I need help with this​

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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The value of m<1 is 65 degrees

From the diagram shown, we have that;

It is important to note that angles on a straight line sum up to 180 degrees

Also, corresponding angles are equal

Then, we have that;

m<2 + m<3 = 180°

Substitute the values

9x + 7 + 5x + 5 = 180

collect like terms

14x = 180 - 12

14x = 168

Make 'x' the subject

x = 168/ 14

x = 12

We have that;

m<3 = 5x + 5 = 5(12) + 5 = 60 + 5 = 65

But m<3 = m<1

m<1 = 65

Thus, the value of m<1 is 65 degrees

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________________________________

Hey!!

Solution,

(x-2)(X+5)=0

Either,

x-2=0

X=0+2

X=2

or,

X+5=0

X=0-5

X=-5

Hope it helps

Good luck on your assignment

____________________________

Answer:

Step-by-step explanation:

Answer:

y/2

Step-by-step explanation:

Answer: y, because ΔABC ~ ΔEDC

Step-by-step explanation:

In the image we can see that angle D is equal to angle B because they are both marked as 65 degrees. Angle BCA is equal to DCE because they are vertical angles and vertical angles are congruent. Know that those are equal to each that must mean CED is equivalent to CAB because that's the last angle that corresponds with another. So, CED is y.

To solve the initial-value problem using the Laplace transform, we start by taking the Laplace transform of the given differential equation and applying the initial conditions.

Taking the Laplace transform of y'' - 6y' + 13y = 0, we have:

s^2Y(s) - sy(0) - y'(0) - 6(sY(s) - y(0)) + 13Y(s) = 0,

Substituting y(0) = 0 and y'(0) = -7, we have:

s^2Y(s) + 6sY(s) + 13Y(s) + 7 = 0.

Now, we can solve for Y(s):

Y(s)(s^2 + 6s + 13) = -7,

Y(s) = -7 / (s^2 + 6s + 13).

To find the inverse Laplace transform of Y(s), we can use partial fraction decomposition or look up the inverse Laplace transform in tables. In this case, the denominator s^2 + 6s + 13 is irreducible and does not factor further.

Using the inverse Laplace transform table, we find that the inverse Laplace transform of Y(s) is given by:

y(t) = -7e^(-3t) sin(2t).

Therefore, the solution to the initial-value problem y'' - 6y' + 13y = 0, y(0) = 0, y'(0) = -7 is:

y(t) = -7e^(-3t) sin(2t).

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The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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To add or subtract given  mixed numbers with different denominators we have a few steps to follow:

first, we have to convert the mixed numbers into improper fractions, and then find the common multiple of both denominators.

Next, convert the fractions as common denominators, and solve the fractions, convert the fraction as mixed numbers.

There is another method to add and subtract the mixed numbers:

first, find the Lowest Common Multiple between the denominators, and multiply the numerator and denominator of each fraction by a number so that they have the LCM as their new denominator.

next, add or subtract the numerators and keep the denominator the same.

finally, if the answer is an improper form, reduce the fraction into a mixed number

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Answer:

f(- 7) = 16

Step-by-step explanation:

substitute x = - 7 into f(x) , that is

f(- 7) = (- 7)² + 3(- 7) - 12 = 49 - 21 - 12 = 28 - 12 = 16

Answer:

             The x intercept:    (1.5, 0)

The slope intercept form:   y = 2x - 3

                      The slope:    m = 2

Step-by-step explanation:

x intercept means y=0

4x - 2y = 6

4x - 2·0 = 6

4x = 6

x = 1.5

The slope intercept form is:  y = mx + b

4x - 2y = 6            {subtract 4x from both sides}

- 2y = - 4x + 6       {dividing both sides by (-2)}

y = 2x - 3            ← slope intercept form

Slope is the number by x, in slope intercept form of line's equation

Answer: z=116 x= 50 1/3

Step-by-step explanation:

64 degrees corresponds to the angle on top of angle z. That means the angle on top of z is also 64 degrees. This same angle and angle z are a linear pair; they sum to 180. 64+z= 180. Subtract 64 from both sides. Z= 116. Angle z and angle (3x-35) are also a linear pair and sum to 180. We know z is 64, so 64+(3x-35) = 180. Combine like terms. 29+3x = 180. Subtract 29 from both sides. 3x = 151. Divide both sides by 3. X= 50 1/3

The value of the angles of the given quadrilateral are;

8) ∠X = 124° = ∠W

∠Y = 56° = ∠Z

9) ∠J = 44° = ∠K

∠L = 136° = ∠M

The sum of angles of a quadrilateral is equal to 180 degrees. Now, in the quadrilateral given, the two angles on the slant side always equal 180 degrees. Thus;

8) From the given trapezium, we can use the definition above to say that;

∠X + ∠Y = 180°

Thus;

(13x - 7)° + (8x - 2)° = 180°

21x - 9 = 180

21x = 189

x = 189/21

x = 9

Thus;

∠X = (13(9) - 7)°

∠X = 124° = ∠W

∠Y = 180° - 124°

∠Y = 56° = ∠Z

9) From the above, we can apply the same to this quadrilateral to get;

7x + 2 + 25x - 14 = 180

32x - 12 = 180

32x = 180 + 12

32x = 192

x = 192/32

x = 6

∠J = (7(6) + 2)

∠J = 44° = ∠K

∠L = 180 - 44

∠L = 136° = ∠M

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On solving the provided question, we can say that in the triangle, Cos A = 4/9 => Cos A =  0.4444444444 = 0.44

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in the triangle

Cos A = 4/9

Cos A =  0.4444444444 = 0.44

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Answer:

Cubic centimetres

Step-by-step explanation:

Cubic centimetres is perfect

As

The statement “there exists a function f such that f(x) < 0, f’(x) > 0, and f”(x) < 0 for all x” is false.

To understand why this statement is false, we must first understand what the symbols mean. The symbol f(x) refers to a function of x, and the symbols f’(x) and f”(x) refer to the first and second derivatives of the function, respectively.

The statement is saying that for all x, the function f(x) will be less than 0, the first derivative f’(x) will be greater than 0, and the second derivative f”(x) will be less than 0.

To show that this statement is false, we need to find an example of a function where this is not the case. Let’s consider the function f(x) = x³. At x = 0, this function is equal to 0, and so f(x) < 0 is not true. Additionally, the first derivative at x = 0 is f’(0) = 0, which is not greater than 0. Thus, the statement is false.

We can also show that this statement is false by looking at the graph of the function f(x). A function with the properties given in the statement would have a graph that looks like a “U” shape, with a minimum point at the origin. However, this is not the case for the function f(x) = x³. The graph of this function is a parabola, which does not have the desired shape.

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The level of measurement that is appropriate for a classification where students are asked to rank their professors as good, average, or poor is the ordinal level of measurement.

Ordinal level of measurement is a statistical measurement level.

It involves dividing data into ordered categories.

For instance, when asked to rank teachers as good, average, or poor, the students' rating of the teachers falls under the ordinal level of measurement.

The fundamental characteristic of ordinal data is that it can be sorted in an increasing or decreasing order.

The numerical values of the categories are not comparable; instead, the categories are arranged in a specific order.

The ordinal level of measurement, for example, provides the order of the data but not the size of the intervals between the ordered values or categories.

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Answer:

  (X_1, X_2) = (2, 4)

  Z = 110

Step-by-step explanation:

You want a graphical solution to ...

  minimize Z = 15 X_1 +20 X_2

  subject to ...

A graph of the reverse of the inequalities is attached. This makes the feasible solution region be white (rather than shaded multiple times), so its vertices are easier to see. (The dashed lines are part of the solution space.)

The vertex of the solution space that minimized the objective function is (X_1, X_2) = (2, 4). The minimum value of Z is 110.

Let the number be x

ATQ

\(\\ \sf\longmapsto 3x+2=18\)

\(\\ \sf\longmapsto 3x=18-2\)

\(\\ \sf\longmapsto 3x=16\)

\(\\ \sf\longmapsto x=\dfrac{16}{3}\)

\(\\ \sf\longmapsto x=5.3\)

\(\\ \sf\longmapsto x\approx 5\)

Answer: To write the proportional relationship between books and months, we can use the formula:

unit rate = (total books) / (total months)

Let's calculate the total books and months for Estelle's reservations:

Two years ago: 24 books in 4 months

Last year: unknown number of books in 36 months

This year: 18 books in 3 months

To find the total number of books for last year, we can use a proportion:

24 books / 4 months = x books / 36 months

Cross-multiplying, we get:

24 * 36 = 4 * x

x = 24 * 9

x = 216

So Estelle reserved 216 books in 36 months last year.

Now we can calculate the unit rate:

unit rate = (total books) / (total months)

unit rate = (24 + 216 + 18) / (4 + 36 + 3)

unit rate = 258 / 43

unit rate = 6

Therefore, the proportional relationship between books and months is:

books = 6 * months

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

Using the Pythagorean theorem,

\(14^2+x^2=18^2 \\ \\ 196+x^2=324 \\ \\ x^2=128 \\ \\ x=\sqrt{128}\)

The common factor, in this case, is a, so the GCF is still a.

What is the greatest common factor (GCF)?

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.

To find the greatest common factor (GCF) of two or more terms, we need to factor each term and then identify the factors that are common to both terms.

In this case, we have the terms 3a and 5a. To find the GCF, we can factor each term as follows:

3a = 3a

5a = 5a

The only common factor between the two terms is a, so the GCF of 3a and 5a is a.

Alternatively, we could have written the terms as:

3a = 3 * a

5a = 5 * a

Hence, The common factor, in this case, is a, so the GCF is still a.

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Answer:

-3

Step-by-step explanation:

Adding a negative number is like subtracting. Subtracting more than the original positive number gets you in to the negative numbers.

Answer:

y = 3x

Step-by-step explanation:

y = 3 and x = 3 doesn't touch 0, 0

The measure of the angle ∠CMD is 45.

We have,

From the figure,

∠FMD = 15

∠BMC = 30

Now,

∠BMF = 90

This can be written as,

∠BMC + ∠CMD + ∠FMD = 90

30 + ∠CMD + 15 = 90

∠CMD = 90 - 45

∠CMD = 45

Thus,

The measure of the angle ∠CMD is 45.

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Option D. 1 + 1/s is the correct choice for a PI controller that has the minimum impact on the root loci of the system.

To minimize the impact of a proportional plus integral (PI) controller on the root loci of a system, the controller should introduce a pole at the origin (s=0) and a zero at a distant location from the origin.

Among the given options, the controller that fits this purpose is D. 1 + 1/s.

The PI controller in option D has a constant term of 1, which introduces a pole at the origin (s=0). It also has a term of 1/s, which introduces a zero at s=infinity, which is a distant location from the origin.

By having a pole at the origin and a zero at a distant location, the PI controller in option D minimizes the impact on the root loci of the system. This configuration ensures stability and avoids significant changes in the system's dynamic behavior.

Therefore, option D. 1 + 1/s is the correct choice for a PI controller that has the minimum impact on the root loci of the system.

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The rate of change of the annual u.s. factory sales in 2000 is 7.7 billion dollars per year

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

s(t) = 0.12t² − t + 5.7

In 2000, we have the value of t to be

t = 2000 - 1990

Evaluate

t = 10

So, we have

s(10) = 0.12 * 10² − 10 + 5.7

Evaluate

s(10) = 7.7

Hence, the rate in 2000 is 7.7 billion dollars per year

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Question

the rate of change of annual u.s. factory sales (in billions of dollars per year) of consumer electronic goods to dealers from 1990 through 2001 can be modeled as s(t) = 0.12t2 − t + 5.7 billion dollars per year

Calculate the rate of change in 2000

Answer:

72.98

Step-by-step explanation:

in the picture shows you the formula for the area of a triangle

Answer:

b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

7%

Step-by-step explanation:

since the formula says si=ptr/100

so we have to separate r which gives us r =(i ×100)/(p×t)

now putting the values (980×100)/(7000×2)

=7

therefore the rate of interest is 7%