What was the purpose of the coordinate graphing system described by Descartes in his book Discourse on Method?
O to use algebraic methods to solve geometric problems
O to prove the universe was Sun-centered
O to represent equations for the queen of Sweden
O to prove his own existence

Answer:

Perimeter: 4+[tex]\pi \\[/tex] mm

Area: [tex]\pi[/tex] mm^2

Step-by-step explanation:

Perimeter:

90/360 * 4[tex]\pi \\[/tex] +2 + 2 = 4+ [tex]\pi \\[/tex]

Area:

90/360 * 4[tex]\pi[/tex] = [tex]\pi[/tex]

Answer: 7.14 mm and 3.14 mm²

Step-by-step explanation:

The perimeter of a figure is the total length on the outside of the figure. A regular circle has a perimeter of [tex]2\pi r[/tex], where r is the radius and [tex]\pi[/tex] is an irrational constant, approximately 3.14.

Due to the right angle, we know that this is a quarter circle, as it is a quarter of 360°, or a full circle. Hence, the curved portion of the quarter circle is [tex]\frac{1}{4}* 2\pi r[/tex] or [tex]\frac{1}{2} \pi r[/tex]. The radius is 2 mm, so this value is

[tex]\frac{1}{2} \pi*2=\pi[/tex]

However, this isn't the total perimeter, as there are straight edges in the figure too. Both edges are radii of the whole circle, so both would be 2mm. Their total is

[tex]2+2=4[/tex]

By adding [tex]\pi[/tex] to 4 we get [tex]\pi +4[/tex] or 7.14 mm.

The  area is the total space enclosed by a figure. The total area of a whole circle is [tex]\pi r^2[/tex], where r is still the radius. Since this is a quarter circle, it would take up a quarter of the area, or [tex]\frac{1}{4} \pi r^2[/tex]. We can plug in 2 for r and solve to get the area.

[tex]\frac{1}{4}\pi*2^2\\\frac{1}{4}\pi*4\\\pi[/tex]

Hence, the area is [tex]\pi[/tex], or around 3.14 mm².

The lower bound of the 90% confidence interval for the gift basket's average shipping weight is 55.605.

Given mean weight of 57 ounces ,sample size 70 ,confidence level 90% and standard deviation of 7.1 ounces.

We have to find the lower bound of the confidence interval for the gift's basket's avrage shipping weight.

We can easily find the confidence interval and its lower bound through theformula of margin of error.

Margin of error is the difference between real values and calculated values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the critical value of confidence level

σ is standard deviation,

n is the sample size

We have to first find the z value for 90% confidence level which is 1.645.

Margin of error=1.645*7.1/[tex]\sqrt{70}[/tex]

=11.6795/8.3666

=1.395

Lower bound of the confidence interval = Mean - margin of error

=57-1.395

=55.605.

Hence the lower bound of the confidence interval for the gift basket's average shipping weight is 55.605.

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Answer: Not similar

Step-by-step explanation:

The polygons are not similar because the ratio of the corresponding sides is not equal (30/18 is not equal to 18/8)

The fraction of the students in Siena's class are girls with brown eyes is 5/12.

Let the fraction of students in Siena's class with brown eyes be a=5/8.

And the fraction of students in Siena's class with brown eyes are girls be b=2/3.

Then, the fraction of students in Siena's class are girls with brown eyes be z=a×b

Therefore, by substituting the fraction values, we get

z=(5/8)×(2/3)

z=5/12.

Hence, 5/8 of the students in Siena's class have brown eyes. 2/3 of the students with brown eyes are girl. Then, the fraction of students in Siena's class are girls with brown eyes is 5/12.

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Answer:

3 elements

Step-by-step explanation:

Let A = solution set of x²-4

B = solution set of x²-3x+2

First, find the solution of each sets:

[tex]\displaystyle{x^2-4=0}\\\\\displaystyle{(x+2)(x-2)=0}\\\\\displaystyle{x=2,-2}[/tex]

Set B:

[tex]\displaystyle{x^2-3x+2=0}\\\\\displaystyle{(x-2)(x-1)=0}\\\\\displaystyle{x=1,2}[/tex]

Now we can write new set as:

A = {2, -2}

B = {1, 2}

The union of A and B means combine both sets together:

A ∪ B = {2, -2, 1, 2}

However, in a set, we do not write duplicate elements, so the union set will be:

A ∪ B = {2, -2, 1}

Hence, there are 3 elements in A ∪ B.

Answer:

(3x+y) (2x-7y)

Step-by-step explanation:

first write -19xy as a difference and you get 6x^2+2xy-21xy-7y^2

and then take the factor 2x from the expression that is 2x(3x+y) and do the same with the -7 that is = -7(3x+y). So this is you answer= (3x+y)(2x-7)

Answer: 1/5

Step-by-step explanation: You just subtract 4/5 from 1, or 5/5. And BOOM! you get 1/5.

The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].

First, we need to determine the value of the vector u by subtracting two vectors whose initial points are at the origin:

[tex]\vec u = (19\,\hat{i} - 8\,\hat{j}) - (21\,\hat{i} + 12\,\hat{j})[/tex]

[tex]\vec u = - 2\,\hat{i} - 20\,\hat{j}[/tex]     (1)

According to the statement, vector v is antiparallel to vector u and its magnitude is five times as the magnitude of vector v, which means that (1) must be multiplied by two scalars:

[tex]\vec v = - 1 \,\cdot \, 5\cdot \vec u[/tex]      (2)

Please notice that antiparallelism is represented by the scalar - 1, whereas the dilation is represented by the scalar 5.

[tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex]

The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].

The statement presents typing mistakes, correct form is shown below:

Vector u has initial points at (21, 12) and its terminal point at (19, - 8). Vector v has a direction opposite that of u, whose magnitud is five times the magnitud of v. Which is the correct form of vector v expressed as a linear combination of the unit vectors i and j?

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Answer:

The answer that you have highlighted is correct.

Step-by-step explanation:

When you are dividing, you divide the exponents

-10 - (-4)

-10 + 4

-6

Answer:

Length= 50

Width=17

Step-by-step explanation:

length= n+8

Since n= 42, Just plug it in. So it would be 42+8 which is 50 for the length

Widith: 1/2n-4

basically since N is given for 42, you do 1/2 multipied by 42 which is 21.

Since you also have to subtract 4 inches it would be 17 for the length

The probability that all three players obtain an odd sum is 3/14.

The probability is the ratio of possible distributions to the total distributions.

I.e.,

Probability = (possible distributions)/(total distributions)

Given that,

There are nine tiles - 1, 2, 3,...9, respectively.

A player must have an odd number of odd tiles to get an odd sum. That means he can either have three odd tiles, or two even tiles and an odd tile.

In the given nine tiles the number of odd tiles = 5 and the number of even tiles = 4.

The only possibility is that one player gets 3 odd tiles and the other two players get 2 even tiles and 1 odd tile.

So,

One player can be selected in [tex]^3C_1[/tex]  ways.

The 3 odd tiles out of 5 can be selected in [tex]^5C_3[/tex] ways.

The remaining 2 odd tiles can be selected and distributed in [tex]^2C_1[/tex] ways.

The remaining 4 even tiles can be equally distributed in [tex]\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}[/tex] ways.

So, the possible distributions = [tex]^3C_1[/tex] × [tex]^5C_3[/tex] × [tex]^2C_1[/tex] × [tex]\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}[/tex]

⇒ 3 × 10 × 2 × 6 = 360

To find the total distributions,

The first player needs 3 tiles from the 9 tiles in [tex]^9C3=84[/tex] ways

The second player needs 3 tiles from the remaining 6 tiles in [tex]^6C_3=20[/tex] ways

The third player takes the remaining tiles in 1 way.

So, the total distributions = 84 × 20 × 1 = 1680

Therefore, the required probability = (possible distributions)/(total distributions)

⇒ Probability = 360/1680 = 3/14.

So, the required probability for the three players to obtain an odd sum is 3/14.

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Answer:

$96

Step-by-step explanation:

Answer:

B. Every integer is also an irrational number.

From the conversation it can be inferred that Paul's approach to getting on the horse is methodical (option c).

A methodical attitude or behavior refers to the preference of people to use an organized method and sequences to perform an activity correctly.

According to the above, it can be inferred that Paul behaves in a methodical manner because he prefers to relate to the horse slowly and in a controlled manner before proceeding to mount it.

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The result of the evaluation of the equation given in the task content is; x =-2.

It follows from the task content that the equation given whose solution is to be determined is;

3[-x + (2 x +1)]=x-1

The equation can be solved as follows;

-3x + 6x +3 = x-1

2x = -4

x = -2

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The slope of given data is a -3.

According to the statement

we have given a some data and we have to find the slope of the data.

So, data given is:

x, has the entries, negative 2, negative 1, 0, 1, 2.

y, has the entries, negative 2, 1, 4, 7, 10.

and we have to find the slope of the data

So, we know that it is a data represent in the graph then

We know that a there is a graphical representation of data.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

And when we observe this data then we see that the there is some increase the y axis value as compare to the x axis values.

So,

For each unit of run in the x-values, there is an increase of 3 in the y-values. The slope is rising over Run so 3/1 = 3

So, The slope of given data is a -3.

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Answer: the answer is a -3

Step-by-step explanation:

https://brainly.com/question/68367When two lines intersect at a point, angles are formed. Some of these angles formed are vertically opposite and thus are equal.

Therefore, the required proof and answer to the question are stated below:

a) m< TRV = 60° (given)

   m<TRS = 4x° (given)

Thus, it can be concluded from the diagram that:

<TRV ≅ m<BRW  (vertically opposite angle property)

Also,

m<TRS ≅ m<VRW (vertically opposite angle property)

But,

m<VRW = m<VRZ + m<ZRW

Thus,

m<TRV ≅ m<BRW = 60°

m<TRV + m<BRW + m<TRS + m<VRW = [tex]360^{o}[/tex]

60° + 60° + m<TRS + m<VRW = [tex]360^{o}[/tex]

m<TRS + m<VRW =   [tex]360^{o}[/tex] - [tex]120^{o}[/tex]

                             = [tex]240^{o}[/tex]

2m<TRS = [tex]240^{o}[/tex] (since m<TRB = m<VRW )

m<TRS = 120

4x = 120

x = [tex]\frac{120}{4}[/tex]

  = [tex]30^{o}[/tex]

Thus, x = [tex]30^{o}[/tex]

b) The missing reason in step 3 is the angle addition postulate.

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The Number of teams is  mathematically given as

N= 30100

Generally, the equation for Number of teams is  mathematically given as

X items are selected from n items by [tex]^nC_x[/tex] ways

[tex]^nC_x = \frac{n!}{ [ (n-x)! * x! ]}[/tex]

Number of teams

N= n(1 child and 3 adults) + n(2 child and 2 adults) + n(3 child and 1 adults) + n(4 child)

N= 16C1 * 15C3 + 16C2 * 15C2 + 16C3 * 15C1 + 16C4 * 15C0

N= 16 * 455 + 120 * 105 + 560 * 15 + 1820

N= 30100

In conclusion, the Number of teams

N= 30100

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[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4x}{y}\right)^{2} \end{gathered}$}[/tex]

To raise 4x/y to a power, raise the numerator and denominator to the power, and then divide.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{(4x)^{2} }{y^{2} } \end{gathered}$}[/tex]

Expand (4x)².

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{4^{2} x^{2} }{y^{2} } \end{gathered}$}[/tex]

Calculates 4 to the power of 2 and gets 16.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \frac{16x^{2} }{y^{2} } \end{gathered}$} }[/tex]

The difference between the tallest and shortest heights is 0.787 × 10

From tallest to shortest:

Difference between tallest and shortest heights =

3.212 x 10⁴ - 2,425

= 3.212 x 10⁴ - 2.425 × 10³

= (3.212 - 2.425) × 10^4 - 3

= 0.787 × 10

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Answer:

$4.86

Step-by-step explanation:

Original price: $5.40

Discount: 10%

Discount amount:

10% of $5.40 = 0.1 × $5.40 = $0.54

Discounted price:

$5.40 - $0.54 = $4.86

Answer:

$4.86

Step-by-step explanation:

There are two approaches to this problem.

1:

You can multiply the original value by 10% and subtract it from the original value. In this case, $5.40-(5.40×10%). This becomes $5.40-$0.54. This is $4.86.

2:

You can simply multiply the original value by 90%. In this case, $5.40×90%. This also becomes $4.86.

Answer:

4. b) an angle

5. b) the angles of a triangle

6. b) opposite, hypotenuse and adjacent

Step-by-step explanation:

4. To find sine, cosine, tangent, you use the sin, cos, tan key of the calculator.

If you are given the value of the sin, cos, tan, and you are looking for the angle, then you use the second function of the calculator.

Answer: b) angle

5. angles of a triangle

6. The sides that form the right angle are the legs. In trig, there is an angle of interest, so to distinguish between the legs, one leg is called the adjacent leg, and the other leg is called the opposite leg. The side opposite the right angle is the hypotenuse.

Answer: opposite, hypotenuse and adjacent

Answer:

[tex]y=0.5x-10.5[/tex]

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we need to find is 0.5.

Substituting into point-slope form and converting to slope-intercept form,

[tex]y+6=0.5(x-9) \\ \\ y+6=0.5x-4.5 \\ \\ y=0.5x-10.5[/tex]

Answer:

x ≤ 2

Step-by-step explanation:

We are given the inequality:

[tex]\displaystyle{2x-3 \leq \dfrac{x}{2}}[/tex]

First, get rid of the denominator by multiplying both sides by 2:

[tex]\displaystyle{2x\cdot 2-3\cdot 2 \leq \dfrac{x}{2}\cdot 2}\\\\\displaystyle{4x-6 \leq x}[/tex]

Add both sides by 6 then subtract both sides by x:

[tex]\displaystyle{4x-6+6 \leq x+6}\\\\\displaystyle{4x \leq x+6}\\\\\displaystyle{4x-x \leq x+6-x}\\\\\displaystyle{4x-x \leq 6}\\\\\displaystyle{3x \leq 6}[/tex]

Then divide both sides by 3:

[tex]\displaystyle{\dfrac{3x}{3} \leq \dfrac{6}{3}}\\\\\displaystyle{x \leq 2}[/tex]

Therefore, the answer is x ≤ 2

Answer: [tex]x \leq 2[/tex]

Step-by-step explanation: Given [tex]2x - 3 \leq \frac{x}{2}[/tex], we multiply 2 by both sides to cancel out the 2 in the denominator (multiplying by a number in a fraction turns it into 1, and since the denominator is one, it is the same as saying the number [or variable] on the numerator by itself.)

We then get [tex]4x - 6 \leq x[/tex].

Adding 6 to both sides, we get [tex]4x \leq x + 6[/tex].

Subtracting x from both sides, we get [tex]3x \leq 6[/tex]

Dividing by 3 from both sides, we get [tex]x \leq 2[/tex]

Hope this helped!

$1799.10

Each year, the amount of money in the account is increased by 8%. This is the same as multiplying by 1.08 each year.

For 10 years, you multiply the original $100,000 by 1.08 a total of 10 times.

This tends to be simplified to:

[tex]100,000 * 1.08^{10}[/tex]

This gives $215892.4997.

This is paid back over 10 years, which is 10 x 12 months, or 120 months.

Divide the $215892.4997 by 120 to get the monthly payment of:

$1799.10 (round to 2 decimal places as it is a currency)

Answer:

circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

[tex] \large{ \boxed{ \tt{A = {\pi \times r}^{2} }}}[/tex]

[tex] \large {\boxed{ \tt{p = 2 \times \pi \times r}}}[/tex]

If the radius is 2 inches and

Use 3,14 for π So:

[tex] \tt{ {A = \pi \times {r}^{2} }}[/tex]

[tex] \tt{A = (3.14 \times 2 \times 2)} [/tex]

[tex] \red{ \boxed{ \bold{A = 12.56 {inches}^{2} }}}[/tex]

440 repeat 11 more times.

400+(400*.1)=440 repeat 11 more times. Remember to use a new value each time.

Vacations can get expensive fast. The average cost per person for a week-long vacation is about $1,200 annually. So, if you've got a family of five, you'll need to sock away at least $6,000 for transportation, hotels, meals, and amusement parks.

Financial experts suggest that the average family vacation costs between 5-10% of your total income. If your family makes $40,000 per year then experts say your yearly family vacation budget should average between $2,000-$4000.

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Answer:

Step-by-step explanation:

Find the roots of x^2-25=0 by solving for x.

Add 25 to both sides

x^2=25

Square root both sides

x=-5

x=5

Answer:

x=5;x=-5

Step-by-step explanation:

It was right for me

The dilation by a scale factor of 2 of the points A(2, 3), B(5, 4), C(3, 6) gives;

a. A'(4, 6), B'(10, 8), C'(6, 12)

b. A'(-2, -2), B'(4, 0), C'(0, 4)

c. The transformation that would carry dilation 1 onto dilation 2 is T(-6, -8)

d. The proportion of the side length of Dilation 1 and Dilation 2 is 1:1

The general formula for finding the coordinates of the image of a point following a dilation is presented as follows;

[tex]D _{(a , \: b)k}(x, \: y) = (a + k \times (x - a) , \: b+ k \times (y - b))[/tex]

Where;

(a, b) = The center of dilation

k = The scale factor of dilation

(x, y) = The coordinate of the pre-image

The given points are;

A(2, 3), B(5, 4), C(3, 6)

a. The scale factor of dilation = 2

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

Therefore;

[tex]D _{(0 , \: 0)2}(2, \: 3) = (0 + 2 \times (2 - 0) , \: 0+ 2 \times (3 - 0)) = (4, \:6)[/tex]

Therefore dilation about the origin, with a scale factor of 2 gives;

Similarly

b. With the center of dilation at (6, 8), we have;

[tex]D _{(6 , \: 8)2}(2, \: 3) = (6 + 2 \times (2 - 6) , \: 8+ 2 \times (3 - 8)) = (-2, \:-2)[/tex]

[tex]D _{(6 , \: 8)2}(5, \: 4) = (6 + 2 \times (5 - 6) , \: 8+ 2 \times (4 - 8)) = (4, \:0)[/tex]

[tex]D _{(6 , \: 8)2}(3, \: 6) = \mathbf{(6 + 2 \times (3 - 6) , \: 8+ 2 \times (6 - 8))} = (0, \:4)[/tex]

c. The difference between the coordinates of the points on dilation 1 and 2 is a shift left 6 places and a shift downwards 8 places

Using notation, we have;

The area of the images of dilation 1 and 2 are equal given that the scale factor is the same.

d. From the above calculation, given that the difference between pre-image point and the center is multiplied by the scale factor followed by the addition of the x and y-values, the lengths of the sides of dilation 1 and 2 are the same, such that we have;

Given that the side lengths are the same, by AAA congruency postulate, we have;

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Answer:

The angle measures are the same.

Step-by-step explanation: