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4 years ago

Use the quadratic formula to solve for the roots of the following equation. x 2 – 4x + 13 = 0

1 answer:

3 0

4±√(−4)2−4⋅(1⋅−13)2⋅1
x=4±2√172⋅1x421721Simplify the denominator.Tap for more steps...x=4±2√172x42172Simplify 4±2√17242172.x=2±√17

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WHAT IS X³-27 SIMPLIFIED

Eduardwww [97]

Answer:

It is (x - 3)³ - 9x(3 - x)

Step-by-step explanation:

Express 27 in terms of cubes, 27 = 3³:

$= {x}^{3} - {3}^{3}$

From trinomial expansion:

${(x - y)}^{3} = (x - y)(x - y)(x - y) \\$

open first two brackets to get a quadratic equation:

${(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)$

expand further:

${(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}$

take y to be 3, then substitute:

$( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)$

5 0

3 years ago

Surface area helpp needed

Firlakuza [10]

Answer:

144 un²

Step-by-step explanation:

Front Parallelogram = 5 x 11 = 55

Two triangles = 3 x 4 = 12

Back Parallelogram = 3 x 11 = 33

Bottom rectangle = 4 x 11 = 44

Total =

55 + 12 + 33 + 44 = 144

units = un²

144 un²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

5 0

3 years ago

An arithmetic sequence is defined by the general term tn = -5 + (n - 1)78, where n ∈N and n ≥ 1. What is the recursive formula o

Gnoma [55]

Answer:

Step-by-step explanation:

In general for arithmetic sequences, recursive formulas are of the form

aₙ = aₙ₋₁ + d,

and the explicit formula (like tₙ in your problem), are of the form

aₙ = a₁ + (n - 1)d,

where d is the common difference. So converting between the two of these isn't so bad. In this case, your problem wants you to have an idea of what t₁ is (well, every answer says it's -5, so there you are) and what tₙ₊₁ is. Using the formulas above and your given tₙ = -5 + (n - 1)78, we can see that the common difference is 78, so no matter what we get ourselves into, the constant being added on at the end should be 78. That automatically throws out answer choice D.

But to narrow it down between the rest of them, you want to use the general form for the recursive formula and substitute (n + 1) for every instance of n. This will let you find tₙ₊₁ to match the requirements of your answer choices. So

tₙ₊₁ = t₍ₙ₊₁₎₋₁ + d ... Simplify the subscript

tₙ₊₁ = tₙ + d

Therefore, your formula for tₙ₊₁ = tₙ + 78, which is answer choice C.

6 0

3 years ago

Read 2 more answers

in a marathon race (42.195 km), the winner’s time is 2 hours, 13 minutes, and 9 seconds, while the second-place time is 2 hours,

algol [13]

in a marathon race (42.195 km), the winner’s time is 2 hours, 13 minutes, and 9 seconds, while the second-place time is 2 hours, 26 minutes, and 6 seconds . The distance is 2.664 km.

D = distance of marathon = 42.195 km = 42195 m

tw = time taken by winner = 2 h 17 min = 2 (60) + 17 = 137 min = 137 (60) = 8220 sec

Vw = speed of winner

speed of winner is given as

Vw = D /tw = 42195/8220

ts = time taken by second place = 2 h 26 min 14 sec = 2 (60)(60) + (26)(60) + 14 = 8774 s

Vs = speed of second place

speed of second place is given as

Vs = D /ts = 42195/8774

distance of the second place holder from the finish line is given as

D' = Vs (ts - tw)

D' = (42195/8774 )(8774 - 8220)

D' = 2664.24 m

D'= 2.664 km

To learn more about distance visit:brainly.com/question/15172156

#SPJ4

7 0

1 year ago

Aaron is reading a graph of equivalent ratios. If one of the ratios is represented as (6, 2), which could be another ratio?

evablogger [386]

There Are Unlimited Equivalent Ratios To This! For One, We Could Simplify This Ratio To 3,1.Another One Would Be 12,4. You See, It Can Be Any Ratio As Long As It Equals(Simplified) To 3/1. I Hope This Helps!

6 0

3 years ago

Read 2 more answers