2 Given (2x + 5)(x - 3) = AX + Bx + C, what is the value of B? O O x a. X O b. X O c. 1 O d. -1

Answer:

V = 108

Step-by-step explanation:

B = 9 x 4 = 36 Height of Triangular prism is 3 so 36 x 3 = 108

The third side of the triangle whose two sides are 11 cm and 19 cm can be between 9 and 29.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

The sides of triangles are 11 cm and 19 cm,

Let the third side of the triangle is x,

Since, a side of a triangle is greater than the difference of two sides and less than the sum of two sides,

implies that,

19-11<x<19+11

8 < x < 30

The possible range of third side is (9,29).  

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Answer:

8cm < x < 30cm

Step-by-step explanation:

To find the range of lengths for the third side of a triangle when two side lengths are known, first, assign a variable for the length of the third side.

Let x be the length of the unknown side.

Use the Triangle Inequality Theorem to write the three inequalities.

x + 11x > 19

x + 19 > 11

11 + 19 > x

Solve each inequality.

x > 8

x > -8

30 > x

Now find the range of values that satisfies all three inequalities.

The range between 8 and 30 satisfies all 3 inequalities. Therefore, this triangle's third side lengths range is 8cm < x < 30cm.

Answer:

Option A

Step-by-step explanation:

By applying Pythagoras theorem in ΔABC,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

AC² = AB² + BC²

AC² = 6² + 5²

AC = \(\sqrt{61}\)

Similarly, by applying Pythagoras theorem in ΔACD,

AD² = AC² + CD²

(10)² = \((\sqrt{61})^2\) + x²

x² = 100- 61

x² = 39

x = √(39)

Option A will be the answer.

Answer:

123cm

Step-by-step explanation:

becuse

Answer:

Down Below

Step-by-step explanation:

b=0.5

g=0.8

1.      3b + 5g = ?

       3×0.5+5×0.8=?

        1.5+4= 5.5 cm

2.      6(3b+5g) = ?

        18b + 30g
        18×0.5+30×0.8

        9+24= 33 cm

3.          2b + 3g

           2×0.5+3×0.8
           1+2.4=3.4 cm

4.   7(2b+3g)
     14b + 21g
     14×0.5+21×0.8
     7+16.8= 23.8 cm

5.     Add number 2 and 4 together
       14b+21g+18b+30g= 32b+ 51g

Take numbers and add them from problems 2 and 4
     23.8+33=56.8 cm

Answer:36

Step-by-step explanation:multiply divide and  subctract

Answer:

[See Below]

Step-by-step explanation:

\(Hey~There!\)

________________________

➜ Solve:

________________________

So based on our work above we can conclude that the equation is equal because when solve it equals \(1\), making \(1=1\).

________________________

\(Hope~this~helps~Mate!\\-Your~Friendly~Answerer,~Shane\) ヅ

The perimeter of television is = 100 inches

The study of measuring geometric shapes and their qualities such as length, volume, shape, surface area, lateral surface area, and so on is known as mensuration. Mensuration will be covered in fundamental mathematics.

let the length be 16x and width be 9x

area given = 576 sq. inches

16x * 9 x = 576

144 \(x^{2}\) = 576

x = 24/12

x = 2

length = 32

width = 18

perimeter = (32 + 18)*2  =100 inches

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The first derivative of the function `g(u) = u(2u - 3)^3` is `g'(u) = 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u) = 12(u - 1)(2u - 3)^2`.

Given function: `g(u)

= u(2u - 3)^3`

To find the first derivative of the given function, we use the product rule of differentiation.`g(u)

= u(2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g'(u)

= u * d/dx[(2u - 3)^3] + (2u - 3)^3 * d/dx[u]`

Using the chain rule of differentiation, we have:

`g'(u)

= u * 3(2u - 3)^2 * 2 + (2u - 3)^3 * 1`

Simplifying:

`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

To find the second derivative, we differentiate the obtained expression for

`g'(u)`:`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g''(u)

= d/dx[6u(2u - 3)^2] + d/dx[(2u - 3)^3]`

Using the product rule and chain rule of differentiation, we have:

`g''(u)

= 6[(2u - 3)^2] + 12u(2u - 3)(2) + 3[(2u - 3)^2]`

Simplifying:

`g''(u)

= 12(u - 1)(2u - 3)^2`.

The first derivative of the function `g(u)

= u(2u - 3)^3` is `g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u)

= 12(u - 1)(2u - 3)^2`.

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The first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

First, let's find the first derivative:

g'(u) = (2u - 3)³ * d(u)/du + u * d/dx[(2u - 3)³]

Using the chain rule, we can differentiate (2u - 3)³ and u as follows:

d(u)/du = 1

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

Plugging these values back into the equation for g'(u), we have:

g'(u) = (2u - 3)² + u * 3(2u - 3)² * 2

= (2u - 3)³ + 6u(2u - 3)²

Simplifying the expression, we have:

g'(u) = (2u - 3)³ + 6u(2u - 3)²

Now, let's find the second derivative:

g''(u) = d/dx[(2u - 3)³ + 6u(2u - 3)²]

Using the chain rule and product rule, we can differentiate each term:

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

d/dx[6u(2u - 3)²] = 6(2u - 3)² + 6u * d/dx[(2u - 3)²]

= 6(2u - 3)² + 6u * 2(2u - 3)

Plugging these values back into the equation for g''(u), we have:

g''(u) = 3(2u - 3)² * 2 + 6(2u - 3)² + 6u * 2(2u - 3)

= 6(2u - 3)² + 6(2u - 3)² + 12u(2u - 3)

= 12(2u - 3)² + 12u(2u - 3)

Simplifying the expression further, we have:

g''(u) = 12(2u - 3)² + 12u(2u - 3)

Therefore, the first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

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True. Statements about averages often present an incomplete picture because they do not provide information about the dispersion or variability of the data.

The statement is true because averages, such as the mean or median, only give a measure of central tendency and do not convey information about the spread or distribution of the data points. Dispersion measures, such as standard deviation or range, are necessary to understand the variability or consistency within the dataset.

Without considering dispersion, it is possible to have datasets with the same average but different levels of variability. Therefore, to gain a comprehensive understanding of a dataset, it is important to consider both the average and the dispersion measures together.

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The required histogram is attached as a picture.

Given the information on how many pages each of the 20 pupils read throughout the summer.

163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431

With frequency on the y axis and class on the x axis.

we observe the histogram and make out that:

class 160 - 220 has the highest frequency of 6 students whereas

400 - 460 has the least with 2 students.

The classes between them range as follows:

220 - 280 has 5 students

280 - 340 has 4 students

340 - 400 has 3 students.

Hence the required histogram is created .

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The surface area of the square pyramid is 115 square meters

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

The square based pyramid

The formula for the surface area of a square pyramid is:

S = a² + 2al

where a is the length of one side of the square base and l is the slant height.

Area of 4 triangles

This is calculated as

A = 1/2 * 5 * 9 * 4 = 90

Area of the square

This is calculated as

A = 5 * 5 = 25

So, we have

Area = 90 + 25

Area = 115

Hence, the surface area of the square pyramid is 115 square meters.

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Answer & Step-by-step explanation:

Step-by-step explanation:

The numerical expression for the cost of 1 dozen eggs is 33.75/15.

Answer:

-32

Step-by-step explanation:

Negative plus negative = Negative

Just add those 2 together,

(-)18 + (-) 14

Which is -32

(-) 32 = -32

Answer:

X=25°

Step-by-step explanation:

\(x = \frac{1}{2} (t2 - 22) \)

\( = \frac{1}{2} (50)\)

\( = 25\)

\(x = 25\)

hope it helps u

Given the following expression:

The similar terms must have the same variable with the same exponents

So, note the following:

So, the given expression will be:

Answer:

3^8

Step-by-step explanation:

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Answer: X= -2.1667 Y= 13

Answer:

the answer to the inequality is C. g<1

The number of dark chocolate AJ sold is 75

Simultaneous equations are two or more algebraic equations that share variables e.g. m and d . They are called simultaneous equations because the equations are solved at the same time.

If the number of Milk chocolate candy is m and the number of dark chocolate candy is d, then

m+d= 200 equation 1

3m+4d= 675 equation 2

to eliminate m we multiply both equations by 3

3m+3d= 600 equation 3

3m+ 4d=675 equation 4

subtract equation 3 from 4

d = 675-600

d= 75

Therefore the number of dark chocolate candy AJ sold is 75.

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The rule that describes the function is (c) Output = (0.5)(Input) + 1.5

The points on the coordinate plane are given as

(negative 1, 1), (1, 2), (3, 3), (5, 4)

Express as numbers

So, we have

(-1, 1), (1, 2), (3, 3), (5, 4)

Divide the input values by 2

So, we have

0.5(Input) => (-1/2, 1), (1/2, 2), (3/2, 3), (5/2, 4)

Add 1.5 to the input values

So, we have

0.5(Input) + 1.5 => (1, 1), (2, 2), (3, 3), (4, 4)

So, we have

Output = 0.5(Input) + 1.5

Hence, the equation is (c)Output = 0.5(Input) + 1.5

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If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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Answer:

384m^2

Step-by-step explanation:

surface area of cube = area of 1 side x 6

area of 1 side = 64m^2

so, surface area = 64 x 6 = 384m^2

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2.23% is the probability of a city with a population of 200,000, and there will be exactly 2 accidental drownings per year.

The Poisson distribution, is useful for modeling the number of events (in this case, accidental drownings) in a fixed interval (here, a year). Given the average rate of 3.0 drownings per 100,000 people per year, we first need to find the expected number of drownings in a city with a population of 200,000.

Expected drownings per year = (3.0 drownings / 100,000 people) * 200,000 people = 6 drownings

Now, we can use the Poisson probability formula to calculate the probability of exactly 2 accidental drownings per year in this city:

P(X = k) = (λ^k * e^(-λ)) / k!

Here, X represents the number of drownings, k is the desired number of drownings (2 in this case), λ (lambda) is the expected number of drownings per year (6), e is the base of the natural logarithm (approximately 2.718), and k! is the factorial of k.

P(X = 2) = (6^2 * e^(-6)) / 2! = (36 * e^(-6)) / 2 = (36 * 0.002478) / 2 = 0.04461 / 2 = 0.022305

Therefore, the probability that in a city with a population of 200,000, there will be exactly 2 accidental drownings per year is approximately 0.0223 or 2.23%.

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The Area of the composite figure = area of the rectangle + area of the triangle = 148.5 cm².

The figure formed by the arrow can be decomposed into a rectangle and a triangle.

The area of the composite figure = area of the rectangle + area of the triangle.

Find the area of the rectangle:

Length = 12 cm

Width = 11 cm

Area of the rectangle = (length)(width) = (12)(11)

Area of the rectangle = 132 cm²

Find the area of the triangle

Base = 11 cm

Height = 15 - 12 = 3 cm

Area of the triangle = 1/2(b)(h) = 1/2(11)(3)

Area of the triangle = 16.5 cm²

Area of the composite figure = area of the rectangle + area of the triangle = 132 + 16.5 = 148.5 cm².

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Answer:

2 1/2

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

No, it is not since 2 points have the same x-coordinate and different y-coordinates.

Answer:

≈ 3.9 miles

Step-by-step explanation:

The third angle in the triangle is

180° - (53 + 78)° = 180° - 131° = 49°

Using the Sine rule in the triangle with distance from 2 being x, then

\(\frac{3}{sin49}\) = \(\frac{x}{sin78}\) ( cross- multiply )

x × sin49° = 3 × sin78° ( divide both sides by sin49° )

x = \(\frac{3sin78}{sin49}\) ≈ 3.9 ( to the nearest tenth )