The two lines graphed on the coordinate grid each represent an equation.


Which ordered pair represents a solution to both equations?
Responses
A (1, 1)(1, 1)
B (1, -1)(1, -1)
C (-1, 1)(-1, 1)
D (-1, -1)(-1, -1)

The requried match to the expression is given as,
x²+ 2x + 2             (x + 1 + i ) (x + 1 − i)
x² - 4x + 8             (x − 2 + 2i)(x − 2 − 2i)
x² + 4                     (x + 2i)(x − 2i)

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
1. expression,
= x²+ 2x + 2

Simplifying the above expression,
= x²+ 2x + 2

We know that,

x = -b ± √{b² - 4ac} / 2a
x = -2 ± √(4 - 8)/2
x = -1 ± i    (i = √-1)

So,
The factored form of the given expression is given as,
= (x + 1 + i ) (x + 1 − i)

Similarly,
x² - 4x + 8 = (x − 2 + 2i)(x − 2 − 2i)
x² + 4 = (x + 2i)(x − 2i)

Thus, following the pattern of each expression to its equivalent standard form can be determined.

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The y-intercept of f(x) = 4^x is f(0) = 4^0 = 1. This means that the graph of f(x) intersects the y-axis at the point (0, 1).

What is the difference between intercept and asymptotes?

The y-intercept of f(x) = 4^x is f(0) = 4^0 = 1. This means that the graph of f(x) intersects the y-axis at the point (0, 1).

The graph of f(x) = 4^x does not have any horizontal asymptotes, since the value of 4^x approaches infinity as x approaches infinity, and approaches 0 as x approaches negative infinity.

The range of f(x) = 4^x is all positive real numbers, since for any positive real number y, there exists a real number x such that 4^x = y.

In contrast, the graph of g(x) = -4^x would have a y-intercept of g(0) = -4^0 = -1. The graph would approach negative infinity as x approaches positive infinity and approach positive infinity as x approaches negative infinity. The range of g(x) = -4^x would be all negative real numbers.

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Answer: 14.46

Step-by-step explanation:

sin 56 = 12/x

0.83 = 12/x

0.83x = 12

x = 12/0.83

x = 14.46

Answer: 14.475

Step-by-step explanation:

Since we are given the angle 56°, this means that the other angle is 34°. We are given the side 12 this means that x, or the hypotenuse, is 14.475.

The hypotenuse is c, b is 12, and a is the side with the 90° angle.

What we do is c = a/sin(a) = b / sin(56°)

The equation to model the value of Maureen's car x years after purchase can be written in the form of y = a(b)^x , where y is the value of the car, x is the number of years after purchase, and a and b are constants.

Using the information given, we can find the values of a and b.

We know that the value of the car one year after purchase is $24,403.

So, we can substitute this value into the equation:

24403 = a(b)^1

We also know that the car's original value is $26,525

So we can substitute this value into the equation:

26525 = a

Now we can use these two equations to find the value of b

24403 = 26525 (b)^1

b = 24403 / 26525

b = 0.9153

So the final equation is:

y = 26525 (0.9153)^x

where y is the value of the car, x is the number of years after purchase, and a = 26525 and b = 0.9153

The type of random variable is continuous

The term called variable in math is known as a quantity that may change within the context of a mathematical problem or experiment.

Here we know that the f1,v random variable can be thought of as the square.

Here the term random variable is known as a set of possible values from a random experiment and the domain of a random variable is called sample space

As we all know that random variables are classified into discrete and continuous variables.

Here the main difference between the two categories is the type of possible values that each variable can take.

The value of the function is continuous one.

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Answer:

x= -4

Step-by-step explanation:

-7(x-2)+4=46

-7x+14+4=46

-7x=46-18

-7x=28

x=28/-7

x= -4

Answer:

-4

Step-by-step explanation:

Hope it helps! =D

We have to show that the set of numbers of the form a + b√2, where a and b are rational numbers, forms a field with respect to addition and multiplication.

To start, we need to show that the set of numbers is closed under addition and multiplication. This means that if we add or multiply two numbers in the set, the result must also be in the set.

For addition, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we add them, we get (a1 + a2) + (b1 + b2)√2. Since a1, a2, b1, and b2 are all rational numbers, their sum is also a rational number. So, the result of adding two numbers in the set is always another number in the set, which means that the set is closed under addition.

For multiplication, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we multiply them, we get (a1a2 + 2b1b2) + (a1b2 + a2b1)√2. Again, since all the numbers involved are rational, the result is also a rational number. This means that the set is closed under multiplication as well.

Next, we need to show that the set satisfies the commutative, associative, and distributive laws for both addition and multiplication. This means that the order in which we add or multiply numbers in the set does not matter, and that addition and multiplication can be combined in a predictable way.

The commutative, associative, and distributive laws for addition and multiplication are well-known for rational numbers, and it can be easily verified that they hold for this set as well.

Finally, we need to show that the set has additive and multiplicative inverses. This means that for each number in the set, there exists another number in the set such that when added (or multiplied) to the original number, the result is 0 (or 1).

It can be shown that for any number of the form a + b√2, its additive inverse is -a - b√2, and its multiplicative inverse is (a / (a^2 + 2b^2)) - (b / (a^2 + 2b^2))√2, assuming that a^2 + 2b^2 is not equal to 0. Both of these are also rational numbers, since they are obtained by dividing rational numbers.

So, we have shown that the set of numbers of the form a + b√2, where a and b are rational numbers, is closed under addition and multiplication, satisfies the commutative, associative, and distributive laws, and has additive and multiplicative inverses. This means that the set of numbers forms a field with respect to addition and multiplication.

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The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.

The rate of change between two variables is shown by the slope of the line in a scatter plot. The slope would show how much the number of performances varies with a change of one unit in the number of practises in the connection between the two numbers.

If the slope is upward, then as the number of practises rises, so do the number of performances. If the slope is negative, then fewer performances will occur as the number of practises rises.

The slope's magnitude tells us how steep the line is, which tells us how strongly the two variables are related.

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When people call into tv contest shows to vote, such as american idol or dancing with the stars, they are an example of a. non probability sample

In general, the probability sampling is the most common sampling technique for studies of public opinion, election polls, and other studies where the results will be applied to a wider population. Therefore, in this case it must provide information that the research methods carried out must represent the wider population.

Probability sampling  can also be interpreted as a sampling method that uses some form of random selection. To be able to get the random selection method, a researcher must prepare several processes or procedures to be able to ensure that different units are in the population and have the same probability of being selected.

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The average number of fills before the line is stopped is 1000 and the standard deviation is 31.62. This means that over many repetitions of the automated filling operation, the number of fills before the line is stopped will tend to be around 1000, with most values falling within 31.62 units of 1000

An electronic scale in an automated filling operation is a device used to measure the weight of packages filled with a certain product. The purpose of the scale is to ensure that each package is filled with the correct amount of product. In this case, the scale stops the manufacturing line after three underweight packages are detected.

a. The average number of fills before the line is stopped can be calculated using the formula for the expected value. The expected value is the average outcome of a random process over many repetitions. In this case, the random process is the number of fills before the line is stopped. The expected value can be calculated as follows: E(x) = 1/p, where p is the probability of an underweight package. Plugging in the value of p = 0.001, we get E(x) = 1/0.001 = 1000. So, the average number of fills before the line is stopped is 1000.

b. The standard deviation of the number of fills before the line is stopped can be calculated using the formula for the standard deviation of a Poisson distribution. The Poisson distribution is a discrete probability distribution that is used to model the number of events in a fixed interval of time or space. In this case, the events are underweight packages. The standard deviation can be calculated as follows: σ = √(λ), where λ is the expected value. Plugging in the value of λ = 1000, we get σ = √(1000) = 31.62. So, the standard deviation of the number of fills before the line is stopped is 31.62.

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The value of b is 0.927. Therefore, the correct answer is option A.

To find b, we need to substitute the given values into a formula for computing the area under a curve. The formula for the area under the curve y=sinx from x=b to x=π is:

Area = ∫πb sinxdx

We do this by splitting the integral into the following two parts:

Area = ∫πbg+∫bg sinxdx

We can evaluate the first integral easily, since bg is a constant:

∫πbg=bg∫π=bgπ

For the second integral, we use integration by substitution:

Let u=x −b, so du=dx. Then the integral can be rewritten as:

∫bg sinx dx=∫bg sin(u+b)du

Where u varies from 0 to π−b. Now that the integral is in a form we can easily integrate:

∫bg sin(u+b)du=∫π−b0 sin(u+b)du

And using the Pythagorean identity:

sin(u+b)=sinubcosb+cosubsinb

We can rewrite the integrand as:

sin(u+b)=sinucosb−cosusinb

And then using integration by parts:

∫π−b0 sin(u+b)du=−cosubcosb|π−b0+∫π−b0 cosusinbdu

And the second integral can be simplified the same way we did the first one.

∫π−b0 cosusinbdu=−sinubsinb|π−b0+∫π−b0 sinubcosbdu

Which can be easily calculated as:

∫π−b0 cosusinbdu=π−b2sinbcosb

Now that both integrals are solved, we can substitute them back into the formula for the area and then solve for b:

Area=bgπ+π−b2sinbcosb

Substituting the value for the Area, we get:

0.4=bgπ+π−b2sinbcosb

Which can be simplified to:

b(π−b)=(π−0.4)/sinbcosb

Solving for b, we get:

b=0.927

Therefore, the correct answer is option A.

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"Your question is incomplete, probably the complete question/missing part is:"

If 0≤b≤π and the area under the curve y=sinx from x=b to x=π is 0.4, what is the value of b?

A) 0.927

B) 1.159

C) 1.982

D) 2.214

The required measurement of the remaining two sides of the given triangle are 8 and 6 meters.

Heron's formula is a formula for calculating the area of a triangle in terms of the lengths of its sides that is credited to Heron of Alexandria.

Given that, a triangle having area of √135 square meter and perimeter 18 meter has a side 4 meter.

Let other two sides be x and y,

Therefore,

x + y + 4 = 18

x + y = 14.....(i)

Now, according to Heron's formula,

Area of a triangle = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c) / 2.

Therefore,

√9(9 - 4)(9 - x)(9 - y) = √135

Squaring both sides

45(9-x)(9-y) = 135

(9-x)(9-y) = 3

81 -9y - 9x + xy = 3

9(x+y)-xy = 78

Put x+y = 14 from eq(i)

9×14-xy = 78

xy = 48

Now finding the factors of 48

48 = (6, 8), (12, 4), (24, 2), (16, 3), (48, 1)

If we consider (6, 8) this is satisfying eq(i)

6+8 = 14

Therefore, we can say the other two sides of the triangle are 8 and 6.

Hence, the required measurement of remaining two sides of the given triangle are 8 and 6 meters.

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The image of the point after the reflection across the y-axis is:

(-13, 8)

Remember that for a general point (x, y), a reflection across the y-axis just changes the sign of the x-component, so the new point will be:

(-x, y)

Here we want to apply this reflection to (13, 8), using the rule above, we can see that the new coordinates after the reflection are:

(-13, 8)

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Answer:

The rate of change of a linear function is its slope, which is the coefficient of the x-term in the equation.

Item I: y = 0.25x + 2

The slope of this line is 0.25.

Item II: y = 2

This is a horizontal line with zero slope, so it has a rate of change of 0.

The slope of Item I is greater than the slope of Item II, therefore option C is correct: "The rate of change of item I is greater than the rate of change of item II".

Step-by-step explanation:

Answer:

Step-by-step explanation:

if you meant just 2 years the answer is 74,845,440 if you meant 2,000 its 74,845,440,000

The number of heartbeats for a person with an average heartbeat of 71.2 BPM for 2,000 years is 86,567,520,000 heartbeats.

The formula to calculate the number of heartbeats in a given period of time is:

Number of heartbeats = Beats per minute (BPM) x Minutes in the period

In this case, the given information is the BPM (71.2) and the period of time is 2,000 years, which is equal to 1,209,600,000 minutes.

Therefore, the number of heartbeats for a person with an average heartbeat of 71.2 BPM for 2,000 years is:

Number of heartbeats = 71.2 BPM x 1,209,600,000 minutes

Number of heartbeats = 86,567,520,000 heartbeats.

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The answer to the question 5/9 divided (- 1/3) as a simplest form is 5/3

What is quotient of a number?

The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.

The question -5/9 divided (- 1/3) can be re-written as

-5/9 ÷ -1/3

-5/9 x -3/1

=15/9

=5/3

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[tex](x + 2)x( {x }^{2} + x + 3)[/tex]

By splitting the range into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of f(x) from x=-2 to x=4 is calculated.

Area = (55 - (-2)^2) + (55 - (1)^2) + (55 - (4)^2) = 55 + 9 + 1 = 65

By splitting the interval into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of

f(x)=55x2 from x=2 to x=4

is calculated. We begin by calculating the area of the rectangle whose right endpoint is at

x = -2. F(-2)

provides the height of this rectangle, which is equal to

55 - (-2)2 = 55 + 4 = 59.

The rectangle's width is

(4 - (-2))/3 = 6/3 = 2.

The area of this rectangle is therefore 59 x 2 = 118. The area of the rectangle with x = 1 as its right terminus can also be determined in a similar manner. This rectangle has a height of f(1), which equals

55 - (1)2 = 55 - 1 = 54.

The rectangle's width is

(4 - (-2))/3 = 6/3 = 2

The area of this rectangle is therefore 54 x 2 = 108. f(4), which equals 55 - (4)2 = 55 - 16 = 39, gives the area of the rectangle with x = 4 as the right endpoint. The rectangle's width is

(4 - (-2))/3 = 6/3 = 2.

The area of this rectangle is therefore 39 x 2 = 78. The sum of the areas of the three rectangles, which equals 118 + 108 + 78 = 304, represents the total area under the graph.

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Answer:

X = 0

Y = 3

Step-by-step explanation:

To solve using substitution, you would solve one equation and substitute it into the other to get that x or y value, then you would use that found value on any original equation.

x+y=3 2x+2y=6

Using the first equation, if we subtract x

y = -x+3

Lets put this into the second equation

2x + 2y = 6

2x + 2(-x+3) = 6

2x + 2x + 6 = 6

4x = 0

x = 0

Now that we have X, we can plug it into any original equation. let's do the first cause it's easier

x+y=3

0+y=3

y=3

We can use the other too

2x+2y=6

2(0)+2y=6

0+2y=6

y=3

Answer:

b)

Step-by-step explanation:

As here it's stated that average of first 9 numbers is 23

so,

sum of 9 numbers = 9×23 = 207

Average of first 5 numbers is 20

so,

Sum of first 5 numbers = 5×20 = 100

Sum of remaining numbers = 207-100 = 107

Average of last five numbers = 25

So,

Sum of last five numbers = 5×25 = 125

Fifth Number = Sum of last five numbers- Sum of remaining numbers

                      = 125 - 107 = 18

Answer:

[tex] \frac{1}x{} [/tex]

Answer:

D

Step-by-step explanation:

Yes... Is D................

Absolute value represents how far you are from zero on the number line.

Examples:

The output of an absolute value function is never negative. Negative distance does not make sense. Therefore, we have no way to reach an output of -7. This is why we have no solutions here.

The value of x for the expression (x – 7)² = 36 is 13. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is  (x – 7)² = 36. The value of x will be calculated as:-

(x – 7)² = 36

(x – 7) = √36

(x - 7) = 6

x = 13

Hence, the value of x for the expression (x – 7)² = 36 is 13. The correct option is A.

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The price of the jeans will be $27 if you apply the function  composition h(x). The price of the jeans will be $30 if you apply the composition j(x). Because it is less expensive.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.

If you first use the coupon and then utilize the shop discount, the price of the jeans is represented by the function h(x). The combination of the functions f(x) and g may be used to calculate the function h(x) (x). If you first apply the shop discount and then utilize the coupon, the cost of the jeans is represented by the function j(x). The combination of the functions g(x) and f may be used to calculate the function j(x) (x).

The price of the jeans will be $27 if you apply the composition h(x). The price of the jeans will be $30 if you apply the composition j(x). Because it is less expensive, the composition h(x) will provide you a bigger discount.

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The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable takes a value less than or equal to z.

In order to model continuous phenomena or quantities that depend on chance, such as time, length, and mass, continuous random variables are utilized.

The likelihood that the random variable takes a value inside that interval is defined as the area under the density function over an interval. Therefore, the probability that the random variable will have a value less than or equal to z is given by the area under the normal curve from negative infinity to z.

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Answer:

Step-by-step explanation:

v + 7/8 = 2/8

v = -5/8

Lexi's reasoning is correct because the theoretical probability of picking a yellow golf ball is 1 out of 2, or 1/2. This is because there are two yellow golf balls in the bag and one ball is being selected.

Theoretical probability is the ratio of the number of outcomes for a certain event to the total number of possible outcomes.

In this case, Lexi found the ratio of one yellow golf ball to the total number of balls in her bag (two balls: one yellow and one green).

This equals a theoretical probability of 1/2 or 0.5, meaning there is a 50% chance of picking a yellow golf ball.

This is the correct way to calculate theoretical probability.

Lexi's reasoning is correct in this situation. The theoretical probability of picking a yellow golf ball is 1 out of 2, or 1/2. This is because there are two yellow golf balls in the bag and one ball is being selected.

This ratio of 1/2 is the same as the theoretical probability of picking a yellow golf ball. Theoretical probability is based on the ratio of the outcomes being considered to the total number of possible outcomes.

In this case, the two yellow golf balls represent the possible outcomes, and the total number of golf balls in the bag is two. Therefore, the theoretical probability of picking a yellow golf ball is 1/2.

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The change in momentum is 22120Ns

The change in momentum (Δp ) is defined as the change in the product of an object's mass and velocity. A force is required to change the momentum of an object. This applied force can increase or decrease the momentum or even change the object's direction.

Therefore the change in momentum = Final momentum - initial momentum

i.e mv -mu

where m is the mass

v is the final velocity

u is the initial velocity

The change of momentum is also called impulse. impulse is the product of the force and the time in applying it.

Change in momentum = force × time

= 2800× 7.90

= 22120 Ns

Therefore the change in momentum of the car is 22120Ns

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The column cells are similarly filled by dividing the column cells by the corresponding column totals.

A table that displays the distribution of a characteristic's occurrence frequency in accordance with a specific set of class intervals.

Two sorts of data, or data in two categories, one pertaining to the columns and the other to the rows, make up a two-way relative frequency table.

                                Response                              

Shift                             Yes                 No                      Total

Day                            67%                  33%                     100%          

Night                         23%                  77%                      100%            

Total                          45%                   55%                    200%        

This table contains information about two categories, day/night and yes/no.

The day/night data percentages are computed along the rows.

The percentages of the yes/no values are calculated along the columns.

Shift                                     Response                              

                         Yes                        No                        Total

Day                  67/100 × 100           33/100 ×100           100

                            = 67%                  =33%                     100%

Night                23/100×100           77/100×100               100

                         = 23%                     =77%                        100%

Total              90/200×100               110/200×100           200

                        = 45%                       =   55%                   200%

To make these computations, divide the row cells by the corresponding row totals.

The column cells are similarly filled by dividing the column cells by the corresponding column totals.

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