What is the solution of following system of equations y=2x-3 4x-3y=31

Answer:

>

Step-by-step explanation:

π / 3 is in radians.

Radian need to be converted into

degree ( ° ).

The value of in degree is 180°

π / 3 = 180 / 3 = 60°

60° > 30°

So,

( π / 3 ) > 30°

Answer:

  (a)  north: 172.5 mph; west: 298.8 mph

  (b)  363.9 mph at 298.9°

Step-by-step explanation:

The components of velocity are found using the formula for polar to rectangular coordinate conversion. The actual ground speed will be the result of adding the velocity vectors of the airplane and wind.

__

The usual formula for converting polar coordinates (r; θ) to rectangular coordinates (x, y) is ...

  (x, y) = r(cos(θ), sin(θ))

When this formula is used with bearing angles, the resulting components are (north, east).

The airplane velocity components are ...

  north: 345·cos(300°) = 172.5 . . . . mph

  east: 345·sin(300°) ≈ -298.8 . . . . mph (or 298.8 mph to the west)

__

The sum of the two velocity vectors is found by a calculator to be ...

  345∠300° +20∠280° = 363.9∠298.9°

If you wanted to calculate this by hand, you would find the components of the wind speed, add them to the components of the plane speed, and convert the rectangular components back to polar coordinates. The usual way that is done is using the formula ...

  r = √(x² +y²)

  θ = arctan(y/x) . . . . paying attention to quadrant

If you use x=northerly component, y=easterly component, then the resulting angle is the bearing angle.

_____

Additional comment

Some calculators are able to convert directly between (x, y) coordinates and (r; θ) coordinates. The calculator shown in the attachment converts (r; θ) coordinates to/from complex numbers. For the purpose here, the real part of the number is the northerly component, and the imaginary part is the easterly component.

The conversion to a complex number is x +iy = r(cos(θ) +i·sin(θ)), sometimes abbreviated r·cis(θ). The notation used here is even more compact: r∠θ. Conveniently, the calculator we used is able to employ this notation.

The sum of the arithmetic series with the parameters  t1 = -2, t3 = 7, and n = 15 is 442.5

The given parameters are:

t1 = -2

t3 = 7

n = 15

Start by calculating the common difference using:

Tn = t1 + (n- 1)d

So, we have:

7 = -2 + (3 - 1) * d

Evaluate

7 = -2 + 2d

Add 2 to both sides

2d = 9

Divide by 2

d = 4.5

The sum  is then calculated using:

[tex]S_n = \frac n2 * (2a + (n - 1) * d)[/tex]

So, we have:

[tex]S_{15} = \frac {15}2 * (2*-2 + (15 - 1) * 4.5)[/tex]

Evaluate

[tex]S_{15} = 442.5[/tex]

Hence, the sum of the arithmetic series is 442.5

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well, since we know the endpoints for the diameter, its midpoint will be where the center of the circle is located, so

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{11}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -4 -10}{2}~~~ ,~~~ \cfrac{ 11 + 5}{2} \right)\implies \left(\cfrac{-14}{2}~~,~~\cfrac{16}{2} \right)\implies \stackrel{center}{(-7~~,~~8)}[/tex]

and if we get the distance between those endpoints, and take half of that, that'd be the radius of it.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{11})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-4 - (-10)]^2 + [11 - 5]^2}\implies d=\sqrt{(-4+10)^2+6^2} \\\\\\ d=\sqrt{6^2+6^2}\implies d=\sqrt{72}~\hfill \stackrel{radius=half~that}{\cfrac{\sqrt{72}}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-7}{ h},\stackrel{8}{ k})\qquad \qquad radius=\stackrel{\frac{\sqrt{72}}{2}}{ r} \\\\\\\ [x-(-7)]^2~~ + ~~[y-8]^2~~ = ~~\left( \frac{\sqrt{72}}{2} \right)^2\implies (x+7)^2~~ + ~~(y-8)^2~~ = ~~18[/tex]

Answer:

Step-by-step explanation:

The frequency table according to the graph looks like

Total number of frequencies is

Sum of data, using the midpoint of frequency ranges

The mean is the average of data

Midpoints of frequency ranges

They are

Now

sum of frequencies

Mean:-

Answer:

3.25 rounded to 3

Step-by-step explanation:

If she liked 1/4 of the colors, then we would divided by 13 by 4 to get 3.25.

She can't like 1/4 of a color though, so we would round to 3.

The percentage of the pages in the user manual that do not have diagrams is 0.8%.

Percentage is a measure of frequency that is is used to determine the  fraction of an amount that is usually expressed as a number out of hundred.

Percentage without diagram = (4/500) x 100 = 0.8%

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Answer:

11.405

Step-by-step explanation:

When rounding numbers, check the digit to the right of the one you're rounding to:

If a = 14.6 is rounded to 1 decimal place then:

If b = 3.25 is rounded to 2 decimal places then:

Therefore, to find the maximum value of a - b, subtract the smallest value of b from the largest value of a:

[tex]\implies \sf a_{max}-b_{min}=14.649999...-3.245=11.405[/tex]

Answer:

[tex](x-2)^2-30[/tex]

Step-by-step explanation:

use the form [tex]ax^2+bx+c[/tex] to find the values of a, b, and c.

[tex]a=1, b= -4, c = -26[/tex]

consider the vertex form of a parabola

[tex]a(x+d)^2+e[/tex]

substitute the values of a and b into the formula [tex]d=\frac{b}{2a}[/tex]

[tex]d=\frac{4}{2(1)}[/tex]

simplify the right side.

find the value of e using the formula [tex]e=c-\frac{b^2}{4a}[/tex]

[tex]e=30[/tex]

The number rounded to the nearest ten will be 1640. The number is grater than the 5 on the scale.

If the digit in the units place is between 0  and 10 i.e., 5, then the unit digit is substituted by 0.

If the digit in the units place is between 5 and 9, that is, > or 5 but less than 10, the units place is replaced by '0,' and the tens place is incremented by 1.

The given number is;

x=1637.984

The number is 7.9 grater than 5. So that the number is rounded to the nearest whole number,i.e.1640

Hence,the number rounded to the nearest ten will be 1640.

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Answer: (7x + 1)(x + 7)

Step-by-step explanation:

[tex]$$Factor the following:$$7 x^{2}+50 x+7$$Factor the quadratic $7 x^{2}+50 x+7$. The coefficient of $x^{2}$ is 7 and the constant term is 7. The product of 7 and 7 is 49 . The factors of 49 which sum to 50 are 1 and 49. So:\\\\ $7 x^{2}+50 x+7\\=7 x^{2}+49 x+x+7\\=7(7 x+1)+x(7 x+1)$ \\\\Factor $7 x+1$ from $7(7 x+1)+x(7 x+1)$ :$$\\\\Answer:(7 x+1)(x+7)$$[/tex]

Answer:

x = -2

Step-by-step explanation:

Step 1: Subtract 7 from both sides.

3x+7−7=1−7

3x=−6

Step 2: Divide both sides by 3.

3x/3 = −6/3

x = −2

Answer:

I think it b

Step-by-step explanation:

I had the same question

Answer:

Sorry

Step-by-step explanation:

Answer:

Shaded square 1: 4

Shaded square 2: 6

Shades square 3: 2

*Sorry all I can get at the moment is the shaded squares I'm still a little new to this

Step-by-step explanation:

Since the figure is a trapezoid, we must use the trapezoid area formula, [tex]A = (b_1 + b_2) / 2 * h[/tex]. By doing so, we can plug in the shown numbers on the image. After that, we multiply.

[tex]A = (8 + 14) / 2 * 5[/tex]

[tex]A = 22/2 * 5[/tex]

[tex]A = 11 *5[/tex]

[tex]A = 55^2[/tex]

The area of the trapezoid is 55 squared yards.

There are several ways you can prove triangles congruent

Just you have to look at these parts of triangles

The ways are

#2

Yes we can form

The rule is that sum of two sides must be greater than third side

check

Answer:

The inverse of f exists

Step-by-step explanation:

Because f  is a function, then the function f  has an inverse

Answer:

3 and 7

Step-by-step explanation:

The LCM of 6 and 9 is 3

The GCF of 21 and 35 is 7

Answer:

224 cm²

Step-by-step explanation:

Look at the figure below.

All sides are in cm. All areas are in cm².

Triangle A:

A = bh/2 = 8 × 21 / 2 = 84

Rectangle B:

A = LW = 9 × 8 = 72

Rectangle C:

A = LW = 4 × 5 = 20

Triangle D:

A = bh/2 = 6 × 16 / 2 = 48

Total area = 84 + 72 + 20 + 48 = 224

Answer: 224 cm²

Answer:

A.  P(A l B) = x

Step-by-step explanation:

For independent events A and B,

P(B | A) = P(B)

P(A | B) = P(A)

P(A ∩ B) = P(A)P(B)

If P(A) = x   and   P(B) = y  then:

⇒ P(B | A) = y

⇒ P(A | B) = x

⇒ P(A ∩ B) = xy

Therefore, the correct solution from the options given is:

A.  P(A l B) = x

Answer:

29.7339181287

The short answer:29.73

Answer: 10 points, please!

Step-by-step explanation:

1. for the medium you want to find the number thats in the middle. so you have to write out all the numbers in order. then you step by step go to the middle and theres your medium.

0, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6, 6, 7, 11

2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6, 6, 7

2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6, 6,
2, 3, 3, 3, 3, 3, 3, 5, 5, 6,

3, 3, 3, 3, 3, 3, 5, 5,

3, 3, 3, 3, 3, 5,

3, 3, 3, 3,
3, 3,

The medium is 3.


2. for the mean you add all the numbers up and then divide based on how many numbers there are.

0 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 3 + 5 + 5 + 6 + 6 + 7 + 11 / 16

64/16

4

the average or mean is 4 which tells us that the average number of kids per houshold is 4. and none of the housholds have 4 children. we know this because of the data in the line plot.

the typical houshold size is either 3 or 4. the medium is 3 and the average or mean is 4.

10 points please

The force vector F in terms of i and j, considering it's magnitude and angle, is represented by:

[tex]V = 11\sqrt{2}i + 11\sqrt{2}j[/tex]

Given a magnitude M and angle [tex]\theta[/tex], the a vector V can be represented as follows:

[tex]V = M\sin{\theta}i + M\cos{\theta}j[/tex]

In this problem, we have that the parameters are as follows:

[tex]M = 22, \theta = 45^\circ[/tex]

Hence:

[tex]V = 22\sin{45^\circ}i + 22\cos{45^\circ}j[/tex]

[tex]V = 22\frac{\sqrt{2}}{2}i + 22\frac{\sqrt{2}}{2}j[/tex]

[tex]V = 11\sqrt{2}i + 11\sqrt{2}j[/tex]

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Answer:

answer is 45 trust me im passing this concept

Step-by-step explanation:

Answer:

x= -2/9

Step-by-step explanation:

step 1: isolate the variable

27x+4 = 9x

-9x. -9x

18x+4 = 0

-4. -4

18x = -4

step 2: isolate the variable by dividing both sides by the coefficient

18x = -4

÷18. ÷18

=

x = -2/9

(x is equal to negative 2 ninths)

Answer:

$45.5

Step-by-step explanation:

Assuming that there is no tax or change in rate its simply $91 divided by two. We know that 45 is half of 91, 45.5 x 2 = 91

The total annual dividend which is received from owning 50 shares of stock A, when Company A Issues a $0.10 quarterly dividend to its shareholders, is $20.

Market value is the current price of a product, company, or something consorting to the stock of the market.

The total annual dividend received from owning 50 shares of stock A has to be found out when Company A Issues a $0.10 quarterly dividend to its shareholders.

For each quarter, the payment of dividend is,

[tex]0.10\times50\\5[/tex]

In a year,

[tex]5\times4\\20[/tex]

Thus, the total annual dividend which is received from owning 50 shares of stock A, when Company A Issues a $0.10 quarterly dividend to its shareholders is $20.

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