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Final answer:

The length of the diagonal between points K(0,3) and L(4,1) in a parallelogram is calculated using the distance formula, which is 2√5 units.

Explanation:

To find the length of the diagonal between the points K(0,3) and L(4,1), we can use the distance formula, which is derived from the Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) in a coordinate plane is calculated by the formula:

d = √((x2 - x1)² + (y2 - y1)²)

For points K(0,3) and L(4,1), this becomes:

d = √((4 - 0)² + (1 - 3)²)

d = √(16 + 4)

d = √20

d = 2√5

The diagonal's length is 2√5 units.

A polynomial expression can be factored by grouping when it has at least four terms. To factor by grouping, group the terms into pairs, factor out the greatest common factor from each pair, apply the distributive property to factor out the common binomial factor, and simplify.

A polynomial expression can be factored by grouping when it has at least four terms. To factor by grouping, follow these steps:

For example, let's consider the polynomial expression 3x^3 - 3x^2 + 2x - 2. We can group the terms as (3x^3 - 3x^2) + (2x - 2). Factor out the greatest common factor from each pair of terms, which gives us 3x^2(x - 1) + 2(x - 1). Applying the distributive property, we can factor out the common binomial factor (x - 1), resulting in (x - 1)(3x^2 + 2). This is the factored form of the original polynomial.

A polynomial expression that can be factored by grouping typically has four terms that are grouped into pairs, with each pair having a common factor. After factoring out the common factors from each pair, if the resulting binomials are identical, the expression can then be factored into the product of two binomials.

The structure of a polynomial expression that can be factored by grouping typically involves four terms with the possibility of factoring pairs of terms separately. To use this method, you would look for common factors in the first two terms and in the last two terms. If a common factor is found in both pairs, you can then factor out these common factors and check if the resulting binomials are identical. If so, you can factor out the binomial, leaving you with a product of two binomials as the factored form of the polynomial.

Here is a step-by-step example:

Thus, you've factored the original polynomial by grouping.

Answer:

[tex]cos(180\°)=-1[/tex]

[tex]sin(180\°)=0[/tex]

Step-by-step explanation:

we know that

In the unit circle the coordinates of the point belong to the x-axis for an angle equal to [tex]180\°[/tex] is [tex](-1,0)[/tex]

we have

[tex]x=1\ units, y=0\ units[/tex]

Applying Pythagoras theorem

[tex]H=\sqrt{1^{2}+0^{2}} =1[/tex]

so

[tex]cos(180\°)=x/H[/tex]

substitute

[tex]cos(180\°)=-1/1=-1[/tex]

[tex]sin(180\°)=y/H[/tex]

substitute

[tex]sin(180\°)=0/1=0[/tex]

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

We have been an equation [tex]x^2-3x-4=x^2-5x+6[/tex]. We are asked to find the solution of our given equation.

[tex]x^2-x^2-3x-4=x^2-x^2-5x+6[/tex]

[tex]-3x-4=-5x+6[/tex]

Adding 5x on both sides of our equation we will get,

[tex]-3x+5x-4=-5x+5x+6[/tex]

[tex]2x-4= 6[/tex]

Upon adding 4 on both sides of our equation we will get,

[tex]2x-4+4= 6+4[/tex]

[tex]2x=10[/tex]

Now, we will divide both sides of our equation by 2.

[tex]\frac{2x}{2}=\frac{10}{2}[/tex]

[tex]x=5[/tex]

Therefore, the solution of our given equation is [tex]x=5[/tex].

The value of x from the expression is 5

Given the equation x²-3x-4 = x²-5x+6

Collect the like terms

x² - x² -3x +5x -4 -6 = 0

Simplify the result

2x - 10 = 0

Add 10 to both sides

2x - 10 + 10 = 10

2x = 10

x = 5

Hence the value of x from the expression is 5

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Answer:

[tex]\sqrt{113}[/tex] is an irrational number.

Step-by-step explanation:

We are asked to find whether square root of 113 is rational or irrational.

We know that a number is rational number when it can be written as a fraction.

Upon finding the value of [tex]\sqrt{113}[/tex], we will get:

[tex]\sqrt{113}=10.6301458127346[/tex]

We can see that [tex]\sqrt{113}[/tex] has neither non-terminating nor a repeating decimal, therefore, it cannot be written as a fraction and it is an irrational number.

19/7 = 114/x

= 114*7 = 798

798/19 = 42

answer is 42

For the table, y = 9x.

 so the price of a short cake is $9


For the graph, y = 4x
so the price of a sweet bread is $4

9-4 = 5

 the short cake is $5 more than the sweet bread

Answer:

If you look at the pictures the question gives you. 5 shortcakes = 45$

5 sweetbreads = 20$.

So you would divide 45 by 5, which gives u 9

Then you would divide 20 by 5, which gives you 4.

Then after you would subtract 9 by 4, which gives you 5$

So your answer for this question would be 5$.

Answer:

A

Step-by-step explanation:

1) LN=LN reflexive property of congruence

2) KN=MN, given

3) <MLN=<KLN, bisected angles are congruent

4) Triangle MNL=Triangle KNL by the HL theorem

To solve sec x/2 = cos x/2, we use the identity sec(θ) = 1/cos(θ). After rearranging, we identify the solution as x = 0 and x = 2π, fitting the interval [0, 2π).

To solve the equation sec x/2 = cos x/2 for the interval [0, 2π), we first need to understand the relationship between secant and cosine functions. Recall that sec(θ) is the reciprocal of cos(θ), thus sec(θ) = 1/cos(θ). Given the equation sec x/2 = cos x/2, we can substitute sec x/2 with 1/cos x/2 to get 1/cos x/2 = cos x/2.

Next, to solve for x, we multiply both sides by cos x/2 to get rid of the fraction: 1 = cos^2(x/2). We know that the square of the cosine function can also be related to the identity cos^2(x) = (1 + cos(2x))/2. Applying this identity, we have 1 = (1 + cos x)/2. Solving for cos x, we get cos x = 1, which occurs at x = 0, 2π in the interval [0, 2π). Therefore, the solution to the equation is x = 0 and x = 2π.

The equation sec x/2 = cos x/2 is solved by finding angles where the cosine of half the angle is either 1 or -1. This leads to solutions x = 0 and x = 2pi within the interval [0, 2pi).

To solve the equation sec x/2 = cos x/2 for the interval [0, 2pi), we can make use of trigonometric identities to simplify and solve for x. The secant function is the reciprocal of the cosine function, so sec(x/2) = 1/cos(x/2). This leads to the equation 1/cos(x/2) = cos(x/2). Solving for cos(x/2), we get cos^2(x/2) = 1, which implies that cos(x/2) = ±1. Therefore, we're looking for angles where the cosine of half the angle is either 1 or -1. This corresponds to angles of 0, pi, and 2pi for cos(x/2) = 1, and pi for cos(x/2) = -1, remembering that we are considering x/2 and need to multiply these results by 2 to solve for x. Accordingly, the solution to the equation within the given interval is x = 0, 2pi, and 4pi (which is equivalent to 0 within one full rotation of the circle), but since we're restricting x to be within [0, 2pi), the accepted solutions are x = 0 and x = 2pi.

The correct answer is X=-3+or-rad33/6

The roots of the quadratic equation 3x^2+3x-2=0 as provided by the quadratic formula are x1 = (3 + sqrt(33))/6 and x2 = (3 - sqrt(33))/6.

The quadratic equation in question is 3x^2+3x-2=0. Here, a=3, b=3, and c=-2. We can solve this equation using the quadratic formula, which, in general terms, is given as: x = [-b ± sqrt(b² - 4ac)] / 2a.

Plugging the coefficients into the quadratic formula, we get:

x = [-3 ± sqrt((3)² - 4*3*(-2))] / 2*3

= [-3 ± sqrt(9 + 24)] / 6

= [-3 ± sqrt(33)] / 6

That gives us two roots: x1 = (3 + sqrt(33))/6 and x2 = (3 - sqrt(33))/6. These are the solutions for the quadratic equation given.

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Answer:

c 2.5 radians

Step-by-step explanation:

As the sample size increases, the distribution of the sample mean tends to become more normal regardless of the population distribution due to the Central Limit Theorem. The mean of the sampling distribution approaches the population mean, and the standard error decreases, resulting in more reliable statistical analyses.

Effects of Increasing Sample Size on the Distribution of the Sample Mean

As the sample size n increases, the distribution of the sample mean tends to become more normal, even if the population distribution is not normal. This is a result of the Central Limit Theorem, which states that the sampling distribution of the mean approaches a normal distribution as n, the sample size, increases. According to the law of large numbers, the mean of the sample means will get closer to the population mean as sample size grows.

When the population is skewed right and we take a simple random sample, the original distribution being non-normal requires a larger sample size to make the sample mean distribution resemble a normal distribution. Generally, sample sizes equal to or greater than 30 are considered sufficient for the sampling distribution to be normal; however, if the original population distribution is further from a normal curve, a larger sample size may be needed to achieve normality.

The practical implication of this is that as sample size increases, the variability (as measured by the standard error) of the sample mean decreases, and this results in a sampling distribution that is more tightly clustered around the true population mean. Therefore, statistical analyses and predictions become more reliable with larger samples.

Answer:

Step-by-step explanation:

Givens:

Basically, the number of computer sold has to subtracted from the inventory, because those are articles that are going out, after being sold, they won't exist in the inventory anymore.

So, this difference between the existence in the inventory and the number of computer sold is best modelled by the second option, because the number of article sold has to subtracted from the inventory, not in the opposite way as the option A states.

If 220 computers is the existence in the inventory, that's the initial condition, which won't variate, because the number of articles in the inventory is represented by y. Also, if they sell 3 computers per day, the expression would be 3x.

Now, after we sell we take out the articles sold from the inventory, then, the function would be:

y = 220 - 3x

Therefore, option B is the answer.

g(x)  = 12(2)x - 1

 h(x)  = 3x  

 We are looking for this :

 g(6) * h(6)     ....so we have....

 12(2)6-1  * 36   =

 12(2)5  * 729  =

 12*32 * 729   =  279,936 points

On the hardest setting of level 6, a player will need 729 points.

The student is asking how many points they will need on the hardest setting of level 6 in a video game according to the function that sets the point requirement.

The function given in the question is [tex]g(x) = 12(2)^x - 1[/tex] and the function for the hardest setting is [tex]h(x) = 3^x.[/tex]

To find the number of points required on the hardest setting for level 6, we plug in x = 6 into the hardest setting function: [tex]h(6) = 3^6.[/tex]

Calculating this gives us h(6) = 729.

Therefore, a player will need 729 points on the hardest setting of level 6.

Answer:

The solution is x = 2 or x = 3  

Step-by-step explanation:

we have to find the solution of the equation

[tex] x=2+\sqrt{(x-2)}[/tex]

[tex]x=2+\sqrt{(x-2)}\\ \\x-2=\sqrt{x-2}\\\\\text{Squaring on both sides }\\\\(x-2)^2=x-2\\\\x^2+4-4x=x-2\\\\x^2-5x+6=0\\\\x^2-2x-3x+6=0\\\\x(x-2)-3(x-2)=0\\\\(x-2)(x-3)=0\\\\x=2\text{ or }x=3[/tex]

Hence, correct option is x = 2 or x = 3

Answer:

C) x = 2 or x = 3

Step-by-step explanation:

Edge 2021

The resale value of the laptop after 3 years will be $949.22

Exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time.

The formula for the exponential decay is

[tex]y = a(1-b)^{x}[/tex]

Where,

y is the final amount

a is the original amount

b is the decay factor

x is the amount of time that has passed

According to the given question.

The initial price of the laptop, a = $2250.

decay factor, b = [tex]\frac{25}{100} = \frac{1}{4}[/tex]

Therefore,

The resale value of the laptop after 3 years

= [tex]2250(1-\frac{1}{4} )^{3}[/tex]

[tex]= 2250(\frac{4-1}{4} )^{3}[/tex]

[tex]= 2250(\frac{3}{4} )^{3}[/tex]

[tex]= 2250\times \frac{27}{64}[/tex]

[tex]= 35.156 \times 27\\=\$ 949.22[/tex]

Hence, the resale value of the laptop after 3 years will be $949.22

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The weight of Anna is: 115 pounds

and the weight of Janet is: 135 pounds.

It is given that:

Janet weighs 20 pounds more than Anna.

This means if the weight of Anna is: x pounds

Then the age of Janet is: (x+20) pounds.

Also,

The sum of their weights is 250 pounds.

i.e.

x+x+20=250

i.e.

2x+20=250

On subtracting both side by 20 we have:

2x=250-20

i.e.

2x=230

On dividing both side by 2 we have:

x=115

Hence, the weight of Anna is:115 pounds.

and the weight of Janet is: 115+20=135 pounds.

78 / 3 3/4 =

78/1 / 15/4 =

78/1 x 4 /15 = 312/15 = 20.8

 20 pieces 3 3/4 inches long can be cut

Answer: $16

Step-by-step explanation:

Let x represents the cost of one subway ticket and y represents the cost of one express ticket.

According to the question, we have the following equations :-

[tex]6x+4y=24.........................(1)\\\\3x+7y=27..................(2)[/tex]

Multiply equation (2) with 2 on both sides , we get

[tex]6x+14y=54....................(3)[/tex]

Subtract equation (1) from equation (3) , we get

[tex]10y=30\\\\\Rightarrow y=\dfrac{30}{10}=3[/tex]

Put the value of y in (2), we get

[tex]3x+7(3)=27\\\\\Rightarrow\ 3x+21=27\\\\\Rightarrow\ 2x=6\\\\\Rightarrow\ x=2[/tex]

Thus, the cost of a subway ticket = $2

The cost of a express ticket = $3

Now, the cost of 5 subway tickets and 2 express tickets will be :-

[tex]5(2)+2(3)=\$16[/tex]

Answer:

answer is b

Step-by-step explanation:

Answer:

1.24 acres or 54,000 feet

by-step explanation:

54000=1.2396694

300*180=54000

Then round up 1.2396694 and u get 1.24