Given that the following statement is true
"If a shape is a polygon, then it is a closed figure."
Which of the following statements must also be true?
A. If a shape is a closed figure, then it is a polygon.
B. If a shape is not a polygon, then it is not a closed figure
C. If a shape is not a closed figure, then it is not a polygon
D. If the shape is not a polygon, then it is a closed figure.

Answer:

1. $539

2. $300

3. C

Step-by-step explanation:

May I have brainliest?

(i) The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].

(ii) The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].

(iii) The rate of increase of the y-coordinate is 1.2 units per second.

(i) By analytical geometry, we know that the slope of a line normal of a curve ([tex]m_{\perp}[/tex]) by the following expression:

[tex]m_{\perp} = - \frac{1}{\frac{dy}{dx} }[/tex] (1)

Where [tex]\frac{dy}{dx}[/tex] is the slope of the line tangent to the curve.

If we know that [tex]x = 1[/tex], then the slope of the normal to the curve is:

[tex]\frac{dy}{dx} = \frac{12}{2\cdot (1)+1}[/tex]

[tex]\frac{dy}{dx} = 4[/tex]

And the slope of a line normal of a curve is:

[tex]m_{\perp} = -\frac{1}{4}[/tex]

By definition of secant curve we calculate the remaining coordinate of the point Q:

[tex]m_{\perp} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex] (2)

Where:

If we know that [tex](x_{P}, y_{P}) = (1, 5)[/tex], [tex](x_{Q}, y_{Q}) = (x, 0)[/tex] and [tex]m_{\perp} = -\frac{1}{4}[/tex], then the remaining coordinate of point Q is:

[tex]-\frac{1}{4} = \frac{0-5}{x-1}[/tex]

[tex]-\frac{1}{4}\cdot (x-1) = -5[/tex]

[tex]-\frac{1}{4}\cdot x +\frac{1}{4} = -5[/tex]

[tex]\frac{1}{4}\cdot x = \frac{21}{4}[/tex]

[tex]x = 21[/tex]

The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].

(ii) The equation of the curve is derived by separating the variables and integrating the resulting expression:

[tex]dy = \frac{12}{2\cdot x + 1}\,dx[/tex]

[tex]\int\, dy = 6\int {\frac{2\,dx}{2\cdot x + 1} }[/tex]

[tex]\int \, dy = 6\int {\frac{du}{u} }[/tex]

[tex]y = 6\cdot \ln u[/tex]

[tex]y = 6\cdot \ln (2\cdot x + 1)+C[/tex]

And the integration constant is found for [tex](x,y) = (1, 5)[/tex]:

[tex]5 = 6\cdot \ln(2\cdot 1 + 1) + C[/tex]

[tex]C = -1.592[/tex]

The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].

(iii) The rate of increase of the y-coordinate by using the differential equation presented in statement and the definition of rate of change:

[tex]\frac{dy}{dt} = \left(\frac{12}{2\cdot x +1}\right)\cdot \frac{dx}{dt}[/tex] (3)

If we know that [tex]\frac{dx}{dt} = 0.3[/tex] and [tex]x = 1[/tex], then the rate of increase of the y-coordinate is:

[tex]\frac{dy}{dt} = \left[\frac{12}{2\cdot (1)+1} \right]\cdot (0.3)[/tex]

[tex]\frac{dy}{dt} = 1.2[/tex]

The rate of increase of the y-coordinate is 1.2 units per second.

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i). The coordinates of Q is equal to:

[tex](x,y) = (21, 0)[/tex]

ii). The equation of the curve is:

[tex]y = 6. In(2.x + 1) - 1.592[/tex]

iii). The rate of increase for y-coordinate when x = 1:

[tex]1.2 units[/tex] per second

i). Using analytical geometry,

[tex]xp[/tex] and [tex]xq[/tex] are the P and Q's x-coordinates.

[tex]yp[/tex] and [tex]yq[/tex] are the P and Q's y-coordinates.

Since ([tex]xp[/tex], [tex]yp[/tex]) = (1,5) and ( [tex]xq[/tex], [tex]yq[/tex]) = [tex](x, 0)[/tex] and m⊥ = - 1/4, the left coordinate of Q's point:-

-1/4 = (0-5)/(x - 1)

∵[tex]x = 21[/tex]

Thus, the coordinates of y = (21, 0)

ii). Through isolating the variables and employing integration:-

[tex]dy = \frac{12}{(2.x + 1)} dx[/tex]

by integration and integration constant (1,5), the equation is:

[tex]y = 6. In(2.x + 1) - 1.592[/tex]

iii). The rate of increase for y-coordinate:

[tex]dy/dt[/tex] = [tex]\frac{(12)}{(2.1 + 1)} .0.3[/tex]

∵ [tex]dy/dt[/tex] [tex]= 1.2[/tex]

Thus, the rate of increase for y-coordinate when x = 1 is 1.2 units per second.

Learn more about "Co-ordinates" here:

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Answer

Maximum point of (-2, 4)

Step-by-step explanation:

the maximum point in this case is the vertex because its the highest point of the graph

Answer:

35.8

Step-by-step explanation:

                [tex]\frac{340.1}{9.5}[/tex]  = 358

 We know that our answer can never be greater than 358 since the dividend

is 340.1 and the divisor is 9.5;

  Also,

  Both values are to one decimal places and we can use this to solve the problem;

  9 can divide 340 in about 37 place with a remainder of 7,

    So, it is appropriate to make the solution 35.8

Answer:

-2

Step-by-step explanation:

-2-4/3-0=-2

you basically take the y value of the first point subtract it from the y value of the 2nd point. you do the same for the x values

Answer:

-2

Step-by-step explanation:

You can use the equation rise over run, which is basically y2-y1 over x2-x1

Y2 is -2 and y4 is 4, x2 is 3  x1 is 0

-2-4 over 3-0=-6/3=-2

Answer:

its 10 with the remainder of 38

Step-by-step explanation:

The result of the division is remainder = 38 and quotient = 10

Division is the opposite of multiplying. When we know a multiplication fact, we can find a division fact: Example: 3 × 5 = 15, so 15 / 5 = 3. Also, 15 / 3 = 5.

Given that, 708 divided by 67

When dividing 708 by 67 will get 10 as quotient and 38 remainder

Hence, the result of the division is remainder = 38 and quotient = 10

Learn more about division, click;

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#SPJ2

Answer:

40

Step-by-step explanation:

divide 320 by 8 and get 40 cause ratio is 1:8 so answer is 40:320

9514 1404 393

Answer:

Step-by-step explanation:

The axes of symmetry are shown and labeled m and n. Reflection across either (or both) axis of symmetry will map the figure to itself. Apparently, you want to designate those reflections as ...

  Ra . . . where a = m

  Rb . . . where b = n

Answer:

hope this pic helps enjoy

Answer:

translation

Step-by-step explanation:

Sliding: moving a shape without rotating or flipping it.

Answer:

B

Step-by-step explanation:

I Can't explain it,I'm sorry

Answer:

4x+12

Step-by-step explanation:

A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame?

(5+2x)+(7+2x)

The perimeter would be 4x+12

Hope I helped!

Please mark Brainliest!!!

Answer:

The answer is A. 4x+12

Step-by-step explanation:

Just took the test on edge 2020 :D

Answer:

that's a lot of clients

Answer:

4

Step-by-step explanation:

8/12 simplifies to 4/6. so x needs to be 4 for it to work

Answer:

bruh 4 days duh

Step-by-step explanation:

Answer:

because AC and BD bis => AX = XC; BX = XD

ΔAXD ≅ ΔCXB (SAS) because: AX = CX

                                                    DX = BX

                                                    m∠AXD = m∠BXC ( 2 opposing angles)

because ΔAXD ≅ ΔCXB (SAS)

=> AD = BC and m∠DAX = m∠BCX

because m∠DAX = m∠BCX => AD//BC

ABCD has AD = BC and AD//BC => ABCD is a parallelogram

Step-by-step explanation:

Answer: the variable is p=6 .

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable

Answer:

p = 6

Step-by-step explanation:

Step 1: Simplify both sides.

3 + 2p − 4 = 11

3 + 2p + −4 = 11

(2p) + (3+−4) = 11 (Combine Like Terms)

2p + −1 = 11

2p − 1 = 11

Step 2: Add 1 to both sides.

2p − 1 + 1 = 11 + 1

2p = 12

Step 3: Divide both sides by 2.

2p/2 = 12/2

p=6

Answer:

I think x= 5

Step-by-step explanation:

because u put 2 where x is supposed to go so it would be -2(2)+9 and -2(2)=-4 and then add 9 and that =5

Answer: I think its Consine

Step-by-step explanation:

Answer:

x=20

Step-by-step explanation:

7+0.20x=5+0.30x              

then take the 7 and subtracet the 2 from it, then take the 0.30 and subtract the 0.20 from it then you should get 2=0.10x      

then to get rid of the 0.10 you take it and divide it from the 2 which gives you 20 then you have 20=x and thats your answer

Answer:

C. There is one solution, because the coefficients of the variables on both sides of the equation are different.

Step-by-step explanation:

The solution is m = 1

~theLocoCoco

Answer: 177

Step-by-step explanation:

Answer:

3=k

Answer:

I hope this helps!

Step-by-step explanation:

1. M is .25

b is 20

so

y= .25x+20

2. y= 3x+2

Answer:

add 2 zeros at the end of all of them

Step-by-step explanation:

Answer:

it's x=50 hope this helps

Answer:

[tex]\frac{50}{5}[/tex] is the answer

Step-by-step explanation:

you would times 10 by 5 and you have your answer