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djyliett [7]
4 years ago
12

Jacob has golf scores of 120, 112, 130, 128, and 124. He wants to have an average golf score of 118. What is the first step in d

etermining what Jacob needs to score in his next golf game?
a. Find the sum of all the numbers in the problem, 120+112+130+128+124+118.

b. Find the average score for the five golf games that Jacob has played.

c. Determine the number of points that he needs in his next golf game.

d. Determine how many total points are needed to have an average of 118.
Mathematics
2 answers:
Harlamova29_29 [7]4 years ago
8 0

Answer:

d

Step-by-step explanation:

Here the sum of 5+1 golf scores, divided by 6, must be 118:

120 + 112 + 130 + 128 + 124 + x

--------------------------------------------- = 118

                         6

Here, 120 + 112 + 130 + 128 + 124 + x is the total number of points needed to have an average of 118.  Answer d is the correct one.

Burka [1]4 years ago
3 0

Answer:

Jacob has golf scores of 120, 112, 130, 128, and 124.

He wants to have an average golf score of 118.

a. Find the sum of all the numbers in the problem, 120+112+130+128+124+118.

120+112+130+128+124+118

= 732

b. Find the average score for the five golf games that Jacob has played.

\frac{120+112+130+128+124}{5}

= 122.8

c. Determine the number of points that he needs in his next golf game.

Jacob will need a golf score of 94  in next game to achieve the average of 118.

Total score = 120+112+130+128+124+x

number of matches = 6

Average score = \frac{614+x}{6}=118

614+x=708

x=708-614

x = 94

d. Determine how many total points are needed to have an average of 118.

Total points needed are 614+94=708

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Gnesinka [82]

\huge \boxed{\mathfrak{Question} \downarrow}

  • Simplify :- 1 + - w² + 9w.

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\large \sf1 + - w ^ { 2 } + 9 w

Quadratic polynomial can be factored using the transformation \sf \: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where \sf x_{1} and x_{2} are the solutions of the quadratic equation \sf \: ax^{2}+bx+c=0.

\large \sf-w^{2}+9w+1=0

All equations of the form \sf\:ax^{2}+bx+c=0 can be solved using the quadratic formula: \sf\frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

\large \sf \: w=\frac{-9±\sqrt{9^{2}-4\left(-1\right)}}{2\left(-1\right)}  \\

Square 9.

\large \sf \: w=\frac{-9±\sqrt{81-4\left(-1\right)}}{2\left(-1\right)}  \\

Multiply -4 times -1.

\large \sf \: w=\frac{-9±\sqrt{81+4}}{2\left(-1\right)}  \\

Add 81 to 4.

\large \sf \: w=\frac{-9±\sqrt{85}}{2\left(-1\right)}  \\

Multiply 2 times -1.

\large \sf \: w=\frac{-9±\sqrt{85}}{-2}  \\

Now solve the equation \sf\:w=\frac{-9±\sqrt{85}}{-2} when ± is plus. Add -9 to \sf\sqrt{85}.

\large \sf \: w=\frac{\sqrt{85}-9}{-2}  \\

Divide -9+ \sf\sqrt{85} by -2.

\large \boxed{ \sf \: w=\frac{9-\sqrt{85}}{2}} \\

Now solve the equation \sf\:w=\frac{-9±\sqrt{85}}{-2} when ± is minus. Subtract \sf\sqrt{85} from -9.

\large \sf \: w=\frac{-\sqrt{85}-9}{-2}  \\

Divide \sf-9-\sqrt{85} by -2.

\large \boxed{ \sf \: w=\frac{\sqrt{85}+9}{2}}  \\

Factor the original expression using \sf\:ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \sf\frac{9-\sqrt{85}}{2}for \sf\:x_{1} and \sf\frac{9+\sqrt{85}}{2} for \sf\:x_{2}.

\large \boxed{ \boxed {\mathfrak{-w^{2}+9w+1=-\left(w-\frac{9-\sqrt{85}}{2}\right)\left(w-\frac{\sqrt{85}+9}{2}\right) }}}

<h3>NOTE :-</h3>

Well, in the picture you inserted it says that it's 8th grade mathematics. So, I'm not sure if you have learned simplification with the help of biquadratic formula. So, if you want the answer simplified only according to like terms then your answer will be ⇨

\large \sf \: 1 + -  w {}^{2}  + 9w \\  =\large  \boxed{\bf \: 1 -  {w}^{2}   + 9w}

This cannot be further simplified as there are no more like terms (you can use the biquadratic formula if you've learned it.)

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