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tatuchka [14]
2 years ago
5

For what values of x is x2-36=5x true?

Mathematics
2 answers:
Inessa05 [86]2 years ago
6 0

Answer:

X = -12

Step-by-step explanation:

x2-36=5x

take away 2x from both sides

-36=3x

divide both sides by 3

X = -12

katrin2010 [14]2 years ago
3 0

Answer:

x=-12

Step-by-step explanation:

x2-36=5x

add 36 to both sides

x2=5x+36

subtract 5x from both sides

x(-3)=36

divide both sides by -3

x=-12

substitute to prove right

(-12)2-36=5(-12)

-24-36=-60

-60=-60

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Answer:

4/35 lottery is easier to win.

Step-by-step explanation:

For the 5/48 lottery, the winning probability is \frac{5}{48} ≈0.1042

For the 4/35 lottery, the winning probability is \frac{4}{35} ≈ 0.1143

Since \frac{4}{35}  >  \frac{5}{48} , the lottery where one chooses 4 of the numbers 1 through 35 is easier to win.

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Subject : Maths<br> Level : High school<br> Topic : Surds<br> Points : 72
Mila [183]

Answer:

  • a = 5

Step-by-step explanation:

<u>Simplify:</u>

  • √5(√8 + √18) =
  • √5*8 + √5*18 =
  • √40 + √90 =
  • √4*10 + √9*10 =
  • 2√10 + 3√10 =
  • (2 + 3)√10 =
  • 5√10

<u>The value of a:</u>

  • a√10 = 5√10
  • a = 5
6 0
3 years ago
Systems of equations substitution y=8 y=x+1
klemol [59]
(8) = x +1

same thing as 8 = 1x

divide both sides by 1 and x = 8 Y= 8
6 0
3 years ago
2. Consider the circle x^2−4x+y^2+10y+13=0. There are two lines tangent to this circle having a slope of 2/3.
likoan [24]

Answer:

a) The coordinates are (0.431, -2.646) and (3.568,-7.354)

b) The tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

Step-by-step explanation:

First, lets complete squares, by taking for each cordinate the square of a linear expression

0= x²−4x+y²+10y+13 = (x-2)²+ 4  + (y+5)²-25+13 = (x-2)²+(y+5)² - 8

Hence (x-2)² + (y+5)² = 8

Lets put y in function of x. We should obtain 2 functions f and g that represent the circle.

(y+5)² = 8 - (x-2)² = -x² + 4x + 4

y = ^+_- \sqrt{-x^2+4x+4} -5

Thus

f(x) = \sqrt{-x^2+4x+4} - 5

g(x) = -\sqrt{-x^2+4x+4} - 5

Lets find the derivate of each function and the points in which they reach the value 2/3. In those points the tangent line will have a slope of 2/3.

We may just find the values of x which the derivate of f is either 2/3 or -2/3.

\frac{-x+2}{\sqrt{-x^2+4x+4}} = ^+_-\frac{2}{3} \Leftrightarrow \frac{x^2-4x+4}{-x^2+4x+4} = \frac{4}{9} \Leftrightarrow 9(x^2-4x+4) = 4(-x^2+4x+4) \\\Leftrightarrow 13x^2-52x+20 = 0

The quadratic has roots

\frac{52 ^+_-\sqrt{1664}}{26}

one root is 3.568, which corresponds with g, and the other root is 0.431, corresponding to f.

Also g(3.568) = - 7.354 and f(0.431) = -2.646

This means that the coordinates are (0.431 , -2.646), (3.568 , -7.354) and the tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

5 0
2 years ago
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