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kaheart [24]
3 years ago
8

Analyze the diagram below and complete the instructions that follow.

Mathematics
1 answer:
valentinak56 [21]3 years ago
4 0

Answer:

x = 6

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

<u>Algebra I</u>

  • Terms/Coefficients/Degrees
  • Expand by FOIL (First Outside Inside Last)
  • Factoring
  • Multiple Roots

<u>Trigonometry</u>

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

  • a is a leg
  • b is another leg
  • c is the hypotenuse

Step-by-step explanation:

<u>Step 1: Identify</u>

<em>a</em> = x + 3

<em>b</em> = x

<em>c</em> = √117

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

  1. Substitute [PT]:                                                                                                (x + 3)² + x² = (√117)²
  2. Expand [FOIL]:                                                                                                 x² + 6x + 9 + x² = (√117)²
  3. Combine like terms:                                                                                       2x² + 6x + 9 = (√117)²
  4. Exponents:                                                                                                      2x² + 6x + 9 = 117
  5. [SPE] Subtract 117 on both sides:                                                                    2x² + 6x - 108 = 0
  6. Factor out GCF:                                                                                               2(x² + 3x - 54) = 0
  7. [DPE] Divide 2 on both sides:                                                                         x² + 3x - 54 = 0
  8. Factor Quadratic:                                                                                            (x - 6)(x + 9) = 0
  9. Solve roots/solve <em>x</em>:                                                                                         x = -9, 6

Since we are dealing with positive values, we can disregard the negative root.

∴ x = 6

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What is m/jsm? (Show Work)
Pie

m<SMJ + m<SME = 180° <em>(Linear pair) ⇒ </em>m<SMJ + 59° = 180°  ⇒ m<SMJ = 121°

m<MJS ≅ m<EJA: <E + <A + <J = 180° ⇒ 90° + 48° + <J = 180°  ⇒ <J = 42°

<u>m<JSM + m<SMJ + m<MJS = 180°  </u><u><em> (Triangle sum) </em></u>

m<JSM  + 121° + 42° = 180°

m<JSM  + 163° = 180°

m<JSM  = 17°

Answer: 17°

6 0
2 years ago
Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 7.0% per year.
fredd [130]

Answer:

The number of years it would take is  n  =  2 \ years

Step-by-step explanation:

From the question we are told that

         The earning per share  is  P = $3.50

          The growth rate is  r  =  7.0%

           The duration is t =  5 \ years

Generally the future value is mathematically represented as

          A =  P(1 + \frac{r}{100} )^n

 Where P is the present value

              n is the time period

         A is the future value which is mathematically evaluated as

               A =  3 * P

substituting value

            A =  3 * 3.50

            A = $ 10.5 0

So

      A =  P(1 + \frac{r}{100} )^n

       10.5 =  3.5(1 + \frac{7}{100} )^n

       10.5 = 3.225^n

Taking log of both sides

       log 10.5 = nlog 3.225

        1.0212 = n(0.5085)

         n  =   \frac{1.0212}{(0.5085)}

         n  =  2 \ years

     

4 0
3 years ago
Which expressions are equivalent to 4(x+1) + 7(x+3)? Select two answers.
Natalija [7]

Answer:

9(x+3) + 2(x+3) or 10(x+2) +(x+5)

Step-by-step explanation:

First you want to distribute the equation.

4(x+1) + 7(x+3) multiplied out is

4x + 4 + 7x + 21

Now we add like terms so it comes out to

11x + 25

Two expressions that can come out to equal 11x + 25 is. 9(x+3) + 2(x+3) or 10(x+2) +(x+5)

7 0
3 years ago
Translate the phrase into an expression: 11 more than one third of a number
skelet666 [1.2K]
1/3x+11.
1/3 of a number can be shown as 1/3x, since the number is not identified.

We can represent 11 more as +11.
This, our expression is 1/3x+11

Hope this helps!
5 0
2 years ago
The polynomial is missing the coefficient of the third and last terms.
bulgar [2K]

In order to divide polynomials using synthetic division, you must be dividing by a linear expression and the leading coefficient (first number) must be a 1. For example, you can use synthetic division to divide by x + 3 or x – 6, but you cannot use synthetic division to divide by x2 + 2 or 3x2 – x + 7. If the leading coefficient is not a 1, then you must divide by the leading coefficient to turn the leading coefficient into a 1. For example, 3x – 1 would becomex minus 1/3 and 2x + 7 would becomex plus 7/2. If synthetic division will not work, then you must use long division.

8 0
2 years ago
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