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3 years ago

Find a polynomial with integer coefficients that satisfies the given conditions.

1 answer:

8 0

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)
\\\\\\
\textit{also recall that }~~~i^2=-1\\\\
-------------------------------\\\\
\begin{cases}
x=5+i\implies &x-5-i=0\\
x=5-i\implies &x-5+i=0
\end{cases}
\\\\\\
(x-5-i)(x-5+i)=\stackrel{\textit{original polynomial}}{0}
\\\\\\\
[(x-5)~~-~~i]~[(x-5)~~+~~i]=0\implies [(x-5)^2~~-~~i^2]=0
\\\\\\
(x^2-10x+25)~~-~~(-1)=0\implies x^2-10x+25+1=y
\\\\\\
x^2-10x+26=y$

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Each of the four angles of a quadrilateral measures 90°. How many rectangles can you construct using this condition?

skad [1K]

The defenition of a rectangle is that it has 4 angles that measure 90 degrees
ther are infinite legnths and inifinite numbers
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3 years ago

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ziro4ka [17]

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3 years ago

Gordon Ramsey made a stew that contained shrimp and potatoes. Shrimp was expensive, so he used three times the amount of potatoe

Burka [1]

Answer:

He bough 1.25 lbs of shrimp and 3.75 lbs of potato.

Step-by-step explanation:

Since the stew is composed of shrimps and potatoes, then the sum of the weighs of these ingredients must be equal to the weigh of the stew, so we have:

$shrimp + potato = 5$

We also know that he bought three times more potatoes than shrimps, therefore:

$potato = 3*shrimp$

Using the second equation on the first one, we have:

$shrimp + 3*shrimp = 5\\4*shrimp = 5\\shrimp = \frac{5}{4} = 1.25$

$potato = 3*shrimp = 3*1.25 = 3.75$

He bough 1.25 lbs of shrimp and 3.75 lbs of potato.

5 0

3 years ago

While the histogram is not perfectly symmetric (there is mild right skewness), it is close enough to being symmetric and mound-s

jek_recluse [69]

Answer:

97.9% ; 12.4% ; 771

Step-by-step explanation:

The approximate percentage who have more Than 469 calories :

P(x > 469)

Mean, m = 1060

Standard deviation, s = 291

Z = (x - mean) / standard deviation

Z = (469 - 1060) / 291

Z = −2.030927

P(Z > - 2.031) = 1 - P(Z < - 2.031)

P(Z > - 2.031) = 1 - 0.0211

P(Z > - 2.031) = 0.9788 = 97.9%

b. What is the approximate percentage of Chipotle meals with calorie amounts between 1372 calories and 1673 calories?

[(1673 - 1060) / 291] - [(1372 - 1060) / 291]

P(Z <2.106) - P(Z < 1.072)

0.9824 - 0.85814

= 0.12426 = 12.4%

c. If a particular meal's calorie amount is equal to the 16th percentile of Chipotle meal calorie amounts, how many calories are in the meal

The Zscore at 16 percentile = -0.994

Zscore = (score - mean) / standard deviation

-0.994 * 291 = score - 1060

−289.254 = score - 1060

Score = −289.254 + 1060

Score = 770.746

Approximately 771

3 0

3 years ago

The sum of two numbers is 27. The larger number is 3 more than the smaller number. What are the two numbers? PLEASE DO NOT GIVE

Contact [7]

Let x and y be the two numbers

Saying "The sum of two numbers is 27" means x+y = 27. The term "sum" is the result of adding. So the first equation is x+y = 27

The second equation is y = x+3 where we assume that y is the larger number of the pair.

So your system of equations will be
x+y = 27
y = x+3

Use substitution to solve this system.
x+y = 27
x+( y ) = 27
x + (x+3) = 27 ... notice how y has been replaced with x+3 (since y = x+3)
x+x+3 = 27
Solve for x and then use this to find y. I'll let you finish up.

If you need more help, then please let me know.

4 0

3 years ago