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igomit [66]
3 years ago
6

Help stuck on this question

Mathematics
1 answer:
Zarrin [17]3 years ago
5 0

Answer:

Find the slope of the original line and use the point-slope formula: y−y1=m(x−x1 )

to find the line parallel to -> y = 6/7 x −2.

<u><em>A: y = 6/ 7x−7</em></u>

<u><em></em></u>

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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
Car travels and average speed of 48 miles per hour how long does it take to travel 180 miles?
Neporo4naja [7]

speed =48mph

distance = 180 miles

we know that

time = distance / speed

time=\frac{180}{48} hours

time=3.75 hours..........Answer

5 0
3 years ago
Read 2 more answers
Is there more than one way to get 2/3/4/5 to the simplest form
seropon [69]
Multiply 2 and 3 also multiply 4 and 5 and then divide the products together like so 2x3 divided by 4x5   so 6 divided by 20
4 0
3 years ago
Rut gon cac phan so sau36\63 30\25 24\32 15\30
Stels [109]
2348833bdjdjfjfj ududdu
4 0
2 years ago
Please help!! :(((((
wel

Answer:

20+4(t)=?

Step-by-step explanation:

try using the vid :P

4 0
3 years ago
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