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2 years ago

11

If using the method of completing the square to solve the quadratic equation x^2-10x-13=0, which number would have to be added t

o "complete the square"?

1 answer:

Maru [420]2 years ago

6 0

Answer: The solution to the problem is based on the solutions

from the subproblems.

x = {8.464101615, 1.535898385}

Step-by-step explanation:

x^2-10x+13=0

Simplifying

x2 + -10x + 13 = 0

Reorder the terms:

13 + -10x + x2 = 0

Solving

13 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.

13 + -10x + -13 + x2 = 0 + -13

Reorder the terms:

13 + -13 + -10x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0

0 + -10x + x2 = 0 + -13

-10x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13

-10x + x2 = -13

The x term is -10x. Take half its coefficient (-5).

Square it (25) and add it to both sides.

Add '25' to each side of the equation.

-10x + 25 + x2 = -13 + 25

Reorder the terms:

25 + -10x + x2 = -13 + 25

Combine like terms: -13 + 25 = 12

25 + -10x + x2 = 12

Factor a perfect square on the left side:

(x + -5)(x + -5) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting

(x + -5) equal to 3.464101615 and -3.464101615.

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A large set of data was collected and analyzed for the majors of college seniors in the US From the scatter plots produced the f

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Using linear function concepts, it is found that the correct statements are given by:

The number of biology degrees increases by about 2,414 each year after 2000.

About 73,000 students graduated with degrees in psychology in 2000.

In 2000, more students graduated with psychology degrees than biology degrees.

<h3>What is a linear function?</h3>

A linear function is modeled by:

$y = mx + b$

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.

In this problem, the number of college seniors who graduated with a bachelor's degree in psychology, in t years after 2000, is modeled by:

P(t) = 2,376t + 73,219.

For biology, the amount is given by:

B(t) = 2,414t + 56,545.

Then, the true statements are given by:

The number of biology degrees increases by about 2,414 each year after 2000.

About 73,000 students graduated with degrees in psychology in 2000.

In 2000, more students graduated with psychology degrees than biology degrees.

More can be learned about linear function concepts at brainly.com/question/24808124

8 0

2 years ago

How are <1 and <2 related

Stella [2.4K]

Answer:

They are adjacent

Step-by-step explanation:

3 0

3 years ago

I want a correct answer you can take your time. If I was born on December 24, two thousand and four and my classmate was born on

cricket20 [7]

Answer:

5years, 3months, 16 days

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3 years ago

For the function defined by f(t)=2-t, 0≤t<1, sketch 3 periods and find:

Oksi-84 [34.3K]

The half-range sine series is the expansion for $f(t)$ with the assumption that $f(t)$ is considered to be an odd function over its full range, $-1$ . So for (a), you're essentially finding the full range expansion of the function

$f(t)=\begin{cases}2-t&\text{for }0\le t$

with period 2 so that $f(t)=f(t+2n)$ for $|t|$ and integers $n$ .

Now, since $f(t)$ is odd, there is no cosine series (you find the cosine series coefficients would vanish), leaving you with

$f(t)=\displaystyle\sum_{n\ge1}b_n\sin\frac{n\pi t}L$

where

$b_n=\displaystyle\frac2L\int_0^Lf(t)\sin\frac{n\pi t}L\,\mathrm dt$

In this case, $L=1$ , so

$b_n=\displaystyle2\int_0^1(2-t)\sin n\pi t\,\mathrm dt$
$b_n=\dfrac4{n\pi}-\dfrac{2\cos n\pi}{n\pi}-\dfrac{2\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{4-2(-1)^n}{n\pi}$

The half-range sine series expansion for $f(t)$ is then

$f(t)\sim\displaystyle\sum_{n\ge1}\frac{4-2(-1)^n}{n\pi}\sin n\pi t$

which can be further simplified by considering the even/odd cases of $n$ , but there's no need for that here.

The half-range cosine series is computed similarly, this time assuming $f(t)$ is even/symmetric across its full range. In other words, you are finding the full range series expansion for

$f(t)=\begin{cases}2-t&\text{for }0\le t$

Now the sine series expansion vanishes, leaving you with

$f(t)\sim\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi t}L$

where

$a_n=\displaystyle\frac2L\int_0^Lf(t)\cos\frac{n\pi t}L\,\mathrm dt$

for $n\ge0$ . Again, $L=1$ . You should find that

$a_0=\displaystyle2\int_0^1(2-t)\,\mathrm dt=3$

$a_n=\displaystyle2\int_0^1(2-t)\cos n\pi t\,\mathrm dt$
$a_n=\dfrac2{n^2\pi^2}-\dfrac{2\cos n\pi}{n^2\pi^2}+\dfrac{2\sin n\pi}{n\pi}$
$a_n=\dfrac{2-2(-1)^n}{n^2\pi^2}$

Here, splitting into even/odd cases actually reduces this further. Notice that when $n$ is even, the expression above simplifies to

$a_{n=2k}=\dfrac{2-2(-1)^{2k}}{(2k)^2\pi^2}=0$

while for odd $n$ , you have

$a_{n=2k-1}=\dfrac{2-2(-1)^{2k-1}}{(2k-1)^2\pi^2}=\dfrac4{(2k-1)^2\pi^2}$

So the half-range cosine series expansion would be

$f(t)\sim\dfrac32+\displaystyle\sum_{n\ge1}a_n\cos n\pi t$
$f(t)\sim\dfrac32+\displaystyle\sum_{k\ge1}a_{2k-1}\cos(2k-1)\pi t$
$f(t)\sim\dfrac32+\displaystyle\sum_{k\ge1}\frac4{(2k-1)^2\pi^2}\cos(2k-1)\pi t$

Attached are plots of the first few terms of each series overlaid onto plots of $f(t)$ . In the half-range sine series (right), I use $n=10$ terms, and in the half-range cosine series (left), I use $k=2$ or $n=2(2)-1=3$ terms. (It's a bit more difficult to distinguish $f(t)$ from the latter because the cosine series converges so much faster.)

5 0

3 years ago

A study by a reputable research organization found that when presented with prints from the same individual, a fingerprint expe

Llana [10]

Answer:

a. 0.6899

b. 0.1642

Step-by-step explanation:

a. Given the probability of success is 0.94 for an expert and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of the events is calculated as:

$P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.94\times0.94\times0.94\times0.94\times0.94\times0.94\\\\=0.6899$

Hence, the probability of correctly identifying the 6 matches is 0.6899

b.Given the probability of success is 0.74 for a novice and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of the events is calculated as:

$P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.74\times0.74\times0.74\times0.74\times0.74\times0.74\\\\=0.1642$

#Hence, the probability of correctly identifying the 6 matches is 0.1642

*I have used the sample size of 6(due to conflicting info/question size).

7 0

3 years ago