In ΔBCD, \overline{BD} BD is extended through point D to point E, \text{m}\angle CDE = (9x-12)^{\circ}m∠CDE=(9x−12) ∘ , \text{m}\angle BCD = (2x+3)^{\circ}m∠BCD=(2x+3) ∘ , and \text{m}\angle DBC = (3x+5)^{\circ}m∠DBC=(3x+5) ∘ . Find \text{m}\angle BCD.M∠BCD.

Answer:

1.5

Step-by-step explanation:

Because the triangle are similar, they possess a proportional relationship in which the one triangle's side length is dilated by a unknown factor (y) to make its corresponding counterpart. Using this knowledge we can make the following two equations

3y=7  & xy=x+2   y is the variable representing the dilation factor

y=7/3 find the value of y

x(7/3)=x+2 substitute the value y into the equation

7/3x =x+2 solve for x

4/3x =2

(3/4)(4/3x)=2(3/4) multiply by the reciprocal

x=1.5

Answer:

large

Step-by-step explanation:

3.95 divided by 12 = 0.33

4.25 divided by 16 = 0.27

4.55 divided by 20 = 0.2275

the 20oz is the least unit price

Answer:

x=2

Step-by-step explanation:

-13x-11=-37                             Original equation

-13x=-26                                 Add 11 to both sides

x=2                                         Divide both sides by -13

Answer:

Step-by-step explanation:

Let the consecutive numbers be 'x' and 'x+1'

according to the conditions of the question

the equation will be

5x + 3(x +1) = 579

= 5x + 3x +3 = 579

8x + 3 = 579

8x = 579 - 3

8x = 576

x = 576/8

x = 72

The solution is, Their rate of change is respectively 0.5.

• A. y = 0.5x - 1

• D. t= 0.5n + 1​

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

The slope-intercept form of the equation of a straight line is:

y=mx+c

where, m= rate of change.

From the given equations, the two that have the same rate of change are:

• A. y = 0.5x - 1

• D. t= 0.5n + 1​

Their rate of change is respectively 0.5.

The correct choices are A and D.

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The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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Answer:

x = 2

Step-by-step explanation:

We Know

UN is 1/2 of LN, so UN must be 10.

Solve for x.

We have

10 = 5x

x = 2

So, x = 2

Answer:

A and C

Step-by-step explanation:

Answer:

  x = 14

Step-by-step explanation:

Extend line AB so that it intersects ray CE at point G. Then angles BGC and BAD are "alternate interior angles", hence congruent.

The angle at B is exterior to triangle BCG, and is equal to the sum of the interior angles at C and G:

  138 = (376 -23x) +(x^2 -8x)

Subtracting 138 and collecting terms we have ...

  x^2 -31x +238 = 0

For your calculator, a=1, b=-31, c=238.

__

Additional comment

You will find that the solutions to this are x = {14, 17}. You will also find that angle BCE will have corresponding values of 54° and -15°. That is, the solution x=17 is "extraneous." It is a solution to the equation, but not to the problem.

For x=14, the marked angles are A = 84°, C = 54°.

Answer:

Step-by-step explanation:

75

The first quartile is 4.5.

The third quartile is 27.5.

A quartile divides data into three points: lower, middle, and upper quartiles, resulting in four groupings of the dataset. The lower quartile, or first quartile, is designated as Q1 and is the 9 halfway number between the dataset's lowest and median values. The median is also in the second quartile, Q2. The upper or third quartile, abbreviated as Q3, is the center point of the distribution that sits between the median and the highest value.

In the question, we are given the number of incidents in which police were needed for a sample of 9 schools in Allegheny County is 8, 39, 6, 12, 45, 16, 3, 0, 15.

We are asked to find the first and the third quartile for the data.

We first arrange the data in ascending order as follows:

0, 3, 6, 8, 12, 15, 16, 39, 45.

We have 9 data points.

Thus, the first quartile is the data at the point (9 + 1)/4 th observation,

or, the first quartile is the data at the point 2.5th observation,

or, the first quartile is the data at the average of 2nd and 3rd observation, = ( 3 + 6 )/2 = 4.5.

Thus, the first quartile is 4.5.

Thus, the third quartile is the data at the point 3(9 + 1)/4 th observation,

or, the third quartile is the data at the point 7.5th observation,

or, the third quartile is the data at the average of 7th and 8th observation, = ( 16 + 39 )/2 = 27.5.

Thus, the third quartile is 27.5.

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Answer:

Step-by-step explanation:gg

The amount of ice cream at $6.9 will be equal to 1.875 quarts.

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 Diante has $3.75 and Rachel has $3.15. They combine their money to buy as much ice cream as they can afford. If ice cream costs $3.68 per quart.

Calculate the total amount of money,

M = 3.75 + 2.15

M = $6.9

The amount of ice cream they can purchase is,

A = 6.9 / 3.68

A = 1.875 quarts

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For f(x) = x5 + x3 + x, the value of f1(3) is 1. Because of the inverse function feature, the value of f(f1(2)) is 2.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

f(x)=x^5 + x^3 + x

f(1)=3

f^-1(3)=1

f[f −1 (x)]=f −1 [f(x)]=x

f(f^(-1)2)=2

The value of f−1(3) is 1 for f(x) = x^5 + x^3 + x. The value of f(f−1(2)) is 2 by property of inverse function.

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The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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Solution:  x∈Ф

No solution

Step-by-step explanation:

\(\sqrt{x} +5+2=\sqrt{x} -7\)

\(5+2=-7\)

\(7=-7\)

\(1=-1\)

x∈Ф

Answer: 45 degrees

Step-by-step explanation:

The rate at which a point object revolves around a fixed origin is referred to as orbital angular velocity.

The speed of a point on its rim = 3150 cm / min.

angular velocity \(\omega\) = 7 rad/sec.

diameter = 15 cm ;

Radius = 7.5 cm.

The speed of a point on its rim = r \(\omega\) = 7.5 x 7 =52.5 cm/s =3150 cm / min

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The unknown angle x in the triangle is 80 degrees

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

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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Answer:

500

Step-by-step explanation:

Add the number of pizzas to find the total, 1020. Since there are 204 thick crusts out of the 1020 pizzas, we can conclude that there is a thick crust in every 5 pizzas. We can make the denominator 2500, making the fraction 500/2500, thus we know there will 500 thick crust pizzas out of the next 2500 pizzas he sells.

Answer:

slope is \(\frac{3}{2}\)

Step-by-step explanation:

Find two points on the line: (1, -3) (3, 0)

\(\frac{0 + 3}{3 - 1}\) = \(\frac{3}{2}\)

Answer:−2.9 and −1.1

Step-by-step explanation:

The number of columns in the first matrix must equal the number of rows in the second matrix in order to multiply matrices with different dimensions.

    3. Determine the dot product of the corresponding row in matrix A          and the corresponding column in matrix B for each element in matrix C.

    4: The final response is matrix C, which is the union of the 2x3 matrix A and the 3x4 matrix B.

     Therefore, the result is a 2x4 matrix, which is produced by taking the dot product of the rows and columns of matrix A and matrix B.

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Winning lottery 5 times most likely, guessing 64-bit key, 128-bit key, hit by lightening.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.

1) Being hit by lightning this year (probability is 1/105) - The probability is the lowest because the odds of being hit by lightning in a given year are relatively low.

2) Guessing a 128-bit key on the first try - The probability of guessing a 128-bit key on the first try is very low because of the large number of possible key combinations.

3) Guessing a 64-bit key on the first try - The probability of guessing a 64-bit key on the first try is lower than guessing a 128-bit key, but still relatively low because of the large number of possible key combinations.

4) Winning a lottery with 1 million (106) contestants five times in a row (the probability is (1/106)5) - The probability of winning a lottery with such large number of contestants is relatively low, but it is still much higher than the first three events.

So the order is:

1) Being hit by lightning this year

2) Guessing a 128-bit key on the first try

3) Guessing a 64-bit key on the first try

4) Winning a lottery with 1 million contestants five times in a row,

Winning lottery 5 times most likely, guessing 64-bit key, 128-bit key, hit by lightening.

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Answer:

b. Non-proportional

Step-by-step explanation:

A table of values that represents a proportional relationship will have the same ratio of every pair in the given table. That is, y/x will result in the same value all through for every given pair.

The table of values given does not show a proportional relationship, because the ratio of y to x of each given pair of values are different and unequal:

y/x = 3/1 ≠ 5/2 ≠ 7/3 ≠ 9/4

Therefore, it is non-proportional.

hope i help

There is a 34% chance that the randomly purchased item from the manufacturer will last longer than 8 years.

The question is asking for the probability that a randomly purchased item from a manufacturer will last longer than 8 years. To answer this question, we must use the normal distribution formula and find the area under the curve between 8 and infinity.

The formula for the normal distribution is as follows:

\(1/(\sigma\sqrt{2\pi}) e^{-((x-\mu)^2)2\sigma^2}\)

Where μ is the mean and σ is the standard deviation.

In this problem, μ = 6.5 years and σ = 0.8 years.

Using the formula, the probability of the randomly purchased item lasting longer than 8 years is 0.34.

To calculate the probability, we use the z-score formula, which is \((x-\mu)/\sigma\). Plugging in 8-6.5/0.8 gives us a z-score of 1.875.

Using the z-table, we can find the area under the curve, which is 0.34. This means that the probability of the randomly purchased item lasting longer than 8 years is 0.34.

Therefore, the answer to the question is that there is a 34% chance that the randomly purchased item from the manufacturer will last longer than 8 years.

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Answer:

2x+2(x+5)) = 24

Step-by-step explanation:

2x+ 2(x+5) = 24

x is represented by the shorter side. Multiply by 2 because of the 2 sides. For the longer side, since it is 5m longer than the shorter side, you have to write (x+5). Multiply by 2 because of the 2 sides. Finally, add them both together since it is the area and set it equal to 24.

The slopes of perpendicular lines are negative reciprocals is proved.

An equation of a straight line is given by

y = mx +c

It is given that

Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular.

Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).

The slopes of lines PQ and P’Q’ can be determined using the formula

\(\rm m = \dfrac{ v _2 - v _1 }{ x _2 -x _1 }\)

The product of these slopes is -1 .

This product shows that the slopes are negative reciprocals

Therefore , The slopes of perpendicular lines are negative reciprocals is proved,

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Answer:

406

Step-by-step explanation:

391+15=406

Answer:

https://tutors.com/math-tutors/geometry-help/volume-of-a-cube

Step-by-step explanation:

Hope this helps :)

Answer:

We combine like terms to get \(10x^{2} + 3x - 6\)

Hope this helps!

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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