1. Which of the following shows the statement 4 less than 12?
a. 4 - 12
b. 12 + 4
c. 12 - 4
d. 4 + 12

Answer:

hi there i think it is B

Step-by-step explanation:

The value of angle CFE in the diagram attached is 51 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

∠AFB = ∠CFD; ∠BFC = ∠DFE

Hence:

∠AFC = ∠CFE

∠AFD = ∠AFC + ∠CFD = ∠AFC + ∠AFB

90 = ∠AFC + 31

∠AFC = 51° = ∠CFE

The value of angle CFE in the diagram attached is 51 degrees.

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Answer:

go down then go right

Step-by-step explanation:

EXPLANATION:

We are given a circle K with radius KG. Note here that line KJ and line KG are both radii of the circle given.

Also we know that a line tangent to a circle at the point of intersecting with the radius forms a 90-degree angle with the radius.

We can now extract the following triangle from the diagram provided;

We now have a right triangle which we shall solve by use of the Pythagorean theorem;

Where we have c as the longest side (hypotenuse) and then a and b are the two other sides. Substituting into the equation above now gives us;

Subtract 36 from both sides;

Take the square root of both sides;

Rounded to the nearest tenth, the answer is;

ANSWER:

1) Let's begin by solving for the measures of the minor triangle

2) Let's use the Law of Sines to find CD, let's convert the measurements into decimal ones to better work:

Let's find the angle D with the Triangle Sum Theorem:

3) Looking back at the graph, we can find BC by finding the angle opposite to this side:

Triangle sum theorem to help us find the angle opposite to BC:

Answer:

They are both the same line

Step-by-step explanation:

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

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

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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Within the Symphony No. 5, right at the beginning (0:00) of this excerpt, the music starts with the introductory section, the so-called "exposition."

The exposition is a crucial section in the sonata form structure commonly found in classical symphonies. It is the initial part of the movement where the main thematic material is introduced and developed. In the case of Symphony No. 5, the excerpt begins with the exposition, which serves as an introduction to the musical ideas that will be further developed throughout the movement. During the exposition, the composer presents the primary themes and motifs that will shape the rest of the piece. It establishes the tonal center and introduces contrasting elements that create tension and interest. In Symphony No. 5, the introductory section of the exposition sets the stage for the thematic material that will unfold, capturing the listener's attention and establishing the musical foundation for the rest of the movement. This section is often characterized by its distinctive melodies, harmonic progressions, and rhythmic patterns that define the musical identity of the symphony.

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512 MINUTES would it take to reach 50% consolidation. (C)

To find the time it would take to reach 50% consolidation, we can use the formula:

T50 = 0.197 * (H^2 / Cv)

Where T50 is the time to reach 50% consolidation, H is the thickness of the specimen, and Cv is the coefficient of consolidation.

Plugging in the given values, we get:

T50 = 0.197 * (3^2 / 5)

T50 = 0.197 * (9 / 5)

T50 = 0.3546

Since the question asks for the time in minutes, we need to convert from days to minutes. There are 1440 minutes in a day, so:

T50 = 0.3546 * 1440

T50 = 510.624

Rounding to the nearest whole number, we get 512 minutes (C).

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Answer:

if the sum of digits is divisible by 3 ,the number is also divisible by 3. Since 210 is divisible by 3, the given number is also divisible by 3.

Answer:

2d-6

Step-by-step explanation:

Since the d is doubled you are multipling then subtracting 6 from the result

Answer:

Yes

Step-by-step explanation:

Hope that this helps :)

P.S. tell me if this is wrong

Answer:

20 seconds

Step-by-step explanation:

Given the following :

Alarm 1 (goes off every 10 seconds)

Alarm 2 (goes off every 5 seconds)

Alarm 3 (goes off every 4 seconds)

If they all go off now, how long will it take all to go off at the same time again.

Obtain the multiples of the time in seconds in which each alarm goes off and select the lowest multiple common to all three;

Multiples of 10 : 10, 20, 30, 40, 50,...

Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40,...

Multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36,....

Hence, the lowest multiple common to all three alarm times is 20.

Hence, all three alarms will go off at the same time again after 20 seconds

The function f(x) = ((x+1)/(x-1))^3 is bijective as it is both injective and surjective, meaning it has a one-to-one correspondence between its domain and codomain.

To prove that f(x) = \(((x+1)/(x-1))^3\)is bijective, we need to show that it is both injective and surjective.

Injectivity: To prove injectivity, we assume that f(x1) = f(x2) and show that it implies x1 = x2. So, let's assume f(x1) = f(x2) and substitute the function values:

\(((x1+1)/(x1-1))^3 = ((x2+1)/(x2-1))^3\)

Taking the cube root of both sides, we get:

(x1+1)/(x1-1) = (x2+1)/(x2-1)

Cross-multiplying and simplifying, we have:

x1 + 1 = x2 + 1

This implies x1 = x2, which shows that the function is injective.

Surjectivity: To prove surjectivity, we need to show that for every y in the codomain, there exists an x in the domain such that f(x) = y. In this case, the codomain is R - {1}.

Let y be an arbitrary element in R - {1}. We can solve the equation f(x) = y for x:

\(((x+1)/(x-1))^3\)= y

Taking the cube root of both sides, we get:

\((x+1)/(x-1) = y^(1/3)\)

Cross-multiplying and simplifying, we have:

\(x + 1 = y^(1/3)(x - 1)\)

Expanding and rearranging terms, we get:

\((x - y^(1/3)x) = y^(1/3) - 1\)

Factoring out x, we have:

\(x(1 - y^(1/3)) = y^(1/3) - 1\)

Dividing both sides by (1 - y^(1/3)), we get:

\(x = (y^(1/3) - 1)/(1 - y^(1/3))\)

This shows that for any y in R - {1}, we can find an x in the domain such that f(x) = y, proving surjectivity.

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The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).

Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).

To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.

Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.

Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.

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Answer:

i dont actually know

Step-by-step explanation:

Answer:

x = 50°

Step-by-step explanation:

The lower right angle in the triangle = 40° ( alternate angle )

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 angles from 180 for x , that is

x = 180° - (90 + 40)° = 180° - 130° = 50°

Answer: 14

Step-by-step explanation:

Well, we know that the formula to fugure out area is :Length times Width

We also know that WIdth is 24. So 24 times __ =5/8.

Now, how do you figure out __? Well, let's first replace that as a variable to make it easier. Let's choose: x   Now, we know that:

x * 24 = 5/8.

To figure out x, we need to do 5/8 divided by 24, right?  When you solve that, the answer would be 15. The closest is 14, so I think the answer is 14.

Answer:

Step-by-step explanation:

(-2)(x+11)=(-8)(-2)

x+11=16

x=5

the given expressions solved by using factorization.

What is factorization of the expression ?

  To factorize an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse.

Here

4) \(x^4-36\)

=> \((x^2)^2 -6^2\)

=> \((x^2-6)(x^2+6)\)

5)64\(c^3+1\)

=> \((4c)^3+1^3\)

=> (4c+1)(\((16c^2+4c+1)\)

6)\(k^3-27\)

=> \(k^3-3^3\)

=>(k-3)(\(k^2+3k+9\))

7)\(54x^3+250y^3\)

=> 2(\(27x^3+125y^3\))

=> 2(\((3x)^3+(5y)^3\))

=> 2 ( 3x+5y)(\(9x^2+15xy+25y^2\))

8)\(3m^4-48n^2\)

=> 3(\((m^2)^2-(4n)^2\))

=> 3\((m^2-4n)(m^2+4n)\)

9)\(a^7b^2-ab^2\)

=> \(ab^2(a^6-1)\\\)

=>\(ab^2(a^3-1)(a^3+1)\)

=> \(ab^2(a+1)(a-1)(a^2-a+1)(a^2+a+1)\)

10)\(x^3y^2-343y^5\)

=> \(y^2(x^3-(7y)^3)\)

=>\(y^2(x-7y)(x^2-7xy+49y^2)\)

11)\(9y^7-144y\)

\(= > 9y(y^6-16)\\= > 9y((y^3)^2-4^2)\\= > 9y(y^3+4)(y^3-4)\)

Hence we can solve by using factorization formula.

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a is the correct answer I Hope it help

We can start by rearranging the equation 5 sin x + 4 cos x = 0 by dividing both sides by cos(x):

5

sin

⁡

�

cos

⁡

�

+

4

=

0

5

cosx

sinx

​

+4=0

Recall that $\frac{\sin x}{\cos x} = \tan x$. So we can substitute this in:

5

tan

⁡

�

+

4

=

0

5tanx+4=0

Now we can solve for $\tan x$:

\begin{align*}

5 \tan x + 4 &= 0 \

5 \tan x &= -4 \

\tan x &= \frac{-4}{5}

\end{align*}

Therefore, the value of $\tan x$ is $\boxed{\frac{-4}{5}}$.

Answer:

\( abc = - \frac{16}{3} \)

Step-by-step explanation:

\( {x}^{ - 2} {y}^{3} \sqrt[3]{ 64{x}^{5} {y}^{3} } = a {x}^{b} {y}^{c} \\ \\ {x}^{ - 2} {y}^{3} \times 4 \times {x}^{ \frac{5}{3} } \times y= a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5}{3} - 2 } {y}^{3 + 1} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5 - 6}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{ - 1}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ a = 4 \\ \\ b = - \frac{1}{3} \\ \\ c = 4 \\ \\ abc = 4 \times ( - \frac{1}{3} ) \times 4 \\ \\ = 16 \times ( - \frac{1}{3} ) \\ \\ abc = - \frac{16}{3} \)

The range between a drug's effective dose and its toxic dose is called the theurapeutic index.

The therapeutic index, often known as the therapeutic ratio, is a numerical evaluation of a drug's relative safety. The amount of a therapeutic agent that has a therapeutic impact is compared to the amount that has a harmful effect.

A range of doses calibrated between efficacy and toxicity, achieving the maximum therapeutic benefit without producing intolerable side-effects or toxicity, is referred to as the therapeutic window or safety window.

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At least 11 students must take the quiz to assure that at least two have exactly the same answers to all five questions.

Determining the minimum number of students required to guarantee that at least two students have the same answers to all five questions on a multiple choice quiz. Under the area of probability and combinatorics.

There are 4 possible answers for each of the 5 questions, so there are a total of \(4^5 = 1024\) possible sets of answers.

Let's consider the opposite scenario where no two students have exactly the same answers to all five questions. In this case, the first student can choose any of the 1024 possible sets of answers. The second student must choose a different set of answers from the first student, so there are 1023 possible sets of answers for the second student. Similarly, the third student must choose a different set of answers from the first two students, so there are 1022 possible sets of answers for the third student. Continuing in this way, the nth student has 1025-n possible sets of answers to choose from.

Therefore, the total number of possible sets of answers for n students is the product of the number of possible sets of answers for each student:

1024 × 1023 × 1022 × ... × (1025-n)

We want to find the minimum value of n such that this product is less than 1024, because that is the maximum number of sets of answers possible. That is, we want to solve the inequality:

1024 × 1023 × 1022 × ... × (1025-n) < 1024

To simplify this expression, notice that each term in the product is very close to 1024, which suggests that we can approximate the product as \(1024^n\). This approximation is valid when n is much smaller than 1024, which is the case here.

Using this approximation, we can rewrite the inequality as:

\(1024^n\)< 1024

Taking the logarithm base 2 of both sides, we get:

n < log2(1024) = 10

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