Evaluate angles s and r, giving reason for your answer​

Answer:

The equation of the line is [tex]y = 2\cdot x + 3[/tex].

Step-by-step explanation:

The data of the table represents a line, also known as a linear function or a first order polynomial if and only if the following property is satisfied:

[tex]\frac{y_{i+1}-y_{i}}{x_{i+1}-x_{i}} = m, m \in \mathbb{R}[/tex] (1)

Now we proceed to check if the table represents a line instead of another kind of function:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{7-5}{2-1} = 2[/tex]

[tex]\frac{y_{3}-y_{2}}{x_{3}-x_{2}} = \frac{9-7}{3-2} = 2[/tex]

[tex]\frac{y_{4}-y_{3}}{x_{4}-x_{3}} = \frac{13-9}{5-3} = 2[/tex]

[tex]\frac{y_{5}-y_{4}}{x_{5}-x_{4}} = \frac{15-13}{6-5} = 2[/tex]

Hence, the data represents a line. From Geometry we know that the equation of the line can be obtained by knowing two distinct points. The formula of the line is described below:

[tex]y = m\cdot x + b[/tex] (2)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]m[/tex] - Slope.

[tex]b[/tex] - y-Intercept.

If we know that [tex](x_{1}, y_{1}) = (1, 5)[/tex] and [tex](x_{2}, y_{2}) = (6, 15)[/tex], then we have the following system of linear equations:

[tex]m + b = 5[/tex] (1)

[tex]6\cdot m + b = 15[/tex] (2)

The solution of the system of linear equations is: [tex]m = 2[/tex], [tex]b = 3[/tex].

The equation of the line is [tex]y = 2\cdot x + 3[/tex].

Answer:

[tex]{ \tt{AB || CD}} \: \: they \: are \: parallel. \\ { \tt{AB \:and \: EF}} \: \: are \: perpendicular \\ { \tt{CD \: and \: EF}} \: \: are \: perpendicular \\ { \tt{GH \: is \: neither \: parallel \: nor \: perpendicular \: to \: any \: other \: line}}[/tex]

Answer:

[tex]y = \frac{ - 13 - \sqrt{489} }{10} [/tex]

Answer:

Step-by-step explanation:

5y^2+15y-2y+4=20

5y^2-13y+4=20

5y^2-13y+4-20=0

5y^2-13y-16=0

This equation is in standard form: ax^2+bx+c=0. Substitute 5 for a, 13 for b, and −16 for c in the quadratic formula.

Answer:

Value of x will be 12.

Step-by-step explanation:

Answer:

A) x + 5y = 20

B) x + 3y = 14

Multiplying A) by -1

A) -x -5y = -20 then adding B)

B) x + 3y = 14

-2y = -6

y = 3

x = 5

Step-by-step explanation:

Answer:

Espero te sirva saludos

Answer:

9

Step-by-step explanation:

Question:

Minimum number of balls to ensure there is at least one ball of each colour marked with each number.

The quantity of distinct numbers are:

red: 4

Yellow 3

Blue 2

So the minimum number of balls to satisfy the given requirements is

4+3+2= 9

Answer:

(2, -3)

Step-by-step explanation:

YEAH

Answer:

x=2; y=-3

Step-by-step explanation:

Answer:

The length is 17 cm.

17+17+9+9 adds up to 52.

Answer:

[tex]a_n=-\frac{9}{4} +\frac{1}{4} *n; \ a_{45}=9.[/tex]

Step-by-step explanation:

1. the difference between two sequent term is: 2- 7/4=7/4 - 3/2 = 3/2 - 5/4=... = 1/4.

2. using the value of the calculated difference it is possible to make up the formula of the given sequence ('n' - the number of term):

[tex]a_n=-\frac{9}{4}+\frac{1}{4} n.[/tex]

3. for n=45:

[tex]a_{45}=-\frac{9}{4}+45*\frac{1}{4}=9.[/tex]

Answer:

x = 75.7 cm

Step-by-step explanation:

sin = opp/hyp

sin63 = x/85

multiply both sides by 85

85 * sin63 = x

Use calculator

75.735554556011268 = x

Rounded

x = 75.7 cm

Answer:

85 miles

Step-by-step explanation:

He needed to travel a total of 210 miles

He had already traveled 125 miles on bus

And he traveled the rest of the length on the train

If we want to find the distance he traveled on train we simply subtract total distance by distance traveled on bus

So distance traveled on train = 210 - 125 = 85

So he traveled a total of 85 miles on train

Answer:

This might be permutation promblem srry if im wrong.

P(6,3)=6x5x4=120

P(4,2)=4x3=12

simplest form 4 : 2 : 2 is 2:1:1

Answer:

B on edge 2021

Step-by-step explanation:

Answer:

y = 3x - 1

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = slope

b = y-intercept

Answer:

y = [tex]\frac{1}{2}[/tex] x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{1}{2}[/tex] and c = - 4 , then

y = [tex]\frac{1}{2}[/tex] x - 4 ← equation of line

Answer:

x = 4      y = 7

Step-by-step explanation:

x + 3 = -1/2x + 9

x = -1/2x + 6

3/2x = 6

x = 4

y = (4) + 3

y = 7

Answer:

1) find the verted of the parabols

[-b/2a, f(-b/2a)]

-32/-32 = 1  .... -16+32+6 = 22

2) take the derivative and set = to 0

-32t+32 = 0

t = 1 .....height = 22

Step-by-step explanation:

Answer:

[tex]V=2080m^3[/tex]

Step-by-step explanation:

The volume formula for triangular prism is  [tex]V=\frac{1}{2}bhl[/tex]

[tex]V=\frac{1}{2}(26)(20)(8)[/tex]

[tex]V=\frac{1}{2}(4160)[/tex]

[tex]V=2080[/tex]

Hope this helps

Answer:

The answer is 2080m^3

Step-by-step explanation:

The formula for volume of a prism is 1/2 x length x width x height

Hope it helps :)

Answer:

35.44

Step-by-step explanation:

(1 +.42)*468 = 664.56

if you add 35.44 you would have 700

Answer:

[tex]\sec \upsilon = -\sqrt{5}[/tex]

Step-by-step explanation:

Given a point in rectangular form and by definition of trigonometric relations, we know that the secant associated to the vector is:

[tex]\sec \upsilon = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex] (1)

If we know that [tex]x = -3[/tex] and [tex]y = 6[/tex], then the secant of the vector is:

[tex]\sec \upsilon = \frac{\sqrt{(-3)^{2}+6^{2}}}{(-3)}[/tex]

[tex]\sec \upsilon = -\sqrt{5}[/tex]

Answer:

a

Step-by-step explanation:

just took the test

Answer:

Step-by-step explanation:

25 200 giây

Answer:

Step-by-step explanation:

Given,

Length of the room = 12m

Width of the room = 5m

Therefore,

Area of the room = l × w

= 12m × 5m

= 60 sq.m (Ans)

Answer:

[tex]39[/tex]

Step-by-step explanation:

[tex]A=lw[/tex]

Area = length * width

[tex]A = 3 * 13[/tex]

[tex]A=39[/tex]

Hope this helps

Answer:

The unknown side is 140

Step-by-step explanation:

Let the unknown side be x

Using ratios

90         90+36

------ = -----------

x            x+56

90         126

------ = -----------

x            x+56

Using cross products

90(x+56) = 126x

Distribute

90x+5040 = 126x

Subtract 90x

5040 = 36x

Divide by 36

140 =x

Answer:

$65,000 was invested in stocks, $ 50,000 in CDs and $ 70,000 in bonds.

Step-by-step explanation:

Since Country Day's scholarship fund receives a gift of $ 185000, and the money is invested in stocks, bonds, and CDs, and CDs pay 4.75% interest, bonds pay 3.3% interest, and stocks pay 7.5% interest, and Country day invests $ 20000 more in bonds than in CDs, if the annual income from the investments is $ 9560, to determine how much was invested in each vehicle, the following calculation must be performed:

55000 x 0.075 + 55000 x 0.0475 + 75000 x 0.033 = 9,212.5

57000 x 0.075 + 54000 x 0.0475 + 74000 x 0.033 = 9,282

65000 x 0.075 + 50000 x 0.0475 + 70000 x 0.033 = 9,560

Therefore, $ 65,000 was invested in stocks, $ 50,000 in CDs and $ 70,000 in bonds.