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Alex_Xolod [135]
3 years ago
14

Last question. 50 points!​

Mathematics
2 answers:
WARRIOR [948]3 years ago
6 0

Answer:

The equation has two solutions which are 2 and -1.5.

Step-by-step explanation:

\small \sf \:  \sqrt{2w {}^{2}  - 19w + 31} + 2  \: = 7 - 2w

Step 1 :- Move constant to the left-hand side and change their sign.

\small \sf ➻ \:  \sqrt{2w {}^{2}  - 19w + 31}  \: = 7 - 2w - 2

Step 2 :- Subtract 2 from 7.

\small \sf ➻\:  \sqrt{2w {}^{2}  - 19w + 31}   \: = 5-  2w

Step 3 :- Square root on both side of expression.

\small \sf ➻ \: (  \sqrt{2w {}^{2}  - 19w + 31} )²  \: = (5-  2w)²

➻ 2w² - 19w + 31 = 25 - 20w + 4w²

Step 3 :- Move expression to the left-hand side and change their sign.

➻ 2w² - 19w + 31 - 25 + 20w - 4w² = 0

Step 4 :- Combine like terms.

➻ -2w² + w + 6 = 0

Step 5 :- Change the sign on both side of equation.

➻ 2w² - w - 6 = 0

Step 6 :- Split the term -w as 3w - 4w.

➻ 2w² + 3w - 4w - 6 = 0

Step 7 :- Factor out w from the first pair and -2 from the second pair.

➻ w ( 2w + 3 ) - 2( 2w + 3 ) = 0

Step 8 :- Factor out w + 3 from the expression.

➻ ( 2w + 3 ) ( w - 2 ) = 0

Step 9 :- Using the zero product property.

➻ 2w + 3 = 0, w - 2 = 0

Step 10 :- Solve for w.

w = \frac{-3}{2} = 1.5 , and w = 2

Thus, This equation has two solutions.

Shkiper50 [21]3 years ago
3 0

<u>w</u><u>=</u><u>-</u><u>1</u><u>.</u><u>5</u>

<u>w</u><u>=</u><u>2</u>

Answer:

Solution given:

\sqrt{2w²-19w+31}+2=7-2w

again

keep square root alone

\sqrt{2w²-19w+31}=7-2w-2

solve subtraction of 7-2

\sqrt{2w²-19w+31}=5-2w

Squaring on both side

(\sqrt{2w²-19w+31})²=(5-2w)²

2w²-19w+31=5²-2*5*2w+4w²

take terms one side

2w²-19w+31-25+20w-4w²=0

-2w²+w+6=0

2w²-w-6=0

doing middle term factorisation

2w²-(4-3)w-6=0

2w²-4w+3w-6=0

take common from each two term

2w(w-2)+3(w-2)=0

(w-2)(2w+3)=0

either

w=2

or

W=-3/2=-1.5

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Answer:

(A) It should choose High school Z for the most consistent attendance among its students.

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Step-by-step explanation:

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(A) It is stated that the school district wants to award the school that has the most consistent attendance among its students.

Now, to check which high school should it choose; we will look for the standard deviation (σ) of each of the three schools because consistency is measured through standard deviation and the school with the lowest standard deviation means that it has the most consistent attendance among its students.

So, after looking at the standard deviation of all the three schools; the High School Z has the lowest standard deviation of 27.5.

This means that it should choose High school Z.

(B) It is stated that the school district wants to award the school with the highest average attendance.

Now, to check which high school should it choose; we will look for the Mean of each of the three schools because average is measured through mean of the data, and the school with the highest mean means that it has the highest average attendance.

So, after looking at the Mean of all the three schools; the High School W has the highest average of 169.

This means that it should choose High school W with the highest average attendance.

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