Θ lies in quadrant III, φ lies in quadrant I. cos θ = -8 /17 , cos φ = 15 /17 . What is cos (θ - φ)?

The roots of the given quadratic equation "x² -5x = -6"  is x = 2 and x = 3   .

The Roots of the Quadratic Equation are defined as the number , which satisfies the equation .

The equation is given as x² -5x = -6 ;

rewriting the given equation ,

we get ; x² -5x +6 = 0 .

= x² -3x -2x +6 = 0    ,...By using split the middle term .

= x(x - 3) -2(x - 3) [tex]=[/tex] 0 ;

= (x - 2)(x - 3) [tex]=[/tex] 0 .

On equating the factors ,  x - 2 = 0    and   x - 3 = 0 ;

Simplifying further ,

we get ;

x = 2   and x = 3 .

Therefore , the roots of the quadratic are  x = 2 and x = 3 .

The given question is incomplete , the complete question is

What are the roots of the quadratic x² -5x = -6 ?

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For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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Reason 1: Distributive Property

The 1/4 x was distributed to each term in the parentheses.

Reason 2: Commutative Property

The individual factors were moved around to put numbers next to numbers and variables next to variables.  (Technically the associative property was also used, to break down the previous parentheses, but I don't think your teacher is thinking about that.)

Reason 3: Associate Property

The similar factors were then regrouped.

Reason 4: Simplify

This is just simplifying.

Reason 1: Distributive property

Reason 2: Commutative property

Reason 3: Associative property

Reason 4: Simplify

What is the property of commutativity?

The rule governing the ordering of variables is the commutative property. It states that the order of the variables does not influence the final answer when they are added or multiplied.

What is the property of associativity?

The associative feature of real numbers relates to grouping variables. It states that altering the grouping of variables added to or multiplied by one another has no effect on the output.

In mathematics, what is a distributive property?

This property states that multiplying the sum of two or more addends by a number yields the same result as multiplying each addend separately by the number and then putting the resulting products together.

First Argument: Distributive Property

[tex]\frac{1}{4x}[/tex]was allocated to each phrase between the parenthesis.

Reason 2: Property of Commutation

The individual elements were rearranged in order to place numbers alongside numbers and variables alongside variables. (Technically, the associative property was also utilized to separate the preceding parenthesis, although I doubt your teacher is aware of this.)

Reason 3: Associative Property

Similar elements were subsequently gathered.

Fourthly: simplify

This is just simplifying.

Reason 1: Distributive property

Reason 2: Commutative property

Reason 3: Associative property

Reason 4: Simplify

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Answer:

like a ratio

Step-by-step explanation:

A multiplicative comparison involves comparing two quantities such that when one is multiplied by a specified number, the other is produced. For example, Sam has twice as many balloons as Sid. Sid has 3 balloons.

As pert the t-test there is sufficient evidence that the average family size in this school district differ from the national average.

Let us assume null and alternate hypothesis.

H₀ = Average family size is 3.18

Hₐ = Average family size is not 3.18

The value of t = (Sample Mean - 3.18) / s/√n

where,

Sample Mean = 3.83

n = 24

s = 1.43

So, t = (3.83 - 3.18) / (1.43 / √24)

t = 2.2268

Degree of freedom = n - 1 = 23

The p-value = 0.0360

As the p-value <0.05, so the null hypothesis will be rejected.

Therefore, there is enough proof to conclude that this school district's average family size is different from the national average.

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Answer:

(3,1)

Step-by-step explanation:

(x+ 6, y -4)

The x tells us the movements are right or left. Right would be a positive movement and left would be a negative movement.

The y tells us the movements are up or down.  Up would be a positive movement and down would be a negative movement.

D is at the point ( -3,5)  

(x + 6, y -4)  Is telling us that from the point of D, move right 6 spaces and down 4 spaces.  You will know be at the point (3,1).

∡ABD and ∡BAD = ∡55°

As we can see Δ ABD is isosceles

so,

∡ABD = ∡BAD (let us assume them to be ∡F)

Therefore

∡ABD+∡BAD+∡ADB = 180°

2∡F+∡ADB = 180°

2∡F + 70° = 180°

∡F = 55°

∡ABD = ∡BAD = 55°

Now

∡ABD + ∡CBD = 180° (Supplementary Angles)

55° + ∡CBD = 180°

∡CBD = 125°

As the sum of all the angles in a triangle is 180°

∡BDC +∡DCB +∡CBD = 180°

∡BDC + 29° +125° = 180°

Hence

∡BDC = 26°

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The triangle KLM and triangle NOP are similar.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The length of side KLM are KL = 18, LM = 19, MK = 20.

The length of side NOP are NO = 54, OP = 57, NP = 60.

The ratio length of sides is

54/18 = 57/19 = 60/20 = 3

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

According to SSS rule triangle KLM and triangle NOP are similar.

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Answer:Square Root Formula

The square root formula of a number, x is given as,

√x = x1/2

Suppose, x is any number such that, x = y × y, the formula to calculate the square root of x will be,

√x = √(y × y) = y

where, y is the square root of any number x. This also means that if the value of y is an integer, then x would be a perfect square.

Step-by-step explanation:

The optimal response is The ranges below encompass all real numbers: From 0 through all actual numbers. The domain of this function is all real numbers since x can be entered with any value.

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

answer to the question is that all real numbers or (−∞,∞)

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The probabilities for exact 8 and less than 8 calls can be obtained as  0.1009 and 0.1785 respectively.

Poisson distribution is applied for the case where the events occur in a specific period of time with constant rate.

The given case belongs to Poisson distribution,

It can be solved as follows,

(a) The probability of exactly 8 calls can be obtained as,

P(Exact 8 calls) =  [tex]e^{-\lambda} \lambda^{x}/x![/tex]

Where x = 8 and λ = 2.1 × 5 = 10.5.

Then, the probability is  obtained as,

⇒ e⁻⁸ × 10.5⁸/8!

⇒ 0.1009

It implies that if 100 calls are selected randomly for the interval of 5 minute, 10 calls can be expected.

(b)  The probability of less than 8 calls can be obtained as

P(Less than 8) = [tex]\sum_{x =1}^{7}e^{-\lambda}\lambda^{x}/ x![/tex]

⇒ P(Less than 8) = 0.1785

It implies that out of 100 randomly selected 5 minute calls, around 18 have less than 8 calls.

Hence, the required probabilities for the given case are 0.1009 and 0.1785 respectively.

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The weight of the object on Mars would be 40 pounds.

What are ratio and proportion?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

An object that weighs 50 pounds on mars weighs 150 pounds on earth.

Let the object weighing 120 pounds on Earth, weighs x pounds on Mars.

We can solve this equation as :

                50/150 = x/120

                 x = 40 pounds

Hence, the weight of the object on Mars would be 40 pounds.

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Answer:

there are 960 calories in 6 cups of cereal.

Step-by-step explanation:

Answer:

Um no?

Step-by-step explanation:

The nature of the roots of the equation 2x^2 - 3x + 5 = 0 is imaginary or unreal.

We know that the general form of a quadratic equation is:

ax^2 + bx + c =0

The equation we have is:

2x^2 - 3x + 5 = 0

Comparing the given equation with the general form of a quadratic equation, we get that:

a = 2, b= -3, and c = 5

We know that if D = b^2 - 4ac < 0, then the roots of the quadratic equation are imaginary or unreal.

Therefore, b^2 - 4ac = (-3)^2 - 4x2x5 = -31 < 0.

Hence, we conclude that the nature of the roots of the give equation is imaginary or unreal.

The question is incomplete, the complete question is:

What is the nature of roots of  2x^2 - 3x + 5 = 0 ?

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Answer:

Shoes rental cost: $7

The equation to find the cost is 19 = 4x + y

Step-by-step explanation:

Each game = $4

There are 3 games

They paid a total of $19.00

We have the equation to find the cost is

19 = 4x + y

Now let's put 3 in for x to solve for the cost of renting shoes!

19 = 4(3) + y

19 = 12 + y

y = $7

So, the equation to find shoe rental cost is 19 = 4x + y, and the cost to rent shoes is $7

Answer:

Step-by-step explanation:

19=4x+y is the equation .------1

here x is number of games.

y is cost to rent shoes.

it is given that x=3

so equation 1 becomes

19-12=y

so y=7

which is shoe rental cost

simple:)

The nature of the roots of the equation x^2 - 5 = 0 is real and unequal.

We know that the general form of a quadratic equation is:

ax^2 + bx + c =0

The equation we have is:

x^2 - 5 = 0

Comparing the given equation with the general form of a quadratic equation, we get that:

a = 1, b= 0, and c = -5

If D = b^2 - 4ac > 0, then we say that the roots of the quadratic equation are real and unequal.

Here, (0)^2 - 4x1x(-5) = 20 >0,

hence we conclude that nature of the roots of the equation x^2 - 5 = 0 is real and unequal.

The question is incomplete, the complete question is:

x^2 - 5 = 0.

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The only SSS members eligible for a monthly disability stipend for life are those who are absolutely and permanently incapacitated.

Members of SSS who have a total or partial permanent disability receive a financial benefit. Depending on the member's number of monthly SSS contribution payments, the reward is either paid as a monthly disability pension or a one-time lump sum benefit.

Cash Benefits for SSS Members with Disabilities:

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The factors of the given expression would be = (x + 2), (x – 3) and (x + 5).

Factorisation of equations is defined as the expression of a given equation as a product of several other factors.

From the equation given; x³ 4x² 11x 30. it's factorisation would be done by getting the first root by trial and error method∶

Since the sum of the coefficients is not zero, 1 is not a root

Let x = -2

⇒ -8 + 16 + 22 – 30 = 0

∴ -2 is or (x + 2) is a factor

Dividing x3 + 4x2 – 11x – 30 by (x + 2)

Quotient = x2 + 2x – 15

⇒ x2 + 5x – 3x – 15 = 0

⇒ x (x + 5) – 3 (x + 5) = 0

⇒ (x – 3) (x + 5) = 0

Other factors are (x – 3) and (x + 5)

∴ (x + 2), (x – 3) and (x + 5) are the roots of the equation

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Commutative property states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another.

The Commutative Property is derived from the word commute, which means to move. It states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another.

The commutative property of addition states that a + b = b + a

The commutative property of multiplication states that a × b = b ×  a.

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Answer: 5a (B)

Step-by-step explanation:

The 3 main root functions are:

(2) They firmly moor the plant.

(3) They support the storage of nutrients and food.

(4) Water and minerals are delivered to the plant by the roots.

The roots of vascular plants are modified plant organs that serve as anchors for the plant and as a means of absorbing water and nutrients into the body of the plant, enabling the plant to grow higher and more quickly.

The majority of the time, roots are found below the soil's surface, but they can also be aerial or aerating, that is, they can rise above the earth or, particularly, above water.

Roots carry out the following tasks:

(1) The soil's nutrients and water are absorbed through roots.

(2) They firmly moor the plant.

(3) They support the storage of nutrients and food.

(4) Water and minerals are delivered to the plant by the roots.

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On solving the provided question, we can say that 50 will therefore be the missing number in the series 2 5 10 x 2637.

What are odd numbers?

A number that is odd is one that can't be partitioned flawlessly into matches. One remains after dividing an odd number by two. The numbers 1, 3, 5, 7, 9, 11, 13, and 15 are consecutively odd. While odd numbers cannot be divided in half, even numbers can. 3, 5, 7, 9, 11, 13, and 15 are unusual cases. Even numbers include 2, 4, 6, 8, 10, 12, and 14.

According to the given question:

Following the numbers 3, 5, 7, 9, 11, and 13, which are all odd numbers, the provided series moves on to 13.

Therefore,

After 37, there will be a break before 50.

50 will therefore be the missing number.

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Answer:

x = (6 i)/5 or x = -(6 i)/5

Step-by-step explanation:

Solve for x:

25 x^2 + 36 = 0

Subtract 36 from both sides:

25 x^2 = -36

Divide both sides by 25:

x^2 = -36/25

Take the square root of both sides:

Answer:  x = (6 i)/5 or x = -(6 i)/5

If all three sides of one triangle are equal to the corresponding three sides of the second triangle, then it is known as the SSS triangle congruency theorem.

The SSS rule states that two triangles are said to be congruent if their respective corresponding three sides are equal.

If all three sets of comparable sides are present, the triangles are congruent.

Using congruence, the side-side-side shortcut can be used (SSS).

Another shortcut is side-angle-side (SAS), which makes use of two sets of sides and an angle between them that is known to be congruent.

Therefore, if all three sides of one triangle are equal to the corresponding three sides of the second triangle, then it is known as the SSS triangle congruency theorem.

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Correct question:

What does the SSS triangle congruency theorem stand for?

The three types of input parameters used in the scripts are: Value, Column, or Table

In this question we need to state the three types of input parameters used in the scripts

We know that a script is a computer language with several commands within a file which are capable of being executed without being compiled.

The input type or input parameters used in the scripts can be Value, Column, or Table. Type option defines whether the input parameter can be one or more columns, or just a single value.

Type option specifies which data types are supported by this input parameter.

The parameters required by a script are specified using comments in the header.

Therefore, Value, Column, or Table are the three types of input parameters used in the scripts.

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Answer:

y=2x

Step-by-step explanation:

plug in the values from the table

for the first one, x=0

2 times x is 0 so y=0

for the second one, x=2

2 times x is 4 so y=4

for the third one, x=4

2 times x is 8 so y=8

for the last one, x=6

2 times x is 12 so y=12

2909/2000

Based on the given conditions, formulate: 16 divided by 11

Evaluate the equation/expression: 1.4545

Convert decimal into fraction: 14545/10000

Reduce the fraction: 2909/2000

Answer: 2909/2000