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leonid [27]
3 years ago
6

a square is put together by two triangles. the hypotenuse is 11 cm and width if 8 cm. find the height of the triangle.

Mathematics
1 answer:
maksim [4K]3 years ago
3 0

Answer:

b ≈ 7.54 cm

Step-by-step explanation:

Pythagorean Theorem

a² + b² = c²

a and b are the sides and c is the hypotenuse

hypotenuse is 11 cm

a side is 8 cm

so

8² + b² = 11²

64 + b² = 121

-64           -64

       b² =  57

    √b² =  √57

       b ≈ 7.54 cm ( use ≈ because its rounded so its not exact)

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Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution? y = x+1 1 X+ 3 2.
Troyanec [42]

Answer:

D. (4, 5)

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Algebra I</u>

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Step-by-step explanation:

<u>Step 1: Define systems</u>

y = x + 1

y = 1/2x + 3

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

  1. Substitute in <em>y</em>:                              x + 1 = 1/2x + 3
  2. Subtract 1/2x on both sides:        1/2x + 1 = 3
  3. Subtract 1 on both sides:              1/2x = 2
  4. Divide both sides by 1/2:              x = 4

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Define original equation:                   y = x + 1
  2. Substitute in <em>x</em>:                                    y = 4 + 1
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<em>We can confirm our answer.</em>

8 0
3 years ago
I need help!!
Natasha2012 [34]

Answer:

The exact solution is

x = \frac{Ln(60)}{7*Ln(5)}

And the approximation to three decimal places is:

x = 0.363

Step-by-step explanation:

Here we have the equation:

5^{7*x} = 60\\

Now we can remember a property of the natural logarithm function:

Ln(a^n) = n*Ln(a)

Now we can apply the Ln( ) function to both sides of that equation to get:

Ln(5^{7*x}) = Ln(60)

Then we get:

7*x*Ln(5) = Ln(60)

Solving that for x we get:

x = \frac{Ln(60)}{7*Ln(5)}  = 0.363

So the exact solution is:

x = \frac{Ln(60)}{7*Ln(5)}

And the approximation to three decimal places is:

x = 0.363

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