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3 years ago

Step by step how to solve this equation by completing the square x^2-16x+-60

Mathematics

1 answer:

anygoal [31]3 years ago

5 0

Answer:

Step-by-step explanation:

x^2-16x+60

(x-6)(x-10) factor the equation

x-6=0

x=6

x-10=0

x=10

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Identify the functions that are continuous on the set of real numbers and arrange them in ascending order of their limits as x t

Studentka2010 [4]

Answer:

g(x)<j(x)<k(x)<f(x)<m(x)<h(x)

Step-by-step explanation:

1. $f(x)=\frac{x^2+x-20}{x^2+4}$

The denominator of f is defined for all real values of x

Therefore, the function is continuous on the set of real numbers

$\lim_{x\rightarrow 5}\frac{x^2+x-20}{x^2+4}=\frac{25+5-20}{25+4}=\frac{10}{29}=0.345$

3. $h(x)=\frac{3x-5}{x^2-5x+7}$

$x^2-5x+7=0$

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function h is defined for all real values.

$\lim_{x\rightarrow 5}\frac{3x-5}{x^2-5x+7}=\frac{15-5}{25-25+7}=\frac{10}{7}=1.43$

2. $g(x)=\frac{x-17}{x^2+75}$

The denominator of g is defined for all real values of x.

Therefore, the function g is continuous on the set of real numbers

$\lim_{x\rightarrow 5}\frac{x-17}{x^2+75}=\frac{5-17}{25+75}=\frac{-12}{100}=-0.12$

4. $i(x)=\frac{x^2-9}{x-9}$

x-9=0

x=9

The function i is not defined for x=9

Therefore, the function i is not continuous on the set of real numbers.

5. $j(x)=\frac{4x^2-7x-65}{x^2+10}$

The denominator of j is defined for all real values of x.

Therefore, the function j is continuous on the set of real numbers.

$\lim_{x\rightarrow 5}\frac{4x^2-7x-65}{x^2+10}=\frac{100-35-65}{25+10}=0$

6. $k(x)=\frac{x+1}{x^2+x+29}$

$x^2+x+29=0$

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function k is defined for all real values.

$\lim_{x\rightarrow 5}\frac{x+1}{x^2+x+29}=\frac{5+1}{25+5+29}=\frac{6}{59}=0.102$

7. $l(x)=\frac{5x-1}{x^2-9x+8}$

$x^2-9x+8=0$

$x^2-8x-x+8=0$

$x(x-8)-1(x-8)=0$

$(x-8)(x-1)=0$

$x=8,1$

The function is not defined for x=8 and x=1

Hence, function l is not defined for all real values.

8. $m(x)=\frac{x^2+5x-24}{x^2+11}$

The denominator of m is defined for all real values of x.

Therefore, the function m is continuous on the set of real numbers.

$\lim_{x\rightarrow 5}\frac{x^2+5x-24}{x^2+11}=\frac{25+25-24}{25+11}=\frac{26}{36}=\frac{13}{18}=0.722$

g(x)<j(x)<k(x)<f(x)<m(x)<h(x)

6 0

3 years ago

Which of the following numbers could not possibly be a probability? Justify your answer. 0.123 negative 0.577 0 What must be tr

dusya [7]

Answer:

First question: -0.577 cannot be a probability.

Second question: The number must be between 0 and 1, inclusive (D)

Third question: -0.577 cannot be a probability.

Step-by-step explanation:

A probability is a real number that is in the interval [0, 1]. Therefore, any number outside this range cannot be considered a probability. Under this premise:

First question: -0.577 cannot be a probability.

Second question: The number must be between 0 and 1, inclusive (D)

Third question: -0.577 cannot be a probability.

3 0

3 years ago

What percent of the bottle of apple juice is water?

Anettt [7]

percent of water is: 32/80*100= 40%

5 0

3 years ago

The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation an

Zigmanuir [339]

The answer is:put the equation xa+yb=1 to the slope intercept form and find its slope and y-intercept.

3 0

3 years ago

$700 at 8% for 6 years is...?

uranmaximum [27]

So if it is simple interest then
700+6 times (8% of 700)=answer

percent means partsout of 100
8%=8/100=0.08
'of' means mutily
700+6 times (0.08 times 700)=700+6 times (0.56)= 700+3.36=703.36
answer is $703.36

3 0

2 years ago