8. Find the domain and range of the 9. Determine the domain and range of the given relation. Is the relation a function? (2,-5),(4,6).(2,0)} d) {(-1,1),(-1,1),(,)} e) {(0,5), (1,5),(2,5), (3,5),(4,5),(5,5)} f) {(5,0),(5,1),(5,2), (5,3),(5,4),(5,5)} a) {(-4,-3), b) {(8,-2), (6,-),(-1,5)} c) {(-√3,3),(-1,1),(0,0), (1,1),(√3,3)}​

We have proven that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form.

Matrices are a type of mathematical structure used to store and analyze data. They are represented as a series of rows and columns, with each cell in the matrix containing a number or other value. Matrices are used to solve systems of equations, perform matrix multiplication and determine the inverse of a matrix. They are also used in linear programming, cryptography, and other areas of mathematics.

Row equivalence is defined as a pair of matrices A and B being row equivalent if there is a sequence of row operations that can transform A into B, or vice versa. This means that if A and B are row equivalent, then A and B can be transformed into one another by a series of row operations.

A reduced row echelon form is defined as a matrix in which all non-zero rows are above any rows of all zeroes and the leading coefficient of each non-zero row is 1. In other words, all of the non-zero rows have a leading coefficient of 1, and any rows of all zeroes are below the non-zero rows.

Therefore, if A and B are row equivalent, then A and B can be transformed into one another by a series of row operations. This means that we can use the same series of row operations to transform A and B into the same reduced row echelon form. This proves that if A and B are row equivalent, then A and B have the same reduced row echelon form.

On the other hand, if A and B have the same reduced row echelon form, then they must have been transformed into the same form by a series of row operations. This means that the same series of row operations must have been used to transform A and B into the same reduced row echelon form, which means that A and B are row equivalent. This proves that if A and B have the same reduced row echelon form, then A and B are row equivalent.
To prove that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form, we can use the definition of row equivalence and the definition of a reduced row echelon form.


Therefore, we have proven that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form.

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From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5

To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".

Looking at the number line, we can see the following values:

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

From this list, the values that "m" could take are:

-2, -3.5, 0, -5

These values are present on the number line, indicating that they are possible values for "m".

Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.

It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.

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Maureen's pension would be $50,035.20.

What is Percentage?

To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

First, we need to calculate the average of Maureen's three highest salaries:

Average = (107,000 + 107,800 + 108,198) / 3

Average = 322,998 / 3

Average = 107,666

Next, we need to calculate 1.56% of this average:

Percentage = 1.56% * 107,666

Percentage = 1,667.84

Finally, we multiply this percentage by the number of years worked to find the pension:

Pension = 30 * 1,667.84

Pension = 50,035.20

So, Maureen's pension would be $50,035.20.

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Answer:

4 cans of paint

Step-by-step explanation:

Half of a can = 1/8 of the outside of the house.

2 halves = whole can of paint

8/2=4

4 cans of paint

The expression "15 more than a number" can be represented using the variable n as n + 15.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
The variable mentioned in the question is n.
To write an expression for 15 more than a number, we have to add the number with 15.
So,
Expression = 15 + n

Thus, the expression "15 more than a number" can be represented using the variable n as n + 15.

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Answer:

70 degrees

Step-by-step explanation:

180-120=60

180-(60+50)=70

Answer: B  - 3 3/4 cubic inches

Step-by-step explanation:

A = BH; B = wl

2 * 1 1/4 = B

B = 2 1/2

H = 1 1/2

2 1/2 * 1 1/2 = 3 3/4

The potential energy of an rock of 40 kg and at a height of 10m is 4000 kgm^2s^2

What is potential energy and its formula?

An object possesses potential energy as a result of its position in relation to other objects. Potential energy is so named because it has the ability to transform into other types of energy, such kinetic energy. the formula for potential energy is mgh where m is the mass, g is the acceleration due to gravity and h is the height of the object.

We are given a rock of mass 40 kg which is at a height of 10m

We substitute the values in the formula to find the potential energy of the rock

Potential energy = m*g*h

Potential energy = \(40*10*10\)

Potential energy = 4000 kgm^2s^2

Hence the potential energy of the rock is 4000 kgm^2s^2

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Events A and B dependent as the occurrence of one event affect the chances of the occurrence of the other event.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

To understand this branch, it is extremely important to know its most basic definitions, such as the formula for calculating probabilities in equiprobable sample spaces, probability of the union of two events, probability of the complementary event, etc.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

Since we have given that

A be the event that Callista drives faster than the speed limit.

P(A)=0.34

B be the event that she gets to a wedding on time.

P(B)=0.45

The probability that she gets to the wedding on time given that she drives faster than the speed limit is 0.85 i.e.

P(A|B)=0.85

but for A and B to be independent ,

P(A).P(B)= P(A and B)

0.34×0.45=0.153

but,

\(P(A|B) = \frac{P(AnB)}{P(B)}\)

P(AnB) = 0.85 x 0.45

P(AnB) = 0.3825

So, P(A∩B) does not satisfy the condition.

Hence, A and B are not independent events.

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The point representing 0 on the real number line is the origin.

A number line is a visual representation of a set of real numbers. It is a straight line that is usually represented horizontally and it has a starting point, usually labeled as 0, which is called the origin.

Numbers to the right of the origin are positive, and numbers to the left of the origin are negative. The numbers on a number line are evenly spaced, and each point on the line represents a specific real number.

Number lines are useful in mathematics to represent numerical relationships, such as order, magnitude, and distance between numbers. They are also useful in teaching mathematical concepts, such as addition, subtraction, and fractions.

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Answer:

10

Step-by-step explanation:

5x+37=87

5x=87-37

5x=50

X=50÷5

X=10

Answer:

Step-by-step explanation:

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Answer:

the answer is 1,963,724,000

The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).

In determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.

Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.

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The minimum SAT score that meets the program requirements is given as follows:

1830.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for the scores are given as follows:

\(\mu = 1497, \sigma = 322\)

The minimum score in the top 15% is the 85th percentile, which is X when Z = 1.035, hence:

\(Z = \frac{X - \mu}{\sigma}\)

1.035 = (X - 1497)/322

X - 1497 = 1.035 x 322

X = 1830.

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Answer:

2 1/12 B)

Step-by-step explanation:

The maximum pressure differential in a stairwell is 58,860 Pa.

The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.

The difference in static water pressure between consecutive floors is 29,430 Pa.

We have,

Assuming a standard atmospheric pressure of 101.3 kPa.

Maximum pressure differential in a stairwell:

Since each stairwell is no more than 20 stories high and each story is approximately 3 m high, the maximum height difference between two floors in a stairwell is:

= 20 x 3

= 60 m

Using the formula for hydrostatic pressure, the maximum pressure differential in a stairwell is:

ΔP = ρgh

= (1000 kg/m³)(9.81 m/s²)(60 m)

= 58,860 Pa

The atmospheric pressure difference between the top of the building and street level:

The atmospheric pressure decreases with increasing altitude.

Using the formula for hydrostatic pressure, the pressure difference between the top of the building and the street level is:

ΔP = ρgh

= (1000 kg/m³)(9.81 m/s²)(300 m)

= 2,943,000 Pa

The difference in static water pressure between consecutive floors:

Assuming a standard density of water of 1000 kg/m³, the difference in static water pressure between consecutive floors is:

ΔP = ρgh = (1000 kg/m³)(9.81 m/s²)(3 m) = 29,430 Pa

Therefore,

The maximum pressure differential in a stairwell is 58,860 Pa.

The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.

The difference in static water pressure between consecutive floors is 29,430 Pa.

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The smallest positive integer Joelle could have multiplied 756 by

15876

This is further explained below.

Generally, A perfect square number is a number in mathematics that, when its square root is calculated, yields a natural number.

To solve this problem we can do:

\(\sqrt{756}\)

By properties of roots

\(\begin{aligned}&\sqrt{756}=\sqrt{6\cdot126} \\&=\sqrt{6 * 6 * 21} \\\\ =\sqrt{6^2 * 21} \\&=6 \sqrt{21}\end{aligned}\)

So, so that the multiplication of 756 by an integer becomes a perfect square, you have to multiply it by 21 to make $21^2$ and thus "eliminate" the root.

756 * 21=15876

In conclusion,  You can verify that 15876is a perfect square since root (15876)=132 and 132 is a natural number

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Answer:

1.029 is greater than 1.0275

Step-by-step explanation:

Answer:

1.029

Step-by-step explanation:

What is greater 1.0275 or 1.029

.027 < .029

So, 1.029 is greater.

According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

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Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

y = ±√100-x

Step-by-step explanation:

To work out the inverse of this function :

We solve for x then swap x and y :

Solving for x :

y = 100 - x²

Add x² to both sides :

x² + y = 100

Subtract y from both sides :

x² = 100-y

Square root both sides :

x = ±√100-y

Now we have solved for x. Now swap x and y :

y = ±√100-x

This is our final answer and is the first option.

Hope this helped and have a good day

Answer:

56.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

   0 5 6

1 6 9 0 4

 − 0    

   9 0  

 − 8 0  

   1 0 4

 −   9 6

       8

the answer is 56

Answer:

1060

Step-by-step explanation:

Answer:

  ∠2 = ∠4 = ∠6 = ∠8 = 114°

  ∠1 = ∠3 = ∠5 = ∠7 = 66°

Step-by-step explanation:

You want to know the measures of all of the angles where transversal t crosses parallel lines m and n. ∠4 is given as 114°.

Where a transversal crosses parallel lines, all of the acute angles are congruent, and all of the obtuse angles are congruent. The obtuse and acute angles form linear pairs, so are supplementary.

In the given figure, the acute angles are numbered using odd numbers, and the obtuse angles are numbered using even numbers.

∠2 = ∠4 = ∠6 = ∠8 = 114°

∠1 = ∠3 = ∠5 = ∠7 = 180° -114° = 66°

Answer:

B.96

Step-by-step explanation: