Is equidistant same as mid point?

The length of AC is approximately 10.85 cm.

To find the length of AC, we can use the Pythagorean theorem.

According to the Pythagorean theorem, in a right triangle where c is the hypotenuse (the side opposite the right angle) and a and b are the other two sides, the relationship between the lengths of the sides is:

c^2 = a^2 + b^2

In this case, we can use AB as one of the legs of the right triangle and BC as the other leg, with AC being the hypotenuse. So we have:

AC^2 = AB^2 + BC^2

AC^2 = (10.2 cm)^2 + (3.7 cm)^2

AC^2 = 104.04 cm^2 + 13.69 cm^2

AC^2 = 117.73 cm^2

To find the length of AC, we take the square root of both sides:

AC = sqrt(117.73 cm^2)

AC ≈ 10.85 cm

Therefore, the length of AC is approximately 10.85 cm.

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The exact value of cscθ is (35 * √(1190)) / 1190.

To find the value of cscθ (cosecant θ) given that cosθ = 1/√35 and sinθ < 0, we can use the reciprocal relationship between sine and cosecant.

Recall that cscθ is the reciprocal of sinθ. Since sinθ is negative, we can determine its value based on the quadrant in which θ lies.

In the unit circle, the cosine is positive in the first and fourth quadrants, while the sine is negative in the third and fourth quadrants.

Given that cosθ = 1/√35 and sinθ < 0, we can conclude that θ lies in the fourth quadrant.

Using the Pythagorean identity, sinθ = √(1 - cos^2θ), we can calculate the value of sinθ:

sinθ = √(1 - (1/√35)^2)

     = √(1 - 1/35)

     = √(34/35)

     = √34 / √35

     = (√34 / √35) * (√35 / √35)     [Multiplying numerator and denominator by √35 to rationalize the denominator]

     = √(34 * 35) / 35

     = √(1190) / 35

Now, since cscθ is the reciprocal of sinθ, we have:

cscθ = 1 / sinθ

     = 1 / (√(1190) / 35)

     = 35 / √(1190)

     = (35 * √(1190)) / 1190.

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Answer:

5 units

Step-by-step explanation:

Area swept by the floor will be the area ofd a sector

Area of a sector = theta/2π * πr²

We are to find the radius r

Given

Area=  25π/12

theta = 30° = π/6

Substitute

25π/12 = 30/360 * πr²

25π/12 = 1/12 * πr²

25/12 = r²/12

r² = 25

r = √25

r = 5

Hence the radius od the part swept by the door is 5 units

22 would be displayed by command print(magic(5)).

The statement print(magic(5)) would display the result of the magic function when called with an argument of 5.

The print function is a commonly used function in programming languages that allows you to display output to the console or terminal. It is used to output text, variables, or other data to the standard output device.

Substituting num = 5 into the function definition, we get:

x = num - 3 = 5 - 3 = 2

return x + 2 * 10 = 2 + 20 = 22

Therefore, print(magic(5)) would display 22.

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Answer:

d) -3

Step-by-step explanation:

The equation of a parabola in vertex form is given as:

y = a(x - h)² + k. Where (h, k) is the vertex of the parabola.

Given that the vertex of the parabola is at (4,-3) i.e h = 4 and k = -3.

The equation of the parabola is given as:

y = a(x - 4)² + (-3)

y = a(x² - 8x + 16) - 3

y = ax² - 8ax + 16a - 3

Given that when x = 5, y = -6. i.e:

-6 = a(5)² - 8a(5) + 16a - 3

- 6 = 25a - 40a + 16a - 3

-6 + 3 = a

a = -3

im pretty sure its 8.94

Constructing a confidence interval for the mean of a distribution based on one sample is Confidence level = 1 - significance level.

The definition of the confidence level is (1-α). Zα is the number of standard deviations from the mean at which X with a certain probability lies. If Z = 1.96 is selected, the likelihood that the real mean falls inside the range is set at 0.95, hence we are asking for the 95% confidence interval.

Let us consider,

Confidence level = c

significance level \(= \alpha\)

\(c = 1 - \alpha\)

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Buying as much auto insurance as you can afford is not the best idea.

Auto insurance is a type of insurance that provides you the following benefits:

Payments are agreed by customers, this means you can pay as much as you can, and by paying more you will have a wider coverage.

Despite this, investing as much money as is possible is not a good idea because incidents such as accidents are not so common and if you never experience one, the insurance is useless.

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In the long run, the proportion of hours the turtle will be hiding is 1, or 100%.

Since the turtle can only be either eating or hiding at any given hour, we know that h + e = 1.

Write the transition matrix as follows:

A =\(\left[\begin{array}{ccc}1&\frac{1}{2} \\\frac{1}{2}&\frac{1}{2}\end{array}\right]\)

The first row of A represents the probability of transitioning from hiding to hiding or from hiding to eating, while the second row represents the probability of transitioning from eating to hiding or from eating to eating.

Find the eigenvector corresponding to the eigenvalue of 1 for the transition matrix A.

Setting up the equation Ax = λx, where λ = 1, we get:

\(\left[\begin{array}{ccc}1&\frac{1}{2} \\\frac{1}{2}&\frac{1}{2}\end{array}\right] \left[\begin{array}{ccc}h\\e\end{array}\right] = \left[\begin{array}{ccc}h\\e\end{array}\right]\)

This gives us two equations:

h + (1/2)e = h

(1/2)h + (1/2)e = e

Simplifying the first equation, we get:

(1/2)e = 0

This implies that e = 0, which means that the turtle spends no time eating in the long run. Using the fact that h + e = 1, we can conclude that the turtle spends all of its time hiding in the long run.

Therefore, the proportion of hours the turtle spends hiding in the long run is 1, or 100%.

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The prime factorization of 735000 is 2² × 3³ × \(5^4\). We can determine that 735000 has 144 divisors using the formula for the number of divisors.

The multiplicative principle can be used to calculate the number of 735000's divisors. The prime factorization of 735000 is given by the basic theorem of mathematics as follows:

735000 = 2³ × 3²× 5³ × 7²

We must take into account all feasible permutations of the prime factors of 735000 in order to determine the number of its divisors. Typically, if a composite number can be divided into prime factors:

n = p1a1 × p2a2 × ... × pkak

where a1, a2,..., pk are positive integers and p1, p2,..., pk are separate prime numbers, then n has the following number of divisors:

(a1 + 1) × (a2 + 1) × ... × (ak + 1)

As we can select any exponent between 0 and ai for each prime factor pi, there are (ai + 1) possibilities for each prime factor, and the sum of all the choices for all prime aspects is the total number of alternatives.

In the case of 735000, we have:

a1 = 3, a2 = 2, a3 = 3, a4 = 2

So the number of divisors of 735000 is:

(3 + 1) × (2 + 1) × (3 + 1) × (2 + 1) = 4 × 3 × 4 × 3 = 144

Therefore, 735000 has 144 divisors.

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Answer:

the only thing I can do is get a refund for the convenience of the day and I'll be there in a few minutes to get a refund for the convenience of the day and I'll be there in a few minutes to get a refund for the convenience of the day and I'll be there in a few minutes to get a

-2 - √3i is a known root not a possible root, option 4 will be the correct answer.

What are real and imaginary roots ?

A real root to an equation is a real number. A complex root to an equation is an imaginary root represented as complex numbers.

In other words real roots can be represented in a number line where as imaginary roots can not.

Here, the given root is -2 + √3i :

It is known that the complex roots comes in pairs that is in form a ±ib, where, a is real part of imaginary root and b is imaginary part.

Therefore, the other root will be -2 - √3i.

So, -2 - √3i is a known root not a possible root, option 4 will be the correct answer.

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Answer:

\( \sqrt{3} \)

Step-by-step explanation:

- since it's an isosceles triangle, the other two angle is the same, so 180-90÷2=45

- i use SOH, CAH, TOA rule and in this case, i use SOH.

Answer:

x = √3

Step-by-step explanation:

Let us use the Pythagoras theorem to find the value of x.

Accordingly,

x² + x² = (√6)²

2x² = 6

Divide both sides by 2.

x² = 3

Put square roots on both sides.

x = √3

Answer:

Step-by-step explanation:

The formulas to find the x and y coordinates of E are:

\(x=\frac{bx_1+ax_2}{a+b}\)  and  \(y=\frac{by_1+ay_2}{a+b}\)  where x1, x2, y1, and y2 are from the coordinates of A and B, and a = 1 (from the ratio) and b = 2 (from the ratio). Filling in to find x first:

\(x=\frac{2(2)+1(-4)}{1+2}=\frac{4-4}{3}=0\)  and now for y:

\(y=\frac{2(-3)+1(9)}{1+2}=\frac{-6+9}{3}=\frac{3}{3}=1\)

The coordinates of E are (0, 1).

Given:

The points are A(2,-3) and B(-4,9).

The point E divides the segment AB in 1:2.

To find:

The coordinates of point E.

Solution:

Section formula: If a point divides a line segment in m:n, then the coordinates of the point is:

\(Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)\)

Using the section formula, the coordinates of point E are:

\(E=\left(\dfrac{1(-4)+2(2)}{1+2},\dfrac{1(9)+2(-3)}{1+2}\right)\)

\(E=\left(\dfrac{-4+4)}{3},\dfrac{9-6}{3}\right)\)

\(E=\left(\dfrac{0)}{3},\dfrac{3}{3}\right)\)

\(E=\left(0,1\right)\)

Therefore, the coordinates of the point E are (0,1).

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6700\\ P=\textit{original amount deposited}\dotfill & \$3600\\ r=rate\to 4.42\%\to \frac{4.42}{100}\dotfill &0.0442\\ t=years \end{cases} \\\\\\ 6700=3600[1+(0.0442)(t)]\implies \cfrac{6700}{3600}=1+0.0442t\implies \cfrac{67}{36}=1+0.0442t \\\\\\ \cfrac{67}{36}-1=0.0442t\implies \cfrac{31}{36}=0.0442t\implies \cfrac{\frac{31}{36}}{0.0442}=t\implies 19.5\approx t\)

Answer: 12xy + 12xyz

Step-by-step explanation:

15xyz - 3xyz = 12xyz + 12xy

Every rectangle with four congruent sides is a square -> True

Every rhombus is a quadrilateral -> True

Every square is a parallelogram -> True

Every quadrilateral is a square -> False.

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

here, we have,

we know that,

Every rectangle with four congruent sides is a square -> True

Every rhombus is a quadrilateral -> True

Every square is a parallelogram -> True

Every quadrilateral is a square -> False.

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It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.

It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying. ​

1) The correct solution is

Given,

a ÷ (2 + 1. 5)

Substituting the value of a which is 14

= 14 ÷ (2 + 1. 5)

= 14 ÷ 3.5

= 4

2) As there is no term which needs to be divided so, the second statement is false.

3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.

4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying. ​

i.e. a ÷ (2 + 1. 5)

14 ÷ 2 + 1. 5

7+1.5

8.5

This is the way Jayden solved the equation due to which he arrived at the wrong solution.

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The Correct question is as below

Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.

1. Jayden's solution is incorrect.

2. Jayden added in the parentheses before dividing.

3. Jayden substituted the wrong value for a.

4. Jayden divided 14 by 2 and added 1.5

Answer:

a = 3

Step-by-step explanation:

Factorize (x+5)(x-4)(x+2)

(x+5)(x-4)(x+2)

=  (x²-4x+5x-20)(x+2)

= (x²+x-20)(x+2)

= (x³+2x²+x²+2x-20x-40)

= x³+3x²-18x -40

Compare with x^3+ax^2

3x² = ax²

3 = a

Rearrange

a = 3

Hence the value of a that makes the expressions identical is 3

Answer:

600,000 is greater than 11,733.83. Or

600,000>11,733.83

Step-by-step explanation:

To compare the values of 600,000 and 11,733.83, we can simply look at the magnitude of the numbers.

600,000 is much larger than 11,733.83. This means that 600,000 is greater than 11,733.83

If a is an nn matrix and the equation axb has more than one solution for some b, then the transformation is not one-to-one. This also means that the transformation is not invertible.

This is because if there is more than one solution for a given b, then there is not a unique inverse for the matrix a. In other words, there is not a unique matrix a-1 such that a-1axb = b for all b.

This means that the transformation cannot be reversed or "undone" uniquely, and therefore it is not invertible. Additionally, this implies that the matrix a is not full rank, meaning that its columns are not linearly independent and there is not a unique solution for the equation ax = 0. These properties are all related and are consequences of the fact that the transformation is not one-to-one.

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1) False (F)

2) True (T)

3) True (T)

4) True (T)

5) True (T)

6) False (F)

7) False (F)

8) True (T)

9) True (T)
10) False (F)

11) True (T)

1) In a commutative ring with unity, every unit is not necessarily a non-zero divisor. For example, in the ring of integers (Z), the unit 1 is not a non-zero divisor since 1 multiplied by any non-zero element gives the same non-zero element.

2) If an ideal I in a commutative ring with unity R contains a unit x, then I = R. This is because the presence of a unit in an ideal implies that every element of the ring can be obtained by multiplying the unit with some element of the ideal, which covers the entire ring.

3) In an integral domain, the left cancellation law holds. This means that if a, b, and c are elements of an integral domain and a ≠ 0, then a * b = a * c implies b = c. This property holds in integral domains.

4) Every finite integral domain is a field. This is known as the finite field theorem, which states that every finite integral domain is a field. In a field, every non-zero element has a multiplicative inverse, and all nonzero elements form a group under multiplication.

5) The sum of two idempotent elements is idempotent. An element in a ring is idempotent if squaring it gives the same element. So, if a and b are idempotent elements in a ring, then (a + b)² = a² + b² + ab + ba = a + b + ab + ba = a + b since a and b are idempotent.

6) The element 6 is not a zero divisor in M₂(Z) (the ring of 2x2 matrices with integer entries). A zero divisor is an element that multiplied by a non-zero element gives the zero element. In M₂(Z), 6 multiplied by any non-zero matrix will not give the zero matrix.

7) There are 2 maximal ideals in Z₁₂ (the ring of integers modulo 12) and no maximal ideals in Z₈ (the ring of integers modulo 8). The number of maximal ideals in a ring is not necessarily related to the number of elements in the ring itself.

8) The polynomial f(x) = x + 5x⁵ - 15x + 15x³ + 25x² + 5x + 25 satisfies the Eisenstein Criteria for irreducibility test and is therefore irreducible over Q (the field of rational numbers).

9) If (1 + x) is an idempotent in Zn (the ring of integers modulo n), then (n - x) is also idempotent. This can be verified by squaring (n - x) and showing that it equals (n - x).

10) Not all non-zero elements in Z[i] (the ring of Gaussian integers) are non-zero divisors. For example, 1 is a non-zero element in Z[i] but is not a non-zero divisor since multiplying it by any non-zero element still gives a non-zero element.

11) In a commutative finite ring R with unity, every prime ideal is a maximal ideal. This property holds in commutative finite rings with unity.

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Answer: 729

Assuming each unit is L x W x H, 7 x 7 x 7 = 729, so thats the volume.

To find the largest area you can enclose with a single-strand electric fence and m units of wire at your disposal, you need to optimize the dimensions of the rectangular plot.

Let's denote the length of the rectangular plot as L and the width as W. The perimeter of the plot can be calculated as P = L + 2W.

Since one side of the plot is already bounded by the river, we have L + W = m. Rearranging this equation, we get L = m - W.

To find the largest area, we need to maximize the function A = L * W. Substituting the value of L, we have A = (m - W) * W.

Expanding the equation, we have A = mW - W^2.

To find the maximum value of A, we take the derivative of A with respect to W and set it equal to zero: dA/dW = 0.

Differentiating, we get m - 2W = 0. Solving for W, we have W = m/2.

Substituting this value back into the equation for L, we have L = m/2.

Therefore, the dimensions of the largest area are L = m/2 and W = m/2.

To find the area, we substitute these values into the equation for A: A = (m/2) * (m/2) = m^2/4.

In conclusion, the largest area that can be enclosed is m^2/4, with dimensions L = m/2 and W = m/2.

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Answer:

u=9.8

Step-by-step explanation:

the minus sign on u and the minus sign on 9.8 cancel out so you get u=9.8.

Answer:

B. no, the relation is not a function

Step-by-step explanation:

Answer:

80x+65 2.465 3.865

Step-by-step explanation:

x being the number of years so in ten years he will have 80x10=800+65=865

80x5=400+65=465 so 5 is the number of years it would take

and i do not understand number 1 but i put a formula just in case that was it

Answer:

Not sure what you're asking here.

Step-by-step explanation:

If you're trying to find the new price just put in your calculator.