Names jocelynn and i was wondering what is the name of the process of rewriting a quadratic equation so that one side is a perfect square trinomial?
i said completing the square but that was not it

First, we know that both triangles already have 2 sides with equal ratios:

AC /RQ = 6/3 =2

AB/QP = 10/5 =2

Now, if RP = 4.5 we will have 3 sides with equal ratios:

CB / RP = 9/4.5 = 2

with this condition, both triangles will be similar by SSS.

Also if they have 2 sides with equal ratios and equal included angles.

m< R = 63

m

There are 10000 pins possible using the 4 numbers

From the question, we have the following parameters that can be used in our computation:

Length of pin = 4 digits

Available digits = 10

Given that the digit of the pins can be repeated, we have

Number of pins = Available digits^Length of pin

So, we have

Number of pins = 10⁴

Evaluate

Number of pins = 10000

Hence, there are 10000 pins possible

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Answer:

y = -x + 1

Step-by-step explanation:

Any point on an angle bisector has equal distance to both sides

Bisector line slope = rise/run = -1    (rise=run and moves from left to right)

equation: y = mx + b

y = -x+b

pass (2.-1)

-1 = -2 + b     B = 1

y = -x+1  

check: (y- -1)/(x-2) = -1

y+1 = -x+2

y = -x + 1

A series is convergent when the sequence of partial sums, which are the sums of the first n terms in the series, approaches a finite limit as n approaches infinity. In other words, the series has a sum that can be found. On the other hand, a series is divergent if the sequence of partial sums does not approach a finite limit. This means the series does not have a sum. So, to determine if a series is convergent or divergent, analyze the behavior of its sequence of partial sums.

A series is a sum of the terms in a sequence. A convergent sequence is one that has a limit as n approaches infinity, meaning that the sequence approaches a specific value. Similarly, a sequence of partial sums is the sum of the first n terms of the series. If this sequence of partial sums converges to a specific value, then the series is convergent. However, if the sequence of partial sums diverges, meaning it does not approach a specific value, then the series is divergent. Understanding whether a series is convergent or divergent is important in various fields such as physics and engineering.
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The expectation E(X) of the given random variable is: (A) E(X) = 45, The variance Var(X) of the given random variable is: (B) Var(X) = 150

A-To calculate the expectation E(X), we multiply each value of X by its corresponding probability and sum them up:

E(X) = (20 * 0.05) + (30 * 0.05) + (40 * 0.35) + (50 * 0.20) + (60 * 0.35) = 1 + 1.5 + 14 + 10 + 21 = 45

B-To calculate the variance Var(X), we need to find the squared deviation of each value from the expected value, multiply it by its corresponding probability, and sum them up:

Var(X) = ( (20 - 45)² * 0.05 ) + ( (30 - 45)² * 0.05 ) + ( (40 - 45)² * 0.35 ) + ( (50 - 45)² * 0.20 ) + ( (60 - 45)² * 0.35 )

= ( 625 * 0.05 ) + ( 225 * 0.05 ) + ( 25 * 0.35 ) + ( 25 * 0.20 ) + ( 225 * 0.35 )

= 31.25 + 11.25 + 8.75 + 5 + 78.75

= 135

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There is a 42.3% chance that the Rangers will win a majority of their seven games against the Islanders, assuming their win percentage stays the same.

We can use the binomial distribution to calculate the probability of the Rangers winning a majority of their games against the Islanders, given their win percentage of 55.1%. Let's denote the probability of the Rangers winning a single game against the Islanders as p.

Since the Rangers and Islanders play seven games against each other, the number of games the Rangers win against the Islanders follows a binomial distribution with parameters n = 7 and p = 0.551.

To find the probability that the Rangers win a majority of these seven games, we need to sum the probabilities of all possible outcomes where they win four or more games. We can use the binomial probability formula to calculate each of these individual probabilities and then sum them up:

P(Rangers win 4 or more games) = P(Rangers win 4 games) + P(Rangers win 5 games) + P(Rangers win 6 games) + P(Rangers win 7 games)

\(= (7 choose 4) * 0.551^4 * (1 - 0.551)^3 + (7 choose 5) * 0.551 ^ 5 * (1 - 0.551)^2 + (7 choose 6) * 0.551^6 * (1 - 0.551) + (7 choose 7) * 0.551^7\)

Using a binomial calculator or a spreadsheet, we can evaluate this expression and find that:

P(Rangers win a majority of their games against the Islanders) = 0.423

Therefore, there is a 42.3% chance that the Rangers will win a majority of their seven games against the Islanders, assuming their win percentage stays the same.

The Binomial distribution is a discrete probability distribution that describes the probability of obtaining a certain number of successes in a fixed number of independent trials, where each trial can have only two outcomes (e.g., success or failure).

The distribution is defined by two parameters: the number of trials n and the probability of success in each trial p. The distribution gives the probability of obtaining k successes in n trials, where k can range from 0 to n.

The formula for the probability mass function of the Binomial distribution is:

\(P(k) = (n choose k) * p^k * (1 - p)^n-k\)

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items. The formula can be used to calculate the probability of obtaining k successes in n trials, given a fixed probability of success p.

The Binomial distribution is used in many areas of statistics, including quality control, epidemiology, and finance, among others. It is also a fundamental building block for more complex statistical models, such as the Poisson distribution and the normal distribution.

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The sum of an arithmetic sequence given a partial sum is 35532.

Firstly, we need to identify the common difference of the arithmetic sequence. This can be done by finding the difference between any two consecutive terms. In this case, subtracting 9 from 3 gives us a common difference of 6.

Next, we determine the number of terms in the sequence. To do this, subtract the first term from the given partial sum and divide the result by the common difference. In this case, subtracting 3 from 639 and dividing by 6 gives us 106 terms.

Finally, we can calculate the sum using the arithmetic series formula: Sn = (n/2)(2a + (n-1)d), where Sn represents the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, we have Sn = (106/2)(2*3 + (106-1)*6). Simplifying this expression, we find that the sum of the arithmetic sequence is 35532.

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Answer: y=1/2x+4

Step-by-step explanation:

Answer:

A full rotation of an object

y+43°= 180°( straight angle)

=>y= 180°-43°

=>y=137°

The critical points are x = π/4 and x = 3π/4, and the extreme values on the interval [0,2] are 1/2 and -1/2,

To find the critical points of f(x) = 2 sin(x) cos(x) on the interval [0, 2] and determine the extreme values, we will first take the derivative of the function and set it equal to zero to find the critical points.

f(x) = 2 sin(x) cos(x)

f'(x) = 2 cos(x) cos(x) - 2 sin(x) sin(x) (using the product rule)

\(f'(x) = 2(cos^2(x) - sin^2(x))\)

f'(x) = 2(cos(2x))

Setting f'(x) equal to zero to find the critical points, we get:

2(cos(2x)) = 0

cos(2x) = 0

2x = π/2, 3π/2, 5π/2

x = π/4, 3π/4, 5π/4

Only the values x = π/4 and x = 3π/4 are in the interval [0,2], so these are the critical points.

Next, we need to determine the extreme values of f(x) at these critical points and the endpoints of the interval [0,2].

We can do this by evaluating the function at these points and comparing the values.

f(0) = 0

f(π/4) = 2(sin(π/4)cos(π/4)) = sin(π/2)/2 = 1/2

f(3π/4) = 2(sin(3π/4)cos(3π/4)) = -sin(π/2)/2 = -1/2

f(2) = 0

Therefore, the function has a maximum value of 1/2 at x = π/4 and a minimum value of -1/2 at x = 3π/4.

There are no extreme values at the endpoints of the interval [0,2].

Thus, the critical points are x = π/4 and x = 3π/4, and the extreme values on the interval [0,2] are 1/2 and -1/2, respectively.

The final answer is: π/4, 3π/4, 1/2, -1/2

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2x²+8x=x²-16

2x²-x²+8x+16=0

x²+8x+16=0

D=b²-4ac

=8²-4×1×16

=64-64

=0

x= -b+VD / 2a

=-8+V0 /2

= -8/2

=-4

The solution is, the solution to the equation is x=-4

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

we need to find the solution to 2x²+8x=x²-16.

so, we have,

the equation is:

2x²+8x=x²-16

2x²-x²+8x+16=0

x²+8x+16=0

now, we know that,

D=b²-4ac

=8²-4×1×16

=64-64

=0

again, we have,

x= -b+VD / 2a

=-8+V0 /2

= -8/2

=-4

Hence, the solution to the equation is x=-4.

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Answer:

15

Step-by-step explanation:

trust me

The formula for sin and cos are opposite side/hypotenuse and adjacent side/hypotenuse respectively.  

Sin and Cos formulae are based on the sides of the right-angled triangle. Along with the tan function, the fundamental trigonometric functions in trigonometry are sin and cos. In contrast to the cosine of an angle, which corresponds to the ratio of the adjacent side to the hypotenuse, the sine of an angle is the ratio of the opposing side to the hypotenuse.

Sine of an angle θ = opposite side/hypotenuse

Cosine of an angle θ = adjacent side/hypotenuse

The figure given in the attachment is a right angled triangle which shows opposite side, adjacent side and hypotenuse side with an angle θ which is specified.

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Answer: y=-64

Step-by-step explanation:

From the first sentence: the value of y varies directly with x:

y∝x

y=cx where c=variation constant

When y=40 x=-5

40=-5c

Therefore c=-8

To find y when x=8

y=cx where c=-8 and x=8

y=-8*8

y=-64

The perimeter of a rectangle is calculated using the formula:

The question gives that the length and width of the rectangle are equal. This means that:

Therefore, the perimeter will be calculated to be:

The perimeter is given to be 32 m. Therefore, the length of the rectangle will be:

Using the formula for the area:

Therefore, the area will be:

The area is 64 square meters.

True , Every matrix transformation is a linear transformation.

Is there a linear transformation for every matrix operation?

Despite the fact that every linear transformation is a matrix transformation, not all linear transformations are matrix transformations.      

                                    Because of this, it's possible that we'll encounter a linear transformation in which we're unable to locate a matrix to carry out the mapping.

What alteration does matrix entail?

In a two-dimensional or three-dimensional space, the transformation matrix converts one vector into another vector, which may be comprehended geometrically.

                                    Stretching, squeezing, rotation, reflection, and orthogonal projection are some of the often utilized transformations.

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The measure of each angle are

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

<4 = 134

So, <4 = <2 = 134 (Vertical opposite angle)

<4= <8= 134 (Corresponding Angle)

<1 + <4 = 180 (Linear Pair)

<1 = 180-134

<1 = 46

<1 = <3= 46 (Vertical opposite angle)

<2= <6= 164 (Corresponding Angle)

<3= <7 (Corresponding Angle)

<1= <5 (Corresponding Angle)

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Answer:

n = 28

Step-by-step explanation:

The angle at the centre is twice the angle on the circle subtended on the same arc, then

35 + m = 0.5 × 98 = 49 ( subtract 35 from both sides )

m = 14

∠ n is at the centre subtended on the same arc as ∠ m , thus

n = 2m = 2 × 14 = 28

Answer:

Step-by-step explanation:

Sum of 25 and square of 2:

Negative reciprocal of 29:

Answer:

Can you attach a picture because its really hard find the answer for me. But I will totally help!!

Step-by-step explanation:

Answer:

Answer B)  (18, 2)

Step-by-step explanation:

Bc I'm just right.

Answer:

  y ≈ 60.6 units

Step-by-step explanation:

Given a triangle with angles 18° and 117°, and sides 21 opposite 18° and y opposite 117°, you want to know the value of y.

The law of sines tells you the ratios of side length to the sine of the opposite angle are the same for all side/angle pairs in the triangle.

  y/sin(117°) = 21/sin(18°)

  y = 21·sin(117°)/sin(18°) ≈ 60.55

The value of y is about 60.6 units.

In the competition model where and are the populations of the competing species, moose and deer, respectively, the coefficient d represents option C  the decrease in the moose population due to interactions with the deer .

In the competition model where  \(N_1\)and \(N_2\) are the populations of the competing species, moose and deer, respectively, the coefficient "d" represents the decrease in the moose population due to interactions with the deer. The competition model is a type of ecological model used to examine the effects of interspecific competition on population dynamics.

This model is widely applied to the interactions between two species that occupy similar niches and compete for limited resources. According to this model, two species are assumed to compete for a shared resource, such as food, water, or territory.

The growth rate of the two species is thus affected by their interactions with each other. The competition model is based on two coupled differential equations:

\(dN_1/dt = r_1N_1(1 - (N_1 + aN_2)/K_1)\) and \(dN_2/dt = r_2N_2(1 - (N_2 + bN_1)/K_2)\)

where \(N_1\)and \(N_2\) are the population sizes of the two species, \(r_1 and r_2\) are their intrinsic growth rates, \(K_1\) and\(K_2\) are the carrying capacities of their habitats, and a and b are the competition coefficients that represent the effects of one species on the other.

The coefficient d represents the decrease in the moose population due to interactions with the deer. Hence, the correct answer is option C.

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A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

9x²

Step-by-step explanation:

3x × 3x= 9x²

That's all

Answer:

h = 7.7 cm

Step-by-step explanation:

you can create a proportion using Law of Sines

sin 90 = sin 31

   15            h

1 = 0.515

15       h

h ≈ 7.7

Answer:

-4x

Step-by-step explanation:

3-7=-4 just add a x

Answer:

$340.

Step-by-step explanation:

Given that some products, such as a pair of trousers in this case, are sold at 2/5 of their value, if the trousers cost $ 850, the following calculation must be performed to determine their sale value:

2/5 = 0.4

850 x 0.4 = X

340 = X

Therefore, selling them at 40% of their value, the trousers' sale value was $ 340.