Write an equation in slope-intercept form for the line perpendicular to y = -2x + 5 and containing the point (8,-3)

Answer: The origins of matrices can be traced back to the 18th century, with the work of mathematicians such as Gabriel Cramer, Leonhard Euler, and Joseph-Louis Lagrange. These mathematicians developed the idea of using arrays of numbers to represent systems of linear equations, which led to the development of the concept of matrices.

The term "matrix" itself was first used by James Joseph Sylvester in 1850, although it had been in use informally for some time before then. In 1858, the English mathematician Arthur Cayley first published a systematic theory of matrices, which further developed the field.

Matrix theory was primarily used in the early days to solve systems of linear equations, but it soon found applications in areas such as linear algebra, multivariate statistics, and even quantum mechanics.

In summary, the origins of matrices can be traced back to the 18th century as an idea to represent systems of linear equations, which developed over time with contributions of many mathematicians over the centuries, and now it plays an important role in many field of mathematics and science.

Step-by-step explanation:

The simplified form of the expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y² is

[1/15(xy)³] and  (x, y) ≠ 0.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Given, An expression 5x³3y² ÷ 27x × 9xy ÷ 25x²y².

= 5x³3y² ÷ 243x⁴y³ ÷ 25x²y².

=  5x³3y² ÷ 25x²y² ÷ 243x⁴y³.

= (3/5)x ÷ 243x⁴y³.

= (3/5)x/(243x⁴y³).

= (3/5)/(243x³y³).

= 1/(81×5x³y³).

= [1/15(xy)³].

The restriction should be x and y can not be equal to zero as it would make the expression undefined.

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This is a separable differential equation, which means we can separate the variables y and x on either side of the equation. To do this, we'll move all the terms involving y to one side and all the terms involving x to the other side.

dy/dx = (1+y²)e^x

We'll divide both sides by (1+y²)e^x:

dy/(1+y²)e^x = dx

Now we'll integrate both sides with respect to their respective variables. The integral of dy/(1+y²) with respect to y is the inverse tangent (tan^-1) function, so we'll use that on the left side:

∫ dy/(1+y²) = ∫dx + C

tan^-1(y) = x + C

On the right side, we'll integrate e^x with respect to x, which gives us e^x. So we have:

tan^-1(y) = e^x + C

We can solve for y by reversing the tan^-1 function:

y = tan(e^x + C)

Where C is an arbitrary constant of integration.

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If you are dealt one card from a​ 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.

Since there are 4 aces in a deck of card 52 first step is to find the number of cards  not aces in a deck of 52

Number of cards  not aces in a deck = 52 -4

Number of cards  not aces in a deck = 48

Now let find the probability that you won't draw an ace.

Probability = 48/52

Probability = 24/26

Probability = 12/13

Therefore we can conclude that the probability is 12/13.

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Luca's average trip will be 58 miles per hour.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

In this case, it took Luca 8 hours to drive 464 miles from Richmond VA to Cleveland, OH. In miles per hour, Luca's average trip will be:

= Distance / Time

= 464 / 8

= 58 miles per hour.

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The equation has one solution.

A value of x that makes the equation true is 6 which when substituted into the equation and simplified makes the equation turn into x = 0.

A value of x that makes the equation false is 8 which when substituted into the equation and simplified makes the equation turn into x = 2.

From the information provided, we have the following equation:

x - 6 = 6 - x

Rearranging the equation by collecting like terms, we have the following solution:

x + x = 6 + 6

2x = 12

x = 12/2

x = 6

Substituting the value "6" into the equation, we have the following solution;

x - 6 = 6 - 6

x - 6 = 0

Assuming x = 8, we have the following solution;

x - 6 = 8 - 6

x - 6 = 2

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Complete Question:

Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.

x - 6 = 6 - x

The equation has _____.

A value of x that makes the equation true is ___ which when substituted into the equation and simplified makes the equation turn into ____.

A value of x that makes the equation false is ___ which when substituted into the equation and simplified makes the equation turn into ___.

Carmen and her dog, Duke walked at a slower rate at 0.625 blocks/min

Carmen and her dog, Duke would take 19.2 minutes to work 12 blocks.

In math, a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in problems.

Carmen/Duke walks 5/8 = 0.625

Terell/Lady walks 8/12 = 0.677

Therefore, from the average time, Carmen and Duke walk slower.

Carmen and Duke will walk 12 blocks in;

= 12/0.625

= 19.2 minutes

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Answer:

8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones

(units) digit T, which means that N = 8000 + 100R + 10S + T. Suppose that the

following conditions are all true:

• The two-digit integer 8R is divisible by 3.

• The three-digit integer 8RS is divisible by 4.

The four-digit integer 8RST is divisible by 5.

The digits of N are not necessarily all different.

The number of possible values for the integer N is

(A) 8

(B) 16

(C) 12

(D) 10

87

(E) 14

Since 8R is divisible by 3, R must be a multiple of 3. The possible values for R are 3, 6, and 9.

Since 8RS is divisible by 4, S must be a multiple of 2. The possible values for S are 0, 2, 4, 6, and 8.

Since 8RST is divisible by 5, T must be 0 or 5.

The possible values for N are therefore:

8000 + 300 + 00 + 0 = 8300

8000 + 600 + 00 + 0 = 8600

8000 + 900 + 00 + 0 = 8900

8000 + 300 + 20 + 0 = 8320

8000 + 600 + 20 + 0 = 8620

8000 + 900 + 20 + 0 = 8920

8000 + 300 + 40 + 0 = 8340

8000 + 600 + 40 + 0 = 8640

8000 + 900 + 40 + 0 = 8940

8000 + 300 + 60 + 0 = 8360

8000 + 600 + 60 + 0 = 8660

8000 + 900 + 60 + 0 = 8960

8000 + 300 + 80 + 0 = 8380

8000 + 600 + 80 + 0 = 8680

8000 + 900 + 80 + 0 = 8980

8000 + 300 + 00 + 5 = 8305

8000 + 600 + 00 + 5 = 8605

8000 + 900 + 00 + 5 = 8905

8000 + 300 + 20 + 5 = 8325

8000 + 600 + 20 + 5 = 8625

8000 + 900 + 20 + 5 = 8925

8000 + 300 + 40 + 5 = 8345

8000 + 600 + 40 + 5 = 8645

8000 + 900 + 40 + 5 = 8945

8000 + 300 + 60 + 5 = 8365

8000 + 600 + 60 + 5 = 8665

8000 + 900 + 60 + 5 = 8965

8000 + 300 + 80 + 5 = 8385

8000 + 600 + 80 + 5 = 8685

8000 + 900 + 80 + 5 = 8985

There are a total of 30 possible values for N. The answer is therefore (E) 14.

Step-by-step explanation:

Using the law of sines, it cannot be affirmed whether the conditional is true or false, as we have no information about the measure of angle B.

We suppose a general triangle, for which:

The lengths and the sine of the angles are proportionally related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The segments in this problem are given as follows:

Hence it can be affirmed that:

BC > AB.

As the measure of angle A is greater than the measure of angle C, hence sin(A) > sin(C) and BC > AB, using the proportional relationship.

As for segment AC, we need the measure of angle B, hence nothing can be affirmed.

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Answer: Set of integers

Integers are positive and negative whole numbers, with 0 included.

Answer: Set of Integers

Step-by-step explanation:

{...,-2,-1,0,1,2...}

since we can see that here is a zero as well as positive and negative numbers, therefore, we call this set, a set of integers.

hope that helps...

Answer: I say 13

Step-by-step explanation:

The measure of angle B is 53°.

The equation used to find B is  

B = [tex]sin^{-1}[/tex](4/5).

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Right triangle ABC.

AB = 6

BC = 10

AC = 8

In order for the triangle to be a right triangle it must satisfy the Pythagorean theorem.

So,

BC² = AB² + AC²

100 = 6² + 8²

100 = 36 + 64

100 = 100

This means,

B

|        \

|             \

|                 \

A_________C

Now,

Sin B = 8/10 = 4/5

B = [tex]sin^{-1}[/tex] (4/5)

B = 53°

Sin C = 6/10 = 3/5

C = [tex]sin^{-1}[/tex] (3/5)

C = 37°

We see that,

∠A + ∠B + ∠C = 180

90 + 53 + 37 = 180

90 + 90 = 180

180 = 180

Thus,

The equation used to find B is  

Sin B = AC / BC = 8/10

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Answer:

Tangent B=8/5

Step-by-step explanation:

Just look at the answer

The range of the absolute function will be from 0 to 9. Then the correct option is A.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The domain means all the possible values of x and the range means all the possible values of y.

From the graph, the range of the absolute function will be from 0 to 9.

Then the correct option is A.

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The complete question is attached below.

The probability that on average these students spend more than $425 on books is given as follows:

0.0009 = 0.09%.

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]

The desired probability is one subtracted by the p-value of Z when X = 425, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{425 - 400}{8}[/tex]

Z = 3.125.

Z = 3.125 has a p-value of 0.9991.

1 - 0.9991 = 0.0009 = 0.09%.

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Answer:

2.25  

4.5

9

18

36

72

144

288

Step-by-step explanation: you take the number and multiply it by itself. but went it comes to the negative numbers you have to divide the number by 2 then take the answer you get from that and add it by itself so 4.5+4.5=9. its pretty simply when you under stand how to do it.

An example of limit in polynomial will be the polynomial function f(x) = x³ + 2x² - 5. As x approaches 2, the value of the function approaches 11. So, the limit of f(x) as x approaches 2 is 11.

A polynomial simply means an expression which is composed of variables, constants and exponents, which are combined using mathematical operations such as addition, subtraction, multiplication and division

In mathematical notation, we can write it as: Here, lim x->2 (x³ + 2x² - 5)

= x³ + 2x² - 5

= 2³ + 2(2²) - 5

= 8 + 8 - 5

= 11

This means that as x gets arbitrarily close to 2, the values of the function gets arbitrarily close to 11.

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4th option: parallelogram

Answer:

5. 6 appointments are cancelled

6. 80  more spots

Step-by-step explanation:

5. Jasmine has 36/24 = 1.5 times as many appointments as cancellations each day.

Since 1.5 times 4 is 6, Jasmine has 6 cancellations each day.

6. Kendrick's kennel has 2 spots for cats for every 7 spots for dogs. If he has a total of 144 spots for both cats and dogs;

Spots for cats = 2x ;

So, spots for dogs will be = 7x ;

Total spots for cats and dogs will be = 2x + 7x = 144 ;

x = 144/9 = 16 ;

So, spots for cats = 2 * 16 = 32 ;

Spots for dogs = 7 * 16 = 112 ;

spots for dogs more than cats are = 112 - 32 = 80 .

Kendrick kennel has 80 more spots for dogs than cats.

Answer: To find the value of g(2+h)-g(2) divided by h, we can use the definition of the derivative. The derivative of a function at a point is a measure of the slope of the function at that point, and it can be calculated by taking the limit of the difference quotient as h approaches 0.

The difference quotient is defined as:

[g(2+h) - g(2)] / h

So, to find the derivative of g at x=2, we can substitute the value of x in the function g(x) and take the limit as h approaches 0:

lim h→0 [g(2+h) - g(2)] / h

Substituting the value of x in the function g(x), we get:

lim h→0 [(2+h)³ - 2(2+h) - (2² - 2*2)] / h

This simplifies to:

lim h→0 [8+6h+h²-2h - 4] / h

Which simplifies to:

lim h→0 [h²+6h+4] / h

And, finally:

lim h→0 [h(h+6)] / h

The limit of a quotient is equal to the quotient of the limits, as long as the limit of the denominator is not 0. In this case, the limit of the denominator (h) is 0, but the limit of the numerator (h(h+6)) is not. Therefore, we can safely take the limit:

h+6

So, the derivative of g at x=2 is h+6. When h=0, the derivative is equal to the function's value at that point, so the value of g(2) is 6.

Therefore, the value of g(2+h)-g(2) divided by h is:

(h+6) - 6 / h

Which simplifies to:

h / h

Which is equal to:

1

So, the final answer is 1.

Step-by-step explanation:

Answer:
Here is a sequence of numbers using the rule "x+8":

x+8=9 (x=1)

x+8=10 (x=2)

x+8=11 (x=3)

x+8=12 (x=4)

x+8=13 (x=5)

x+8=14 (x=6)

Here is the sequence of ordered pairs:

(1, 9)

(2, 10)

(3, 11)

(4, 12)

(5, 13)

(6, 14)

Step-by-step explanation:

the area of a trapezoid is

(a + b)/2 × x

a and b being the 2 bases. and x, as requested, is the height.

A

it does not matter which base is which, as long as we keep using them consistently.

so, let's assume a is the first base :

a = x + 5

and then for the second base

b = 2x - 1

now we use that in the main formula :

(x + 5 + 2x - 1)/2 × x = (3x + 4)/2 × x = (3x² + 4x)/2

A = (3/2)x² + (4/2)x = (3/2)x² + 2x ft²

B

now the height is increased by 4 ft.

that means we need to replace x by x + 4.

(3/2)(x+4)² + 2(x+4) = (3/2)(x² + 8x + 16) + 2x + 8 =

= (3/2)x² + (24/2)x + (48/2) + 2x + 8 =

= (3/2)x² + 12x + 24 + 2x + 8 =

= (3/2)x² + 14x + 32 ft²

with x being the original height, of course.

Answer:

62 degrees.

Step-by-step explanation:

I think this because it appears that ABC makes a 90 degree angle and I would think that you would just subtract 28 from 90 and get 62.

Hope it helps! =D

The probability Richard marker is 11.The probability of anything occurring is known as probability.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

According to question:-

11/1 = 11

11/1 = 11

The probability Richard marker is 11.The probability of anything occurring is known as probability.

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Answer:

Step-by-step explanation: