The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit.


What are the slope and y-intercept of the line that models this situation? I

The sine of an acute angle is less than one because it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio is always less than one.

To what does sin equate?

In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.

It's also the same reason why the cosine of an acute angle is always less than one because it is the ratio of the adjacent side of the angle to the hypotenuse.

It's important to note that this is only true for acute angles, angles smaller than 90 degrees.

For obtuse angles, greater than 90 degrees, the sine and cosine values are greater than one.

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A Pythagorean triple is a set of three positive integers a, b, and c that satisfies the equation a2 + b2 = c2.

In this case, the triple is (3, 4, 5) and (5, 12, 13).

The equation for the first triple is 32 + 42 = 52.

3² = 9

4² = 16

9 + 16 = 25

25 = 25

The equation for the second triple is 52 + 122 = 132.

5² = 25

12² = 144

25 + 144 = 169

169 = 169

Therefore, both sets of numbers are Pythagorean triples because they both satisfy the equation a2 + b2 = c2.

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The Third side of a triangle if the two sides are given and one angle is given can be found by using the Cosine Law .

What is Cosine Law ?

The Cosine Law states that the square of any one side of the triangle is equal to difference between  sum of squares of the other two sides and double of product of other sides and cosine of the angle included between them.

In mathematical terms it  means that ;

let a , b be the the know sides and "c" be the unknown side of the triangle ABC , and the known angle be = angle C ;

So , the side c will be ⇒ [tex]c^{2}= a^{2} +b^{2} - 2ab\times Cos(C)[/tex] ;

Therefore , the Cosine Law helps in finding the missing third side .

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The quadratic functions that have an axis of symmetry at x = -2 are given as follows:

The standard definition of a quadratic function is given by the rule presented as follows:

y = ax² + bx + c, in which a is different of zero.

The axis of symmetry is given by the x-coordinate of the vertex, hence it's equation is defined as follows:

x = -b/2a.

Meaning that the correct options are given by the first and by the fourth options in this problem.

For the first function, we have that:

a = 1, b = 4.

Hence the axis of symmetry is obtained as follows:

x = -4/2 = -2.

For the fourth function, we have that:

a = -2, b = -8.

Hence:

x = -8/4 = -2.

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The given equation gives two solution. We can find solution by using quadratic formula or discriminant.

A linear equation in two variables is an equation of the form ax + by + c = 0 where a, b, c ∈ R. So a and b ≠ 0. When we consider a system of linear equations we can find the number of solutions by comparing the coefficients of the variables of the equations.

How do you find how many solutions are in a quadratic equation?

if the discriminant is positive. Then the quadratic equation has two solutions.

if the discriminant is equal. Then the quadratic equation has one solution.

if the discriminant is negative. Then the quadratic equation has no solution.

Here we have

a=5    b=-7   c=4

Disc= [tex]b^2[/tex]-4ac

Disc= [tex](-7)^2[/tex]-4(5)(4)

Disc= 49+80

      =129

Disc >0    it has two solutions.

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Complete question is: How many solutions are there for 5x^2+7x-4=0?

a) 0

b) 1

c) 2

d) 3

Surface Area : Volume = 6 : s

A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.

Surface Area of a Cube = 6a² in a square units

Volume of cube = a³ cubic units

where a is the side length of the cube.

Given length of the cube = s

Surface Area of cube A = 6s²

Volume of cube V = s³

Ratio between Surface Area and volume:

Surface Area / Volume = 6s² / s³

Surface Area / Volume = 6 / s

Surface Area : Volume = 6 : s

Hence the ratio between Surface area and volume of cube is 6 : s.

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The value of the legs of the triangle would be hypotenuse/√2.

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

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From the table for Drew's week 1 classes:

Domain = {English, Math, History, Biology, Biology Lab}

Range = {60. 90, 45, 0}

A function's domain is the set of values that can be plugged into it. This set contains the x values in a function such as f. (x). A function's range is the set of values that it can take. This is the set of values that the function returns when we enter an x value. They are the y values.

A function can be thought of as a machine on an assembly line. On one end of the assembly line, there are a few screws and bolts, and on the other end, there is a car. The function is represented by the machine in the middle. The domain consists of the screws and bolts that we insert into the machine (our function).

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A. The net of a triangular prism is a flattened version of the prism that shows all the faces of the prism.

The prism's base is a right triangle with a base of 3 units and a height of 4 units. The prism is six units tall. The net of the triangular prism would look like a rectangle with a length of 3 units and a width of 4 units. On top of this rectangle, there would be two smaller triangles, each with a base of 3 units and a height of 6 units.

B. To calculate the surface area of the prism, we need to add the area of all the faces.

The base of the prism is a right triangle with an area of (1/2) (3 units) (4 units) = 6 square units.

The two triangular faces have an area of (1/2) (3 units) (6 units) = 9 square units each.

The rectangular face has an area of (3 units) (6 units) = 18 square units.

So, the total surface area of the prism is:

6 square units (base) + 9 square units (triangular face) + 9 square units (triangular face) + 18 square units (rectangular face) = 42 square units.

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Answer:

y=(this is a fraction) 4/3 times x-3

Step-by-step explanation:

In 2x^3, 3 is the greatest degree of the exponent. 2x^3 is a cubic polynomial as a result.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An example of a polynomial of a single indeterminate x is x² − 4x + 7.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.

For instance, the polynomial 3x+2x-5.

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

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A function is generally indicated by f.

A mathematical expression that indicates a relationship between an independent variable and a dependent variable.

In other word, a function shows a relation between a set of input values to a set of output values in where each input value is connected to only a particular output value.

A function is generally, expressed by letters such as f, g and h and so on.

It is said that f(x) is a function of x or g(x) and h(x) are a function of x when functions are denoted by g or h.

For an input value of an independent variable x, the output value is denoted by f(x) that is equal to a dependent variable such as y. We can write, y = f(x)

The set of x value are the domain of function, and the set of f(x) value are the ranges of a function.

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Complete question is: What is the value of f in a function?

Answer: x=-1/4 and x=-1

Step-by-step explanation:

The answer choices you give are extremely hard to figure out, so I hope my explanations and answers help.

The quadratic formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]. Once we figure out a, b, c, we can plug them into the formula and solve for x.

The standard form equation is ax²+bx+c=0. The equation given matches this so we know that:

a=4

b=5

c=1

Plug them into the formula. There is a [tex]\pm[/tex] symbol, which stands for "plus or minus". This means we solve the formula with addition and subtractions separately. We should have 2 solutions at the end. Let's do them separately to show work.

Solution 1: addition

[tex]x_1=\frac{-5+\sqrt{5^2-4(4)(1)} }{2(4)}[/tex]             [exponents]

[tex]x_1=\frac{-5+\sqrt{25-4(4)(1)} }{2(4)}[/tex]             [multiply]

[tex]x_1=\frac{-5+\sqrt{25-16} }{8}[/tex]                    [inside square root]

[tex]x_1=\frac{-5+\sqrt{9} }{8}[/tex]                          [square root]

[tex]x_1=\frac{-5+3}{8}[/tex]                            [add]

[tex]x_1=\frac{-2}{8}[/tex]                                [divide top and bottom by 2]

[tex]x_1=-\frac{1}{4}[/tex]

Solution 2: subtraction

[tex]x_2=\frac{-5-\sqrt{5^2-4(4)(1)} }{2(4)}[/tex]             [exponents]

[tex]x_2=\frac{-5-\sqrt{25-4(4)(1)} }{2(4)}[/tex]             [multiply]

[tex]x_2=\frac{-5-\sqrt{25-16} }{8}[/tex]                    [inside square root]

[tex]x_2=\frac{-5-\sqrt{9} }{8}[/tex]                          [square root]

[tex]x_2=\frac{-5-3}{8}[/tex]                            [subtract]

[tex]x_2=\frac{-8}{8}[/tex]                                [divide]

[tex]x_2=-1[/tex]

I am not able to find the answer choices, but we know that x=-1/4 and x=-1.

The median's class interval is 20 hours and 30 minutes. And the average number of hours is thought to be 26.17.

The median is the exact middle value of a dataset after it has been sorted. A measure of central tendency is the distance between the bottom 50% of data and the top 50% of values. The methods for determining the median will vary depending on whether you have an odd or even number of data points.

the class interval that have  median.

total is frequency is as -

∑f = 30

median class of corresponds to half of the value

∑th is the  value

i.e.  15th value.

least cumulative frequency higher than or equal to 15 is obtained by accumulating frequencies starting at the top.

[tex]2+8+9=19[/tex]

So, corresponds to the class interval  = [tex]20 < h\leq 30.[/tex]

Hence, median class is [tex]20 < h\leq 30.[/tex]

Since this is a grouped data we use the midpoint

The median:-

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yes, (-2,4) is the solution of the system of equation 4x² - 4y = 0.

To check whether the given points are the solution of the given system of equation 4x² - 4y = 0. We have to put the values of x = -2 and y = 4 in the given equation. If we get the result equals zero then (-2, 4) is the solution of 4x² - 4y = 0 and if the result is a non-zero number then (-2, 4) is not the solution of 4x² - 4y = 0.

⇒4x² - 4y = 0

⇒4(-2)² - 4 × 4 = 0

⇒4 × 4 - 4 × 4 = 0

⇒0 = 0

Here we get the result equal to zero, hence (-2,4) is the solution of the system of equation 4x² - 4y = 0.

--This question is incomplete, the complete question is

''Is (-2,4) a solution of the system of equation 4x² - 4y = 0?''--

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Answer:

  (a)  11

Step-by-step explanation:

You want the degree of the monomial 7m^6n^5.

The degree of a monomial is the sum of the exponents of its variables.

  m has an exponent of 6

  n has an exponent of 5

The degree is 6+5 = 11.

The 30-60-90 triangle is shaped like half of an equilateral triangle.

A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest.

The side opposite to the 60° angle is the longer leg, and finally, the side opposite to the 90° angle is the largest side of the right triangle, also known as the hypotenuse.

30°-60°-90° Triangle Rule:

In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the 30-60-90 triangle rule.

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The Normal probability for all sample of 5 that the sample mean will be greater than 22 pounds is approximately 0.05. In this Question The normal probability distribution and the central limit theorem were used.

The most prevalent continuous probability distribution is the Normal (or Gaussian) distribution. As the curve becomes closer to zero on either side of the mean, the function calculates the likelihood that a given event will fall between any two real number limits. The area under the normal curve is always one.

Central limit theorem

The central limit theorem implies that the distribution of the sample means will be roughly normally distributed if you have a population with mean and standard deviation and take sufficiently enough random samples from the population with replacement.

Normal probability distribution, ; Problems of normally distributed samples are solved using the z-score formula.

Mean standard deviation , the z-score of a measure X is given by:

Z = x-μ/σ

Given ,

The distribution of backpack with mean deviation = 19.7 pounds

And the standard deviation = 3.1 pounds

The number of standard deviations is measured by the Z-score. The average is used as the measure.

We glance at the z-score table after determining the Z-score to determine the p-value connected to it.

The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value.

1 is subtracted from the p value.

We calculate the likelihood that the measure exceeds X.

P(ä > 22) is the probability of the sample means being above 22.

For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.

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Answer:

c

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 6.5 when x = 1.3

6.5 = 1.3k ( divide both sides by 1.3 )

5 = k

y = 5x ← equation of variation

Isolating for a variable: rearranging an equation so that a variable is on its own. This is done by performing inverse operations until a variable is isolated.

[tex]P-9=-3w+9-9[/tex]

[tex]p-9=-3w[/tex]

[tex]\frac{p-9}{-3}=\frac{-3w}{-3}[/tex]

[tex]-\frac{P-9}{3} =w[/tex]

To read a linear equation, first, identify the constants and the variable, then determine the coefficient of the variable.

A linear equation is an equation that contains two variables and can be written in the form of ax + b = 0, where 'a' and 'b' are constants and 'x' is the variable.  This coefficient will indicate how the variable is related to the constants. Then, solve the equation by isolating the variable to determine its value.

To read a linear equation, start by identifying the constants and the variable. The constant is the numerical value that is not connected to the variable. For example, in the equation "2x + 4 = 0", the constants are '2' and '4'. The variable is the letter that represents the values that can change. In this equation, the variable is 'x'.

Next, determine the coefficient of the variable. The coefficient is the numerical value in front of the variable. It represents how the variable is related to the constants. In this example, the coefficient of 'x' is '2'. This means that the value of 'x' will be twice as much as the constants.

Once the constants, variables, and coefficients have been identified, the equation can be solved.

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A. ∠F corresponds to ∠F' is True.

B. Segment EE' is parallel to segment FF' is False.

C. The distance from point D' to the origin is One-third the distance of point D to the origin is True.

D. The measure of ∠E' is One-third the measure of ∠E is False.

E. △DEF ~ △D'E'F' is True.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Given:

As triangle DEF was dilated according to the rule DO, One-third(x, y)(one-third x, one-third y) to create similar triangle D'E'F'.

and, The center of dilation = (0, 0)

Also, Triangle FDE has points: (- 9, 3), (- 9, 9), (- 6, 6).

Triangle F'D'E' has points : (- 3, 1), (- 3, 3), (- 2, 2)

A) ∠F corresponds to ∠F'. ( True)

B) Segment EE' is parallel to segment FF'. (False)

As they intersect each other at the origin.

C) The distance from point D' to the origin is One-third the distance of point D to the origin.    ( True)

Now, the length of DE

D = √(-9-0)² + (-9-0)²

D = 9√2

and, length of D'E'

D = √(-3-0)² + (-3-0)²

D = 3√2

Thus, DE / D'E' =  3√2/  9√2 = 1/3

D) The measure of ∠E' is One-third the measure of ∠E. ( False)

E)  △DEF ~ △D'E'F'.  ( True)

As they are similar triangles.

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Answer:

A. ∠F corresponds to ∠F'.

C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.

E. △DEF ~△D'E'F'

Step-by-step explanation:

got it right on edge 23

Using the provided equations, Applying the addition method in the system of equations, The answer is x=-2 and y =-6.

An equation is a statement of equality between two expressions, usually containing one or more variables. Equations can be used to express mathematical relationships and can be solved to find the value of the variables. Equations can take many forms, such as linear equations, quadratic equations, and differential equations. They can also be represented graphically.

The addition method to solve a system of equations is a way to solve a system of two linear equations by adding them together. The goal is to eliminate one variable by adding or subtracting the equations. We can eliminate one variable by adding the equations together. To do this, we'll add the left-hand side of the first equation to the left-hand side of the second equation and add the right-hand side of the first equation to the right-hand side of the second equation. It is important to note that the addition method works only when the coefficients of the variable you want to eliminate are opposite in sign.

4x-5y=22

3x+2y=-18

multiplying first equation with 3 and second equation with 4 and subtracting them , we eliminate x and solve for y,

y=-6

put y=-6 in first equation , we get x,

x=-2

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Answer:

find 3 consecutive numbers such that twice the first , 3 times the second and 4 times the third together make 191 ?

Let n-1,n and n+1 be three consecutive numbers.

Given

2(n-1)+3n+4(n+1)=191

2n-2+3n+4n+4=191

9n+2=191

9n = 189

n = 21

So, n-1=20 and n+1=22

So the answer is 20,21,22

[tex] \huge \bold{\color{red}{ANSWER}}[/tex]

[tex]\pmb { \orange{Given }:} \sf{ Three \: Consecutive \: numbers}[/tex]

[tex]\pmb{\orange{To find}: } \sf{Least \: of \: the \: numbers}[/tex]

[tex]\pmb{\orange{Solution}: }[/tex]

[tex]\sf{Let \: the \: three \: consecutive \: numbers \: be }[/tex]

[tex] \sf\red x, \red {x+1}, \red{x+2}[/tex]

[tex]\sf{Twice \: the \: number = 2\red x}[/tex]

[tex]\sf{3 \: times \: the \: Second \: number = 3(\red{ x+1})}[/tex]

[tex]\sf{4 \: times \: the \: third \: number= 4(\red {x+2})}[/tex]

☆ according to question

[tex] \pmb{2\red x + 3(\red{x+1})+4(\red{x+2})= 191}[/tex]

[tex] \pmb{2\red{x} + 3\red{x}+3+4\red{x}+8= 191}[/tex]

[tex] \pmb{9\red{x}=191-11 = 180}[/tex]

[tex] \pmb{\red{x}=20}[/tex]

[tex] \sf{∴the \: three \: Consecutive \: numbers \: are} [/tex]

[tex] \pmb{\pink{20}, \pink{21}, \pink{22}}[/tex]

_________________......

[tex] \purple{ \pmb{LearningLifeII}}[/tex]

Answer:

Step-by-step explanation: You can add all of these numbers with a calculator. but be sure what are the numbers telling you what to do. So always focus on the words that are going to mention about the numbers.

The correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.

A quadrilateral with at least one pair of parallel sides is called a trapezoid.

Given that, Samara placed the congruent sides of these two triangles together to form a quadrilateral.

2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.

If we construct such quadrilateral, we will get a trapezoid with one angle a right angle.

Hence, the correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.

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Answers:

1. B its a trapezoid

2. D it has two right angles

3. E it has 2 sides that are parallel

Step-by-step explanation:

B) The length of GB is 3 in the given triangle.

The centroid of a triangle is the point at which the three medians of the triangle intersect. A median of a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. The three medians divide the triangle into six smaller triangles, each with a vertex at the centroid.

The ratio in which the centroid divides a median of a triangle is 2:1. That is, the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.

So, if G is the centroid and B is the midpoint of the side opposite to point A, the ratio of EG: GB is 2:1.

so the length of GB = EG/2

so the length of GB = 3

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Complete question:

In ΔAEC, G is the centroid , as shown in the figure .

if EG = 6 ,find GB

A) 2

B) 3

C) 6

D) 9

The total number of coins Piper has in her collection is 100 coins.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Piper has a coin collection. She keeps 12 of the coins in her box, which is 2% of the collection.

Let, The total number f coins in the box be 'x'.

Therefore, 2% of 'x' is 12 which can be numerically expressed as,

(2/100)×x = 12.

0.02x = 12.

x = 2/0.02.

x = 100.

So, She has 100 coins in her box.

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The conditions for inference are: The customers who are surveyed are chosen independently at random, so we can assume that the survey results are independent.

The amount of grams or mole equivalents of solute present in a solution that contains one liter is what is referred to as normalcy according to the accepted definition. The amount of moles of reactive units in a compound is what we mean when we say it is equal.

The conditions for inference are met.

However, to conclude that more than 50% of customers who dine at his restaurant would rate the food as excellent, we need to conduct a statistical test such as a one-sample proportion test or a confidence interval. The manager would need to compare the proportion of the customers who rated the food as excellent from the survey with the proportion of customers who would rate the food as excellent. This would allow to see if the data provides convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent.

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Answer:

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

According to the two-tangent theorem, two tangent segments drawn to one circle from the same external point are congruent.

That is:

We have EF = 10 units, it means EG is also 10 units.

The perimeter of triangle EHP is:

We can substitute:

Then the perimeter is: