The correct answer is option A. For P= -1/2 0 1/2 1/2 0 -1/2 0 0 1 D= 0 4 0 0 0 4 -1 0 0. The matrix can be diagonalized using the eigenvectors.
To diagonalize the matrix, the eigenvectors must be found first. The eigenvectors can be found by solving the characteristic equation and finding the eigenvalues. The eigenvalues of the matrix are 2 and -1. The eigenvectors associated with each eigenvalue are determined by solving the eigenvalue equation.
The eigenvectors for the matrix are [1, -2], [1, 2], [1, 0], and [0, 1]. After the eigenvectors are found, the matrix can be diagonalized by constructing the transformation matrix P. The transformation matrix P is composed of the normalized eigenvectors. The transformation matrix P is: P=[-1/2, 0, 1/2, 1/2, 0, -1/2, 0, 0, 1], and the diagonal matrix D is composed of the eigenvalues.
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how do i find the unit rate for 30 inches per 5 years
per year unit rate becomes 6 inches. This can be solved using the concept of unit rate.
What is an unit rate?A unit rate is a price for one of anything. This is expressed as a proportion with such a base of one. For instance, you would cover 7 yards on average every second if you covered 70 yards in 10 seconds. The ratios of 70 yards in 10 seconds and 7 yards in 1 second are both rates, however, the latter is a unit rate.
A rate is the ratio of two different measurement units, whereas a unit rate seems to be the ratio of two different units of measurement for just a single object.
unit rate for 30 inches per 5 years:
= 30 inches / 5 years
= 6 inches / 1 year
Thus, per year unit rate becomes 6 inches.
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Consider the parent function f(x) below and graph
The exponential function formula for the parent function is found to be
[tex]f(x) = 2^x[/tex]
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The general formula to find an exponential function is [tex]f(x) = ab^x[/tex]
From the given graph, we take two points on the graph : (1,2) and (2,4)
Substituting in the above equation, taking f(x) as y
[tex]ab^1 = 2\\\\ab^2 = 4[/tex]
Solving the above equations, we get
a= 1, b=2
So the parent function [tex]f(x) = 2^x[/tex].
Now using this function we can graph [tex]f(2x), -3f(x), 2f(2x)\\[/tex].
[tex]f(2x) = 2^{2x} = 4^x\\\\-3f(x) = -3 * 2^x\\2f(2x) = 2 * 4^x[/tex]
Therefore using the Desmos, the above exponential functions are graphed.
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Last year at a certain high school, there were 75 boys on the honor roll and 120 girls on the honor roll. This year, the number of boys on the honor roll increased by 24% and the number of girls on the honor roll increased by 10%. By what percentage did the total number of students on the honor roll increase
The total number of students on the honor roll increased by 20%.
Given that, 75 boys and 50 girls on the honor roll
=> boys increased by 24% = 75*24/100 = 18
So, the number of boys is increased by 18.
=> girls increased by 14% = 50*14/100 = 7
So, the number of girls is increased by 7.
After the increment, the number of boys and girls on the honor roll is 93 and 57, respectively.
Thus, the total number of students increased = 18+7 = 25
Therefore, the percentage increment in total = 25 / 125 * 100 = 20%
Hence, The total number of students on the honor roll increased by 20%.
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PLEASE HELP !!
What is the missing reason for line 6 in this proof?
CPCTC
This acronym stands for "corresponding parts of congruent triangles are congruent". The triangles being congruent leads to their corresponding pieces being the same length. It's like saying if two houses are identical, then the front doors must be identical as well. Notice how this builds off the fact the triangles are proven congruent in line 5.
The lines represented by the equations y= -1/3x+2and 5y+15x=-40
The two lines are neither parallel nor perpendicular to each other.
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 two equations of the lines are y= -1/3x+2 and 5y+15x=-40.
y= -1/3x+2
5y+15x=-40.
5y = -15x - 40
y =-3x - 40/3
Here the slopes of the lines are,
m₁= -1 / 3
m₂ = -3
For the lines to be parallel the slopes should be equal and for the lines to be perpendicular the slopes should be inverse and reciprocal.
Here the slopes are neither equal nor have the inverse reciprocal.
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11. Solve the inequality.
g-6> -1
Answer:
g>5
Step-by-step explanation:
Simply add 6 to both sides to get g>5
Find the lengths of the diagonals of rectangle WXYZ.
WY = 14x + 10
XZ = 11x + 22
The length of each diagonal is
units.
The length of each diagonal is √(196x^2 + 816x + 324) units.
What is the formula for diagonal length?The diagonal of a rectangle can be estimated using the hypotenuse formula, such as using the Pythagorean theorem calculator.
WX^2 = WY^2 + XZ^2
Given that WY = 14x + 10 and XZ = 11x + 22, we can substitute those values in the equation:
WX^2 = (14x + 10)^2 + (11x + 22)^2
WX^2 = 196x^2 + 816x + 324
WX = √(196x^2 + 816x + 324)
The same goes for the other diagonal, WZ.
WZ = √(196x^2 + 816x + 324)
So, the length of each diagonal is √(196x^2 + 816x + 324) units.
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How do you tell if a graph is linear quadratic or exponential?
A linear graph is one whose equation is in the form y = mx + b, where m and b are constants. A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants.
To determine if a given graph is linear, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = mx + b.
For example, if the two points on the graph are (2, 3) and (5, 7), then plugging these values into the equation gives us:
y = mx + b
3 = m*2 + b
7 = m*5 + b
Solving this system of equations gives m = 2 and b = -1, so the equation of the line is y = 2x - 1.
A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. To determine if a given graph is quadratic, calculate the equation of the parabola by finding three points on the graph and plugging them into the equation y = ax^2 + bx + c.
For example, if the points on the graph are (1, 6), (2, 13), and (3, 24), then plugging these values into the equation gives us:
y = ax^2 + bx + c
6 = a*1^2 + b*1 + c
13 = a*2^2 + b*2 + c
24 = a*3^2 + b*3 + c
Solving this system of equations gives a = 4, b = -5, and c = 6, so the equation of the parabola is y = 4x^2 - 5x + 6.
An exponential graph is one whose equation is in the form y = a*b^x, where a and b are constants. To determine if a given graph is exponential, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = a*b^x.
For example, if the two points on the graph are (2, 16) and (3, 24), then plugging these values into the equation gives us:
y = a*b^x
16 = a*b^2
24 = a*b^3
Solving this system of equations gives a = 2 and b = 2, so the equation of the line is y = 2*2^x.
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What does log () do in mathematics?
Log () helps to determine the single number to be multiplied.
Log stands for logarithm in algebra. The inverses of equations using exponents are called logarithms. Logs can be used to determine how many times one number needs to be multiplied to get another in its most basic form. For instance, to get 100 in the base-10 system, 10 must be multiplied by 10. In a base-10 system, the logarithm of 100 is therefore 2.
Log () expresses the power or exponent that a base number must be raised to or multiplied by in order to create another number in an ideal world. In situations where the user has data values that are significantly greater or lower than the other values, log scales are quite helpful. When displaying major percentage variations between data points, the user can also utilize a log scale.
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how do I find the slope of these points
(8,-4) and (2,-4)
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]
How do you know if its logarithmic or exponential?
The difference between logarithmic and exponential functions can be determined by looking at the form of the equation and by performing a calculation.
A logarithmic equation is written as log_b(x) = y, where b is the base and x and y are variables. An exponential equation is written as b^x = y, where b is the base and x and y are variables.
To determine if an equation is logarithmic or exponential, begin by comparing the form of the equation to the two equations above. If the equation is written in the form of log_b(x) = y, then it is a logarithmic equation. If the equation is written in the form of b^x = y, then it is exponential.
To perform a calculation, plug in a known value for x and then solve for y. For example, if the equation is log_2(x) = 4, then plug in x = 8. The calculation would then be:
log_2(8) = 4
This is a logarithmic equation, as the form of the equation matches log_b(x) = y.
If the equation is b^x = 16, then plug in x = 4. The calculation would then be:
2^4 = 16
This is an exponential equation, as the form of the equation matches b^x = y.
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Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. complete the diagram to show smaller and larger batches that would taste the same as lin's favorite blend. please
help it's due tomorrow
Answer:
that is the persons username I got it from
Step-by-step explanation:
3 and 7
6 and 14
9 and 21
12 and 28
15 and 35
Step-by-step explanation:
If the two numbers they give you are 9 and 21, then the cranberry's are 3 ounces and the apples are 7 fliud ounces, then you can divide and multiply them to your will.
What is the equation of the line graphed below?
Answer: -2/3x is the slope and the beginning amount is 5 so the equation would be -2/3x+5.
Step-by-step explanation:
Once you find the slope using the formula rise/run you will get 2/3 but since the slope is going downwards it would be -2/3 which gives you the mx. Now to find the beginning amount look where the line intersects the graph which will give you the equation.
CORRECT ANSWER WITH **STEPS** GETS BRAINLIEST
for the following questions, determine what values of x makes the rational expression equal to zero.
1. x+6 / x-4
2. (x+4)(x-2) / (x+6)
3. 2x+10 / 3x-12
thanks.
what is f for 1/8f = 3
Answer:
F = 24
Step-by-step explanation:
simplify 1/8
(1/8 x F) - 3 = 0
3 = 3/1 = 3 x 8/ 8
F x (3 x 8) / 8 F - 24/ 8
F - 24/ 8 = 0
F - 24/ 8 = 0 x 8
Answer:
24
Step-by-step explanation:
You want to know f for 1/8f = 3.
UndoMultiply the given equation by 8 to undo the multiplication by 1/8:
8(1/8f) = 8(3)
f = 24 . . . . . . . . simplify
The value of f is 24.
<95141404393>
For two weeks the highest temp each day was recorded in four different cities. Line L, M, N, & P are graphs of the temp over time in Lubbock, Memphis, New Orleans, & Phoenix. Which statement is true?
A. the high temp in Lubbock increased as time passed
B. the high temp in Memphis decreased steadily
C. Initially, the high temp was warmer in Phoethen in Memphis
D. The high temp in Phoenix rose faster than the temp in New Orleans
batch of hot chocolate is made with 21 teasoons of cocoa and 7 cups of milk.
How many teaspoons of cocoa are needed for every cup of milk?
On the double number line below, fill in the given values, then use
multiplication or division to find the missing value:
cups of milk
Answer:
Step-by-step explanation:
Ya
For what value of k is 4x 2 8xy k * y 2 9 The equation of a pair of straight lines?
The value 'k' for which '4x^2 + 8xy + ky^2 = 9' is the second degree equation of a pair of straight lines is 4.
Therefore the answer is 4.
A general second-degree equation of a pair of straight lines is given by:
ax² + 2hxy + by² + 2gx + 2fy + c = 0
Where a, b, c, d, e, and f are constants, x and y are variables.
For the equation to represent a pair of straight lines, the following conditions must be met :
abc + 2fgh - af² - bg² - ch² = 0
In the equation 4x^2 + 8xy + ky^2 = 9, a = 4, h = 4, b = k, g = f = 0 and c = -9.
That is 4×k×(-9) + 2×0×0×4 - 4×0² - k×0² + 9×4² = 0
4×k×9 = 9×4²
k = 4
--The question is incomplete, complete question is given below--
"For what value of k is 4x^2 + 8xy + ky^2 = 9 the equation of a pair of straight lines?"
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2 1/3 grams of spice A was mixed with 4 1/7 grams of spice B. The ratio of spice A to spice B is 1:
The ratio of spice A to spice B is : 49/87
Here, 2 1/3 grams of spice A was mixed with 4 1/7 grams of spice B.
First we convert the improper fraction into a proper fraction.
For improper fraction2 1/3,
2 1/3
= (2 × 3)/3 + 1/3
= 6/3 + 1/3
= (6 + 1)/3
= 7/3 which is a proper fraction.
and for 4 1/7
= (4 × 7)/7 + 1/7
= 28/7 + 1/7
= (28 + 1)/7
= 29/7
The ratio of spice A to spice B would be,
(2 1/3) / (4 1/7 )
= (7/3) / (29/7)
= (7/3) × (7/29)
= (7 × 7)/(3 × 29)
= 49/87
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Please help
me find the product
Answer:
cant answer sorry i didnt realize it was an equation
Step-by-step explanation:
subtract x2+2x+1-(x-3)
Answer:
(x to the second power)+x+4
Step-by-step explanation:
Ur welcome
Find the equation for the line running
to y = -5x + 5 and passes through the
perpendicular
point (10,7).
let's reword this a bit differently, since it looks jumbled
let's find the equation of a line that is perpendicular to y = -5x + 5, and it also passes through (10 , 7), well, keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-5}x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -5 \implies \cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5} \implies \cfrac{1}{ 5 }}}[/tex]
so we're really looking for the equation of a line with a slope of 1/5 and that it passes through (10 , 7)
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \\\\\\ y-7=\cfrac{1}{5}x-2\implies {\Large \begin{array}{llll} y=\cfrac{1}{5}x+5 \end{array}}[/tex]
50 POINTS!! Pls make sure the answers are correct and the work is shown
Answer all pls and show work
Answer:
it 33 pts not 50
The sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, write and solve a compound inequality to show the possible heights of the third tree.
A. 8 ≤ x ≤ 16
B. 8 ≤ x ≤ 18
C. 32 ≤ x ≤ 42
D. 56 ≤ x ≤ 66
The compound inequality that shows the possible heights of the third tree is 8 ≤ x ≤ 18
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, hence:
Sum of three palm tree heights = x + 8 + 16 = x + 24
The sum of three palm tree heights range from 32 to 42 feet. Hence:
32 ≤ x + 24 ≤ 42
32 - 24 ≤ x ≤ 42 - 24
8 ≤ x ≤ 18
The solution to the compound inequality is 8 ≤ x ≤ 18
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THIS IS A TEST!!!
HOW DO YOU SOLVE FOR X?
If you get this right, or you give an explanation. ill mark you as blranliest.
Answer:
[tex]x = \frac{9}{5} [/tex]
Step-by-step explanation:
[tex] - 7( - 7 \times ( - x - 1)) = 6 (- \times ( - 2x - 3))[/tex]
[tex] - 7 + 7x + 7 = 6 + 2x + 3[/tex]
[tex]7x - 2x = 6 + 3 + 7 - 7[/tex]
[tex]5x = 9[/tex]
[tex] \frac{5x}{5} = \frac{9}{5} [/tex]
[tex]x = \frac{9}{5} [/tex]
What is the domain and range of a composite function?
The domain of a composite function is the set of all possible inputs for both functions, and the range is the set of all possible outputs.
A composite function is the combination of two or more functions. The domain of a composite function is the set of all possible inputs for both functions. This means that the domain is the set of all the possible inputs that can be used in either of the functions that make up the composite function. The range of a composite function is the set of all possible outputs. This means that the range is the set of all the possible outputs that can be obtained by the combination of the two or more functions. When graphing a composite function, it is important to remember that the domain and range of the composite function are the union of the domain and range of the individual functions in the composite function. The domain and range of a composite function can be determined by first determining the domains and ranges of the individual functions and then combining them.
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Give your answer in the form y=ma + c, where m and c are integers or
fractions in their simplest forms.
Bookwork code, $79
Canalda
allowst
What is the equation of line H?
33
Line
Watch video
Answer? Helllppo
If p(x) = b² - 16b +32 and q(x) = -32b-32 what values of x does p(x)=q(x)?
The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.
Given that,
The functions are p(x) = b² - 16b +32 and q(x) = -32b-32
We have to find the x value when the functions are equivalent to each other.
We know that,
Take the functions
p(x) = b² - 16b +32 and q(x) = -32b-32
When the function are equivalent
p(x) = q(x)
b² - 16b +32 = -32b-32
b² - 16b +32 +32b+32=0
b² + 16b +64 = 0
Now find the factors for 64
64 = 8×8
b² + 8b + 8b +64 = 0
Taking common terms
b(b + 8) + 8(b + 8)=0
(b + 8)(b + 8)=0
b=8
Therefore, The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.
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Suppose that 15 inches of wire costs 90 cents. At the same rate, how many inches of wire can be bought for 72 cents?
Answer:
12 inches-----------------------------
15 inches of wire costs 90 cents, then 1 inch of wire costs:
90/15 = 6 centsThe length of wire for 72 cents:
72/6 = 12 inchesUse polar coordinates to find the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 36 and outside the cylinder x^2 + y^2 = 1.
The required volume of the given solid is (√16 - r²) -(-√16 - r²).
What is volume?The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.
Volume and the notion of length are connected.
Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.
The cubic meter (m3), a derived unit, is the SI unit of volume.
So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.
We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.
The solid's volume is (√16 - r²) -(-√16 - r²).
Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).
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Correct question:
Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.