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Galina-37 [17]
3 years ago
8

Given: ∆ABC, AC = 12, AB = BC = 10 Find: m∠A, m∠C, m∠B

Mathematics
1 answer:
4vir4ik [10]3 years ago
3 0

Answer:

  • m∠A ≈ 53.13°
  • m∠B ≈ 73.74°
  • m∠C ≈ 53.13°

Step-by-step explanation:

An altitude to AC bisects it and creates two congruent right triangles. This lets you find ∠A = ∠C = arccos(6/10) ≈ 53.13°.

Since the sum of angles of a triangle is 180°, ∠B is the supplement of twice this angle, so is about 73.74°.

  m∠A = m∠C ≈ 53.13°

  m∠B ≈ 73.74°

_____

The mnemonic SOH CAH TOA reminds you of the relation between the adjacent side, hypotenuse, and trig function of an angle:

  Cos = Adjacent/Hypotenuse

If the altitude from B bisects AC at X, triangle AXB is a right triangle with side AX adjacent to the angle A, and side AB as the hypotenuse. AX is half of AC, so has length 12/2 = 6, telling you the cosine of angle A is AX/AB = 6/10.

A diagram does not have to be sophisticated to be useful.

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nlexa [21]

Answer:

\frac{8^x}{2^y} = 4096

Step-by-step explanation:

Rules:

  1. \frac{a^m}{a^n}=a^{m-n}
  2. a^m\times a^n= a^{m+n}
  3. (a^m)^n=a^{m\times n}

Given that,

3x-y =12

Therefore

\frac{8^x}{2^y}

=\frac{(2^3)^x}{2^y}  [ since 8=2^3 ]

=\frac{2^{3x}}{2^y}   [ applying 3rd rule]

=2^{3x-y} [ applying 2nd rule]

=2^{12}   [ since 3x-y =12]

=4096

3 0
3 years ago
Solve: 4x - 8 &gt; 32 <br>A) X &lt;10 <br>B)x &gt; -10 <br>C) X &gt; 10 <br>D) X &lt; -10​
larisa [96]

Answer:

C) x > 10

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

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtract Property of Equality

Step-by-step explanation:

<u>Step 1: Define</u>

4x - 8 > 32

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

  1. Add 8 on both sides:                    4x > 40
  2. Divide 4 on both sides:                x > 10

Here we see that any value <em>x</em> greater than 10 would work as a solution to the inequality.

7 0
2 years ago
Right triangle has a shorter leg of 5, a longer leg of 7. What is the length of the hypotenuse? Round to the nearest hundredth.
bagirrra123 [75]
The answer is 8.602
5 0
2 years ago
Given function of f(x) = 2x - 1 and fg(x) = 10x + 3, find the function of g(x)​
denis-greek [22]

Answer:

The function of g(x) = 5x + 2

Step-by-step explanation:

Let us use the composite function to solve the question

∵ f(x) = 2x - 1

∵ f(g(x)) = 10x + 3

→ f(g(x)) means substitute x in f(x) by g(x)

∴ f(g(x)) = 2[g(x)] - 1

→ Equate the two right sides of f(g(x))

∴ 2[g(x)] - 1 = 10x + 3

→ Add 1 to both sides

∴ 2[g(x)] - 1 + 1 = 10x + 3 + 1

∴ 2[g(x)] = 10x + 4

→ Divide each term into both sides by 2

∵ \frac{2[g(x)]}{2} = \frac{10x}{2} + \frac{4}{2}

∴ g(x) = 5x + 2

∴ The function of g(x) = 5x + 2

7 0
2 years ago
Dx+hy=j   what does x=
DerKrebs [107]
dx+hy=j\\\\dx=j-hy\ /:d\ \ \ \ and\ \ \ \ d \neq 0\\\\x= \frac{j-hy}{d}
3 0
3 years ago
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