Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
DAC
A
Statements
Reasons
00
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
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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

Answer: the answer wwas c

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

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:

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

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:

A.

Step-by-step explanation:

It just is trust

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 ≥ 3x-1

x+3y ≤ 6

Step-by-step explanation:

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:

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:

x= -9

Step-by-step explanation:

=-9 hope this helped.

Answer:

4.5

Step-by-step explanation:

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:

B) 15/8

Step-by-step explanation:

Use the SOH-CAH-TOA acronym:

• SOH: Sin(θ) = Opposite / Hypotenuse

• CAH: Cos(θ) = Adjacent / Hypotenuse

• TOA: Tan(θ) = Opposite / Adjacent

Tangent of A would be "opposite" over "adjacent". The side of the triangle opposite angle A would be 15, and the side adjacent to angle A would be 8 -- the value of tan(A) is 15/8.

Tan(A) cannot be 15/7, because 7 is the hypotenuse. Remember that the hypotenuse of a right triangle is the side opposite the 90° angle -- here, angle B is the 90° angle.

Answer: 2/5

Step-by-step explanation:

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:

-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:

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:

$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:

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:

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:

-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.

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:

y= -40

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:

Here is the answer.

Step-by-step explanation:

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: