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How many more unit tiles must be added to the function f(x)=x2−6x+1 in order to complete the square?

Valentin [98]

<h2>8 unit tiles should be added</h2>

Step-by-step explanation:

Function given is $f(x)=x^{2}-6x+1$ . We wish to add more unit tiles to the function so that it becomes a complete square.

Since the given function is of order 2, the side of the square will be order 1. Let us assume a general order 1 expression $ax+b$ to be the side of the square.

As the function forms the square after adding some $p$ unit tiles, $f(x)+p=(\text{Side of square})^{2}$

$x^{2}-6x+1+p=(ax+b)^{2}=a^{2}x^{2} +2abx+b^{2}$

From comparision, $a^{2}=1; 2ab=-6; b^{2}=1+p\\a=1; b=-3\\(-3)^{2}=p+1\\p=8$

∴ 8 more unit tiles are required to complete the square.

10 0

2 years ago

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Need to find the volume. measurements in picture, please help.

o-na [289]

Answer:

V = 288.5 $yd^{3}$

Step-by-step explanation:

To find the volume of a cone, use this equation:

$V = \pi r^{2}\frac{h}{3}$

r = radius

h = height

We aren't given the height of the cone, just the length of the side. To find the height use the Pythagorean Theorem:

$a^{2}+ b^{2}= c^{2}$

The value of 12.1 yds is the hypotenuse and the radius is the value of one of the legs. So, set it up like this:

$a^{2}+5^{2} =12.1^{2}$

Now, solve:

$a^{2}+25= 146.41$ Distribute the square

$a^{2} = 121.41$ Subtract 25 from 146.41

$\sqrt{a^{2} }=\sqrt{121.41}$

a = 11.01862

So, the height is equal to 11.01862 yds.

Now, we can plug everything into the volume equation:

$V = \pi (5)^{2}\frac{11.01862}{3}$

Simplify (use calculator):

V = 288.5 $yd^{3}$

So, the volume of the cone is equal to 288.5 $yd^{3}$

5 0

2 years ago

Find the probability that when a couple has four children, at least one of them is a boy. (Assume that boys and girls are equa

erma4kov [3.2K]

Answer:

The probability that at least, one of the four children the couple has is a boy is 0.8.

Step-by-step explanation:

Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..

Note that it is possible to have the following for 4 children:

1. 4 boys, 0 girls

2. 3 boys, 1 girl

3. 2 boys, 2 girls

4. 1 boy, 3 girls

5. 0 boys, 4 girls.

To have at least, one boy, out of the 5 options, only 4 is possible.

1. 4 boys, 0 girls.........YES

2. 3 boys, 1 girl ...........YES

3. 2 boys, 2 girls.........YES

4. 1 boy, 3 girls.............YES

5. 0 boys, 4 girls..........NO

The probability is therefore,

(Probability of event = 4) ÷ (Total possible outcome = 5)

P = 4/5 = 0.8

3 0

3 years ago

32 rounded to the nearest ten

alekssr [168]

Answer:

30

Step-by-step explanation:

7 0

3 years ago

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You just won the lottery! As your prize you will receive $1,500 a month for 150 months. If you can earn 7 percent, compounded mo

Paladinen [302]

Answer: the worth of the prize today is $150000

Step-by-step explanation:

We would apply the formula for determining present annuity. It is expressed as

PV = R[1 - (1 + r)^- n]r

Where

PV represents the present value of the investment.

R represents the regular payments made(could be weekly, monthly)

r = represents interest rate/number of interval payments.

n represents the total number of payments made.

From the information given,

r = 0.07/12 = 0.0058

n = 150

Therefore,

PV = 1500[1 - (1 + 0.0058)^- 150]/0.0058

PV = 1500[1 - (1.0058)^- 150]/0.0058

PV = 1500[1 - 0.42]/0.0058

PV = 1500[0.58]/0.0058

PV = 1500 × 100

PV = $150000

6 0

2 years ago

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