1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dmitrij [34]
2 years ago
11

guys it's really important I'm begging you to answer as many as possible!!!!! it's a practice paper due tomorrow please answer a

s much as you can!​

Mathematics
1 answer:
alexira [117]2 years ago
3 0

Step-by-step explanation:

5b.

P (6, -1), Q (1, 3), R (x, 8)

the distance between points is found via Pythagoras for right-angled triangles, as the distance is the Hypotenuse c, and the coordinate differences of x and y are the "legs".

for PQ

c² = (6-1)² + (-1 - 3)² = 5² + (-4)² = 25 + 16 = 41

now we need find the x, so that we get 41 as the square of the distance for QR

41 = (1-x)² + (3-8)² = (1-x)² + (-5)² = (1-x)² + 25

aha ! the 41 and 25 terms are the same as above.

that means (1-x)² must be equal to 16.

=>

1-x = 4 => x = -3

or

1-x = -4 => x = 5

so, R could be either (-3, 8) or (5, 8).

5c.

(4 + sqrt(7))/(2×sqrt(7) + 5) = a + b×sqrt(7)

let's use the old trick of

(a+b)(a-b) = a² - b²

to get rid of the sqrt(7) in the denominator.

we multiply with

(2×sqrt(7) - 5)/(2×sqrt(7) - 5)

=>

(4 + sqrt(7))×(2×sqrt(7) - 5) / (2×sqrt(7) + 5)×(2×sqrt(7) - 5) =

= (8×sqrt(7) - 20 +2×7 - 5×sqrt(7)) / (4×7 - 25) =

= (3×sqrt(7) - 6) / 3 = sqrt(7) - 2

now, we see

sqrt(7) - 2 = a + b×sqrt(7)

a = the sum of every term without sqrt(7) = -2

b = the sum of all factors of sqrt(7) = 1

6a.

similar triangles.

EBA and DFA are similar triangles due to the parallel baselines and the sharing of the same "legs" and therefore using the same angles.

and that means that all the lengths of lines in one triangle are the result of the lengths of the corresponding lines in the other triangle multiplied by the same factor.

since E is the midpoint of AD, that means this factor is 2 :

AE×2 = AD.

therefore, FA = AB×2 and AB = FA/2

that proves that B is the midpoint of FA.

that also means that L is the midpoint of DF.

and DF = EB×2 or EB = DF/2

as L is the midpoint of DF, it means that LF = DF/2 = EB.

6b.

x - 2/x = 5

i.

let's square everything.

(x - 2/x)² = 25

x² - 2×2x/x + 4/x² = 25

x² - 4 + 4/x² = 25

x² + 4/x² = 29

ii.

let's multiply with (x - 2/x) again.

(x² + 4/x²)×(x - 2/x) = 29×5

x³ - 2x²/x + 4x/x² - 8/x³ = 145

x³ - 2x + 4/x - 8/x³ = 145

x³ - 8/x³ - 2×(x - 2/x) = 145

x³ - 8/x³ - 2×5 = 145

x³ - 8/x³ = 155

6c.

I can't draw here, but let's transform the equations into regular line equations :

2y - x = 8

2y = x + 8

y = (1/2)x + 4

when assuming x = 0 for one point. and y = 0 for a second point we get (0, 4) and (-8, 0)

y - 2x = 1

y = 2x + 1

same trick as above with x = 0 and y = 0 :

(0, 1) and (-1/2, 0). but we could also use x=1 to get an integer as x coordinate for the second point: (1, 3)

7a.

i.

the radius is half the diameter = (18+8)/2 = 13 cm

ii.

the shortest chord through M creates a right-angled triangle with the radius from 0 to the point on the circle, where the chord ends as the Hypotenuse. one leg is M0, which is

13 - 8 = 5 cm

the other leg is half of the length of the chord, as the chord goes up and down of AB.

so,

13² = 5² + x²

169 = 25 + x²

144 = x²

x = 12 cm

so, the whole chord is 2×12 = 24cm long.

7b.

3/(sqrt(6) + sqrt(3)) rationalized is

3×(sqrt(6) - sqrt(3)) / (sqrt(6) + sqrt(3))×(sqrt(6) - sqrt(3))

3×(sqrt(6) - sqrt(3)) / (6 - 3) =

3×(sqrt(6) - sqrt(3)) / 3 = sqrt(6) - sqrt(3)

1/(sqrt(3) + sqrt(2)) rationalized is

(sqrt(3) - sqrt(2)) / (sqrt(3) + sqrt(2))×(sqrt(3) - sqrt(2))

(sqrt(3) - sqrt(2)) / (3 - 2) = sqrt(3) - sqrt(2)

4/(sqrt(6) + sqrt(2)) rationalized is

4×(sqrt(6) - sqrt(2)) / (sqrt(6) + sqrt(2))×(sqrt(6) - sqrt(2))

4×(sqrt(6) - sqrt(2)) / (6 - 2) =

4×(sqrt(6) - sqrt(2)) / 4 = sqrt(6) - sqrt(2)

so, we have in total

sqrt(6) - sqrt(3) + sqrt(3) - sqrt(2) - sqrt(6) + sqrt(2) = 0

the whole expression is eliminating every term and is simply 0.

You might be interested in
7 more than 5 times a number is 122
Luba_88 [7]

Answer:

The number is 23.

Step-by-step explanation:

5n + 7 = 122               Subtract 7 on both sides

     5n = 115                 Isolate the variable by dividing 5 on both sides

        n = 23

<h3><u><em>Hope this helps!!! </em></u></h3><h3><u><em>Please mark this as brainliest!!! </em></u></h3><h3><u><em>Thank You!!! </em></u></h3><h3><u><em>:)</em></u></h3>
4 0
3 years ago
[PICTURE ATTACHED] HEEELLPPP
Natali5045456 [20]
The answer to this question would be 8,4,4
6 0
3 years ago
Read 2 more answers
How many U.S. dollars have the same value as 1 euro?
Natalija [7]

Answer:

1.13 dollars is equivalent to 1 euro

Step-by-step explanation:


7 0
3 years ago
Read 2 more answers
What is the main piece of computer software on which every other piece of software relies?
andrew-mc [135]
The main piece of computer software on which every other piece of software relies is referred to as the "operating system". It is responsible for all the major channels of communication between the software and the hardware. 
6 0
3 years ago
What is the decimal 25/75
Charra [1.4K]

Answer:

0.3

Step-by-step explanation:

1. break it down 25/75

2. the answer 1/3 not the real answer

3.turn decimal form

4.  0.3

3 0
3 years ago
Other questions:
  • Simplify 42 ⋅ 48.<br><br> 416<br> 410<br> 1616<br> 1610
    15·2 answers
  • What is 3/15 in simplest form
    14·1 answer
  • at noon it was -18 °F in Billings MT At the some time it was 32 °F in mesa AZ how much warmer was mesa than billings at noon​
    9·1 answer
  • 4x - 3 = 2x + 7 what would the answer be??
    9·1 answer
  • Math pls help me big time
    11·2 answers
  • Kelly flies a distance of 2,100 miles. the trip takes 4 2/3 hours
    12·1 answer
  • PLEASE HLEP WITH A FREAKING IXL
    7·2 answers
  • 3. Penny's family decided to go to the Splash Park.
    14·1 answer
  • One positive integer is 2 less than twice another. The sum of their squares is 628. Find the integers.
    10·1 answer
  • The path of a ball is modelled by the quadratic function ℎ(t) = −5(t − 2)^2 + 23 where
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!