in δjkl, k = 6.3 inches, j = 8.8 inches and ∠j=127°. find all possible values of ∠k, to the nearest 10th of a degree.

Two sides are congruent to each other.

The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.

A triangle with all sides of different lengths. All angles are different, too. So no sides are equal and no angles are equal.

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Answer:

Two sides are congruent to each other.

The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.

A triangle with all sides of different lengths. All angles are different, too. So no sides are equal and no angles are equal.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

3(-2y) +2y = -4

-6y+2y=-4

-4y=-4

y=1

Considering the logarithmic loudness equation, the relative intensity of 120 decibels is of \(R = 10^{12}\).

The equation is:

\(L = 10\log{R}\)

In which:

For this problem, we have that L = 120, hence the relative intensity is found as follows:

\(120 = 10\log{R}\)

\(\log{R} = 12\)

\(R = 10^{12}\)

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The function to model the water used by the car wash on a shorter day is (C) \(4x^{3} +7x^{2} -14x-6\).

To find the function to model the water used by the car wash on a shorter day:

Given that the amount of water used on normal days is given by the equation:

The amount of decrease in water used is modeled by the equation:

To get the function \(C(x)\) that models the water used by the car wash on a shorter day you subtract equation (2) from equation (1).

Therefore, the function to model the water used by the car wash on a shorter day is (C) \(4x^{3} +7x^{2} -14x-6\).

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The correct question is shown below:

The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day.

(A) c(x) = 5x3 7x2 − 14x − 6

(B) c(x) = 4x3 7x2 − 14x 6

(C) c(x) = 4x3 7x2 − 14x − 6

(D) c(x) = 5x3 7x2 − 14x 6

Answer:

A number plus 3, sum is 5.

Answer:

-----------------------

Dilation results in similar figures.

Each side of the image is 3 times larger hence the area is 3*3 = 9 times larger since area is the product of two dimensions.

So the area of the image is:

The surface area of the rectangular prism figure is S = 838 cm²

Given data ,

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

So, the value of S is given by

The heights of the prism is represented as 7cm.

S = ( 11 x 20 ) + ( 7 x 20 ) + ( 4 x 20 ) + 2( 5 x 7 ) + 2( 6 x 4 ) + ( 6 x 20 ) + ( 5 x 20 ) + ( 3 x 20 )

On simplifying the equation , we get

S = 220 + 140 + 80 + 70 + 48 + 120 + 100 + 60

S = 838 cm²

Therefore , the value of S is 838 cm²

Hence , the surface area is S = 838 cm²

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i) The dispersion relation for the given equation is ± (v / 6) * k.

ii) The group velocity for the given equation is ± v / 6.

iii) The phase velocity is ± v / 6.

To find the dispersion relation, as well as the group and phase velocities for the given equation, let's start by rewriting the equation in a standard form:

82y(x, t) - 8\(t^2\) + 84y(x,t) = -2 * 8\(x^4\)

Simplifying the equation further:

8(2y(x, t) - \(t^2\) + 4y(x,t)) = -16\(x^4\)

Dividing both sides by 8:

2y(x, t) - \(t^2\) + 4y(x,t) = -2\(x^4\)

Rearranging the terms:

6y(x, t) = \(t^2\) - 2\(x^4\)

Now, we can identify the coefficients of the equation:

Coefficient of y(x, t): 6

Coefficient of \(t^2\): 1

Coefficient of \(x^4\): -2

(i) Dispersion Relation:

The dispersion relation relates the angular frequency (ω) to the wave number (k). To determine the dispersion relation, we need to find ω as a function of k.

The equation given is in the form:

6y(x, t) = \(t^2\) - 2\(x^4\)

Comparing this with the general wave equation:

A * y(x, t) = B * \(t^2\) - C * \(x^4\)

We can see that A = 6, B = 1, and C = 2.

Using the relation between angular frequency and wave number for a linear wave equation:

\(w^2\) = \(v^2\) * \(k^2\)

where ω is the angular frequency, v is the phase velocity, and k is the wave number.

In our case, since there is no coefficient multiplying the y(x, t) term, we can set A = 1.

\(w^2\) = (\(v^2\) / \(A^2\)) * \(k^2\)

Substituting the values, we get:

\(w^2\) = (\(v^2\) / 36) * \(k^2\)

Therefore, the dispersion relation for the given equation is:

ω = ± (v / 6) * k

(ii) Group Velocity:

The group velocity (\(v_g\)) represents the velocity at which the overall shape or envelope of the wave propagates. It can be determined by differentiating the dispersion relation with respect to k:

\(v_g\) = dω / dk

Differentiating ω = ± (v / 6) * k with respect to k, we get:

\(v_g\) = ± v / 6

So, the group velocity for the given equation is:

\(v_g\) = ± v / 6

(iii) Phase Velocity:

The phase velocity (\(v_p\)) represents the velocity at which the individual wave crests or troughs propagate. It can be calculated by dividing the angular frequency by the wave number:

\(v_p\) = ω / k

For our equation, substituting the dispersion relation ω = ± (v / 6) * k, we have:

\(v_p\) = (± (v / 6) * k) / k

\(v_p\) = ± v / 6

Therefore, the phase velocity for the given equation is:

\(v_p\) = ± v / 6

To summarize:

(i) The dispersion relation is ω = ± (v / 6) * k.

(ii) The group velocity is \(v_g\) = ± v / 6.

(iii) The phase velocity is \(v_p\) = ± v / 6.

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Answer:

Step-by-step explanation:

sin(x) = (17/19)

sin inverse of (17/19) = x

x = 63.45°

Answer: the ANSWER IS 11 sqt

Step-by-step explanation:

Factor 1331 into its prime factors

          1331 = 113

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          121 = 112

Factors which will remain inside the root are :

          11 = 11

To complete the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          11 = 11

The simplified SQRT looks like this:

        11 • sqrt (11)  

Simplified Root :

11 • sqrt(11)

Solving a system of equations, it is found that the value of a is of -191.75 and the value of b is of 278.25.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

Multiplying the first equations by 17 and the second by -5, we have that the system is:

Then, adding them:

4a = -767

a = -767/4

a = -191.75

Then:

\(b = \frac{49 - 7a}{5} = \frac{49 - 7(-191.75)}{5} = 278.25\)

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Answer:

area=3/5      

length=7/8    

width=?

so  3/5=7/8 times ?

multiply both sides by 8/7 to clear fraction (7/8 times 8/7=56/56=1 and 1 times ?=? so)

24/35=?  

the width= 24/35 mile

Answer:

(x,y)

Step-by-step explanation:

x comes first always

(x,y)

so 2 would be the x value and 3 would be the y value

There is only one different square root of A.(a) To find the square roots of matrix A = [2 2; 2 2]: Let's consider two matrices B1 and B2: B1 = [1 1; 1 1]; B2 = [-1 -1; -1 -1].

Now, let's check if BB = A for each matrix: B1B1 = [1 1; 1 1] * [1 1; 1 1] = [2 2; 2 2] = A; B2B2 = [-1 -1; -1 -1] * [-1 -1; -1 -1] = [2 2; 2 2] = A. Both B1 and B2 satisfy BB = A, so they are two possible square roots of matrix A. (b) For matrix A = [5 0; 0 9], let's consider a matrix B: B = [√5 0; 0 √9] = [√5 0; 0 3] .We can see that BB = [√5 0; 0 3] * [√5 0; 0 3] = [5 0; 0 9] = A.

Thus, there is only one different square root of A. (c) Not every 2x2 matrix has a square root. For a square root of a matrix to exist, the matrix must be positive definite or positive semidefinite. If the eigenvalues of the matrix are negative or complex, there won't be any real square root. Additionally, if the matrix has zero eigenvalues with multiplicities greater than one, it may not have a unique square root. Therefore, the existence of a square root for a 2x2 matrix depends on its eigenvalues and their properties.

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The correct option is a low return rate; eliminating interviewer bias. Mail surveys have the concern of low return rate but have the advantage of eliminating interviewer bias.

A mail survey is a form of a self-administered survey in which the questionnaire is sent to the respondent through the post. Mail surveys are convenient because they allow participants to respond on their schedule and in the privacy of their own homes.

Mail surveys have the concern of a low return rate but have the advantage of eliminating interviewer bias. The concern of mail surveys is a low return rate. One of the greatest advantages of mail surveys is that they do not require any interaction between the researcher and the respondent. Mail surveys' response rate is typically lower than phone or face-to-face surveys. However, it eliminates interviewer bias.

Interviewer bias occurs when the interviewer's characteristics or behavior have an impact on the participant's responses. Interviewer bias can occur in face-to-face interviews or phone surveys. Respondents may attempt to please the interviewer or present themselves in a more favorable light than they otherwise would in order to avoid social disapproval.

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Answer: $149.8

Step-by-step explanation:

Find the 1% of the 140 which is 1.4 because 140/100 = 1.4

Times by 7 to get 7%. 1.4 x 7 = 9.8

Add them together. 140+9.8 = 149.8

Answer:

tan(57°) = 12/x

x tan(57°) = 12

x = 12/tan(57°) = 7.793

Answer:

x ≈ 7.8

Step-by-step explanation:

using the tangent ratio in the right triangle

tan57° = \(\frac{opposite}{adjacent}\) = \(\frac{12}{x}\) ( multiply both sides by x )

x × tan57° = 12 ( divide both sides by tan57° )

x = \(\frac{12}{tan57}\) ≈ 7.8 ( to the nearest tenth )

The shape consist of a rectangle and a semi circle

The area of a rectangle is the product of its length and width while that of a semicircle pir^2

The radius of the semicircle is = 12/2

= 6 ft

The length and width of the rectangle are 16 ft and 12 ft respectively.

Hence the area of the shape

= 12 * 16 + 3.14 *6^2

= 192 + 113.04

= 305.04 sq ft

Answer:

26 miles

you welcomeeeeee

Answer:

Yes,

\(y^{6} x\)

Step-by-step explanation:

\(y^{5} xy = y^{5} *y*x = y^{6} x\)

Lagrange multipliers is a method used to find extrema of a function subject to equality constraints by introducing auxiliary variables called Lagrange multipliers.

To find the maximum and minimum value of the function f(x, y, z) = 2x - 3y, subject to the constraint x^2 + 2y^2 + 3z^2 = 1, we can use the rule of Lagrange multipliers.

First, we set up the Lagrangian function L(x, y, z, λ) as follows:

L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z) - c)

where g(x, y, z) represents the constraint function \(x^2 + 2y^2 + 3z^2\), and c is the constant value 1.

Take the partial derivative with respect to x, y, z, and λ, we get:

∂L/∂x = 2 - 2λx

∂L/∂y = -3 - 4λy

∂L/∂z = 0 - 6λz

∂L/∂λ = \(x^2 + 2y^2 + 3z^2 - 1\)

Setting these derivative equal to zero and solving the resulting equations simultaneously will give us the critical points.

From the 1st equation, we have: 2 - 2λx = 0, which gives λx = 1.

From the 2nd equation, we have: -3 - 4λy = 0, which gives λy = -3/4.

From the 3rd equation, we have: -6λz = 0, which gives λz = 0.

From the 4th equation, we have: \(x^2 + 2y^2 + 3z^2 - 1\) = 0.

Considering the constraint equation and the values obtained for λ, we can solve for the critical points by substituting the values back into the original equations.

By analyzing the critical points, including boundary points (where the constraint is satisfied), we can determine the maximum and minimum values of the function f(x, y, z) = 2x - 3y subject to the given constraint \(x^2 + 2y^2 + 3z^2 = 1\).

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The area of the surface generated by revolving the curve about the x-axis is 9664π  / 3 square units.

Given: The equation of the curve is y = 4√x on [21,77]

The formula for finding the surface area of a curve rotated about the x-axis on some interval [a, b] is given by:

\(S = \int\limits^b_a {2\pi f(x)\sqrt{1 +(f'(x))^{2} } } \, dx\)

where S is the surface area,

f(x) is y

a and b is the given interval such that a ≤ x ≤ b or [a, b]

Now in this question,

f(x) = 4√x

a = 21, b = 77

f'(x) = 4 * 1 / 2√x = 2 / √x

f'(x) = 2 /√x

Placing the respective values in the equation we get,

\(S = \int\limits^{77}_{21} {2\pi. 4\sqrt{x} \sqrt{1+(\frac{2}{\sqrt{x} } )^{2} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x} \sqrt{1+\frac{4}{x} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x} * \frac{\sqrt{x + 4} }{\sqrt{x} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x+4} } } \, dx\)

we know the formula for the integral

\(\int\limits^b_a {\sqrt{ax + b} } \, dx = \frac{2}{3a}(ax+b)^{\frac{3}{2} } | { {{b} \atop {{a}}} \right.\)

Therefore, by applying the formula, we get:

\(S = 8\pi *\frac{2}{3}(x+4)^{\frac{3}{2} } | { {{77} \atop {{21}}} \right.\)

\(S = \frac{16\pi }{3} \{ (77+4)^{\frac{3}{2}} - (21+4)^{\frac{3}{2} }\}\)

\(S = \frac{16\pi }{3} \{ (81)^{\frac{3}{2}} - (25)^{\frac{3}{2} }\}\)

\(S = \frac{16\pi }{3} \{729 - 125\}\)

\(S = \frac{16\pi }{3} * 604\)

\(S = \frac{9664\pi }{3}\)

Hence, The area of the surface generated by revolving the curve about the x-axis is 9664π  / 3 square units

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Disclaimer: The given question is incomplete. The complete question is mentioned below:

Find the area of the surface generated when the given curve is rotated about the x-axis y= 4sqrt(x) on [21,77]

The area of the surface generated by revolving the curve about the x-axis is ___ square units (type an exact answer, using pi as needed)

The functions of fat cells are:

Store energy

Hold body heat

Absorb shocks.

Adipocytes, sometimes referred to as fat cells, are specialized cells that serve as major sources of fat-based energy storage. They are essential to maintaining the equilibrium between energy intake and energy expenditure, which is known as energy homeostasis. Triglycerides, the primary building block of body fat, is accumulated in the adipose tissue when we consume more energy (calories) than we expend.

Leptin and adiponectin are two hormones secreted by fat cells that control insulin sensitivity, metabolism, and hunger. For instance, leptin helps to control body weight by alerting the brain when we've eaten enough to eat. Contrarily, adiponectin enhances insulin sensitivity and possesses anti-inflammatory properties.

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The distance between point \((8, \sqrt{17})\) and the center (0,0) is of 9 units, which is less than the radius, hence the correct option is:

Yes, the distance from the origin to the point \((8, \sqrt{17})\) is of 9 units.

Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

In this problem, we have a circle with center at (0,0) and radius 10. Hence, every point that is less than 10 units of distance from point (0,0) will be on the circle.

The distance of \((8, \sqrt{17})\) is:

\(D = \sqrt{(8 - 0)^2+(\sqrt{17} - 0)^2}\)

\(D = \sqrt{81}\)

D = 9 units.

9 < 10, hence the correct option is:

Yes, the distance from the origin to the point \((8, \sqrt{17})\) is of 9 units.

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Answer:

l = 2, m = - 1, n = - 6

Step-by-step explanation:

A scalar matrix has its diagonal elements equal and all other elements zero, so

2l - 4 = 0 ( add 4 to both sides )

2l = 4 ( divide both sides by 2 )

l = 2

---------------------------------------

3l + n = 0

3(2) + n = 0

6 + n = 0 ( subtract 6 from both sides )

n = - 6

--------------------------------------

3m - n = 3

3m - (- 6) = 3

3m + 6 = 3 ( subtract 6 from both sides )

3m = - 3 ( divide both sides by m )

m = - 1

Answer: 50.5

Step-by-step explanation:

If it’s mathswatch you don’t need an explanation just type in the answer it gives you all the marks <3

The value of the angle,x=50.531°. The angle is obtained by the sin law.

A triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

From the sin rule;

\(\rm \frac{AB}{sin \angle ACB} =\frac{BC}{sin \angle BAC} \\\\ \rm \frac{5.6}{sin \angle ACB} =\frac{9.3}{sin \angle 50^0} \\\\ \angle ACB=27.49^0\)

For the same angles;

\(\rm \angle ACB=\angle BCD\)

From the exterior angle theorm ;

\(\rm \angle BCD+\angle CBD= \angle ADB\)

∠CBD=x

∠ABD=78°

Putting the obtained values;

27.469°+x=78°

x=78°-27.469°

x=50.531°

Hence,the value of the angle,x=50.531°.

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The term central location or central tendency relates to the way data tend to cluster around some middle or central value

It is a number located towards the center of the distribution of the values of a series of observations, that are called measures, in which the set of data is located. The most commonly used measures of central tendency are: mean, median and mode.

Statistics is a branch of mathematics that allows you to collect, organize and analyze data according to the need you have, for example: to obtain a result, compare information, make better decisions, among many other things.

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