kuta software infinite algebra 2 the law of cosines

When an increase in one variable is associated with an increase in a second variable, the two variables are known as positively correlated. The correlation coefficient is the measure of the degree of the relationship between two variables.

The correlation coefficient ranges from -1 to 1. A positive correlation coefficient indicates a positive relationship between two variables, while a negative correlation coefficient indicates an inverse relationship between two variables.

A positive correlation coefficient signifies that as one variable increases, the other variable also increases. For instance, the correlation between a person's height and weight is positive because as their height increases, so does their weight.

In the same way, as a person's income increases, so does their level of expenditure. Positive correlations can be either strong or weak.A strong correlation is indicated by a correlation coefficient close to 1, while a weak correlation is indicated by a correlation coefficient closer to zero.

For example, the correlation between a person's weight and the number of hours they exercise per week is strong. When a person's exercise time increases, so does their weight loss. In conclusion, when an increase in one variable is associated with an increase in a second variable, the two variables are positively correlated.

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Answer:

\(9 - x = 1\)

\(9-x-9=1-9\)

\(-x=-8\)

\(\cfrac{-x}{-1}=\cfrac{-8}{-1}\)

\(\boxed{x=8}\)

\(-252 = 21k\)

\(21k=-252\)

\(\cfrac{21k}{21}=\cfrac{-252}{21}\)

\(\boxed{k=-12}\)

Answer:

x= -6   k=-12

Step-by-step explanation:

15-9 is 6.   9+6=15 9-(-6)=15 because when two negatives are together they make a positive. (--)=+      K=-21 because -252/21 is -12.

Answer:

no

Step-by-step explanation:

Answer: No

Step-by-step explanation: plz mark me brainliest. EF are 5 lengths away from each other and FG is 15 so no

Answer:

\(400m^3\)

Step-by-step explanation:

Use the formula \(V=\frac{1}{3}Ah\)

Where h=the height of the pyramid (12cm)

A=the base area of the pyramid, also known as the area of the square (10cm*10cm=100cm)

So, inserting this into the equation:

\(V=\frac{1}{3} (100)(12)\)

\(V=\frac{1}{3} (1200)\)

\(V=400m^3\)

Answer:

33%

Step-by-step explanation:

48-15=33

33/100*100=33%

The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:

Step-by-step explanation:

Answer:

Check Explanation

Step-by-step explanation:

The diagram for this question is missing, but from the setup of the question, it is evident that the triangle to obtain cos α from is a right angled triangle.

It is evident from the options provided that the right angled triangle is one with dimensions of 20, 21 and 29.

These three dimensions perfectly form a Pythagorean triple.

So, the value of cos α now depends on the setup of the triangle.

From trigonometric relations, if α is an angle in the right angled triangle, cos α is given mathematically as

Cos α = (Adj/Hyp)

For this Pythagorean triple,

Hyp = hypotenuse side = 29

Adj = Adjacent side = 20 or 21, depending on the triangle's setup.

If the adjacent is 20,

Cos α = (20/29), option A is correct.

If the adjacent is 21,

Cos α = (21/29), option C is correct.

Hope this Helps!!!

Answer:

its b

Step-by-step explanation:

Answer: the answer B sorry if its wrong

Step-by-step explanation: have a nice day buddy

In an LRC circuit problem, the term "C" stands for capacitance (option b).

An LRC circuit consists of three primary components: an inductor (L), a resistor (R), and a capacitor (C). These components are connected in series, and the circuit allows the analysis of the behavior of electrical energy in the presence of these components.

The inductor (L) stores energy in the form of a magnetic field when current flows through it, while the resistor (R) dissipates energy in the form of heat as the current passes through it. The capacitor (C), on the other hand, stores energy in the form of an electric field as it holds a charge across its plates.

Capacitance is a measure of a capacitor's ability to store electrical energy per unit voltage. It is typically measured in farads (F). The capacitance of a capacitor is dependent on its physical properties, such as the surface area of its plates, the distance between the plates, and the dielectric material between the plates.

In an LRC circuit, the interplay of the inductor, resistor, and capacitor components creates a complex electrical behavior that depends on the circuit's characteristics and the applied voltage or current. The analysis of LRC circuits typically involves solving differential equations that describe the relationships between voltage, current, and the properties of the components.

In summary, the term "C" in an LRC circuit problem represents capacitance, which is a measure of a capacitor's ability to store electrical energy per unit voltage. The LRC circuit's behavior results from the combined action of the inductor, resistor, and capacitor components.

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Measure of angle:

∠A  = 36.86°

∠B = 90°

∠C = 53.13 °

Measure of side ,

AB =  28

BC = 21

CA = 35

Given triangle ABC.

Right angled at B.

Now, using trigonometric ratios to find angle A , B , C .

Right angled at B : ∠B = 90°

Angle A,

SinA = 21/35

∠A = 36.86

Angle C,

SinC = 28/35

∠C = 53.13

Now measures of side.

To find the length of side use sine rule .

Sine rule:

a/sinA = b/sinB = c /sinC

a = opposite side of angle A .

b = opposite site of angle B .

c = opposite side of angle C.

AB = 28

BC = 21

CA = 35

Hence the sides and angles of the triangles are measured .

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The total utility of 4 units is 50 and the marginal utility is 5

Total utility is the sum of satisfaction that is derived from the consumption of units of a good or service.

Total utility can be determined by adding the marginal utility of each unit that is consumed.

Total utility of consuming 4 units = marginal utility of the first unit + marginal utility of the second unit + marginal utility of the third unit + marginal utility of the fourth unit  

20 + 15 + 10 + 5 = 50

Marginal utility is the change in total utility when consumption increases by unit. Marginal utility is 5

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I am not completley sure but i think its (3)

This involves finding the tangent vector, computing the dot product, and integrating over the curve.

The line integral of a vector field F along a curve parameterized by r(t) can be evaluated by computing the dot product of F and the tangent vector r'(t) and integrating over the curve. In this case, the vector field F is given as F = <2³ + zy², 42²z + 2yz, 4 - 2²>.

To evaluate the line integral, we need to parameterize the curve on the sphere S defined by a² + y² + z² = 9. Let's denote the parameterization as r(t) = <a(t), y(t), z(t)>. We then calculate the tangent vector r'(t) and compute the dot product F·r'(t).

Since S is a sphere, we can use spherical coordinates to parameterize the curve. Let's assume a = 3cos(t), y = 3sin(t)cos(u), and z = 3sin(t)sin(u). We differentiate each component with respect to t to find r'(t)

After obtaining r'(t), we substitute it into F·r'(t) and integrate over the appropriate range of t and u. This integration will yield the value of the line integral.

The process involves several calculations and substitutions, which would be more appropriate to present in a mathematical format.

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hi <3

1) as the value ahead of the tenths position is a 5, you would round up.

this gives you the answer of 1.6

2) as the value ahead of the hundredths position is a 4, you would round down.

this gives you the answer of 1.55

3) as the value ahead of the thousandths position is an eight, you would round up.

this gives you the answer of 1.555

hope this helps :)

The electric field (E-field) associated with the given potential function V(x, z) = 4bx^2 + 4az^3 - 3cz^3 is E = -8bx i - (12az^2 - 9cz^2)j.

To find the electric field (E-field) associated with the given potential function, we need to calculate the negative gradient of the potential. The E-field is given by the following formula:

E = -∇V

Where ∇ is the gradient operator. In this case, the potential function V(x, z) is defined as:

V(x, z) = 4bx^2 + 4az^3 - 3cz^3

To calculate the E-field, we need to take the partial derivatives of V with respect to x and z and then apply the negative sign. Let's calculate each component separately:

Partial derivative with respect to x (dV/dx):

dV/dx = 8bx

Partial derivative with respect to z (dV/dz):

dV/dz = 12az^2 - 9cz^2

Now, we can write the E-field vector as:

E = -∇V = -(dV/dx)i - (dV/dz)j

Substituting the calculated partial derivatives, we have:

E = -8bx i - (12az^2 - 9cz^2)j

Therefore, the electric field (E-field) associated with the given potential function V(x, z) = 4bx^2 + 4az^3 - 3cz^3 is:

E = -8bx i - (12az^2 - 9cz^2)j

Note that the positive constants b and c are included in the E-field expression.

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The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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The error Justin made in his calculation is "He should have added the values in the numerator before dividing by 2".

The correct answer choice is option B

(x + y + 5) / 2

Where,

x and y are his parents’ current heights in inches,

Mom’s height = 54 inches

Dad’s height = 71 inches

Substitute into the expression

(71 + 54 + 5) / 2

= 130/2

= 65 inches

Justin's work:

( 71 + 54 + 5 ) / 2

= 71 + 27 + 5

= 103 inches

Therefore, Justin should have added the numerators before dividing by 2.

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The average commute distance of all 50,000 heads of households in the town is estimated as 8.7, and this estimate is likely to be off by 0.28 or so.

The population mean = 8.7

population standard deviation = s/√n

s = 9

n = 1000

= 9/√1000

= 0.28

The conclusion is that the estimate is 8.7 and it is off by 0.28.

CI = bar X ± Z∝/2(s/√n)

= 8.7±1.645(0.28)

= 8.7 ± 0. 47

Confidence interval = 8.23, 9.17

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The ratios, 1 : 4 and 2 :6 are not equivalent.

Ratio shows the relationship that exist between two or more numbers. Ratio is used to compare two or more numbers. It shows the number of times that one value is contained within other value(s).

In order to determine if the ratios are equivalent, express 2 : 6 in its simplest form. To do this, divide 2 and 6 by 2, a common  multiple of both numbers.

2 :6 in its simplest form is 1 : 3

Since, 1 : 3 is different from 1 : 4, the ratios are not equivalent.

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The long polynomial division of the given equation is \(\ 2x^2-5x+4-\frac{6}{5x+1}\).

What is long polynomial division?

Polynomial long division is a generalized variant of the well-known arithmetic operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.

We have,

            \(10x^{3} -23\pi x^{2} +15x - 2\)   £ \(5x+1\)

By taking long division

                        \(= \:\frac{10x^3-23x^2+15x-2}{5x+1} \\)

                        \(= \quad 2x^2-5x+4-\frac{6}{5x+1}\)

                        \(= \ 2x^2-5x+\frac{20x-2}{5x+1}\)

                        \(= \ 2x^2-5x+4+\frac{-6}{5x+1}\)

By simplifying we get,

                        \(= \ 2x^2-5x+4-\frac{6}{5x+1}\)

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Answer:

x < 3

Step-by-step explanation:

The arrow pointing to the left, along with the highlighted line indicates that it is looking for answers less than the given value, which is signified by the dot. The open dot on the value indicates everything less than, but not equal to the value, therefore, the answer is; x < 3.

Answer:

x = - 9

y = 5

Step-by-step explanation:

EQ1 + EQ2

Substitute the value of X in either EQ1 or EQ2

Answer:

A square pyramid is composed of an eight-sided square base, four triangular sides, five vertices, and five vertices. This pyramid has a square base with a peak at the top. The fact that a square pyramid is a polyhedron was noted.

Step-by-step explanation:

The three-dimensional geometric shape of a square pyramid has a square base and four triangular sides that are joined at the vertex. Five facets make up its polyhedron shape (pentahedron). Four triangles joined at the vertex and a square base make up a square pyramid. Three sides, a square base, and a central vertex characterize the triangle side faces. The tallest point of the pyramid is known as its "apex." The base is represented by the bottom square. Faces are the three triangular vertices of the triangle. When viewed from the bottom up, a pentahedron is a five-sided, three-dimensional shape that resembles a square pyramid.

The test statistic of the data on the concentration of calcium in precipitation in Chautauqua, New York, is 1. 46.

The test statistic (t0) can be calculated using the following formula:

t0 = ( x bar - μ0 ) / (s / √n )

First, calculate the sample mean :

= (0.087 + 0.313 + 0.183 + 0.07 + 0.108 + 0.12 + 0.262 + 0.065) / 8

= 0.151 mgL

Given the sample mean, the test statistic would be:

= ( x bar - μ0 ) / ( s / √n )

= ( 0. 151 - 0. 11 ) / ( 0. 087 / √8 )

= 1. 46

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The statement that correctly compares the two functions include the following: D. They have different y-intercepts but the same end behavior.

In Mathematics and Geometry, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear equation or function, generally occur at the point where the value of "x" is equal to zero (x = 0).

By critically observing the graph and the functions shown in the image attached above, we can reasonably infer and logically deduce the following y-intercepts:

y-intercept of f(x) = (0, 4).

y-intercept of g(x) = (0, 8).

Additionally, the end behavior of both functions f(x) and g(x) is that as x tends towards infinity, f(x) and g(x) tends towards zero:

x → ∞, f(x) → 0.

x → ∞, g(x) → 0.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

He got 5 questions wrong so he scored a 75%

Step-by-step explanation:

I hope this helps :)

Answer:

15 questions correct

Step-by-step explanation:

So you know that Diego took a 20 question quiz and got 75% on it so you have to find 75% of 20. 75% is also 3/4, so 3/4x20=60/4=15.  Therefore, he got 15 questions correct.

Hope this helps

Answer:

y=mx+b y=4/3x-3

Step-by-step explanation:

b= your y-slope which is -3

from -3. Count your rise until it reaches an equal run

3= run (count left or right)

4 = rise (count up or down)

y=

\( \frac{4}{3} \)

y=4/3x-3

Answer:

im not sure

Step-by-step explanation:

im not sure

Answer:

Step-by-step explanation:

The graph of y= -3/2x + 1 is given in attachment with slope -3/2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given line is  y= -3/2x + 1

slope is -3/2

We have to find few values of x and y.

When x=0

y=1

When x=1

y=-1/2

When x=2

y=-2

Hence, the graph of y= -3/2x + 1 is given in attachment with slope -3/2.

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Space-time is a concept used in physics and engineering to describe the combination of three-dimensional space and time as a unified four-dimensional continuum.

It incorporates the idea that space and time are interconnected and cannot be treated separately. In terms of a formula, the concept of space-time is often represented using the equation:

s = vt

where:

s represents the spatial distance or displacement in three-dimensional space,

v is the velocity or speed of an object or event,

t is the time elapsed.

The formula signifies that the distance covered in space (s) is equal to the product of the velocity (v) and the time (t). It demonstrates the interconnectedness of space and time, implying that changes in one dimension affect the other.

By considering space and time as part of a single entity, the concept of space-time enables the formulation of theories like Einstein's theory of relativity, where the curvature of space-time influences the behavior of objects and the propagation of light. It provides a framework for understanding the dynamic nature of the universe and the fundamental role of space and time in describing physical phenomena.

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Answer:

20

Step-by-step explanation:

Since 40% 0f 50 is 20???