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Digiron [165]
3 years ago
14

Solve by using square root: 4(x-1)^2+2=10

Mathematics
2 answers:
WITCHER [35]3 years ago
5 0
4(x-1)^2+2=10 \\
 4(x-1)^2=8\\
(x-1)^2=2\\
x-1=-\sqrt2 \vee x-1=\sqrt2\\
x=1-\sqrt2 \vee x=1+\sqrt2
Scilla [17]3 years ago
3 0
4(x-1)^2+2=10\\\\4(x^2-2x+1)+2-10=0\\\\4 x^2-8x+4+2-10=0\\\\4 x^2-8x-4=0\ \ / :4\\\\x^2-2x-1=0\\\\x_{1}=\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{2-\sqrt{ (-2)^2-4*1*(-1)}}{2 }=\frac{2-\sqrt{ 8}}{2 }=\frac{2- \sqrt{ 4*2}}{2 }=\\\\=\frac{2-\sqrt{ 8}}{2 }=\frac{2(1- \sqrt{ 2})}{2 }=1- \sqrt{ 2}\\\\x_{2}=\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{2+\sqrt{ (-2)^2-4*1*(-1)}}{2 }=\frac{2(1+ \sqrt{ 2})}{2 }=1+ \sqrt{ 2}

Answer:\ x=1- \sqrt{2}\ \ or\ \ x= 1+ \sqrt{ 2}


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A 3 L bottle of oil costs $36 and contains 12 cups. Dinesh puts 1 cup of oil, 10 garlic gloves and 1 cup of lemon juice in each
lys-0071 [83]

Answer:

$15

Step-by-step explanation:

Let's start by figuring out how much 1 cup of oil costs.

12 cups of oil is 36$

Let's set up a proportion.

12/36=1/x

Cross Multiply

12x=36

Divide both sides by 12.

x=3

1 cup of oil is $3.

Dinesh makes 5 batches of hummus, and each batch requires 1 cup of oil.

5*1=5

This means he needs 5 cups of oil.

5*3=15

He used $15 worth of oil in the 5 batches of his recipe.

However, since it is impossible to buy 5/12 bottles of oil, he would have needed to spend $36.

7 0
3 years ago
F(t) = t - 6<br> f(u + 6) =
vovikov84 [41]

Answer:

  f(u +6) = u

Step-by-step explanation:

Put (u+6) in place of t and simplify:

  f(u+6) = (u+6) -6

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4 0
3 years ago
Candice is preparing for her final exam in Statistics. She knows she needs an 65 out of 100 to earn an A overall in the course.
sertanlavr [38]

Answer:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean  Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 =  

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean  2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to  of the values.

Therefore, Scores between 72 and 90 =  

= 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 =  

= 2.5 X 12 = 30.

That is, 30 students have scored below 54.

Step-by-step explanation:

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