Find the coordinates of the intersection of the diagonals of ABCD
with vertices A(0, 2), B(8, 2), C(4, − 4), and D(−4, − 4).
The coordinates of the intersection of the diagonals are ( , )

The value of the variable is equal to 0

Algebraic expressions are described as those mathematical expressions that are known to consist of terms, coefficients, constants, variables and factors.

These algebraic expressions are also composed of arithmetic operations, such as;

From the information given, we have that;

4x+4=4x-4

To determine the value of x, take the steps;

collect the like terms, we have;

4x - 4x = -4 - 4

subtract the values, we have;

0 = -8

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3) Sin B = 5/9.43, Cos B = 8/9.43, Tan B = 5/9.43

4) Angle A is 40 degrees

5) x is  23.8 mm

A specific type of triangle known as a right triangle has a single angle that is exactly 90 degrees, or a right angle. The sides that make up the right angle are the legs and the hypotenuse.

The Pythagorean theorem connects the side lengths of a right triangle by stating that the square of the hypotenuse's length is equal to the sum of the squares of the legs' lengths.

Cos A = 47/61

A = Cos-1(47/61)

= 40 degrees

5) The marked side can be obtained from;

Cos 28 = 21/x

x = 21/Cos 28

x = 23.8 mm

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The volume of the composite solids that consists of rectangular prisms is: A. 190 m³.

Note that the formula for finding the volume of a rectangular prism is given as:

Volume of rectangular prism = length * width * height.

Find the volume of each rectangular prism and add them together:

Volume of prism 1:

length = 10 m

width = 4 m

height = 3 m

Volume = 10 * 4 * 3 = 120 m³

Volume of prism 2:

length = 10 m

width = 1 m

height = 7 m

Volume = 10 * 1 * 7 = 70 m³

Total Volume = 120 + 70 = 190 m³.

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Answer:

[tex]\left \{ {{R + L = 27} \atop {1.99*L+1.29*R=43.23}} \right.[/tex]

Step-by-step explanation:

The critical value for a confidence level of 98% with a sample size of 32 is given as follows:

t = 2.4528.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.

(df is one less than the sample size).

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The volumes of the figures are

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

V = 22/7 * (32/2)² * 14

Evaluate

Volume = 11264

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

(2r)² = 40² - 32²

(2r)² = 576

So, we have

r = 12

So, we have

V = 22/7 * (12)² * 32

Evaluate

Volume = 14482.28

The rectangular prism

The volume is calculated as

V = lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 8 * 12 * 39

Evaluate

Volume = 3744

The triangular prism

The volume is calculated as

V = 1/2lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 1/2 * 11 * 5.4 * 16

Evaluate

Volume = 475.2

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * (33/2)³

Evaluate

Volume = 18824.14

The sphere

The volume of a sphere is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * 2.8³

Evaluate

Volume = 91.99

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a) Approximately 778.7 grams of thorium 234 will be left after 0.5 years.

b) Approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

(a) To find the amount of thorium 234 left after 0.5 years, we can use the equation:

[tex]A_t = A_0 e^{(-10.498t)}[/tex]

where A₀ is the initial amount, which is 1000 grams, t is the time in years, and At is the amount after t years.

Substituting t = 0.5, we get:

[tex]At = 1000 e^{(-10.498\times0.5)} = 778.7 \ grams[/tex]

Therefore, approximately 778.7 grams of thorium 234 will be left after 0.5 years.

(b) To find the time at which 115 grams of thorium 234 will be left, we can use the same equation and solve for t:

[tex]A_t = A_0 e^{(-10.498t)[/tex]

Dividing both sides by A₀ and taking the natural logarithm of both sides, we get:

ln(At/A₀) = -10.498t

Substituting At = 115 grams and A₀ = 1000 grams, we get:

ln(115/1000) = -10.498t

Solving for t, we get:

t = (ln(115/1000)) / (-10.498) ≈ 2.1 years

Therefore, approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

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Step-by-step explanation:

The sum of the interior angles of a n-gon is equal to  ( n-2)(180) degrees

 for this 6-gon   the sum is   (6-2) * 180 = 720 degrees

    (145 + 165 + 58 + 130 + 125 + x )    degrees = 720 degrees

           x = 97 degrees

Answer:

Exact form: 2.5185185185185

Simplified form: 2.52

Fraction form: 63/25

Step-by-step explanation:

Answer:

The exact volume of the cylinder is 72π cubic centimeters, or approximately 226.19 cubic centimeters to two decimal places.

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula:

[tex]\boxed{V = \pi r^2 h}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned} \implies V&=\sf \pi \cdot 3^2 \cdot 8\\&=\sf \pi \cdot 9 \cdot 8\\&=\sf 72\pi \;cm^3\\&= \sf 226.19\; cm^3\;(2\;d.p.)\end{aligned}[/tex]

Therefore, the volume of the cylinder is 72π cubic centimeters, or approximately 226.19 cubic centimeters to two decimal places.

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

Here, we have,

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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with scaling factor = 1/2 ,

the coordinate location of the dilated posit C is ( 2,-3)

Answer: 23.80

Step-by-step explanation:

[tex]\sqrt{19^2+18^2-2*19*18cos(80)}[/tex]

As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.

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

The function is given below:

y = |2x + 7|

The translated function is as follows:

y = |2(x - 1) + 7|

y = |2x - 2 + 7|

y = |2x + 5|

As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.

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The piecewise rule for the pattern is given as follows:

A piece-wise function is a function that has different definitions, depending on the input of the function.

The pattern for this problem is given as follows:

1,6,9,1,6,9.

The period of the pattern is given as follows:

3 units.

The pattern of the function is constant, meaning that all the outputs for an input that is a multiple of 3 are of 1, if the remainder of the division is of 1 the output is of 6, and if the remainder of the division is of 2 the output is of 9.

Hence the pattern is defined as follows:

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After considering the given details we conclude that the height of the picture frame is 12, under the condition that the diagonal of a picture frame is 18 inches the base of the picture frame is 12.

The height of the picture frame can be evaluated applying  the Pythagorean theorem. The Pythagorean theorem projects that in a right triangle, the square of the length of the hypotenuse (the diagonal of the picture frame) is equivalent to the summation of the squares of the lengths of the other two sides (the height and base of the picture frame).

Therefore , in this case, we have a right triangle with a hypotenuse of 18 inches and a base of 12 inches. We can evaluate for the height as follows:
height²+ 12² = 18²
height² = 18² - 12²
height² = 144
height = √(144)
height = 12
Hence, the height of the picture frame is 12 inches rounded to the nearest tenth.
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The total area of the composite figure is 17 square centimeters.

Remember that the area of a rectangle is equal to the product between its dimensions.

We can separate the figure into two rectangles, one of these rectangles is of 1cm by 2cm, then its area is:

A = 1cm*2cm = 2cm²

The other rectangle is of 3cm by 5cm, then its area is:

A' = 3cm*5cm = 15cm²

Adding that we get a total of:

total area = 2cm² + 15cm² = 17cm²

That is the area of the figure.

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Hello!

it's a multiplication

The value of cos(θ) value of cos(0) when the sine of the angle is -0.5 in the third quadrant is -sqrt(0.75).

To solve this problem, we need to use the fact that the sine and cosine functions are related through the Pythagorean identity: [tex]sin^2[/tex](0) + [tex]cos^2[/tex](0) = 1.
Since we know that the sine of angle 0 in the third quadrant is -0.5, we can use the unit circle to find the corresponding x-coordinate (cosine value) of the angle.
In the third quadrant, the angle is between 180 and 270 degrees, which means that the x-coordinate (cosine value) is negative.

We can draw a right triangle with the hypotenuse on the unit circle and the angle in the third quadrant, and use the Pythagorean theorem to find the length of the adjacent side (the x-coordinate).
The hypotenuse has a length of 1 because it is on the unit circle, and the opposite side (the y-coordinate) has a length of -0.5 because we know that the sine of the angle is -0.5. Using the Pythagorean theorem, we can solve for the length of the adjacent side (the x-coordinate):
[tex]cos^2[/tex](0) + (-0.5)2 = 1
[tex]cos^2[/tex](0) + 0.25 = 1
[tex]cos^2[/tex](0) = 0.75
Taking the square root of both sides, we get:
cos(0) = +/- sqrt(0.75)
Since we know that the cosine value is negative in the third quadrant, we can take the negative square root:
cos(0) = -sqrt(0.75)

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The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].

Option D is the correct answer.

We have,

The expression:

2/5 - 15 + 8 - 1/5 + 3

Now,

To make the simplification easier,

We combine the fraction and like terms together.

So,

[2/5 + (-1/5)] + [8 + 3 + (-15)]

This can be seen as applying the properties of commutative and associative.

Thus,

The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].

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The statements that justify why the table does not represent a probability distribution are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Considering that the number of outcomes cannot be negative, negative probabilities do not exist.

For a distribution, the sum of all the probabilities must be of one, hence:

-1/3 + 2/5 + 1/5 + 2/5 = 1 - 1/3 = 2/3 -> Different of one.

The table is given by the image presented at the end of the answer.

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The area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex]

To find the area of a regular decagon, we need to know either the side length or the apothem (the perpendicular distance from the center to a side). In this case, you have provided the radius of the decagon, which is 14 units.

For a regular decagon, the apothem (a) is related to the radius (r) by the formula:

[tex]a = r * cos(\pi/10)[/tex]

Let's calculate the apothem using the given radius:

[tex]a = 14 * cos(\pi/10) =12.149[/tex]

Now, we can calculate the area (A) of the regular decagon using the formula:

[tex]A = (5/2) * a^2 * tan(\pi/10)[/tex]

[tex]A = (5/2) * (12.149)^2 * tan(\pi/10) =195.7[/tex]

Rounding to the nearest tenth, the area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex].

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The ball's height is 11 meters after approximately 6.83 seconds and 0.17 seconds.

The height of the ball after t seconds is given by the equation h = 1 + 30t - 5t^2. To find all values of t for which the ball's height is 11 meters, we need to solve the equation [tex]1 + 30t - 5t^2 = 11[/tex].

[tex]30t - 5t^2 - 10 = 0[/tex]

[tex]t^2 - 6t + 2 = 0\\\\t = (6 \pm \sqrt{6^2 - 4(1)(2)}) / 2\\\\\t = (6 \pm \sqrt{32}) / 2\\\\t = (6 \pm 4\sqrt2 / 2\\\\t = 3 \pm 2\sqrt2[/tex]

Therefore, the values of t for which the ball's height is 11 meters are approximately 6.83 seconds and 0.17 seconds.

Rounding to the nearest hundredth, we get:

t ≈ 6.83 or t ≈ 0.17

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Median: 212

Mode: 212

The median and mode of the data set are 273 and 212 respectively.

The median is the value that splits the mathematical numbers or expressions in half. The median value is the middle number of data points. To find the median first arrange the data points in ascending order.

To find the median, we need to arrange the numbers in order from least to greatest:

3, 4, 5, 212, 212, 334, 414, 823

There are 8 numbers in total, so the median is the average of the two middle numbers, which are 212 and 334.

Median = (212 + 334)/2 = 273

To find the mode, we need to identify the number(s) that occur most frequently. In this case, 212 appears twice, so it is the mode.

Mode = 212

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Based on the information and the image, we can infer that it does correspond to a polygon.

A polygon is a term used in geometry to refer to a closed plane figure made up of three or more line segments called sides. Polygons are classified according to the number of sides they have. For example:

Based on the above information, we can infer that the image corresponds to an irregular polygon with 20 sides.

Note: This question is incomplete. Here is the complete information:

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The greatest common factor (GCF) of the three monomial, 21x³y⁵, 63x⁵y² and 45x¹y³ is 3xy²

The greatest common factor (GCF) of the three monomials, 21x³y5, 63x5y² and 45x¹y³ can be obtained as follow:

First, we shall determine the factors of each monomials. This is illustrated below:

21x³y⁵ = 3 × 7 × x × x × x × y × y × y × y × y

63x⁵y² = 3 × 3 × 7 × x × x × x × x × x × y × y

45x¹y³ = 3 × 3 × 5 × x × y × y × y

Finally, we shall determine the greatest common factor (GCF) from the factors listed above. This is shown below:

3 × x × y × y = 3xy²

Thus, we can conlude that the greatest common factor (GCF) of the three monomials is 3xy²

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Answer: 3 1/3

Step-by-step explanation:

if the width of the rectangle is equal to “x” then the length is equal to 3x+2

The area is 40ft^2

so: 40=(3x+2)(x)

Then we simplify and subtract 40 in both sides:

0=3x^2+2x-40

Then we will use the quadratic formula to solve for x

X=(-2-sqr(2^2-4(3)(-40)))/2*3

And

X=(-2+sqr(2^2-4(3)(-40)))/2*3

then x is either equal to 3 1/3 or -4, since the answer cannot be negative, the answer is 3 1/3

The inequality representing the amount Jeremiah spends on dinner daily is x ≥ $14.50. Two examples of amounts Jeremiah might spend are $16.75 and $22.00.

1. To represent the amount Jeremiah spends on dinner daily, we can use the inequality symbol "≥" (greater than or equal to) since it says "at least." Let's use the variable x to represent the amount.

2. The inequality representing the amount Jeremiah spends is x ≥ $14.50.

3. Example 1: Jeremiah might spend $16.75 on dinner, which satisfies the inequality since $16.75 is greater than $14.50.

4. Example 2: Jeremiah might spend $22.00 on dinner, which also satisfies the inequality as $22.00 is greater than $14.50.

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The simplest form of the expression by the use of the distributive property is;

[tex]12x^2 + 24x + 9[/tex]

In mathematics, the distributive property, which explains how multiplication interacts with addition or subtraction, is a fundamental concept. By allocating or multiplying a number or term to each term enclosed by a set of parenthesis, it enables you to simplify expressions.

The distributive property is frequently employed in algebraic expressions, equation simplification, and polynomial operations. By spreading out the multiplication over addition or subtraction, it aids in simplifying complex statements and makes calculations easier to understand.

We know that;

[tex]3(4x^2 + 8x + 3)\\12x^2 + 24x + 9[/tex]

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