
0.6 = k
So the final answer is: P(x) = 0.6 · (x-2)^2 · (x-0) · (x+2)
4. Reginald created a mosaic from 6" square tiles.
If the completed mosaic was 2 feet by 3 feet, how
many square tiles did he use?
Reginald used 2 square tiles to make the mosaic
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The area is the product of the length and width. Hence:
Area = length * width
Reginald created a mosaic from 6" square tiles. Therefore:
Area of tiles = 6 in * 6 in = 36 in²
If the completed mosaic was 2 feet by 3 feet, Hence:
Area of mosaic = 2 feet * 3 feet = 6 feet
1 feet = 12 in
6 feet = 6 feet * 12 in per feet = 72 in²
Number of tiles = Area of mosaic / area of tiles = 72 in² / 36 in² = 2
Reginald used 2 tiles
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A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the volume of 15 bags in cubic yards.
Answer:
285.76 kilograms 1.1 cubic yard
Step-by-step explanation:
Answer:
1.11121 cubic yards.
Step-by-step explanation:
First, let's convert the weight of 1 bag of garden soil from pounds to kilograms:
1 lb = 0.45359237 kg
42 lbs = 42 * 0.45359237 kg = 19.05 kg
So, the weight of 1 bag of garden soil is 19.05 kilograms.
Next, let's find the weight of 15 bags of garden soil:
15 bags * 19.05 kg/bag = 285.75 kg
So, 15 bags of garden soil weigh 285.75 kilograms.
Next, let's find the volume of 15 bags of garden soil in cubic yards:
1 cubic foot = 0.037037 cubic yards
2 cubic feet * 15 bags = 30 cubic feet
30 cubic feet = 30 * 0.037037 cubic yards = 1.11121 cubic yards
So, 15 bags of garden soil have a volume of 1.11121 cubic yards.
Mary is driving at 60 mph. She decreases her speed by 5 mph every second. Which signed number
represents the change in her speed after 5 seconds?
Answer:
35 mph
Step-by-step explanation:
5×5=25
60-25=35.
what is the equation of a line that is parallel to the line that is given by the equation x=-4?
The equation of the line which is parallel to the line x = -4 will be x = -3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the equation of the line is x = -4. The y-intercept is zero for the line.
The equation of the line parallel to the equation will be,
x = -3
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Is 8 a solution to 3/4x=6?
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
YES, x = 8
Step-by-step explanation:
plug in 8 for x and see if both sides are equal
3/4 times 8 = 24/4 or 6
Answer:
Yes, 8 a solution to 3/4 x=6 !Step-by-step explanation:
If we solve it as....
[tex]\mathrm{\cfrac{3}{4}x=6}[/tex]
[tex]\mathrm{4\times\cfrac{3}{4}x=6\times\:4}[/tex]
[tex]\mathrm{3x=24}[/tex]
[tex]\mathrm{\cfrac{3x}{3}=\cfrac{24}{3}}[/tex]
[tex]\mathrm{x=8}[/tex]
Yes, 8 would be the solution!
___________________
Hope this helps!
