The augmented matrix for the system of equations is [tex]\left[\begin{array}{ccc}\frac{6}{5} \\\frac{1}{10} \\\frac{23}{5} \end{array}\right][/tex]
What is matrix ?A matrix is a rectangular array or table where data is organized into rows and columns, and "matrixes" is the plural version of matrix. It doesn't matter how many columns and rows they have. Matrices can be used for a variety of operations, including addition, multiplication, transposition, and scalar multiplication. When executing these matrix operations, certain guidelines must be followed. For example, matrices can be added to or subtracted from if only their rows and columns are the same, whereas they can be multiplied if only their first and second sets of columns are exactly the same.
A =[tex]\left[\begin{array}{ccc}1&-2&0\\-5&8&2\\0&4&1\end{array}\right] \left[\begin{array}{ccc}X\\Y\\Z\end{array}\right] =\left[\begin{array}{ccc}1\\4\\5\end{array}\right][/tex]
Ax = B
multiply by [tex]A^{-1}[/tex] to both side
[tex]A^{-1}[/tex]Ax = [tex]A^{-1}[/tex]B
x = [tex]A^{-1}[/tex]B
[tex]\left[\begin{array}{ccc}0&\frac{-1}{5} &\frac{2}{5} \\\frac{-1}{2} &\frac{-1}{10} &\frac{1}{5} \\\ 2&\frac{2}{5} &\frac{2}{5} \end{array}\right][/tex]= [tex]A^{-1}[/tex]
X = [tex]\left[\begin{array}{ccc}0&\frac{-1}{5} &\frac{2}{5} \\\frac{-1}{2} &\frac{-1}{10} &\frac{1}{5} \\\ 2&\frac{2}{5} &\frac{2}{5} \end{array}\right][/tex][tex]\left[\begin{array}{ccc}1\\4\\5\end{array}\right][/tex]
X = [tex]\left[\begin{array}{ccc}\frac{6}{5} \\\frac{1}{10} \\\frac{23}{5} \end{array}\right][/tex]
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please solve this question
We have a random variable, the time it takes to wash the dishes, that is uniformly distributed between 7 minutes and 16 minutes.
We have to calculate the probability that this random variable will have a value between 11 and 15 minutes.
We can calculate this probability as:
[tex]P(11Answer: the probability is 0.44.Solve the equation.
−3=z−8
z=
The answer is 5
Step-by-step explanation:
-3=z-8
put +8 underneath -8. Then cross it out.
Put +8 underneath -3. -3+8=5
The answer is 5.
I hope this helped you!
Line segments JK and JL in the xy-coordinate plane both have a common endpoint /(-4, 11) andmidpoints at M, (2,16) and M, (-3, 5), respectively.What is the distance between M, and M.? Round to the nearest tenth
SOLUTION
From the question, since the coordinates of the mid-points JK and JL has been given as M (2,16) and M, (-3, 5), respectively.
To find the distance between these two mid-points, we simply use the distance formula to do that.
The distance formula is given as
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ where\text{ d is the distance } \end{gathered}[/tex]Applying these to the points M (2,16) and M, (-3, 5), we have
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(-3-2)^2+(5-16)^2} \\ d=\sqrt{(-5)^2+(-11)^2} \\ d=\sqrt{25+121} \\ d=\sqrt{146} \\ d=12.083045 \\ d=12.1\text{ units } \end{gathered}[/tex]Hence the answer is 12.1 units
If f(x) = -x³ + x² + x, find f(-3)
A 15-gallon gas tank. If you can drive 330 miles on a full tank of gas, what is the unit rate of miles per gallon he gets?
please help thank you
A dinner theater charges $20 per person. Your table can hold a maximum of five people. Does the situation represent a function?
If so, find the domain and range. If not, leave this blank.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Domain: Response area
Range: Response area
The situation represents a function, while the domain and the range are 0 <= x <= 5 and 0 <= y <= 100, respectively
How to determine if the situation is a function?From the question, we have
Charges = $20 per person
Let the number of people be x and the total charges be y
So, we have
y = 20x
The above equation is a linear function
The domain and the rangeFrom the question, we have
Total number of people per seat = 5
So, the domain is 0 <= x <= 5
Substitute 5 for x in y = 20x
y = 20 x 5
Evaluate
y = 100
So, the range is 0 <= y <= 100
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Use the properties of equality to solve each equation r + 18 = 26
To solve this equatio you use the next property:
Subtraction Equal Property: it is used in expressions with adds. State that you can substract the same amount from both sides of the equation and maintain euality.
In this case, to solve r you substract 18 in both sides of the equation:
[tex]r+18-18=26-18[/tex]As 18-18 is 0;
[tex]r=8[/tex]Then, The solution of r+18=26 is r=8what is the answer to -6 2/5 + 7/3
Need help, please.Quick answer is okay
xplanation:
Step 1. e are given the following zeros of a polynomial function.
- 1 with a multiplicity of two, which means that is a zero two times:
[tex]\begin{gathered} x_1=1 \\ x_2=1 \end{gathered}[/tex]and the other two zeros are:
[tex]\begin{gathered} x_3=2+\sqrt{2} \\ x_4=2-\sqrt{2} \end{gathered}[/tex]And we need to find the equation that has these four zeros.
tep 2. 2R
[tex]f(x)=(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]tep 3. S
[tex]f(x)=(x-1)(x-1)(x-(2+\sqrt{2}))(x-(2-\sqrt{2}))[/tex]tep 4. S
[tex]f(x)=(x-1)(x-1)(x-2-\sqrt{2})(x-2+\sqrt{2})[/tex]tep 5. T
[tex]f(x)=(x^2-2x+1)(x-2-\sqrt{2})(x-2+\sqrt{2})[/tex]Then, let's multiply the second and third parentheses:
[tex]f(x)=(x^2-2x+1)(x^2-2x+x\sqrt{2}-2x+4-2\sqrt{2}-x\sqrt{2}+2\sqrt{2}-2)[/tex]Multiple terms cancel and the result is:
[tex]f(x)=(x^2-2x+1)(x^2-4x+2)[/tex]tep 6. TT
[tex]f(x)=x^4-4x^3+2x^2-2x^3+8x^2-4x+x^2-4x+2[/tex]Combining like terms:
[tex]f(x)=x^4-6x^3+11x^2-8x+2[/tex]This is shown in option D.
Answer:
D
[tex]f(x)=x^4-6x^3+11x^2-8x+2[/tex]
1. The total number of pancakes that can be made for a pancake breakfast fundraiser is directly related to the
amount of batter that is available. If 28 cups of batter make 112 pancakes, then which of the following is
closest to the number of pancakes that can be made with 45.4 cups of batter?
If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.
What is unitary method?The unitary approach is a technique for problem-solving that involves first calculating the value of a single unit, then multiplying that value to figure out the required value.
Given Data
28 cups of batter to make 112 pancakes
To make 1 unit
28 cups of batter = 112 pancakes
1 cup of batter = 4 pancakes
If we have 45.4 cups of batter, we can make,
1 cup of batter = 4 pancakes
45.4 cup of batter = 45.4(4)
45.4 cup of batter = 181 pancakes ( approximately )
If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.
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What are the order pairs for y=2/5x?(14,35)(30,1250,2010,440,2425, 5/2
Ok
y = 2/5x
ok
a) y = 2/5(14)
y = 28/5
y = 5.6 the first one is not an order pair
b) y = 2(30)/5
y = 60/5
y = 12 the second one is an order pair
c) y = 2/5(50)
y = 100/5
y = 20 the third one is an order pair
d) y = 2/5(10)
y = 20/5
y = 4 the four one is an order pair
e) y = 2/5(40)
y = 80/5
y = 16 the fifth one is not an order pair
f) y = 2/5(25)
y = 50/5
y = 10 the sixth one is not an order pair.
The solutions are (30, 12), (50, 20) and (10, 4)
step by step explanations for the following
g(x)=4x-5
f(x)= -2x-3
find (f•g) (-8)
and problems on the paper numbers 5-8 please
Answer:
5. [tex]\bold{(g \circ f)(-3) = 16}}[/tex]
6. [tex]\bold{h(h(-3x)) = -12x + 15 }}[/tex]
7. [tex]{\bold{f\left(g\left(x-3\right)\right):\quad 3x-21}}[/tex]
8. [tex]\bold{\text \bold g(f(-3x)) = -36x + 15}}[/tex]
Step-by-step explanation:
These are examples of composite functions.
What is a composite function?
A function by definition is a process that takes a collection of inputs and produces a corresponding collection of outputs in such a way that the process produces one and only one output value for any single input value.
Since we consider a function a process it makes sense to think of two functions acting in sequence to produce a single output. The output from one function is fed into the second function.
A composite function can be written as:Note that we can have [tex]f[/tex][tex]g[/tex] as the outer function, in which case the notation will be [tex](g \circ f)(x)[/tex] or [tex]g(f(x))[/tex]
Problem Solution
5. [tex]g(x) = x + 3 \;\text and\; f(x) = 3x + 4[/tex]
Find [tex](g \circ f)(-3) = g(f(-3))[/tex]
6. [tex]h(x) = 2x + 5[/tex]
Find [tex]h(h(-3x))[/tex]
[tex]7.\;\;\;g\left(x\right)\:=\:x-\:3,\:f\left(x\right)\:=\:3x\:-\:3\\\\\text{Find } \:f\left(g\left(x-3\right)\right)[/tex]
[tex]\mathrm{For}\:g=x-3\:\mathrm{substitute}\:x\:\mathrm{with}\:x-3[/tex].[tex]\bold{8.\;\;g(x) = 3x + 3, f(x) = 4x + 4}\\\\\bold{\text{Find } g(f(-3x))}[/tex]
[tex]\text {For}\:f(x) =4x+4\:\mathrm{substitute}\:x\:\mathrm{with}\:-3x}[/tex]HELP WITH 1 AND 2 PLEASE 20 POINTS AND BRAINLIEST SHOW YOUR WORK!!!!!!
1. The least number of hours that.Kee can work is 7 hours.
2. The maximum number of miles that Julie will drive will be 272 miles.
How to illustrate the information?1. Lee makes $64 per hour and he wants to make no less than $400 each hours for the trip. The number of hours will be:
Let the number of hours = h
64h >= 400
Divide
h >= 400/64
h >= 6.25
The least hour should be 7 hours.
2. The maximum number of miles that Julie will drive will be:
44(3) + 0.25m = 200
m = number of miles
132 + 0.25m = 200
0.25m = 200 - 132
0.25m = 68
m = 68 / 0.25
= 272
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What is −12÷2/3?
Responses
−36
−24
−18
−8
denmark uses kroner as its currency. Before a trip to denmark. Mia wants to exchange
$1700 for kroner.
bank a
dollars kroner
80 408
100 510
120 612
Denmark uses kroner as its currency. Before a trip to Denmark. Mia will get 8670 Kroner in exchange for $ 1700.
bank A
Dollars ($) Kroner
80 408
100 510
120 612
Since $ 80 = 408 Kroner
=> $ 1 = 408 / 80 = 5.1 Kroner . . . . . . conversion rate of $ to Kroner)
=> $ 1700 = 1700 x 5.1 = 8670 Kroner
Hence Mia will get 8670 Kroner in exchange for $ 1700
The exchange rate of conversion from $ to Kroner is arrived at by applying Unitary System of calculation in arithmetic (mathematics).
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coffee loses 12% of its weight when roasted. How much fresh coffee do you need to obtain 14 2/25 lb of roasted coffee
16 fresh coffee are needed to obtain 14 2/25 lb of roasted coffee.
How to calculate the number of fresh coffee needed ?Coffee loses 12% of it's weight when it is roasted
The number of fresh coffee that is needed to obtain 14 2/25 lb of roasted coffee can be calculated as follows
let y represent the number of fresh coffee needed
100%-12%
= 88%
= 88/100
= 0.88
14 2/25
= 352/25
= 14.08
The number of fresh coffee can be calculated as follows
0.88y= 14.08
y= 14.08/0.88
y= 16
Hence to obtain 14 2/25 lb of roasted coffee, 16 fresh coffee is required.
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Answer:
16 lbs
Step-by-step explanation:
Calculate the circumference of a circle with a radius of 15 inches .Use 3.14 for pi.Round answer to the nearest tenth ,if necessary
The circumference of a circle whose radius is 15 inches measures 94.2 inches.
How to find the circumference of the circle?For a circle of radius R, the circumference is given by the formula:
C = 2*pi*R
Where pi is 3.14
In this case, we know that the radius is 15 inches, then we can write:
R = 15 in
Replacing that in the circumference formula we get:
C = 2*3.14*15 in = 94.2 inches.
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use this equation to write an equation that has many /infinite solutions, no solution one solution y =3x + 4
the initial expression is:
[tex]y=3x+4[/tex]So this equation has already one solution
Now if we want to have infinit solution we an rest 3x so:
[tex]\begin{gathered} y=3x-3x+4 \\ y=4 \end{gathered}[/tex]So x can have any value, so there are infinit solutions
And to have no solutions we can add 5 -y at the left an
write the expression as a power and evaluate it. 16*32
The expression as power [tex]16^{3/2}[/tex] is 64.
What are exponents and power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
Given:
[tex]16^{3/2}[/tex]
using law of exponent
[tex]x^{(a * b)} = (x^a)^b[/tex]
Now, splitting 16 as 4 square
[tex]16^{3/2}[/tex]
=(4²[tex])^{3/2}[/tex]
=4³
=4 x 4 x 4
=64
Hence, expression as power [tex]16^{3/2}[/tex] is 64.
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Answer: 16^2.25
This is the correct answer thanks
Simplify fully the following
2√5 × 5√5
2√3 x 3√8
how do i solve this
We are basically asked to perform the product of expressions that contain complex numbers a s roots of polynomials. So it is essential to identify the complex root in order to facilitate our products that otherwise could be really time consuming.
First product:
(x + 3 + 5i) (x + 3 - 5i) we are going to write as: ((x +3) +5i) ((x+3) - 5i). So this is going to be interpreted as a difference of squares (a + b) ( a - b) = a^2 - b^2:
((x +3) +5i) ((x+3) - 5i) = (x+3)^2 - (5i)^2 = (x+3)^2 - (-25) = (x+3)^2 + 25
We are using the fact that (i)^2 = -1 to convert - 25 (i)^2 = + 25
Now we solve the square of the binomial (x+3) , that is:
(x+ 3)^2 = x^2 + 6x + 9
Now this combined with + 25 gives: x^2 + 6x + 34 This is one of the options in blue background shown at the tops (the fourth one starting from the left)
Second product:
(x - 4i) (x + 4i) which is an easirer product than the one above because we can solve it just using difference of squares: (a - b) (a + b) = a^2 - b^2:
(x - 4i) (x + 4i) = x^2 - (4i)^2 = x^2 - 16 (i)^2 = x^2 +16
This is the second expression in blue background from left to right.
Third product:
(x - 6 + i) (x - 6 - i) for which we apply the same technique as in the first product we solve above:
(x - 6 + i) (x - 6 - i) = ((x - 6) + i) ((x - 6) - i) = (x-6)^2 - (i)^2 = (x-6)^2 - (-1) = (x-6)^2 + 1 = x^2 - 12 x + 36 + 1 = x^2 - 12 x + 37 which is the very first expression in blue background in the image you uploaded.
Olease move the bue background boxes so as to match the indicated products.
Hi I need help on my homework only number 1
) Let us assume that the interest was compounded annually. The formula for calculating compound interest is expressed as
A = P(1 + r/n)^nt
where
A is the amount after t years
P is the principal or initial amount invested
r is the interest rate
n is the number of compounding periods in a year
t is the number of years
From the information given,
P = 130
r = 4% = 4/100 = 0.04
n = 1 because it was compounded once in a year
t = 10
By substituting the values into the formula, we have
A = 130(1 + 0.04/1)^1 * 10
A = 130(1.04)^10
A = 192.43
Rounding to the nearest whole number, the amount after 10 years is $192
PLS HELP!! 20 POINTS ASAP
18 5/12+ 8 10/17 + 23 7/12 + 28 7/17
Answer:
79
Step-by-step explanation:
same thing as 79/1
Hey I really need help on this question
We have
[tex]9x+5y-10[/tex]We will substitute the values given
x=6 y=1
[tex]9(6)+5(1)-10[/tex]we solve the operations in order to obtain the result
[tex]54+5-10=49[/tex]the answer is 49
I need help with the whole question
Given:
[tex]\begin{gathered} f(x)=2x^2-4x-6 \\ g(x)\text{ = 3x-4} \\ h(x)\text{ = }\frac{2}{x} \\ \end{gathered}[/tex]1.1.1 The equation of the reflection of g(x) in the x-axis is of the form:
The rule for the reflection in the x-axis:
[tex](x,y)\rightarrow\text{ (x,-y)}[/tex]Applying the rule:
[tex]\begin{gathered} g^{\prime}(x)\text{ = -g(x)} \\ =-(3x\text{ -4)} \\ =\text{ 4 -3x} \end{gathered}[/tex]Hence, g'(x) = 4-3x
1.1.2 The equation of the reflection of h(x) in the y-axis.
The rule for reflection in the y-axis:
[tex](x,y)\rightarrow\text{ (-x,y)}[/tex]Applying the rule:
[tex]h^{\prime}(x)\text{ = }\frac{2}{-x}[/tex]Hence, h('x) = 2/-x
1.1.3 The values of k for which :
[tex]k=2x^2-4x-6[/tex]Re-arranging:
[tex]\begin{gathered} 2x^2-4x-6-k\text{ =0} \\ 2x^2-4x\text{ -(6+k) = 0} \end{gathered}[/tex]Using the rule that for an equation to have non-real roots, the discriminant (D) must be less than zero.
[tex]\begin{gathered} D=b^2-4ac \\ (-4)^2\text{ -4(2)-(6+k) }<\text{ 0} \end{gathered}[/tex]Simplifying we have:
[tex]\begin{gathered} 16\text{ +48+8k }<\text{ 0} \\ 64\text{ + 8k }<\text{ 0} \\ 8k\text{ }<\text{ -64} \\ \text{Divide both sides by 8} \\ \frac{8k}{8}\text{ }<\frac{-64}{8} \\ k\text{ }<\text{ -8} \end{gathered}[/tex]Hence, the values of k for which the equation has non-real roots is that k must be less than -8
1.1.4 The average gradient of f(x) between x=-4 and x=0:
First, we need to find the value of f(x) at x=-4.
[tex]\begin{gathered} f(-4)=2(-4)^2\text{ -4(-4) -6} \\ =\text{ 32+16 -6} \\ =\text{ 42} \end{gathered}[/tex]Next, we must find the value of f(x) at x=0:
[tex]\begin{gathered} f(0)=2(0)^2-4(0)\text{ -6} \\ =\text{ -6} \end{gathered}[/tex]Using the average gradient formula:
[tex]\begin{gathered} \text{Average gradient = }\frac{y_B-y_A}{x_B-x_A} \\ =\text{ }\frac{-6-42}{0-(-4)} \\ =\frac{-48}{4} \\ =\text{ -12} \end{gathered}[/tex]Hence, the average gradient is -12
Question
Simplify the expression:
(4/9)^3
Answer:
Step-by-step explanation:
(4^3/(9^3)
= 64/729 or0.09
Help me please
15+ points
The equation is y=5x+16.
How to form the required equation?The formula y=mx+b is expressed in slope-intercept form. We are aware of the slope (m) as well as a point (-2,6). We now require the y-intercept (b).We need to enter the information we are aware of in order to solve the y-intercept (b).Y = 6, M = 5, and X = -2 are known values. The equation must be like this: 6=5(-2)+bContinuing, 5(-2) is just 5 times -2, or -10. The new formula is 6=-10+b.Since we must repeat this process for both sides, we must add 10 to the right side to cancel it out and 10 to the left to obtain b. 6+10=-10+10+bB must therefore be 16 because of this.The last step is to construct the equation, where all that is required is to correct the values of m and b in the slope-intercept equation y=mx+b. We know that m is 5 and b is 16.y - 6 = 5(x - (-2)) y=5x+16Therefore, y=5x+16 is the solution.To learn more about equations, refer
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Match each unit of measurement on the right with the appropriate measurement system on the left. The answer options on the left will be used more than once.Metric system U. S. Customary SystemCentiliterYardPoundMilligramMileKilometer
Metric system:
Centiliter
Miligram
Kilometer
U.S. Customary System:
Yard
Pound
Mile
The boxplot below shows salaries for Construction workers and Teachers.ConstructionTeacher20254530 35 40Salary (thousands of S)50If a person is making the median salary for a construction worker, they are making more than what percentage ofTeachers?They are making more than% of Teachers.Check Answer
It is known that that the median divides the range into half.
And the first and third quartiles are the landmark for 25% and 75% of the data values.
Therefore, a dot plot is divided into 4 parts, each of ehich represents 25% of the population.
In the given dot plot diagram, it is observed that the mean of the construction worker's salary, coincide with the upper quartile of the salary., at $45,000
It means that 50% population of construction workers is getting at most $45,000 while 75% population of teachers is getting at most $45,000.
So if a construction worker is making the median salary i.e. $45,000, so he/she will be making more than 75% of the teachers.