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Nezavi [6.7K]
2 years ago
12

Solve the equation algebraically. Calculus section 1.5 of textbook 2^x + 2^-x = 5

Mathematics
1 answer:
natulia [17]2 years ago
8 0

The value of x from the given expression is \frac{5+\sqrt{29}}{2log2} \\

<h3>Solving quadratic expression</h3>

Given the algebraic expression below;

2^x + 2^-x = 5

This can also be expressed as:

1/2^x+ 1/2^x = 5

Let P = 2^x, such that;

P + 1/P = 5

P²-1/P = 5

P²-1 = 5P

P²-5P-1=0

On factrorizing, then;

P = \frac{5+\sqrt{29}}{2} \\

Since 2^x = P, then;

2^x=\frac{5+\sqrt{29}}{2} \\\\xlog2=\frac{5+\sqrt{29}}{2} \\\\x=\frac{5+\sqrt{29}}{2log2} \\

Hence the value of x from the given expression is \frac{5+\sqrt{29}}{2log2} \\

Learn more on algebraic equation here: brainly.com/question/723406

#SPJ1

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Prove triangle AOC is congruent to triangle BOD​
marta [7]

Step-by-step explanation:

We are given two Triangles and we need to prove them congruent . In ∆AOC and ∆BOD , we have

\to AC = BD ( given ) \\\\\to OD = OA \\\\\to \angle CAO =\angle BDO (Since\ BD || AC )

Therefore by AAS congruent condition we can say that ,

\implies\red{ \triangle AOC \cong \triangle BOD }

Hence Proved!

8 0
3 years ago
Anyone want to help me with this? I will mark brainliest and thanks
Degger [83]

Answer:

x = -8

m∠BDC = 68°

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Geometry</u>

  • Definition of a Line: A line is 180°

Step-by-step explanation:

<u>Step 1: Set up Equation</u>

m∠BDC + m∠CDA = 180°

(-7x + 12)° + (-8x + 48)° = 180°

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Combine like terms:                    -15x + 60 = 180
  2. Isolate <em>x</em> term:                              -15x = 120
  3. Isolate <em>x</em>:                                       x = -8

<u>Step 3: Find m∠BDC</u>

  1. Define:                    m∠BDC = (-7x + 12)°
  2. Substitute in <em>x</em>:       m∠BDC = (-7(-8) + 12)°
  3. Multiply:                  m∠BDC = (56 + 12)°
  4. Add:                        m∠BDC = 68°
6 0
3 years ago
Liz walks 1/2 mile in 20 minutes on Monday and 3 3/4 in 150 minutes on Sunday is this proportional or non -proportional
ratelena [41]

Answer:

non proportional

Step-by-step explanation:

1/2 doesnt go into 3/4 and 20 doesnt go into 150

4 0
3 years ago
Read 2 more answers
Find a focus for this conic section. 9x^2+25y^2-200y+175=0
Katena32 [7]
First of all we have to figure out what type of a conic this is.  We know it's not a parabola because it has both an x-squared term and a y-squared term.  There's a plus sign separating the squared terms so we know it also cannot be a hyperbola.  It's either a circle or an ellipse.  If this was simply a circle, though, we would not have leading coefficients on the squared terms (other than a 1).  Circles have a standard form of (x-h)^2+(y-k)^2=r^2.  That makes this an ellipse. Let's group together the x terms and the y terms and move the constant over and complete the squares to see what we have.  9x^2+25y^2-200y=-175.  Since there's only 1 term with the x squared expression we cannot complete the square on the x's but we can on the y terms.  First, though, the rule for completing the square is that the leading coefficient has to be a 1 and ours is a 25, so let's factor it out. 9x^2+25(y^2-8y)=-175.  To complete the square we take half the linear term, square it, and add it to both sides.  Our linear term is 8.  Half of 8 is 4, and 4 squared is 16. So we add a 16 into the parenthesis, BUT we cannot disregard that 26 sitting out front there.  It refuses to be ignored.  It is still considered a multiplier.  So what we are really adding on to the right side is 25*16 which is 400.  9x^2+25(y^2-8y+16)=-175+400 which simplifies to 9x^2+25(y^2-8y+16)=225.  The standard form of an ellipse is \frac{(x-h)^2}{a^2}+ \frac{(y-k)^2}{b^2} =1 if its horizontal axis is the transverse axis, or \frac{(x-h)^2}{b^2}+ \frac{(y-k)^2}{a^2}=1 if its vertical axis is the transverse axis.  Notice that the a and b moved as the difference between the 2 equations.  A is always the larger value and dictates which ellipse you have, horizontal or vertical.  Our equation has a 225 on the right, so we will divide both sides by 225 to get that much-needed 1 on the right: \frac{x^2}{25}+ \frac{(y-4)^2}{9}=1.  Because 25 is larger than 9, this is a horizontal ellipse, our a value is the square root of 25 which is 5, and our b value is the square root of 9 which is 3.  The center is (0, 4).  You want the focus and now we can find it.  The formula for the focus is c^2=a^2-b^2 where c is the distance from the center to the focus.  We have an a and a b to find c: c^2=25-9, which gives us that c=4.  The focus is 4 units from the center and always lies on the transverse axis.  It shares a y value with the center and moves from the x-coordinate of the center the value of c.  Our center is (0, 4) so our y value of the focus is 4; our x coordinate of the center is 0, so the x value of the focus is 4.  The coordinates of the focus are (4, 4).
8 0
3 years ago
3/8 x 8/9 = to in simplest form<br><br><br> 50 POINTS PLEASE ANSWER
SpyIntel [72]
24/72 which simplifies to 12/36 which then simplifies to 6/18 which then also simplifies to 3/9 then also simplifies to 1/3.
6 0
3 years ago
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