Write a linear function that passes through the points (3, -7) and (0, 15)

The equation in the form of the given expression is (0)² + (1)² = 1

According to some of the trigonometry identity

sin 0 = 0

cos 0 1

Given the expression below

sin^2 0+cos^2 0=1

This can also be expressed as:

(sin0)² + (cos0)² = 1

Substitute

(0)² + (1)² = 1

Hence the equation in the form of the given expression is (0)² + (1)² = 1

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Answer: 105 dollars

Step-by-step explanation:

Let's say that the original price x dollars, we can use the equation to find the original price.

80%x = 84

x = 105

Answer:

$105

Step-by-step explanation:

The multiplier is 0.8

To get the price after the discount,the original price was multiplied by 0.8(100 - 20 = 80% = 0.8

Therefore to obtain the original price from the price after the discount, we use reverse percentage:

$84 ÷ 0.8 = $105

Answer: [tex]\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}[/tex]

Step-by-step explanation:

Let the smallest angle be x.

Then, the middle angle is x+30.

The largest angle is 2x+30.

Angles in a triangle add to 180 degrees, so:

[tex]x+x+30+2x+30=180\\\\4x+60=180\\\\4x=120\\\\x=30[/tex]

So, the angles measure [tex]\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}[/tex]

The measures of all three angles are 30°,60°, and 90°.

A triangle is a 3-sided polygon occasionally (though not frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which may be the same.

Find the measures of all three angles:

The three angles be a, b and c.

Angle “a" = x

Angle “b" = x + 30°

Angle “c" = “a" + “b"

                = x + x + 30°

                = 2x + 30°

Total angle in a triangle = 180°

Therefore;

“a" + “b" + “c" = 180°

Births; (x + (x + 30°) + (2x + 30°)) = 180°

So,

4x + 60° = 180°

x = (180° - 60°) ÷ 4

x = 30°

Plugging this value of x into the earlier equations for angles “a,” “b,” and “c."

“a" = x = 30°

“b" = x + 30° = 60°

“c" = 2x + 30° = 90°

The measures of all three angles are 30°,60°, and 90°.

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a. The value of cos2θ = -119/169

b. The value of cosθ = -5/13

The question involves trigonometric identities

Trigonometric identities show the relationship between trigonometric ratios.

Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.

Using trigonometric identity

cos2θ = 1 - 2sin²θ

Substituting sinθ = 12/13  into the equation, we have

cos2θ = 1 - 2sin²θ

cos2θ = 1 - 2(12/13)²

cos2θ = 1 - 2(144/169)

cos2θ = 1 - 288/169

cos2θ = (169 - 288)/169

cos2θ = -119/169

So, the value of cos2θ = -119/169

Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.

Using trigonometric identity

cosθ = √(1 - sin²θ)

Substituting sinθ = 12/13  into the equation, we have

cosθ = √(1 - sin²θ)

cosθ = √[1 - (12/13)²]

cosθ = √[1 - (144/169)]

cosθ = ±√(169 - 144)/169

cosθ = ±√25/169

cosθ = ±5/13

θ is the quadrant II, it means that 90° ≤ θ ≤180° it means that cosθ is negative.

So, cosθ = -5/13

So, the value of cosθ = -5/13

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The volume of the solids are 240 cubic yards and 125.6 cubic cm

The complete question is added as an attachment

Solid 1

The shape is a rectangular prism.

The volume of a rectangular prism is

Volume = Length * Width * Height

So, we have

Volume = 8 yd * 5 yd * 6 yd

Evaluate

Volume = 240 cubic yards

Hence, the volume of the solid is 240 cubic yards

Solid 2

The shape is a cylinder.

The volume of a rectangular prism is

Volume = πr²h

So, we have

Volume = 3.14 * 2^2 * 10

Evaluate

Volume = 125.6 cubic cm

Hence, the volume of the solid is 125.6 cubic cm

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Based on the given summation notation, the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n

The expression is given as:

43Σn=1(3+9n)

As a general rule, if a summation notation is represented using the following expression

Σ(a + bn)

The equivalent expression of the above summation notation is

Σa + bn

Where the variable a is a constant in the expression

This means that:

Σ(a + bn) = Σa + bn

Using the above equation as a guide, we have the following equivalent equation

43 Σ n=1 (3+9n) = 43 Σ n=1 3 + 43 Σ n=1 9n

Hence, based on the given summation notation; the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n

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Answer:

D on 3dg I took the best

Step-by-step explanation:

The following statements are considered to be propositions:

Deductive reasoning can be defined as a type of logical reasoning that typically involves drawing conclusions based on a given set of rules and conditions or from one or more premises (factual statements) that are assumed to be generally (universally) true.

A proposition can be defined as a type of statement (assertion) that is typically used to express an opinion or a judgement, with either a true or false answer.

This ultimately implies that, a proposition refers to a type of statement (assertion) that is either a true or false.

In this context, we can infer and logically deduce that the following statements are considered to be propositions:

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Part 1)  [tex]\displaystyle \frac{1}{n^2}[/tex] or 1/(n^2) goes in the box.

Part 2)  The series converges

======================================================

Work Shown:

[tex]\displaystyle L = \lim_{n\to \infty} \frac{a_n}{b_n}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{\frac{n+3}{n^3-5n+8}}{\frac{1}{n^2}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n+3}{n^3-5n+8}\times\frac{n^2}{1}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n^3+3n^2}{n^3-5n+8}\\\\\\[/tex]

[tex]\displaystyle L = \lim_{n\to \infty} \frac{\frac{n^3}{n^3}+\frac{3n^2}{n^3}}{\frac{n^3}{n^3}-\frac{5n}{n^3}+\frac{8}{n^3}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{1+\frac{3}{n}}{1-\frac{5}{n^2}+\frac{8}{n^3}}\\\\\\\displaystyle L = \frac{1+0}{1-0+0}\\\\\\\displaystyle L = 1\\\\\\[/tex]

Because L is finite and positive, i.e. [tex]0 < L < \infty[/tex], this means that the original series given and the series  

[tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}[/tex]  

either converge together or diverge together due to the Limit Comparison Test.

But the simpler series is known to converge (p-series test).

Therefore, the original series converges as well.

The two series likely don't converge to the same value, but they both converge nonetheless.

Answer:

See below

Step-by-step explanation:

The derivative of the function is the slope

2x^2 - x -1       take derivative  ( f ' )

4x -1                 equate to 7

7 = 4x -1

x = 2        sub into the original equation to find y = 5

The number with the given characteristics is 17

Let the tens be x and the units be y.

So, the number is 10x + y

The relationship between the digits is

y = x + 6

The relationship between the number and the reverse is

2(10x + y + 10y + x) = 6 + 10 * (10x + y)

Simplify the second equation

2(11x + 11y) = 6 + 100x + 10y

Open the brackets

22x + 22y = 6 + 100x + 10y

Substitute y = x + 6

22x + 22(x + 6) = 6 + 100x + 10(x + 6)

Expand

22x + 22x + 132 = 6 + 100x + 10x + 60

Collect like terms

22x + 22x - 100x - 10x = 6 + 60 - 132

Evaluate the like terms

-66x = -66

Divide by -66

x = 1

Substitute x = 1 in y = x + 6

y = 1 + 6

y = 7

Recall that the number is 10x + y

So, we have

Number = 10 * 1 + 7

Evaluate

Number = 17

Hence, the number is 17

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Answer:

See below

Step-by-step explanation:

Here is HOW to solve this problem:

b = pounds of blue candy      then   r =  11-b = pounds of red candy

.79b = cost of blue candy             1.29 (11-b) = cost of red candy

   these two costs sum to   11.19  

.79b    + 1.29 ( 11-b)  = 11.19        Now you can solve for 'b'  the 'r' = 11-b

Answer:

Red candy =5

Blue candy = 6

Step-by-step explanation:

Let the pounds of red candy be x and blue candy y. Then y=11-x

Also 1.29x + 0.79y=11.19

1.29x+0.79(11-x)=11.19

0.5x=11.19–8.69

0.5x=2.5

X=5

Red candy =5

Blue candy = 6

Answer:

Step-by-step explanation:

I think you are trying to use synthetic division for

[tex]x^{4} -2x^{3} -2x^{2} +3x-5[/tex] divided by x-3

First  

x -3 = 0 , make it equal to 0 and add 3 to both sides

x = 3

Then we write all the coefficients and continue with

a pattern of multiply by 3 and add to the next coefficient.

See attachment.

The price at which equilibrium is achieved is $20.

The equilibrium point is the point where the lines of the demand and supply functions meet.

From the question, we understand that price is plotted on the vertical axis (i.e. the y-axis).

Also from the question, the lines intersect at point (15, 20).

The y-coordinate of the intersection point is 20 in this scenario.

Hence, the price at which equilibrium is achieved is $20.

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Answer:

b

Step-by-step explanation:

Answer:

a) A = 3, B = 8.

b) C = 2, D = 25

Step-by-step explanation:

See the image below.

Answer:

X is less than and equal to 4

Answer:

7, 9

Step-by-step explanation:

Let x and y represent the two positive integers.

We can write x in terms of y. The question states "one positive integer is 5 less than twice another". Let "one positive integer" represent x.

Therefore:

[tex]x=2y-5[/tex]

We also know that the sum of the squares of the two positive integers is 130. Using this information, we can write another equation.

[tex]x^2+y^2=130[/tex]

These two equations form a system of equations.

[tex]x=2y-5[/tex]

[tex]x^2+y^2=130[/tex]

We can solve this system of equations by the substitution method. Using this method, we substitute [tex]2y-5[/tex] for [tex]x[/tex].

[tex](2y-5)^2+y^2=130[/tex]

Expand [tex](2y-5)^2[/tex] . Notice that [tex](a-b)^2=a^2-2ab+b^2[/tex] :

[tex](2y-5)^2=4y^2-20y+25[/tex]

[tex]4y^2+y^2-20y+25=130[/tex]

Subtract 25 from both sides

[tex]4y^2+y^2-20y=105[/tex]

Add like terms

[tex]5y^2-20y=105[/tex]

Divide both sides by 5

[tex]y^2-4y=21[/tex]

Subtract 21 from both sides

[tex]y^2-4y-21 = 0[/tex]

Factor the equation

[tex]y^2-7y+3y-21=0\\y(y-7)+3(y-7)=0\\(y-7)(y+3)=0\\y=7\text{ or} \ -3[/tex]

Since the question states that the two integers are positive, one of the integers is 7.

We can use this information to find the other integer.

[tex]x=2y-5\\x=2(7)-5\\x=14-5\\x=9[/tex]

[tex]CHECK:\\x^2+y^2=7^2+9^2=49+81=130 \Rightarrow Correct![/tex]

Therefore the two integers are 7 and 9.

Answer:

scalene

Step-by-step explanation:

hidhihihihihihi

No graph for the polar equation because here sin 0 is 0.

According to the statement

we have given that a polar equation and we have to represent in the graph.

So, For this purpose, we know that the

The expression of a point as an ordered pair. is known as polar notation, the equation of a curve expressed in polar coordinates is known as a polar equation.

The given polar equation is

r = 1-3 sin 0

here the value of r is 0.

so, No graph is possible for the given statement

because here the value of r is 0 and for zero value there is a no graph possible.

So, No graph for the polar equation because here sin 0 is 0.

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The number of ways that the dancers can line up is; 518400 ways

The fundamental counting theorem is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n1 * n2 * n3.....*nₙ

Total = 12

Dancers on Green = 6

Dancers on blue = 6

Number of ways for those wearing green = 6!

Dancers wearing green must be in the first position and so 6 places are left for the blue dancers.

Number of ways to arrange those wearing blue = 6!

Thus;

Number of ways that the dancers can line up = 6! * 6! = 518400 ways

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Applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.

In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.

In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.

According to the congruent chords theorem, NS = PS, thus:

8 = 2x - 6

8 + 6 = 2x

14 = 2x

Divide both sides by 2

14/2 = 2x/2

7 = x

x = 7

LP = 1/2(12)

LP = 6 units.

In summary, applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

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Answer:

1/4

Step-by-step explanation:

Rebecka already chose a retriever, so the puppies left for Aaron to pick are:

2 poodles

2 terriers

1 retriever

Total: 4

Number of retrievers left after Rebecka's pick: 1

p(Aaron picks retriever) = 1/4

The book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.

Current year book value

Land and buildings $707,150

Machinery, equipment, and internal-use software $671,793

Office furniture and equipment $106,073

Other fixed assets related to leases $855,652

Less Accumulated depreciation and amortization ($898,081)

Book value $1,442,587

Preceding year book value

Land and buildings $410,147

Machinery, equipment, and internal-use software  $530,363

Office furniture and equipment $91,930

Other fixed assets related to leases $643,507

Less Accumulated depreciation and amortization  ($749,579)

Book value $926,368

Therefore the book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.

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The speed of the plane will be 875km/h and the speed of the wind will be 125km/h.

It should be noted that the speed is calculated as:

= Distance/Time

Based on the information, the DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr.

Therefore, (v + w) = 3000/3

v + w = 1000 .... I

(v - w) = 3000/4

v - w = 750 .... ii

We'll then add both equations together. Therefore, the speed of the plane will be 875km/h and the speed of the wind will be 125km/h.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Take HJ = a, GH = b and GJ = c

put the value of a from equation 1 in equation 2

now, put the value of a and c in equation 3

Now, we need to find HJ (a)

[tex]{ \qquad \large \sf {Conclusion} :} [/tex]

The mean, median, and mode are;

median=77

Mean=73.33

Mode= 78, 67

This is further explained below.

Generally, The middle number in a list that is arranged from smallest to greatest is referred to as the median. On the list, the value that occurs most often is known as the mode. Therefore

median=77

Generally, In mathematics, particularly statistics, the term "mean" may refer to a number of different concepts. The purpose of each mean is to summarize a certain collection of data, often for the purpose of gaining a better understanding of the overall value of a specific data set.

A dataset's mean (also known as the arithmetic mean, which is distinct from the geometric mean) is calculated by dividing the sum of all of the values in the dataset by the total number of values in the dataset. It is the measure of central tendency that is used the most often, and it is sometimes referred to as the "average."

[tex]mean=\frac{\sum x}{n}\\\\Mean=\frac{78+67+98+50+67+78+67+77+78}{9}[/tex]

Mean=73.33

Mean=73.3 in one dp

In conclusion, The mode is the number that appears the most often, or the number that stands out as having the most occurrences overall. The number 2 is the mode of the sequence 4, 2, 4, 3, 2, 2 because it appears three times, which is more than any other number in the sequence.

The mode of 78, 67, 98, 50, 67, 78, 67, 77, 78  is

Mode= 78, 67

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The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.

The percentage represented as; 20% can be expressed as a fraction.

This follows from the fact that the percentage, % symbol translates to divided by 100.

Consequently, we must note that the 20% translates to; 20/100 = 1/5.

Hence, the 20% tip is one-fifth of the total amount.

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Answer:

37°

Step-by-step explanation:

• recall that the sum of the interior angles of a triangle

  is equal to 180°

Then

The measure of the two other angles :

= 180 - 106

= 74°

The measure of each of the equal angles :

= 74 ÷ 2

= 37°

Answer:

the 2 angles r 37

Step-by-step explanation:

the angles of triangle sums up to 180, and lets call the unknown angle x, since they're both equal, x+x=2x

so when 3 angles of triangle adds up, we get 180

106+2x=180

2x=180-106
2x=74, divide both sides by 2 to get x

x=74/2

x=37

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