Find the inverse of the following matrix,
if it exists.
[ -1 0 1]
A = [ 2 2 0]
[ 1 0 1]

Answer:

#1 No

#2 Yes

#3 No

#4 No

Hope this helps!

The following exponential rule is called the Product Rule.

What is exponential rule ?

Exponential rules are mathematical rules that govern the manipulation of exponential expressions, which involve terms that have a base raised to a power. Exponential rules are important in many areas of mathematics and science, particularly in algebra, calculus, and statistics.

According to the question:
The following exponential rule is called the Product Rule. It states that when multiplying two powers with the same base, you can add their exponents. The rule is:

[tex]a^m * a^n = a^(m+n)[/tex]

For example, [tex]2^3 * 2^4 = 2^(3+4) = 2^7 = 128[/tex]. This rule is fundamental in simplifying expressions and solving equations involving exponential functions.

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The answer is 7x^(8) + 9x^(7) - 2x^(3) + 2x^(2) - 5x + 9.

To add (7x^(8)-6x^(3)+2x^(2)+9) and (9x^(7)+4x^(3)-5x), we need to combine the like terms in both expressions. Like terms are terms with the same variable and exponent.

Combine the like terms in the first expression:
7x^(8) + 0x^(7) - 6x^(3) + 2x^(2) + 0x + 9

Combine the like terms in the second expression:
0x^(8) + 9x^(7) + 4x^(3) + 0x^(2) - 5x + 0

Add the two expressions together:
(7x^(8) + 0x^(8)) + (0x^(7) + 9x^(7)) + (-6x^(3) + 4x^(3)) + (2x^(2) + 0x^(2)) + (0x - 5x) + (9 + 0)

Simplify the expression:
7x^(8) + 9x^(7) - 2x^(3) + 2x^(2) - 5x + 9

Write the answer in descending order:
7x^(8) + 9x^(7) - 2x^(3) + 2x^(2) - 5x + 9

Therefore, the answer is 7x^(8) + 9x^(7) - 2x^(3) + 2x^(2) - 5x + 9.

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Answer:

Skeleton hand holding a piece of candy maybe?

Or a jack-o-lantern but its a poison apple.

OR a drawing of a witch's face in the reflection of a cauldron.

Step-by-step explanation:

Spooky Graveyard: Draw a creepy graveyard scene with tombstones, skeletons, and ghosts.

Jack-O-Lanterns: Draw a bunch of different jack-o-lanterns with different expressions and designs.

Haunted House: Draw a haunted house with creaky doors, broken windows, and bats flying around.

Witch's Cauldron: Draw a witch's cauldron bubbling with potions and ingredients.

Trick or Treaters: Draw a group of trick or treaters dressed up in costumes going from house to house.

Scary Trees: Draw a spooky forest with twisted, gnarled trees that look like they could come to life at any moment.

Monster Mash: Draw a bunch of different classic Halloween monsters, like Frankenstein's monster, vampires, and werewolves.

Zombie Apocalypse: Draw a post-apocalyptic scene with zombies wandering around and survivors trying to stay alive.

Black Cats: Draw some cute or creepy black cats with glowing eyes.

Halloween Candy: Draw a big pile of Halloween candy with all your favorite treats.

A pumpkin: Draw a simple pumpkin shape and add eyes, nose, and mouth. You can also add a stem on top and some vines on the sides.

Ghosts: Draw some simple white shapes for ghosts and add eyes and a mouth. You can also draw a white sheet around the ghost to make it look more spooky.

Skeletons: Draw a basic skeleton shape and add some bones. You can also add some spooky decorations, like spider webs or bats.

Witch hats: Draw a simple witch hat shape and add some details, like a buckle or a spider. You can also add some stars or a crescent moon in the background.

Bats: Draw a bat shape and add some details, like wings and ears. You can also draw a moon or some stars in the background to make it look more Halloween-like.

The statements that correctly interpret the scatter plot on the ages of the used cars is :

The scatter plot shows the number of miles that a car of a certain age would be expected to have driven. The data has a positive association to show that the older a car is, the more miles it would have driven.

There is a cluster of data points at 2 , 23 to show that a car of the age 2 would have been driven the same amount of miles in general.

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In interval notation, the the solution set in interval notation. (5)/(y-4)<9 is   (41/9, ∞).

Inequality is a mathematical statement that two values or expressions are not equal. It is represented by symbols, like >, <, or ≠, and is used to compare quantities or values.

To solve the inequality (5)/(y-4)<9, we need to isolate the variable on one side of the inequality. We can do this by multiplying both sides of the inequality by (y-4) and then simplifying.

(5)/(y-4)<9

5 < 9(y-4)

5 < 9y - 36

41 < 9y

y > 41/9

This means that any value of y greater than 41/9 will satisfy the inequality.

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A school fundraising event sold a total of 223 tickets and generated a total revenue of $955.90, 89 adult tickets and 134 child tickets were sold.

Let's use the following variables to represent the number of tickets sold:

Using this, we can write the following system of equations:

a + c = 223 (the total number of tickets sold is 223)

6.60a + 2.75c = 955.90 (the total revenue generated is $955.90)

To solve this system of equations, we can use any method of our choice, such as substitution or elimination. Here, we will use the elimination method:

(2.75a + 2.75c) - (6.60a + 2.75c) = 613.25 - 955.90

-3.85a = -342.65

Therefore, 89 adult tickets and 134 child tickets were sold during the fundraising event. We were given the total number of tickets sold and the total revenue generated by the school fundraising event. We used this information to set up a system of equations that describes the relationship between the number of adult tickets sold, the number of child tickets sold, and the total revenue generated. We solved this system of equations using the elimination method to find the number of adult and child tickets sold. The final answer is 89 adult tickets and 134 child tickets sold.

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(a) Yes, At α = .025, the sample show that portfolio A has significantly greater variance in rates of return than portfolio B. The correct hypotheses for this problem are H0: σA2/σB2 ≤ 1 versus H1: σA2/σB2 > 1.

The appropriate hypotheses are H0: σA2/σB2 ≤ 1 versus H1: σA2/σB2 > 1.  This is because we are testing if portfolio A has significantly greater variance in rates of return than portfolio B.

If the null hypothesis is true, then the ratio of the variances will be less than or equal to 1, meaning that portfolio A does not have greater variance than portfolio B. If the alternative hypothesis is true, then the ratio of the variances will be greater than 1, meaning that portfolio A does have greater variance than portfolio B.

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5(3)/(10),  5.338,  5.37,  (21)/(4).

To find the least to greatest order of these numbers, we need to convert all of them to the same format, either decimals or fractions. In this case, it is easier to convert the fractions to decimals.
5(3)/(10) = 5.3/10 = 0.53
(21)/(4) = 21/4 = 5.25

Now we can compare all of the numbers in decimal form:
0.53, 5.338, 5.37, 5.25

Next, we can arrange them in ascending order:
0.53, 5.25, 5.338, 5.37

Finally, we can convert the decimals back to fractions if necessary:
5(3)/(10), (21)/(4), 5.338, 5.37

Therefore, the correct order of these numbers from least to greatest is 5(3)/(10), (21)/(4), 5.338, 5.37.

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The undefined numbers are p = 0, p = 2, q = 0, and q = -2 for the given expression.

In arithmetic, the operation and interpretation of a function to make it simpler or easier to grasp is known as simplifying, and the process itself is known as simplification.

First, let's simplify the expression:

(4p - 8)/(p³ - 2p²) - (q + 2)/(q³ + 2q²) × (p/2q - p)

= 4(p - 2)/(p²(p - 2)) - (q + 2)/(q²(q + 2)) × p(1/2 - q)

= 4/p - 4/p² - p/2q² + p²/2q

= (8q² - 8pq - p³ + 2p²q)/(2pq²(p - 2))

Now, let's find the undefined numbers, which are the values of p and q that make the denominators equal to zero.

For the first fraction, p³ - 2p² = p²(p - 2) = 0 when p = 0 or p = 2.

For the second fraction, q³ + 2q² = q²(q + 2) = 0 when q = 0 or q = -2.

Therefore, the undefined numbers are p = 0, p = 2, q = 0, and q = -2.

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This is a geometric sequence because each term is obtained by multiplying the previous term by a constant value of 1/2. Option B

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the preceding term by a fixed non-zero number called the common ratio.

It can be represented by the formula a, ar, ar^2, ar^3, ..., where a is the first term and r is the common ratio. For example, 2, 4, 8, 16, 32 is a geometric sequence with a = 2 and r = 2.

In a geometric sequence, the ratio between any two consecutive terms is always the same.  For example: 2, 4, 8, 16, 32, 64, ... is a geometric sequence with a common ratio of 2.

This is a geometric sequence in 2,1,1/4,1/2,… because each term is obtained by multiplying the previous term by a constant value of 1/2. Option B

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Answer: transfers

Step-by-step explanation: now make sure you submit in time.

The greatest possible distance from  Austin to san Antonio is 335.77 mi, b. the Least possible distance to Austin to san Antonio is 120.03 mi.

Describe Distance?

Distance refers to the physical length or space between two points or objects. It is an important concept in mathematics, physics, and everyday life. Distance can be measured in various units such as meters, feet, kilometers, miles, or light-years, depending on the context and scale of the measurement.

In mathematics, distance is often measured using the Euclidean distance formula, which calculates the distance between two points in a plane or in three-dimensional space. The formula is given by:

[tex]d = √((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where d is the distance between the two points, (x1, y1) and (x2, y2).

In physics, distance is often used to describe the separation between two objects or particles. The distance between two objects can affect the strength of gravitational or electromagnetic forces between them. Distance is also an important concept in special relativity, where it is affected by the relative motion of observers and the distortion of spacetime.

a. Greatest possible distance from  Austin to san Antonio= Distance from Austin →Houston → san Antonio.

Austin - Houston = 146.43 mi

Houston - San Antonio = 189.34 mi

Total  distance= 146.43+ 189.34= 335.77 mi

b. Least possible distance to Austin to san Antonio= the shortest distance = x

By pythagoras theorem

[tex](189.34)²= (146.43)²+ x²x²= (189.34)²- (146.43)²x²= 35849.63- 21441.744x²= 14407.89x=√14407.89x= 120.03[/tex]

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The complete question is:

The solution of the quadratic equation is x=24/2 and x=-6/2.

To solve the quadratic equation 3x2-27x+60=0, you can use the method of factoring. You can factor this equation by taking out the common factor of 3 from the terms.

That leaves us with x2-9x+20=0, which can be factored into (x-10)(x-2)=0. To solve, you set each factor equal to 0, so x=10 and x=2 are the solutions.

If you forget how to factor on a multiple choice test, you can use other methods such as completing the square or the quadratic formula.

For this equation, completing the square would involve adding and subtracting 92/4 to both sides, which would give us (x-9/2)2=225/4. To solve, you would then take the square root of both sides, resulting in x-9/2=±15/2, or x=24/2 and x=-6/2.

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The solution set for the inequality is (-1, ∞) in interval notation. To solve the inequality, we need to isolate the variable on one side of the inequality sign. We can do this by using the following steps:

Step 1: Divide both sides of the inequality by 8 to simplify the equation.
8(2x+3)>8 → (2x+3)>1

Step 2: Subtract 3 from both sides of the inequality to isolate the variable.
(2x+3)>1 → 2x>-2

Step 3: Divide both sides of the inequality by 2 to find the value of x.
2x>-2 → x>-1

Step 4: Write the solution set using interval notation. Since the inequality sign is ">", we use a parenthesis to indicate that the solution does not include the endpoint -1.
x>-1 → (-1, ∞)

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The percentage of races with a finishing time between 64.5 and 65.5 seconds is given as follows:

68%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The measures in this problem are within one standard deviation of the mean, as:

Hence the percentage is of 68%.

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Answer:

2/3 (-9+3) simplifies to 2/3 (-6) which is equal to -4.

Step-by-step explanation:

To simplify 2/3(-9+3), we need to start by simplifying the expression inside the parentheses, which is -9+3=-6. Therefore, we can rewrite the expression as 2/3(-6).

Now we can apply the distributive property of multiplication over addition/subtraction to simplify further. This property states that a(b+c) = ab + ac. So, 2/3(-6) can be written as:

2/3 x -6 = 2/3 x (-1 x 6) = 2/3 x (-1) x 6 = -2/3 x 6

Now we just need to multiply -2/3 by 6, which gives us -12/3 or -4. Therefore, 2/3(-9+3) simplifies to -4.

Answer:

I assume the inequality is

[tex]\sf{ \dfrac{2c}{3} + 1 > 7}[/tex]

[tex]\sf{ \dfrac{2c}{3} > 7-1}[/tex]

[tex]\sf{ 2c> 18}[/tex]

[tex]\sf{ c > 9}[/tex]

The simple interest rate for this loan is 12.4%.

To find the simple interest rate, we can use the formula for simple interest, which is:
Simple Interest = Principal x Rate x Time

In this case, we are given the simple interest (\$496), the principal (\$12,000), and the time (4 months). We can plug these values into the formula and solve for the rate.
\$496 = \$12,000 x Rate x (4/12)

Simplifying the equation, we get:
\$496 = \$4,000 x Rate

Dividing both sides by \$4,000, we get:
Rate = 0.124

To convert this to a percentage and round to one decimal place, we multiply by 100 and round:
Rate = 0.124 x 100 = 12.4%

Therefore, the simple interest rate for this loan is 12.4%.

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The correct answer is option B) 1/3.

To evaluate the algebraic expression for the given value(s) of the variable(s), we need to substitute the value of x into the expression and simplify.

The expression is: x+4/4x+8

Substitute x = 3 into the expression:

3 + 4/(4*3) + 8

Simplify:

3 + 4/12 + 8

3 + 1/3 + 8

Combine the terms:

11 + 1/3

Convert to a common denominator:

33/3 + 1/3

Simplify:

34/3

Divide:

11 1/3

So the answer is 1/3, which is option B.

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The value of (x-y)² is m^2-4n.

To find the value of (x-y)², we can use the formula for the difference of squares:
(x-y)² = (x+y)² - 4xy

We are given that x+y = m and xy = n, so we can substitute these values into the formula:
(x-y)² = m² - 4n

Therefore, the value of (x-y)² is m²-4n.

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Surface area of a box with 12 as length, 10 as height and 3 as width is 372 square units.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

We have to find the surface area of a box

12 = length,

10 = height and

3 = width.

surface area =2lw+2lh+2hw

=2(12×3)+2(12×10)+2(10×3)

=2(36)+2(120)+2(30)

=72+240+60

=372 square units

Hence, surface area of a box with 12 as length, 10 as height and 3 as width is 372 square units.

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The restrictions for this equation are that y must be greater than or equal to 0, since the square root of a negative number is not a real number. So, the restrictions for this equation are y ≥ 0.

To solve the equation √y + 6 = 4, we first need to isolate the square root on one side of the equation. We can do this by subtracting 6 from both sides of the equation:
√y = 4 - 6
√y = -2

Now, we need to square both sides of the equation to get rid of the square root:
y = (-2)^2
y = 4

So, the solution to the equation is y = 4. However, we need to verify this solution by plugging it back into the original equation:
√(4) + 6 = 4
2 + 6 = 4
8 = 4

This is not true, so there are no solutions to the equation.

The restrictions for this equation are that y must be greater than or equal to 0, since the square root of a negative number is not a real number. So, the restrictions for this equation are y ≥ 0.

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17. Yˉ is the set of all positive, odd integers.
18. Xˉ is the set of all integers that are not in X, which is {6, 7, 8, 9, 10...}.
19. Yˉ is the set of all positive, odd integers, which can be expressed in set-builder notation as Yˉ = {2n + 1 | n ∈ Z+}.
20. X∩Y is the set of all elements that are in both X and Y, which is {2}.
21. X∪Y is the set of all elements that are in either X or Y, which is {1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20...}.
22. Xˉ∩Y is the set of all elements that are in both Xˉ and Y, which is {6, 8, 10, 12, 14, 16, 18, 20...}.
23. Xˉ∪Y is the set of all elements that are in either Xˉ or Y, which is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20...}.
24. X∩Yˉ is the set of all elements that are in both X and Yˉ, which is ∅ (the empty set).
25. X∪Yˉ is the set of all elements that are in either X or Yˉ, which is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20...}.
26. Xˉ∩Yˉ is the set of all elements that are in both Xˉ and Yˉ, which is {6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20...}.
27. Xˉ∪Yˉ is the set of all elements that are in either Xˉ or Yˉ, which is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20...}.

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By the concept of vertically opposite angles, m∠MDH = 44°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know, Pair of vertically opposite angles are equal.

Therefore, 2y + 130 = 3y + 127.

y = 3.

So, 2y + 130 = 136°

Again, ∠PDG = ∠MDH.

Now, 2∠PDG = 360° - 2(136°)

2∠PDG = 360° - 272°.

∠PDG = 44° = ∠MDH.

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No, she will not earn enough money to buy the $59 pair of headphones after working 4(3)/(4) hours. She needs $23.375 more.

To find out how much money she will earn after working 4(3)/(4) hours, we can multiply her hourly wage by the number of hours she works:

7(1)/(2) dollars/hour × 4(3)/(4) hours

Transform the mixed fractions into improper fractions, then multiply.

15/2 dollars/hr x 19/4 hours = 285/8 = 35.625 dollars

So, she will earn $35.625 after working for 4(3)/(4) hours.

To find out how much more money she needs to buy the $59 pair of headphones, we can subtract the amount she earned from the cost of the headphones:

$59 - $35.625 = $23.375

So, she needs $23.375 more to buy the $59 pair of headphones.

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B) The left end of the cable is 15 m above the roadway. The y-intercept of the graph represents the height of the left end of the cable, which is 15 m above the roadway.

Intercept is the point where a line intersects with an axis on a graph. It is the point at which a line crosses the x-axis or y-axis. Intercepts are important when analyzing relationships between variables, and they can help to draw conclusions about how two variables are related. For example, if a line has a negative slope, the y-intercept will be a positive number, indicating that as the x-value increases, the y-value will decrease. In linear regression, the intercept is the average value of the dependent variable when the independent variable is equal to zero. It is also used to determine the value of a linear equation when given the value of one of its variables.

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The equivalent expressiοn οf  2x+3y-x-(8+1) is x+3y-9.

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne math οperatiοn, and a sentence. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. An expressiοn's structure is as fοllοws: (Mathematical Operatοr, Number/Variable, and expressiοn).

Like terms in mathematics are summands in a sum that differ οnly by a small number. Regrοuping similar terms is pοssible by adding their cοefficients. Like terms in a pοlynοmial expressiοn are thοse that, pοssibly with different cοefficients, cοntain the same variables raised tο the same pοwers.

The given expressiοn is 2x+3y-x-(8+1).

First, cοmbine like terms:

= (2x-x) +3y-(8+1)

= x +3y-9

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What is Trapezium ?

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional shape that appears as a table when drawn on a sheet of paper. In Euclidean Geometry, a quadrilateral is defined as a polygon with four sides and four vertices. Hence, a trapezium also has four sides, four angles and four vertices.

ABCD is a trapezium, AB || DC

The area of ABCD = 180 cm²

AB = 17 cm

CD = 13 cm

Formula Used:

Area of trapezium = 1/2 x height x (Sum of parallel sides)

Calculation:

Area of trapezium = 1/2 x height x (Sum of parallel sides)

⇒ 180 = 1/2 x height x (AB + CD)

⇒ 180 x 2 = Height x (17 +13)

Height=360/30

Height = 12

.:. The height of the trapezium is 12 cm.

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