False, for both statements.
For the first statement, let A be an n x n matrix. If for two vectors y and z of Rⁿ we have Ay = Az, it does not necessarily mean that y=z. It is possible that A is a singular matrix, meaning that it does not have an inverse. In this case, there could be multiple vectors that would give the same result when multiplied by A. Therefore, it is not always true that y=z.
For the second statement, if A is a matrix of size n x n such that A³ = Iⁿ (where Iⁿ is the identity matrix of size n), it does not necessarily mean that A is invertible. It is possible for a matrix to have a power that equals the identity matrix, but not have an inverse. For example, consider the matrix A = [[0,1],[0,0]]. A² = [[0,0],[0,0]], and A³ = [[0,0],[0,0]], which is equal to I². However, A does not have an inverse, as its determinant is 0. Therefore, it is not always true that A is invertible if A³ = Iⁿ.
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Ps show work :D
Will mark BRAINLIST!!!
Given trigonometric equation is equal to 2 so the it has been proved.
what is trigonometric identity?
A trigonometric identity is a mathematical equation that expresses a relationship between trigonometric functions of an angle. These identities are true for all values of the angle, and they allow us to simplify expressions involving trigonometric functions, manipulate them algebraically, or evaluate them more easily.
Trigonometric identities include basic relationships such as [tex]sin^2(x) + cos^2(x) = 1,[/tex] as well as more complex identities involving multiple functions such as the Pythagorean identity.
According to the question:
Let us begin by applying the trigonometric identity[tex]cos^2(x) + sin^2(x) = 1,[/tex]which is true for any angle x. Solving for[tex]cos^2(x)[/tex], we get [tex]cos^2(x) = 1 - sin^2(x).[/tex]
Using this identity, we can rewrite the given equation as
[tex]1 - sin^2((1/8)^2) + 1 - sin^2(3n/8) + 1 - sin^2(5n/8) + 1 - sin^2(7n/8) = 2[/tex]
Simplifying, we get:
[tex]4 - (sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8)) = 2[/tex]
Rearranging, we get:
[tex]sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8) = 2[/tex]
Now, let us apply the trigonometric identity [tex]sin^2(x) + cos^2(x) = 1[/tex], which is true for any angle x. Solving for [tex]sin^2(x),[/tex] we get [tex]sin^2(x) = 1 - cos^2(x)[/tex].
2=2
Therefore, the equation is true
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The length of the base is 45 inches and the height of the ramp is 28 inches.
Enter the length, z of the ramp in inches.
Based, on the given information, the length of the ramp z, is equal to 53 inches.
What is a Right Angled Triangle?A triangle is said to be right-angled if one of its internal angles is 90 degrees, or if any one of its angles is a right angle. The right triangle or 90-degree triangle is another name for this triangle. In geometry, the right triangle is significant.
A triangle is said to be right-angled if one of its edges is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the parts that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equivalent to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three edges are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposing the 90° angle, the hypotenuse in this case is the longest side. When the positive number sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
In this question, the base, the height and the length of the ramp form a right angled triangle.
To find the length, we will use Pythagoras theorem, which states that,
(hypotenuse)² = (base)²+ (height)²
Substituting the values, we get
x²=45²+ 28²
x²= 2809
x=√2809
x=53 inches
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Simplify $\frac{\sqrt{40\cdot9}}{\sqrt{49}}$.
The simplified expression of the given expression is [tex]\frac{6\sqrt{10}}{7}$.[/tex]
What is expression ?
An expression is a mathematical phrase that can contain numbers, variables, operators, and symbols. It can be a combination of terms, factors, and/or coefficients, and may involve addition, subtraction, multiplication, division, exponents, roots, and/or other mathematical operations. Expressions can be simplified, evaluated, or manipulated using algebraic rules and properties.
We can simplify the expression as follows:
[tex]\frac{\sqrt{40\cdot9}}{\sqrt{49}}=\frac{\sqrt{4\cdot10\cdot3\cdot3}}{\sqrt{7\cdot7}}\\ \\ \\=\frac{\sqrt{4}\cdot\sqrt{10}\cdot\sqrt{3}\cdot\sqrt{3}}{\sqrt{7}\cdot\sqrt{7}}\\ \\ \\=\frac{2\cdot3\sqrt{10}}{7}\\ \\ \\={\frac{6\sqrt{10}}{7}}.[/tex]
Therefore, the simplified expression of the given expression is [tex]\frac{6\sqrt{10}}{7}$.[/tex]
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Solve the equation. 4(x - 2) = 2(2x + 6) 4x – [?] = [__] + [__] First we must use the distributive property to expand our equations. Hint: Calculate and enter the value of 4•2. ______________
The equation 4(x - 2) = 2(2x + 6) has no solution.
To solve the equation 4(x - 2) = 2(2x + 6), we must first use the distributive property to expand the equations. The distributive property states that a(b + c) = ab + ac.
Using the distributive property, we can expand the equation as follows:
4(x - 2) = 2(2x + 6)
4x - 8 = 4x + 12
Next, we must isolate the variable on one side of the equation. We can do this by subtracting 4x from both sides of the equation:
-8 = 12
This equation is not true, so there is no solution to the equation 4(x - 2) = 2(2x + 6).
In conclusion, the equation 4(x - 2) = 2(2x + 6) has no solution.
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Which of the following lists the sides of the triangle in order of length, from longest to shortest?
Answer: EF, DF, DE
Step-by-step explanation:
The smaller the opposite angle, the smaller the side, and vice versa.
∠EDF = 85°
∠DEF = 60° (Because the total degrees in a triangle must be 180°)
∠DFE = 35°
EF, DF, DE
Hope this helps!
write an expression and then solve. three less than one-fourth of the the product of eight thirds and nine
Step-by-step explanation:
3 - (1/4)×(8/3 × 9)
3 - (1/4)×(8×9/3)
3 - (1/4)×(8×3)
3 - (1/4)×24
3 - 24/4
3 - 6 = -3
work. 32. Write an equation for a function that has the shape of y=x^(2), but shifted right 2 units and down 1 unit.
The answer of equation for the function is y=(x-2)^(2)-1.
The equation for a function that has the shape of y=x^(2), but shifted right 2 units and down 1 unit is y=(x-2)^(2)-1.
To shift a function to the right, we subtract the amount of the shift from the x variable.
In this case, we want to shift the function 2 units to the right, so we subtract 2 from x: (x-2).
To shift a function down, we subtract the amount of the shift from the entire function.
In this case, we want to shift the function down 1 unit, so we subtract 1 from the entire function: (x-2)^(2)-1.
Therefore, the equation for the function is y=(x-2)^(2)-1.
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What are the quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+2?
When [tex]3x^{4}-x^{2}[/tex] is divided by [tex]x^{3}-x^{2}+2[/tex], the quotient is 3x and the remainder is [tex]5x^2-2x[/tex].
To see why, we perform long division as follows:
[tex]3x[/tex]
[tex]x^3 - x^2 + 2 | 3x^4 + 0x^3 - x^2 + 0x + 0[/tex]
[tex]- 3x^4 + 3x^3 - 6x^2[/tex]
-----------------------
[tex]3x^3 - 7x^2[/tex]
[tex]- 3x^3 + 3x^2 - 6x[/tex]
-------------------
[tex]5x^2 - 2x[/tex]
The divisor is [tex]x^3 - x^2 + 2[/tex] and the dividend is [tex]3x^4 - x^2[/tex]. We start by dividing the highest degree term of the dividend by the highest degree term of the divisor, which gives 3x. We then multiply the divisor by this quotient and subtract the result from the dividend. We repeat this process with the resulting polynomial until the degree of the remainder is less than the degree of the divisor.
In this case, the remainder is [tex]5x^2-2x[/tex], which has a degree of 2 (less than the degree of the divisor). Therefore, we have found the quotient and remainder of the division.
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A quadrilateral has two angles that measure 216° and 102°. The other two angles are in a ratio of 10:11. What are the measures of those two angles?
(I would do this, but I'm in a rush right now sorry!)
Answer:
20° and 22°
Step-by-step explanation:
Quadrilaterals are shapes with 360°. Since we are given two known angles, we can subtract them from 360. 360 - 216 - 102 = 144 - 102 = 42
Because the others are in a ratio of 10:11, the only possible degree combination will be 20° and 22°
Multiply.
2 1/4 x 5
Answer with a mixed number in simplest form.
Answer: 11 1/4
Step-by-step explanation:
To multiply fractions, you must use the improper form so...
2 1/4 x 5 =
9/4 x 5 =
45/4 =
11 1/4
Hope this helps!
Please help me i have a screenshot
2 1/8 pints
2.125 pints
find the sale price of a $36 item after a 50% discount
Answer:$18
Step-by-step explanation: Since 50% is half of a hundred and the item is half off, you multiply 36 by 0.5 and get $18. This is the price of the item with the sale and the the discount
Answer:
18$
Step-by-step explanation:
go to Safari and look it up is how I got the answer
Isha is a pet sitter.
She earns $5 for each cat.
She earns $12 for each dog.
Last week, Isha pet sat for 11 cats and 7 dogs.
How much money did Isha earn pet sitting last week?
Answer: $139.00
Step-by-step explanation: 5x11 = 55
12x7 = 84
55+84=139
Distributive Property of 7/8(4+8b)
Answer: 7/2 + 7b
Step-by-step explanation:
When applying the distributive property, you want to start by identifying which value you are distributing. That value in this case will be 7/8.
7/8 is going to be multiplied with 4, then multiplied with 8b, and you will then find the sum of those to products:
( (7/8) * 4 ) + ( (7/8) * (8b) )
The first product simplified will be 7/2.
The second product simplified will be 7b.
The sum of those two products is: 7/2 + 7b.
Hope this helps.
Calculate the simple interest earned on an investment of $6740 at 5% per year for 3 years. Give the answer to the nearest cent.
intrest=$
Answer:
1011.00
Step-by-step explanation:
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Sam went to play video games in Video Game Central arcade. Video Game Central charges $10 to get into the arcade and then $1 per game played
The mentioned relationship is an additive relationship as the total cost is not proportional to the number of games played.
To represent the relationship between the total cost, y, and the number of games played, x, we can create a table, graph, and equation as follows:
Number of games played (x) Total cost (y)
0 10
1 11
2 12
3 13
4 14
5 15
The equation that represents this relationship is: y = 1x + 10
Where 10 is the fixed cost to enter the arcade and 1 is the cost per game played.
To represent this relationship graphically, we can plot the points from the table on a graph. Refer to the image attached with this answer.
This graph shows that the relationship between the total cost and the number of games played is a straight line with a positive slope.
This relationship is an additive relationship because the total cost is not proportional to the number of games played. If the relationship was proportional, the cost per game played would remain constant regardless of the number of games played. In this case, the cost per game played is always $1, but the total cost increases by $1 for each additional game played.
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The complete question is :
Sam went to play video games in Video Game Central arcade. Video Game Central charges $10 to get into the arcade and then $1 per game played. Represent the relationship between total cost, y, and number of games played, x using a table, graph and equation. Is this relationship a proportional or additive relationship? Explain.
For the piecewise function, find the values h(- 8), h(-3), h(2), and h(5). -2x 10, for x< -7 2. x+3, forx22 h(x) = for 7sx<2 h(-8) = h(-3) = h(2) = h(5)
The numeric values of the piece-wise function are given as follows:
h(-8) = 26.h(-3) = 16.h(2) = 4.h(5) = 7.How to calculate the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression.
A piece-wise function is a function that has different definitions, based on the input interval of the function.
For x < 2, the function is defined as follows:
h(x) = -2x + 10.
Hence the numeric values on the interval are obtained as follows:
h(-8) = -2(-8) + 10 = 26.h(-3) = -2(-3) + 10 = 16.For x >= 2, the function is defined as follows:
h(x) = x + 2.
Hence the numeric values on the interval are obtained as follows:
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Kayleigh walks 5/8 to school every day how far does she walk to school in 5 days
Answer:
Step-by-step explanation: First you do 5*5 and get 25. Then you do 25/8 and get 3 1/8.
How are the side lengths of the preimage and dilated image related?
Answer:
The dilated image has half the dimensions of the pre-image
So the pre-image is dilated by a scale factor of 1/2 (0.5)
Step-by-step explanation:
The side lengths of the dilated image is related to the preimage by a division of 2
How to determine the how the side lengths are relatedFrom the question, we have the following parameters that can be used in our computation:
The figure
Where we have
Pre-Image = PQRS
Image = P''Q'R'S'
From the figure, we can see that
The side lengths of P''Q'R'S' is half of the side lengths of PQRS
This means that
(x, y) = 1/2(x, y)
Hence, the transformation is (x, y) = 1/2(x, y)
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Find all values of 1 for which det(A) = 0, using the method of this section. A=|λ-6 0 0| . |0 λ 4| . |0 5 λ-1| λ 1=_____ λ 2=_____ λ 3=_____ Fill the upper blank with the greater value of lif it exists. Fill the blank with the symbol "x" if there is no corresponding 1.
A = |λ-6 0 0| . |0 λ 4| . |0 5 λ-1| λ 1= 4.79 λ 2= 4.79 λ3 = 4.79, as the highest value of lif it exists is 4.79. therefore X=4.79
To find the values of λ for which det(A) = 0, we need to solve the equation det(A) = 0. The matrix determinant of a 3x3 matrix A is given by:
[tex]det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)[/tex]
In this case, the matrix A is:
A = |λ-6 0 0|
|0 λ 4|
|0 5 λ-1|
So, the determinant of A is:
[tex]det(A) = (λ-6)(λ(λ-1) - 4*5) - 0(0(λ-1) - 4*0) + 0(0*5 - λ*0)[/tex]
Simplifying the equation, we get:
[tex]det(A) = (λ-6)(λ^2 - λ - 20)[/tex]
Setting det(A) = 0, we can find the values of λ:
[tex](λ-6)(λ^2 - λ - 20) = 0[/tex]
This equation has three solutions:
[tex]λ 1 = 6λ 2 = (-1 + √81)/2 ≈ 4.79λ 3 = (-1 - √81)/2 ≈ -5.79[/tex]
So, the answer is:
λ 1 = 6
λ 2 = 4.79
λ 3 = -5.79
The greater value of λ is λ 2 = 4.79.
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What is the solution of this inequality?
Answer: C
Step-by-step explanation:
vIf you go out to eat with 3 friends and your meal was $54.55, and you should tip the waiter 20%. If the bill is shared equally, how much should each person pay?
Each person should pay $16.37.
Calculate the costIf the meal was $54.55 and you should tip the waiter 20%, the total cost of the meal would be $54.55 + ($54.55 * 0.20) = $65.46.
If the bill is shared equally among 4 people, each person should pay $65.46 / 4 = $16.37.
Therefore, each person should pay $16.37 for the meal. Step-by-step explanation:
1. Calculate the tip by multiplying the cost of the meal by 20% (0.20): $54.55 * 0.20 = $10.91
2. Add the tip to the cost of the meal to get the total cost: $54.55 + $10.91 = $65.46
3. Divide the total cost by the number of people to get the cost per person: $65.46 / 4 = $16.37
4. The final answer is $16.37 per person.
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When 3x^(2)-22x+26 is divided by a polynomial, the quotient is 3x-4 and the remainder is 2 . Find the polynomial.
The polynomial that 3x^(2)-22x+26 is divided by is x - 6.
To find the polynomial that 3x^(2)-22x+26 is divided by, we can use the formula:
Dividend = Quotient * Divisor + Remainder
In this case, the dividend is 3x^(2)-22x+26, the quotient is 3x-4, and the remainder is 2. We can plug these values into the formula and solve for the divisor:
3x^(2)-22x+26 = (3x-4) * Divisor + 2
Next, we can rearrange the equation to isolate the divisor:
Divisor = (3x^(2)-22x+26 - 2) / (3x-4)
Divisor = (3x^(2)-22x+24) / (3x-4)
Now, we can use polynomial long division to find the divisor:
```
3x - 4 | 3x^2 - 22x + 24
- (3x^2 - 4x)
-------------
-18x + 24
- (-18x + 24)
-------------
0
```
Therefore, the divisor is x - 6.
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What is the solution of this inequality?
The whole number that is a solution for the inequality x ≥ 4 but is not a solution for the inequality x > 4 is 4.
Option B is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
here,
We have,
x ≥ 4 and x > 4
Now,
x ≥ 4 means that x can be 4 and greater than 4.
x > 4 mean x is greater than 4.
So,
4 is a solution to x ≥ 4 but not a solution to x > 4.
Thus,
4 is the whole number.
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36.7 divided by 0.7
Answer:
52.4285714286
Step-by-step explanation:
use a calculator
Answer: 52.4
Step-by-step explanation:
According to the Funda equation of the given polynomial equatior f(x)=-3x^(2)+4x-1
The solutions to the given polynomial equation are x = 1/3 and x = 1.
According to the given polynomial equation f(x)=-3x^(2)+4x-1, we can find the values of x by using the quadratic formula, which is x = (-b ± √(b^(2)-4ac))/(2a).
In this equation, a = -3, b = 4, and c = -1.
Plugging these values into the quadratic formula, we get:
x = (-(4) ± √((4)^(2)-4(-3)(-1)))/(2(-3))
Simplifying this equation, we get:
x = (-4 ± √(16-12))/(-6)
x = (-4 ± √4)/(-6)
x = (-4 ± 2)/(-6)
Therefore, the two possible values of x are:
x = (-4 + 2)/(-6) = -2/(-6) = 1/3
x = (-4 - 2)/(-6) = -6/(-6) = 1
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Write the standard equation of an ellipse with vertices at (2,-2) and (12,-2) and covertices at (7,1) and (7,-5).
(a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1
(b) (x+7)^2 / 25 + (y-2)^2 / 9 = 1
(c) (x-7)^2 / 9 + (y+2)^2 / 25 = 1
(d) (x+7)^2 / 100 + (y-2)^2 / 36 = 1
(e) (x-7)^2 / 100 + (y+2)^2 / 36 = 1
The correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.
The standard equation of an ellipse is (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1, where (h,k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the covertices.
In this case, the center of the ellipse is the midpoint of the vertices and covertices, which is (7, -2). The distance from the center to the vertices is 5 (12-7) and the distance from the center to the covertices is 3 (1-(-2)).
Therefore, the standard equation of the ellipse is (x-7)^2 / 25 + (y+2)^2 / 9 = 1, which corresponds to answer choice (a).
So the correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.
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College Algebra -3.1Modeling with Quadratics Angry Birss: * Cire cact aniwns. Hhe enty the fusctien to obraln yoar answerc. - Show all nocensary cakiadsina. - Wine your ancurers is complrte aeatrnces 1. Whor is the s-inerreept and nhat does a repreiert? 2. What is the ponatire eimerreps and whas doest throsetinaly tepereset? socirt?
The x-intercept is (-3,0) and the y-intercept is (0,9).
The x-intercept of a quadratic function is the point where the function intersects with the x-axis. This point represents the value of x for which the function is equal to 0. The x-intercept can be found by setting the function equal to 0 and solving for x.
The y-intercept of a quadratic function is the point where the function intersects with the y-axis. This point represents the value of y for which the function is equal to 0. The y-intercept can be found by setting x equal to 0 and solving for y.
1. The x-intercept of the function is (-3,0) and it represents the point where the function intersects with the x-axis.
2. The y-intercept of the function is (0,9) and it represents the point where the function intersects with the y-axis.
To find the x-intercept, set the function equal to 0 and solve for x:
0 = x^2 + 6x + 9
0 = (x+3)(x+3)
x = -3
To find the y-intercept, set x equal to 0 and solve for y:
y = 0^2 + 6(0) + 9
y = 9
Therefore, the x-intercept is (-3,0) and the y-intercept is (0,9).
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Find the unit rate.
Drove 275 miles in 5 hours
.02 miles per hour
275 miles per hour
50 miles per hour
55 miles per hour
Answer: 55 miles per hour.
To find the unit rate, divide the miles traveled by the time taken:
275 miles ÷ 5 hours = 55 miles per hour
Step-by-step explanation:
Does someone mind helping me with this problem? Thank you!
The amount we would have after 40 years will be $8183.27
What is an exponential growth?Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Given that, an amount increasing exponentially every two years and with a rate of 15% and the amount is $500, we need to find the amount we would have after 40 years.
Since, the amount is increasing exponentially every two years, therefore,
T = 40 / 2 = 20 years
A = P(1+0.15)²⁰
A = 500(1+0.15)²⁰
A = 500(1.15)²⁰
A = 8183.27
Hence, the amount we would have after 40 years will be $8183.27
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