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2 years ago

What is the equation x^2+12x-3=16 written in the form (x-p)^2=q using the method of completing the square ?

Mathematics

1 answer:

Alexus [3.1K]2 years ago

3 0

Step-by-step explanation:

${x}^{2} + 12x - 3 = 16$

${x}^{2} + 12x = 19$

${x}^{2} + 12x + 36 = 19 + 36$

$(x + 6) {}^{2} = 55$

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The side of each of the equilateral triangles in the figure is twice the side of the central regular hexagon. What fraction of t

lana [24]

Answer:

The fraction is 1/4

Step-by-step explanation:

we know that

The area of an equilateral triangle, using the law of sines is equal to

$A=\frac{1}{2}x^{2}sin(60^o)$

$A=\frac{1}{2}x^{2}(\frac{\sqrt{3}}{2})$

$A=x^{2}\frac{\sqrt{3}}{4}$

where

x is the length side of the triangle

In this problem

Let

b ----> the length side of the regular hexagon

2b ---> the length side of the equilateral triangle

step 1

Find the area of the six triangles

Multiply the area of one triangle by 6

$A=6[x^{2}\frac{\sqrt{3}}{4}]$

$A=3x^{2}\frac{\sqrt{3}}{2}$

we have

$x=2b\ units$

substitute

$A=3(2b)^{2}\frac{\sqrt{3}}{2}\\\\A=6b^{2}\sqrt{3}\ units^2$

step 2

Find the area of the regular hexagon

Remember that, a regular hexagon can be divided into 6 equilateral triangles

The area of the regular hexagon is the same that the area of 6 equilateral triangles

$A=3x^{2}\frac{\sqrt{3}}{2}$

we have

$x=b\ in$

substitute

$A=3(b)^{2}\frac{\sqrt{3}}{2}$

step 3

To find out what fraction of the total area of the six triangles is the area of the hexagon, divide the area of the hexagon by the total area of the six triangles

$3(b)^{2}\frac{\sqrt{3}}{2}:6b^{2}\sqrt{3}=\frac{3}{2} :6=\frac{3}{12}=\frac{1}{4}$

3 0

3 years ago

Mashcka [7]

To solve this we are going to use the formula for compounded interest: $A=P(1+ \frac{r}{n})^{nt}$
where
$A$ is the final amount after $t$ years
$P$ is the initial amount
$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year
$t$ is the time in years

We know for our problem that $P=1380$ , $r= \frac{5}{100} =0.05$ , and $t=3$ . Since the interest is compounded daily, it is compounded 365 times in year; therefore, $n=365$ . Lets replace those values in our formula to find $A$ :
$A=P(1+ \frac{r}{n})^{nt}$
$A=1380(1+ \frac{0.05}{365})^{(365)(3)}$
$A=1603.31$

We can conclude the amount in Diane's after 3 years will be <span>$1,603.31</span>

4 0

3 years ago

The probability of a chance event is 0.5, it is __________ to happen when compared to a chance event with a probability of 1.

nignag [31]

Answer:

less likely

Step-by-step explanation:

Probability is between 0 and 1 so 1 is guaranteed to happen and 0 is guaranteed to not happen

3 0

2 years ago

Read 2 more answers

can someone help me figure this out?? My sisters at work rn she usually helps me with algerbra pleasee help!