Which one of Aiko's steps makes a false assumption? Why is it false?
Aiko's Proof:
1. Draw 2 rectangles. Label one ABCD and the other PQRS
2. Translate rectangle ABCD by the directed line segment from A to P.A' and P now coincide. The points coincide because that's how we defined
our translation
3. Rotate rectangle A'B'C'D' by angle D'A'S. Segment A"D" now lies on ray PS. The rays coincide because that's how we defined our rotation.
4. Dilate rectangle A"B"C"D" using center A" and scale factor AD. Segments A"D" and PS now coincide. The segments coincide because A" was
the center of the rotation, so A" and P don't move, and since D" and S are on the same ray from A", when we dilate D" by the right scale factor, it
will stay on ray PS but be the same distance from A" as S is, so S and D' will coincide.
5. Because all angles of a rectangle are right angles, segment A'B' now lies on ray PQ. This is because the rays are on the same side of PS and
make the same angle with it (If A'B' and PQ don't coincide, reflect across PS so that the rays are on the same side of PS.)
6. Dilate rectangle A"B"C"D" using center A" and scale factor AB Segments A'"'**" and PQ not coincide by the same reasoning as in step 4.
7. Due to the symmetry of a rectangle, if 2 rectangles coincide on 2 sides, they must coincide on all sides.

First let us know about Polynomial –

Types of polynomials based on the degree–

[tex]\qquad[/tex] ☀️ Constant polynomial :-

Example : 6 (6x⁰ : degree of x : 0)

[tex]\qquad[/tex]☀️ Quadratic polynomial :-

Example : 3x² + 7x + 6 (3x² : degree of x : 2)

[tex]\qquad[/tex]☀️ Cubic polynomial :-

Example : 5x³ + 3x² + 7x + 6 (5x³ : degree of x : 3)

[tex]\qquad[/tex][tex] \purple{\bf \longrightarrow (1) p(x) = 6x² – 7x + 2 + q(x) = 6x³ – 7x + 15}[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 6x² – 7x + 2 + (6x³ – 7x + 15)[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 6x² + 6x² – 7x – 7x + 2 + 15[/tex]

[tex]\qquad[/tex][tex]\purple{ \bf \longrightarrow 6x³ + 6x² – 14x + 17}[/tex]

[tex]\qquad[/tex][tex]\pink{\bf \longrightarrow (2) h(x) = 7x³ – 6x + 1 + f(x) = 7x² + 17x – 9}[/tex]

[tex]\qquad[/tex][tex]\sf \longrightarrow 7x³ – 6x + 1 + (7x² + 17x – 9)[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 7x³ + 7x² – 6x + 17x + 1 – 9[/tex]

[tex]\qquad[/tex][tex]\pink{\bf\longrightarrow 7x³ + 7x² + 11x – 8}[/tex]

1) The degree of the polynomial is 3.

2) The degree of the polynomial is 3.

Answer:

  c = -1/2

Step-by-step explanation:

Put the known values in the equation and solve for the unknown.

  k = cd² +e

  3 = c(2²) +5

  -2 = 4c . . . . . . . subtract 5

  -1/2 = c . . . . . . divide by 4

Answer:

7

Step-by-step explanation:

Terms are the numbers and/or variables within an equation. For example you have 5 terms in that equation:

[tex]3x^2+7y^3+2x+9y-5y^2[/tex]

The first term is: [tex]3x^2[/tex]

The second term is: [tex]7y^3[/tex]

The third term is: [tex]2x[/tex]

The fourth term is: [tex]9y[/tex]

The fifth term is: [tex]-5y^2[/tex]

Coefficients are the numbers in front of variables (this includes negative/subtraction signs). For example you have 5 coefficients in this equation:

The first coefficient is: 3

The second coefficient is: 7

The third coefficient is: 2

The fourth coefficient is: 9

The fifth coefficient is: -5

Answer:

8cups

Step-by-step explanation:

if it takes 4-cups for 4-dozen. That's 1-cup each dozen so 8-dozen is 8-cups

Answer:

Option D.

Step-by-step explanation:

A  function is a relation in which one input (x-value) is assigned to exactly one output (y-value).

Since option D's x-values do not repeat, then it is a function.

Hope this helps.

Answer:

It is False

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

y1 = 5.2

y2 = 1

x1 = 0

x2 = -1.5

Solution:

m = ( y2 - y1 ) / ( x2 - x1 )

m = ( 1 - 5.2 ) / ( -1.5 - 0 )

m = -4.2 / -1.5

m = 2.8

then

y - y1 = m ( x - x1 )

y - 5.2 = 2.8 ( x - 0 )

y - 5.2 = 2.8x - 0

y = 2.8x + 5.2

Answer:

8

Step-by-step explanation:

Answer:

Ask your teacher to explain it. I think that the answer is one hundred and thirty-two dollars.

Step-by-step explanation:

The simple interest  follows this formula:

I = C x r% x t

– C would be the capital; the money that is provided (in this case, $1600)

– r would be the rate, which could be annual, monthly, etc. In this scenario, it's  not specified. Therefore, we assume that it's annual as the time is given in years. (It would be equal to 2,75, but don't forget about the percent symbol %, which is equal to 1/100)

– Finally, t stands for time.

Remember that both time and rate must be in the same measurement (annual, monthly, etc).

You multiple everything, and the result is $132

Answer:

Royce took out a 3 year loan to purchase a car at 4.5% simple interest. If he pays $405 in interest, how much principal did he borrow?

Answer:

Solution here,

Principal=?

Time =3 year

Rate of percent= 4.5

SIMPLE intrest=$405

Now

Principal=(SIMPLE INTREST × 100)/(TIME × RATE)

=$40500/13.5

=$3000

Answer: I believe he is wrong because when I had to do this it was (a+b)(a+b)-ab

Answer: u < 6

Step-by-step explanation: 2 + u < 8

u < (8-2)

u < 6

Answer:$1375 in interest and $6875 total.

Step-by-step explanation:

Explanation:

We're given that

Note that P(A)*P(B) = 0.53*0.17 = 0.0901 which is somewhat similar to 0.901 but not entirely the same. We have an extra zero between the decimal point and the nine. So this indicates that [tex]P(A)*P(B) \ne P(\text{A and B})[/tex]. Therefore, events A and B are not independent. We consider them dependent.

Answer:

[tex]y=-\frac{1}{3}x-4[/tex]

Step-by-step explanation:

To find the slope perpendicular to this, take the negative reciprocal of the slope. Basically, invert both the fraction and the negative/positive so that 3 becomes -1/3.

Now, using the new slope and the given point, we can find the y-intercept. Plug the 3 known variables into the equation:

[tex]y=mx+b\\-7=(-\frac{1}{3})(9)+b[/tex]

Then, solve for b:

[tex]-7=-3+b\\-4=b\\b=-4\\[/tex]

Finally, with both the slope and the y-intercept, you can write the equation of the line:

[tex]y=-\frac{1}{3}x-4[/tex]

Answer:

Equation in slope intercept form: y = -2x -1

Step-by-step explanation:

First you must convert this equation from standard form to slope intercept form (y=mx+b).

Subtract 6x on both sides to get 3y = -6x - 3. Then divide by 3 on both sides to get y = -2x - 1.

Now to graph:

First we will plot the y-intercept, which will be (0,-1). The point will be on the y-axis, since that's the point in which the line will cross.

Next we will go down 2 units and over to the right 1 unit, until we get to the next point.

(Picture is attached above for your convenience⤴⤴⤴)

Hope this helps you :)

Answer:

Step-by-step explanation:

Wind, friction and terrain (flat versus hilly) all oppose motion of the bike.  Air resistance increases as the bicyclist goes faster (there's none at 0 mph, a significant amount at 30 mph, a greater amount at 40 mph, and so on).

Answer:

  A.  Function 1

Step-by-step explanation:

The slope of Function 2 can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-8 -(-2))/(3 -0) = -6/3

__

The slope of function 1 can be found by comparing the equation to the slope-intercept equation for a line:

  y = mx + b . . . . . . equation with slope m and y-intercept b

The slope of Function 1 is -7/3.

-7/3 is more negative than -6/3, so Function 1 has the more negative slope.

Using compound interest, it is found that he must invest $45,225 now.

Compound interest:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In this problem:

Then:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]1000000 = P\left(1 + \frac{0.069}{12}\right)^{12(45)}[/tex]

[tex]P = \frac{1000000}{(1.00575)^{540}}[/tex]

[tex]P = 45225[/tex]

He must invest $45,225 now.

To learn more about compound interest, you can take a look at https://brainly.com/question/25781328

Answer:

He must invest $45,225

Answer:

h(t) = -16t2 + 184t + 18

at the ground h = 0

hence;  -16t2 + 184t + 18 = 0  

solving this quadratic equation using the quadratic formula ; a = -16, b = 184, c = 18 ; x = (-b +-(b2 - 4ac)1/2)/2a

gives t = 11.597 seconds and rounded to the nearest tenth, t = 11.6 (note that the negative root has no practical significance)

Step-by-step explanation:

Step-by-step explanation:

Start by multiplying both sides by cosα:

1 + sinα + (cos²α)/(1+sinα) = 2

sinα + (cos²α)/(1+sinα) = 1

Now multiply both sides by 1+sinα:

sinα + sin²α + cos²α = 1 + sinα

sin²α + cos²α = 1 Q.E.D.

Thats the answer and method i used

Answer: 1:15pm

Step-by-step explanation:

Answer:

A)

Step-by-step explanation: