Quadrilateral ABCD is shown. Two students each perform a different reflection on the original figure.

Use the drop-down menus to give the coordinates of point B' after each reflection.

Answer: D.  5.3 m

Step-by-step explanation:

The ladder leaning against the wall causes it to forma  right angle.  

The right angle has two sides , which is  the two legs, and the hypotenuse.

Using the formula a^2 + b^2 = c^2 , a  and b are the two legs and c is the hypotenuse. In this case, a will be the wall, b will be 1.5 m  and the ladder which is 5.5 m will be the hypotenuse.  

Input the values for a and c to sole for b using the formula.

1.5^2 + b^2 = 5.5^2

2.25 + b^2 = 30.25

-2.25                 -2.25

   b^2 = 28

   b = [tex]\sqrt{28}[/tex]

  b = 5.2915   rounded to one decimal place is the same as rounding it to the nearest tenth, and 5.29 rounded to the nearest tenth is 5.3.

Height of top of ladder above the ground  that is resting on the wall, correct to one decimal place is 5.3 m

hence option D is correct.

According to Pythagoras theorem

In a right triangle

[tex]\rm H^2 = P^2 + B^2[/tex]

[tex]\rm P = \sqrt {H^2 - B^2 }.........(1)\\where \\H = Hypotenuse \; of \; right\; triangle\\B = Base\; of \; the \; right\; triangle \\P = Perpendicular \; of \; the\; right\; triangle[/tex]

In the given situation the the ladder forms the right triangle with the wall

Length of the ladder = 5.5 m

Length of the base of ladder from the wall = 1.5 m

Let K be the height of top of ladder above the ground  that is resting on the wall.

Hence  from equation (1) we can write

[tex]\rm K = \sqrt{5.5^2 - 1.5^2} = \sqrt{28} = 5.291 \approx \bold{5.3}[/tex]  m

Height of top of ladder above the ground  that is resting on the wall, correct to one decimal place is 5.3 m

hence option D is correct.

For more information please refer to the link given below

https://brainly.com/question/16426393

9514 1404 393

Answer:

  a.  270 miles

Step-by-step explanation:

In 3/4 of an hour, the plane will fly 3/4 of 360 miles, so 270 miles.

Answer:

20 (D)

Step-by-step explanation:

2.5 miles in 1/8 of a mile

so multiply by 8 to get 1 hour

2.5 * 8 = 20

Answer:

Polly=30

Andy=60

Phoebe=180

Step-by-step explanation:

Polly=x

Andy=2x

Phoeby 3(2x)=6x

x+2x+6x=270

9x=270

x=30

Polly=x=30

Andy = 2x=60

Phoebe=6x=180

Answer:

-9 is real, 9i is imaginary, C

Step-by-step explanation:

-9 is real because you can literally draw nine things.

9i is imaginary because i is √-1 and square roots of negatives are imaginary.

It is complex because complex expressios are written as a+bi.

Answer:

n<-0.6

Step-by-step explanation:

7.2>0.9(n+8.6)

8>n+8.6

-0.6>n

n<-0.6

So there would be an open circle at the point -0.6 (because the "less than" sign shows that -0.6 is not included), and then an arrow pointing left to show solutions that are less than -0.6

I will assume you know what buttons to press.

Answer:

Step-by-step explanation:

7.2>0.9(n+8.6)

n< -0.6

(-∞,-0.6)

open circle on -0.6 and go to the left

Answer:

4

Step-by-step explanation:

PLZ MARK BRAINLIEST

Answer:

y=1.5x

Step-by-step explanation:

3/2=1.5

9/6=1.5

Answer:

(-7. -8) Just flip the signs.

Answer:

[tex]\boxed {\boxed {\sf (-8,-7)}}[/tex]

Step-by-step explanation:

When a point is reflected over y=-x, the following change occurs:

[tex](x,y)[/tex]    ⇒  [tex](-y, -x)[/tex]

We are given the point (7,8).

Essentially, we change the signs for both coordinates, then flip the x-coordinate and y-coordinate.

1. Change the signs

[tex](7,8)[/tex]    ⇒    [tex](-7,-8)[/tex]

2. Flip the x and y coordinates

[tex](-7,-8)[/tex]   ⇒    [tex](-8,-7)[/tex]

So the image of (7,8) after a reflection over y=-x is (-8,-7)

Answer:

y= -40

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

Answer:

4.702 does not represent 4.701

Step-by-step explanation:

#teamtrees #WAP (Water And Plant)

Answer:

WHAT ARE THE NUMBERS?

Step-by-step explanation:

YOU DIDNT WRITE THEM

Answer:

I'm not sure but maybe this will help

Step-by-step explanation:

- 3 and 3 are located on opposite sides of zero. They are the same distance from zero. 3 and -3 are called opposites.

Answer: 2/5

Step-by-step explanation:

Answer:

Here is the answer.

Step-by-step explanation:

Answer:

90$

Step-by-step explanation

Step 1: You need to find how much was the 60% discount

Step 2: To find that multiply .6 by 50 you will get 30

Now you know how much was 60% discount

Step 3: Add   30(the discount) + 50(the prce sally pays) = 90 (the oriagnal price)

Answer:

-4/3

Step-by-step explanation:

I think :\

I like ice cream :D

Answer:

-4/3

Step-by-step explanation:

We can use the slope formula

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

    = ( -4-8)/(8 - -1)

    = ( -4-8)/(8+1)

    = -12/9

   = -4/3

Answer: the answer wwas c

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

$8.75 per book

Step-by-step explanation:

26.25/3 = 8.75

Answer:

$8.75

Step-by-step explanation:

26.25 divided by 3 = 8.75

Answer:

x= -9

Step-by-step explanation:

=-9 hope this helped.

Answer:

A.

Step-by-step explanation:

It just is trust

Answer:

a is 840 ,b is 525

Step-by-step explanation:

At the end of each year, its value is down to 79%, which is 0.79 times its value at the start of the year.  Keep this up for n years and the value is

V(n) = $20,000 (0.79)n,

where n is the number of years elapsed from when the value was $20,000.  Just plug in n=5 and n=8, evaluate, and get your 2 answers.

Answer:

A. 5 years

Step-by-step explanation:

21% of 20,000 is 4200, mutiply that by 5 and get $20,000

Answer:

y ≥ 3x-1

x+3y ≤ 6

Step-by-step explanation:

Answer:

16x^2-25y^2/400

Step-by-step explanation:

The 16 and 25 are grouped and both over the 400. I really hope this helps pls consider giving brainliest I would really appreciate it.

Answer:

1. y < 4

2. x </= -3

3. y >/= 2

4. x > -2

5. x </= 2

6. x < 0

7. t > -2

8. N >/= 3

9. n < -4

10. x < 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

α and β are the roots of the equation:

Sum of the roots is:

Product of the roots is:

Solving the following expressions:

(i)

----------------

(ii)

[tex] \huge \underline{\tt Question} :[/tex]

If α and β are the roots of the equation ax² + bx + c = 0, where a, b and c are constants such that a ≠ 0, find in terms of a, b and c expressions for :

[tex] \\ [/tex]

[tex] \huge \underline{\tt Answer} :[/tex]

[tex] \\ [/tex]

[tex] \huge \underline{\tt Explanation} :[/tex]

As, α and β are the roots of the equation ax² + bx + c = 0

We know that :

[tex] \tt : \implies \alpha + \beta = \dfrac{-b}{a}[/tex]

and

[tex] \tt : \implies \alpha\beta = \dfrac{c}{a}[/tex]

[tex] \\ [/tex]

Now, let's solve given values :

[tex] \bf \: \: \: \: 1. \: \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2}[/tex]

[tex] \tt : \implies \dfrac{\beta ^2 + \alpha ^2}{\alpha ^2 \beta ^2}[/tex]

[tex] \tt : \implies \dfrac{\alpha ^2 + \beta ^2}{\alpha ^2 \beta ^2}[/tex]

[tex] \\ [/tex]

Now, by using identity :

[tex] \tt : \implies \dfrac{(\alpha + \beta)^2 - 2 \alpha\beta}{(\alpha\beta)^2}[/tex]

[tex] \\ [/tex]

Now, by substituting values of :

[tex] \tt : \implies \dfrac{\Bigg(\dfrac{-b}{a}\Bigg)^2 - 2 \times \dfrac{c}{a}}{\Bigg(\dfrac{c}{a}\Bigg)^2}[/tex]

[tex] \tt : \implies \dfrac{\dfrac{b^2}{a^2} - \dfrac{2c}{a}}{\dfrac{c^2}{a^2}}[/tex]

[tex]\tt : \implies \dfrac{\dfrac{b^2}{a^2} - \dfrac{2ac}{a^{2} }}{\dfrac{c^2}{a^2}}[/tex]

[tex]\tt : \implies \dfrac{\dfrac{b^2 - 2ac}{a^2 }}{\dfrac{c^2}{a^2}}[/tex]

[tex]\tt : \implies \dfrac{b^2 - 2ac}{\cancel{a^2} } \times \dfrac{ \cancel{a^2}}{c^2}[/tex]

[tex]\tt : \implies \dfrac{b^2 - 2ac}{c^2 }[/tex]

[tex] \\ [/tex]

[tex] \underline{\bf Hence, \: \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2} = \dfrac{b^2 - 2ac}{c^2 }}[/tex]

[tex] \\ [/tex]

[tex] \bf \: \: \: \: 2. \: \alpha ^3 + \beta ^3 [/tex]

[tex] \\ [/tex]

By using identity :

[tex] \tt : \implies (\alpha + \beta)(\alpha ^2 - \alpha\beta + \beta ^2)[/tex]

[tex] \tt : \implies (\alpha + \beta)(\alpha ^2 + \beta ^2 - \alpha\beta)[/tex]

[tex] \\ [/tex]

By using identity :

[tex] \tt : \implies (\alpha + \beta)(\alpha + \beta)^2 -2 \alpha\beta - \alpha\beta)[/tex]

[tex] \tt : \implies (\alpha + \beta)((\alpha + \beta)^2 -3 \alpha\beta)[/tex]

[tex] \\ [/tex]

Now, by substituting values of :

[tex] \tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg( \bigg(\dfrac{-b}{a} \bigg)^2 -3 \times \dfrac{c}{a}\Bigg)[/tex]

[tex] \tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2}{a^2} - \dfrac{3c}{a}\Bigg)[/tex]

[tex]\tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2}{a^2} - \dfrac{3ac}{a^{2} }\Bigg)[/tex]

[tex]\tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2 - 3ac}{a^2} \Bigg)[/tex]

[tex]\tt : \implies \dfrac{-b}{a} \times \dfrac{b^2 - 3ac}{a^2} [/tex]

[tex]\tt : \implies \dfrac{ - b(b^2 - 3ac)}{a \times a^2} [/tex]

[tex]\tt : \implies \dfrac{ - b^3 + 3abc}{a^3} [/tex]

[tex] \\ [/tex]

[tex] \underline{\bf Hence, \: \alpha ^3 + \beta ^3 = \dfrac{ - b^3 + 3abc}{a^3}}[/tex]

Answer:

Step-by-step explanation:

you could distribute and combine like terms

y=(x+4)2+8

y=2x+8+8

y=2x+16

Answer:

line t = -9/8

Step-by-step explanation:

Parallel lines have the same slope, so line t will have a slope of -9/8 as well