kiara takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. the cut she makes is 20 centimeters long and the width of the paper is 12 centimeters. what is the paper's length?

When given triangles are given then the value of x and y is 5 and 14 respectively.

When BC is similar to EF.

19= 4x-1

19+1=4x

20=4x

x=5

When DE is similar to AB

y-6 =8

y=8+6

y=14

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

A pair of triangles are said to be similar if two pairs of corresponding angles in those triangles are congruent. We can conclude that the third pair must also be equal if the first two angle pairs are. When all three pairs of angles are equal, the sides of the three triangles must also be proportionate.

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The solution of the equation y/7=-11 is y=-77

To solve the equation `y/7=-11`, we can multiply both sides of the equation by 7.

This is because we can isolate y on one side of the equation by undoing the division as follows:

y/7 = -11

Multiply both sides by 7:

7(y/7) = 7(-11)

We get:

y = -77

Therefore, the solution to the equation y/7 = -11 is y = -77, as shown above.

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The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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The area of the regular hexagon with a side length of 12 feet and an apothem of 10 feet is \(216\sqrt{3}\) feet.

To find the area of a regular hexagon, you can use the formula:

\(Area = (3 *\sqrt{3} *side~length^2) : 2\)

Given that the side length of the hexagon is 12 feet, we can substitute this value into the formula:

Area = \((3 * \sqrt{3} * 12^2) : 2\)

Simplifying further:

Area = \((3 * \sqrt{3} * 144) : 2\)

Area = \(216\sqrt{3}\)

Therefore, the area of the regular hexagon with a side length of 12 feet and an apothem of 10 feet is \(216\sqrt{3}\) feet.

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The area of the regular hexagon with a side length of 12 feet and an apothem length of 10 feet is approximately 936 square feet.

To find the area of a regular hexagon, you can use the formula:

Area = (3 × √3 × s²) / 2,

where "s" represents the length of a side.

Given that the side length (s) of the hexagon is 12 feet, we can substitute this value into the formula:

Area = (3 × √3 × s²) / 2

Area = (3 × √3 × 12²) / 2

= (3 × √3 × 144) / 2

= (3 × √3 × 144) / 2

= (3 × √3 × 12 × 12) / 2

= (3 × √3 × 144) / 2

= (3 × √3 × 144) / 2

= (3 × √3 × 144) / 2

= (3 × √3 × 144) / 2

= (3 × √3 × 144) / 2

= (3 × √3 × 144) / 2

≈ 936 square feet.

Therefore, the area of the regular hexagon with a side length of 12 feet and an apothem length of 10 feet is approximately 936 square feet.

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Answer:

\(ax^{2} +bx+c^{2}=0\)

Step-by-step explanation:

A quadratic equation is a equation that takes the form: \(ax^{2} +bx+c^{2} = 0\)

   Ex. Using our definition of quadratic equations, \(ax^{2} +bx+c^{2}=0\),

          We can set a = 2, b = 1, c = 6:

               \(2x^{2} +x+6^{2}=0\)

               \(2x^{2} +x+36=0\)

          Which can then be solved (if you are trying to solve it) as:

               \((2x+9)(x-8)=0\)

                \(x=\frac{9}{2}, 8\)

The volume of a shape is the amount of space in the shape

The radius of the cylinder is 3 mm

The given parameters of the cone are:

Radius = 3mm

Height = 6mm

The volume of the cone is:

\(V =\frac 13\pi r^2h\)

So, we have:

\(V =\frac 13\pi * 3^2 * 6\)

The volume of a cylinder is:

\(V= \pi r^2h\)

The height is:

Height = 2 mm

So, we have:

\(V= \pi r^2 * 2\)

The volumes are equal.

So, we have:

\(\pi r^2 * 2 = \frac 13\pi * 3^2 * 6\)

Divide the common factors

\(r^2 = \frac 13 * 3^2 * 3\)

Evaluate the products

\(r^2 = 9\)

Take the square roots of both sides

\(r = 3\)

Hence, the radius of the cylinder is 3 mm

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The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Saturday restocked (S) = 3 * Thursday restocked (T) - 12

Total restocked (S+T) = 228

Substituting S in the second equation gives T = 72

Therefore, S = 204.

To solve this problem, we can use a system of two equations with two variables. Let's call the number of machines restocked on Thursday "T" and the number restocked on Saturday "S". We can then translate the information given in the problem into equations:

S = 3T - 12 (Saturday restocked 12 less than 3 times Thursday restocked)

S + T = 228 (the total number of machines restocked on both days is 228)

We now have two equations with two variables, which we can solve using substitution or elimination. Substituting equation 1 into equation 2, we get:

(3T - 12) + T = 228

Simplifying this equation, we get:

4T - 12 = 228

Adding 12 to both sides, we get:

4T = 240

Dividing both sides by 4, we get:

T = 60

We can now use equation 1 to find S:

S = 3T - 12

S = 3(60) - 12

S = 180 - 12

S = 168

Therefore, the company restocked 60 machines on Thursday and 168 machines on Saturday.

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Saturday restocked (S) = 3 * Thursday restocked (T) - 12

Total restocked (S+T) = 228

Substituting S in the second equation gives T = 72

Therefore, S = 204.

To solve this problem, we can use a system of two equations with two variables. Let's call the number of machines restocked on Thursday "T" and the number restocked on Saturday "S". We can then translate the information given in the problem into equations:

S = 3T - 12 (Saturday restocked 12 less than 3 times Thursday restocked)

S + T = 228 (the total number of machines restocked on both days is 228)

We now have two equations with two variables, which we can solve using substitution or elimination. Substituting equation 1 into equation 2, we get:

(3T - 12) + T = 228

Simplifying this equation, we get:

4T - 12 = 228

Adding 12 to both sides, we get:

4T = 240

Dividing both sides by 4, we get:

T = 60

We can now use equation 1 to find S:

S = 3T - 12

S = 3(60) - 12

S = 180 - 12

S = 168

Therefore, the company restocked 60 machines on Thursday and 168 machines on Saturday.

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

Step-by-step explanation:

Actually 75067 x 2= 150134

Let's create a vector F(x, y, z) with at least two variables in its components:

F(x, y, z) = (xy + 2z)i + (yz + 3x)j + (xz + y)k

Now, let's find the gradient, divergence, and curl of this vector:

1. Gradient (∇F):

The gradient of a vector is given by the partial derivatives of its components with respect to each variable. For our vector F(x, y, z), the gradient is:

∇F = (∂F/∂x)i + (∂F/∂y)j + (∂F/∂z)k

Calculating the partial derivatives:

∂F/∂x = yj + zk

∂F/∂y = xi + zk

∂F/∂z = 2i + xj

Therefore, the gradient ∇F is:

∇F = (yj + zk)i + (xi + zk)j + (2i + xj)k

2. Divergence (div F):

The divergence of a vector is the dot product of the gradient with the del operator (∇). For our vector F(x, y, z), the divergence is:

div F = ∇ · F

Calculating the dot product:

div F = (∂F/∂x) + (∂F/∂y) + (∂F/∂z)

Substituting the partial derivatives:

div F = y + x + 2

Therefore, the divergence of F is:

div F = y + x + 2

3. Curl (curl F):

The curl of a vector is given by the cross product of the gradient with the del operator (∇). For our vector F(x, y, z), the curl is:

curl F = ∇ × F

Calculating the cross product:

curl F = (∂F/∂y - ∂F/∂z)i - (∂F/∂x - ∂F/∂z)j + (∂F/∂x - ∂F/∂y)k

Substituting the partial derivatives:

curl F = (z - 3x) i - (z - 2y) j + (y - x) k

Therefore, the curl of F is:

curl F = (z - 3x)i - (z - 2y)j + (y - x)k

That's it! We have calculated the gradient (∇F), divergence (div F), and curl (curl F) of the given vector F(x, y, z) by finding the partial derivatives, performing dot and cross products, and simplifying the results.

Answer:

(x-4)(x+4)

Step-by-step explanation:

This is a special case. Eventually, it will be helpful to memorize these, but for now, this special case is (a-b)(a+b)=(a^2)-(b^2). In this case, a=x and b=4 because the square root of 16 is 4. Plug in your numbers and then you have: (x-4)(x+4) which is your answer!

I hope this helped! :)

If your looking for a true or false answer because I didn't know what type of problem that you were asking, the answer is false because you haven't factored the equation, if anything, you simplified it. factoring would be what we did above.

Answer:

option a

Step-by-step explanation:

in figure 1: 4n+8 = 4×1=4+8=12

figure 2:4n+8 =4×2=8+8=16 and so on

Answer:

x = {- 8, 2}

Step-by-step explanation:

Since, B is between line AC.

\(\therefore AB + BC = AC\\

\therefore x^2 - 3x + 9x = 16\\

\therefore x^2 - 3x + 9x - 16=0\\

\therefore x^2 + 6x - 16=0\\

\therefore x^2 + 8x - 2x- 16=0\\

\therefore x(x +8) - 2(x + 8)=0\\

\therefore (x+8)(x-2)=0\\

\therefore x + 8 = 0\: or \: x-2=0\\

\therefore x = - 8 \:or\: x = 2\\

\huge \orange {\boxed {\therefore x = \{-8,\: 2\}}} \)

Answer:

The code is 8415

Step-by-step explanation:

Answer:I think CBD

Step-by-step explanation:

Answer:

In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign.

Answer:

D. 57

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The variance and standard deviation of the heart rate for the 5 team members after running a mile is 71.5 and 8.4557.

Variance is a measure of how much a data point deviates from the mean. Variance, according to Layman, is a measure of how much a set of data (a number) varies from its mean (mean). Variance means finding the expected difference in deviation from the actual value.  

mean = (180+189+199+200+197)/5=193

variance=

= (169+16+36+49+16)/4 = 71.5

  standard deviation =\(\sqrt{variance}\)

= \(\sqrt{71.5}\) =  8.4557

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The probability of drawing a seven and then a four when randomly drawing two cards without replacement is 0.0045 or approximately 0.45%.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement can be calculated using the following steps:

First, we need to determine the total number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement. This can be found using the combination formula:

C(52,2) = 52! / (2! * (52-2)!) = 1,326

Next, we need to determine the number of favorable outcomes where we draw a seven and then a four.

There are four sevens and four fours in a deck of 52 cards, so the probability of drawing a seven on the first draw is 4/52. Since we are not replacing the card, there are now 51 cards left in the deck, and three of them are fours. Therefore, the probability of drawing a four on the second draw is 3/51.

The probability of drawing a seven and then a four is the product of the probabilities of drawing a seven on the first draw and a four on the second draw:

P(seven and then four) = (4/52) * (3/51) = 0.0045 or approximately 0.45%.

Therefore, the probability of drawing a seven and then a four when without replacement is 0.0045 or approximately 0.45%.

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Answer:

No solutions (x ∈ empty set)

Step-by-step explanation:

The absolute value of a number is the distance of that number to zero. Distance has to be greater or equal to zero, so therefore, there is no such "x" so that the absolute value of x is -5.

Hope this helps :)

Answer: D: 2/3

Step-by-step explanation: the numbers you can get is 2, 1, 3, or 5, and the chance of rolling a certain number on a die is 1/6, so for 4 numbers it would be 4/6.

Tell me if I’m wrong

Sample space=6

Getting 2 or an odd no

Probability

p(E)

Answer:

-9n+8

Step-by-step explanation:

Similar triangles may or may not be congruent.

Question 1 to 6:

Triangles XYZ and NPQ are similar triangles.

This means that:

Angles Z and Q, lines YZ and PQ, angles P and Y, angles X and N, lines NQ and XZ, lines PN and YX are corresponding sides and angles

Question 7 to 12:

Triangles LMN and CBA are similar triangles.

This means that:

\(\mathbf{7z+6 = 5y}\)

\(\mathbf{2y-12 = z + 12}\)

Collect like terms

\(\mathbf{2y= z + 12+12}\)

\(\mathbf{2y= z + 24}\)

Make z the subject

\(\mathbf{z = 2y -24}\)

Substitute \(\mathbf{z = 2y -24}\) in \(\mathbf{7z+6 = 5y}\)

\(\mathbf{7(2y -24) + 6 = 5y}\)

\(\mathbf{14y -168 + 6 = 5y}\)

\(\mathbf{14y -162 = 5y}\)

Collect like terms

\(\mathbf{14y -5y = 162}\)

\(\mathbf{9y = 162}\)

Divide both sides by 9

\(\mathbf{y = 18}\)

Recall that: \(\mathbf{z = 2y -24}\)

\(\mathbf{z = 2 \times 18 - 24}\)

\(\mathbf{z = 12}\)

\(\mathbf{L = 60}\)

\(\mathbf{LN = 2y - 12}\)

\(\mathbf{LN = 2 \times 18 - 12}\)

\(\mathbf{LN = 24}\)

\(\mathbf{C = L}\)

\(\mathbf{C = 60}\)

\(\mathbf{AC = LN}\)

\(\mathbf{AC = 24}\)

Question 13:

The congruent parts are: KL and RQ,  KJ and RS, QS and LJ

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The value of dfbetween in the analysis of variances is 2. Thus option D is correct option.

According to the statement

we have given that the df total = 29 and df within = 27. And we have to find the value of the df between.

So, For this purpose, we know that the

Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts.

So, Df between values are the values between the value of dftotal and dfwithin.

Here df total = 29 and df within = 27

So, df between = df total - df within

Substitute the values in it then

df between = df total - df within

df between = 29 - 27

df between = 2.

So, The value of dfbetween in the analysis of variances is 2. Thus option D is correct option.

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After one week, Reggie has 195 trade cards. He buys 16 more trade cards every week. he have 371 trading cards after 12th week.

According to the question, given that

After one week, Reggie has 195 trade cards. He buys 16 more trade cards every week.

he have trading cards in the 12th week = 195 + 16 * (12 - 1)

                                                                    = 195 + 16 * 11

                                                                     = 195 + 176

                                                                      = 371

Therefore, we get after solve  371 trading cards after 12th week.

Mathematicians refer to equations with a degree of 1 as linear equations. The largest exponent of terms in these equations is 1, which equals. These can also be broken down into linear equations with one variable, two variables, three variables, etc. A linear equation with the variables X and Y has the conventional form a X + b Y - c = 0, where a and b are the corresponding coefficients of X and Y and c is the constant.

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Reggie has 195 trade cards after a week. Each week, he purchases 16 additional trading cards. After the 12th week, he had 371 trading cards.

In response to the query, assuming that

Reggie has 195 trade cards after a week. Each week, he purchases 16 additional trading cards.

he have trading cards in the 12th week = 195 + 16 * (12 - 1)

                                                                   = 195 + 16 * 11

                                                                    = 195 + 176

                                                                     = 371

As a result, by the end of the 12th week, we have solved 371 trade cards.

Equations with a degree of 1 are referred to be linear equations by mathematicians. In these equations, the term with the biggest exponent is equal, or 1. These can also be reduced to linear equations involving one, two, three, etc. variables. The standard form of a linear equation with the variables X and Y is a X + b Y - c = 0, where a and b are the corresponding coefficients of X and Y, and c is the constant.

Answer:

15/5 = 3

3 x 2 = 6

There are 6 men in the dance recital.

The engineer should take a sample size of approximately 40 to be 95% confident of being in error by only 0.125 minutes.

To calculate the sample size for estimating the cycle time, the engineer can use the formula for continuous data:

E = (zα/2) * (σ / √n)

where:
E is the maximum allowable error (0.125 minutes),
zα/2 is the z-value for a 95% confidence level (which corresponds to a 0.025 alpha level),
σ is the standard deviation (0.4 minutes), and
n is the sample size (unknown).

Rearranging the formula, we have:

n = (zα/2)^2 * (σ^2 / E^2)

Plugging in the given values, we get:

n = (1.96)^2 * (0.4^2 / 0.125^2)

Simplifying the equation, we have:

n ≈ 3.8416 * (0.16 / 0.015625)

n ≈ 3.8416 * 10.24

n ≈ 39.494

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Answer: i) Q=7*P   ii) if P=5 => Q=35 iii) if Q=42 => P=6

Step-by-step explanation:

Q is directly prportional to P that means that

Q/P=k=const ( where k is the prportionality coefficient)

So k= 28/4=7

So i)  Q= 7*P

ii) Q=5*7=35 if P=5 =>Q=35

iii) P=42/7=6   if Q=42 => P=6