I) if y varies directly as x and inversely as the square root of z, and y = 1/6 when x = 20 and z = 6, determine y when x = 14 and z = 5

Answer:

B. x ≥ 1

Step-by-step explanation:

The resulting polynomial in standard form (b)  –4g^4 –3g³ +4g² +5g +3

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

The simplification process is described and partially carried out. We are to finish by combining like terms and writing the result in standard form.

Given

Add: (g² – 4g^4 + 5g + 9) + (–3g³ + 3g² – 6)

Combine Like Terms

g²  + (–4g^4) + 5g + 9 + (–3g³) + 3g²  + (–6)

The like terms are the g² terms and the constants;

= (1 +3)g² + (–4g^4) +5g +(9 +(–6)) +(–3g³)

 = 4g² +(–4g^4) +5g +3 +(–3g³)

Write in Standard Form

In this form, the terms are written in order of decreasing degree.

= –4g^4 –3g³ +4g² +5g +3

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Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.

Here.

Given : Cosθ = -1/6

To find : Tanθ

Since cosθ is in second quadrant

Thus,

Cosθ = B/H

According to pythagoras theorem,

H²= B²+ P²

=> 6² = 1² + P²

=> 36-1 =P²

=>P= √35

So ,

value of Tanθ comes out to be

=> tanθ = - √35 /1

=>tanθ = - √35

Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

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On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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The total amount each member of the Nantucket recreation center have to pay after the discount is given by the equation A = $ 840

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount for each person after discount be represented as A

Now , the equation will be

The total number of people in the group = 36

The standard fare for each person = $ 1200

So , the total cost of the fare = total number of people x standard fare for each person

Substituting the values in the equation , we get

The total cost of the fare = 1200 x 36

The total cost of the fare = $ 43,200

Now , the discount percentage = 30 %

So , the amount after discount = total cost of the fare - total cost of the fare x discount percentage

Substituting the values in the equation , we get

The amount after discount = 43,200 - ( 30/100 ) x 43,200

The amount after discount = 43200 - 12960

The amount after discount = $ 30,240

Now ,

Total amount for each person after discount A =amount after discount / 36

Total amount for each person after discount A = 30,240 / 36

On simplifying the equation , we get

Total amount for each person after discount A = $ 840

Therefore , the value of A is $ 840

Hence , the amount is $ 840

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Answer:

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

We see two sides and one angle marked as congruent on both triangles.

The congruent angle is not included.

It means we can neither state it is ASA nor SAA as both of these require two congruent angles.

Answer:

20x²

-5xy

14y²

Step-by-step explanation:

17x² + 3x² = 20x²

-3xy - 2xy = -5xy

14y²

[tex]\huge\text{Hey there!}\\\\\\\mathsf{\dfrac{3}{21}}\\\\\mathsf{= \dfrac{3\div3}{21\div3}}\\\\\mathsf{= \dfrac{1}{7}}\\\\\huge\text{Therefore, your\ answer\ should\ be: \huge\boxed{\mathsf{\dfrac{1}{7}}}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

5√2

Step-by-step explanation:

Hello!

To simplify the radical, we can identify perfect square factors in the radicand or the number inside the square root.

We know that 50 is 25 times 2, so we can expand the radical like this...

Now we can simplify each radical:

The simplified form is 5√2.

The y-intercept of the quadratic function f(x) = (x - 8)(x + 3) is (0, -24).

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.

This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

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The collection of values that can be plugged into a function's domain are called its parameters.

A specific area of thinking, action, or interest is referred to as a domain, particularly one over which someone has authority. [formal]...the great artists who experimented with several mediums. Alternative words: region, globe, field, department [informal] More Domain synonyms.

The domain is used to facilitate user navigation and increase accessibility. Slugs are links that consist of the domain plus the text "/text."

Let y = f(x) be a function where x and y are the independent and dependent variables. The chosen x-value is said to fall within the domain of f if a function f offers a means of effectively producing a single value y while using a value for x to that end.

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Intercept = 1

Equation - y = -(2/5)x + 1

The null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

What is the null hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Here,

We have to find out the slope of the line predicted by the null hypothesis if we are doing a linear regression.

We concluded that the null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.

Hence, the null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

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a. The trigonometric ratio tanθ = -√(sec²θ - 1)

b. The trigonometric ratio secθ = -1/√(1 - sin²θ)

Trigonometric ratios are the following mathematical expressions sinθ, cosθ, tanθ,secθ,cosecθ and cotθ.

Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity

tan²θ + 1 = sec²θ

Making tanθ subject of the formula, we have that

tan²θ = sec²θ - 1

tanθ = ±√(sec²θ - 1)

Since in Quadrant II, tanθ is negative, we choose the negative answer.

So, tanθ = -√(sec²θ - 1)

Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity

secθ = 1/cosθ and

sin²θ + cos²θ = 1

Making cosθ subject of the formula, we have that

cos²θ = 1 - sin²θ

cosθ = ±√(1 - sin²θ)

So, secθ = 1/cosθ

= ±1/√(1 - sin²θ)

Since in Quadrant III, secθ is positive, we choose the positive answer.

So, secθ = -1/√(1 - sin²θ)

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The inverse of +5 as calculated is found to be +1 / 5.

To find the inverse of +5 we can simply reciprocate it and the result will be the required answer.

reciprocal of +5 = 1 / 5.

Therefore, the answer is 1 / 5.

The opposite or reciprocal of a number or term in math is known as it's inverse. There are two types of inverse in math, the additive inverse and the multiplicative inverse.

The multiplicative inverse of a number for any n is given as 1/n.  It is also called as the reciprocal of a number and 1 is called the multiplicative identity. On the other hand subtraction is the inverse of addition.

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The expression for the sentence that is twice the difference of a number and six is given as follows:

2(n - 6).

The sentence for this problem is defined as follows:

"Twice the difference of a number and six."

The number is unknown, hence the variable that represents the number is given as follows:

n.

The difference between the number and six is given by the subtraction of n by 6, as follows:

n - 6.

(the - symbol represents the subtraction).

The expression twice is equivalent to a multiplication of the expression n - 6 by 2, as follows:

2(n - 6).

(the multiplication symbol is implicit before the parenthesis, meaning that the distributive property is applied).

Which is the expression that represents the sentence given at the beginning of the answer.

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Answer:

F.

Step-by-step explanation:

y = k/x where k is a constant

given that x = 4 when y = 3, we have:

3 = k/4

So, k =12.

The equation of variation is:

y = 12/x

When x = 15

y = 12/15 = 4/5.

So not 12 so this is False,

The distance between town a and b is 175 mi.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Given that, a map drawn move to the scale 2 cm : 100 mi. on the map town b is 3.5 centimeters from town a and town c is 2 centimeters past town b

Since, 2 cm = 100 mi

1 cm = 50 mi

Therefore, 3.5 cm = 50×3.5 = 175 mi

Hence, the distance between town a and b is 175 mi.

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On solving the provided question we can say that - here in equation we have [tex]y = 160+ 2 *t= > y = 160 + 2X 30 = > y= 160+ 60 = > y = 220 pounds[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex]y = 160+ 2 *t\\y = 160 + 2X 30\\y= 160+ 60\\y = 220 pounds[/tex]

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The value of YZ = 2 units.

The Latin words "col" and "linear" are combined to form the word "colinear." "Col" stands for "together," and "Linear" is a line. Collinear points are hence points that are situated along a single line. Numerous instances of collinearity can be observed in daily life, such as a line of pupils standing together.

Given X, Y, and Z are collinear. Y is between X and Z.

so XY + YZ = XZ

given XY = 12 units and XZ = 14 units

XY + YZ = XZ

12 + YZ = 14

YZ = 14 - 12

YZ = 2 units

Hence measure of YZ is 2 units.

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On solving the provided question, we can say that it is right angle triangle provided, so  cos 60 = 3/H => 1/2 = 3/H => H = 6

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.

it is right angle triangle provided,

so

cos 60 = 3/H

1/2 = 3/H

H = 6

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Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.

An algorithm is a process for carrying out a computation or resolving a challenge. Algorithms work as a detailed set of guidelines that lead hardware- or software-based routines through a series of predetermined actions step by step. Algorithms are frequently used in all areas of IT.

Here,

The halting problem, which claims that no program can be created that can anticipate whether or not any other program will halt after a finite number of steps, is an intractable algorithmic challenge.

The inability to solve the stopping problem directly affects software development.

Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.

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A 45°-45°-90° triangle looks like Right Angle Triangle.

A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.

45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2 . The measures of the sides are x, x, and x√2.

In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg, and the Opposite side to 45 = 1/√2 * Hypotenuse.

The 45-45-90 triangle has three unique properties that make it very special and unlike all the other triangles.

Hence, a 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.

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Answer: no question=no answer

Step-by-step explanation:

Linear graphs have the following form: y = mx + b, where m is the slope of the line and b is the y-intercept.

To calculate the slope, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Exponential graphs have the following form: y = ab^x, where a and b are constants. To calculate the constants, you can use the formula y = a + b^x, where (x, y) are two points on the graph and a is the y-intercept.

Quadratic graphs have the following form: y = ax^2 + bx + c, where a, b, and c are constants. To calculate the constants, you can use the formula y = ax^2 + bx + c, where (x, y) are two points on the graph and c is the y-intercept.

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The answer to the Linear expression 7(3n + 2) - 3n - 5 is 18n + 11

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

From the expression 7(3n + 2) - 3n - 5

By expanding the bracket, we have

21n + 14 - 3n - 5

By collecting like terms, we have

21n - 3n + 14 - 3

18n + 11

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The ratio of the green houses to the the total number of houses is 17:103

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here, The number of green houses as 17 and total number of houses altogether 103

Therefore the required ratio is 17:103

Hence, The ratio of the green houses to the the total number of houses is 17:103

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9) x = 6

10) x = 1

11) x = 0

12) x = 6

This can be solved from the property of parallelogram.

A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles.

Properties are:

9) As we know, from the property of parallelogram,

SR = TQ and ST = RQ

Now, 4 + 2x = 3x - 2

or, x = 6

10) As we know, from the property of parallelogram,

EF = DC and ED = FC

17x + 1 = 18x

or, x = 1

11)  As we know, from the property of parallelogram,

YZ = XW and YX = ZW

2x + 9 = 9

2x = 0

x = 0

12)  As we know, from the property of parallelogram,

TU = SV and TS = UV

6 + 2x = 4x - 6

or, 2x = 12

or, x = 6

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