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Otrada [13]
2 years ago
14

I need #1 done (show work) will give brainliest

Mathematics
1 answer:
allochka39001 [22]2 years ago
6 0

Step-by-step explanation:

<u>Statement                                                        Reason                               </u>

∠5 and ∠7 are vertical angles                        Vertical angles theorem

m∠5 = m∠7                                                      Definition of vertical angles

m∠5 = -2(3x - 4), m∠7 = 3(x - 3) - 1                  Given

-2(3x - 4) = 3(x - 3) - 1                                       Substitution property of equality

-6x + 8 = 3x - 9 - 1                                            Distributive property

3x + 6x = 8 + 10                                               Addition property

9x = 18                                                              Addition property

x = 18/9                                                             Division property

x = 2                                                                  Proved

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If a wheelchair-marathon racer moving at 13.1 miles per hour expends energy at a rate of 645 calories per hour, how much energy
Anna71 [15]

Answer:

1290 calories

Step-by-step explanation:

Given: The racer moves at 13.1 miles per hour expends energy at a rate of 645 calories per hour.

To find: Energy in calories, required to complete a marathon race 26.2 miles at this pace.

Solution: We have,

The racer moves at 13.1 miles per hour.

The racer expends energy at a rate of 645 calories per hour.

So, energy expended while moving 13.1 miles =645 calories.

Now, energy expended while moving 1 mile =\frac{645}{13.1} calories.

So, energy expended while moving 26.2 miles =\frac{645}{13.1}\times 26.2=645\times 2=1290 calories.

Hence, 1290 calories of energy is required to complete a marathon race 26.2 miles at this pace.

6 0
3 years ago
Please help! ! Timed !******
lord [1]

Answer:

(fоg)(x) =  x

Step-by-step explanation:

f(x) = (x-1)/3

g(x)=3x+1

(fоg)(x) = f(g(x)) = ((3x+1)-1) / 3 = 3x / 3 = x

3 0
3 years ago
For the functions f(x) = x^2+ 8x + 2 and g(x) = -5+9, find (f•g)(x)and (f.g)(-1).
Ne4ueva [31]

Answer:  (f·g)(x) = -5x³ - 31x² + 62x + 18

               (f·g)(-1) = -70

(fog)(x) = 25x² - 130x + 155

(fog)(-1) = 310

<u>Step-by-step explanation:</u>

f(x) = x² + 8x + 2          g(x) = -5x + 9

(f·g)(x) = (x² + 8x + 2)(-5x + 9)

          = -5x³ + 9x²

                    - 40x² + 72x

            <u>                    - 10x + 18</u>

          = -5x³ - 31x² + 62x + 18

(f·g)(-1)= -5(-1)³ - 31(-1)² + 62(-1) + 18

         =  -5(-1)  - 31(1)    - 62      + 18

         =    5     -   31      - 62      + 18

         =  -70

****************************************************************************************

(fog)(x) = (-5x + 9)² + 8(-5x + 9) + 2

           = 25x² - 90x + 81

                       - 40x + 72

              <u>                   +   2</u>

           = 25x² - 130x + 155

(fog)(-1) = 25(-1)² - 130(-1) + 155

            =   25    +  130    + 155

            = 310

<em>It wasn't clear if you wanted multiplication or composition so I solved both.</em>

6 0
3 years ago
Set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-
lapo4ka [179]

She invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.

<h3><u>Distributions</u></h3>

Given that Sylvia invested a total of $27,000, and she invested part of the money in a certificate of deposit (CD) that earns 3% simple interest per year, she invested in a stock that returns the equivalent of 7% simple interest, and she invested in a bond fund that returns 2%, and she invested three times as much in the stock as she did in the CD, and earned a total of $1140 at the end of 1 yr, to determine how much principal did she put in each investment, the following calculation must be made:

  • 9000 x 0.07 + 3000 x 0.03 + 15000 x 0.02 = 630 + 90 + 300 = 1020
  • 9900 x 0.07 + 3300 x 0.03 + 13800 x 0.02 = 693 + 99 + 276 = 1068
  • 12,000 x 0.07 + 4,000 x 0.03 + 11,000 x 0.02 = 840 + 120 + 220 = 1,180
  • 11400 x 0.07 + 3800 x 0.03 + 11800 x 0.02 = 798 + 114 + 236 = 1148
  • 10800 x 0.07 + 3600 x 0.03 + 12600 x 0.02 = 756 + 108 + 252 = 1116
  • 11160 x 0.07 + 3720 x 0.03 + 12120 x 0.02 = 781.2 + 111.6 + 242.4 = 1135.2
  • 11190 x 0.07 + 3730 x 0.03 + 12080 x 0.02 = 783.3 + 111.9 + 241.6 = 1136.8
  • 11250 x 0.07 + 3750 x 0.03 + 12000 x 0.02 = 787.5 + 112.5 + 240 = 1140

Therefore, she invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.

Learn more about distribution in brainly.com/question/10250387

7 0
2 years ago
What is the product of the polynomials below? (4x^2-2x-4)(2x+4)
Travka [436]

Answer:  8x³ + 12x² - 16x - 16

<u>Step-by-step explanation:</u>

  (4x² - 2x - 4)(2x + 4)

= (2x + 4)(4x² - 2x - 4)

= 2x(4x² - 2x - 4)  +  4(4x² - 2x - 4)

=   8x³ - 4x² - 8x   +  16x² - 8x - 16

=   8x³ + (-4x² + 16x²) + (-8x - 8x) - 16

=   8x³ + 12x² - 16x - 16

7 0
3 years ago
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