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3 years ago

6

on Monday camila spent 4 2/6 hours studying on Tuesday spent another 3 5/6 hours studying what is the combined length of the tim

e she spent studying

1 answer:

erastova [34]3 years ago

5 0

She spent 8 1/6 hours studying

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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

If Clare earns $75 the next week from delivering newspapers and deposits it in her account, What will her account balance be the

alexira [117]

Answer: $15

Step-by-step explanation:

-$50 + $75 = $15

3 0

3 years ago

nydimaria [60]

Answer:

29 nickels, 12 dimes

If the number of nickels is 7 less than three times the number of dimes, the answers should be 29 nickels and 12 dimes. Hope it helps!

7 0

3 years ago

Read 2 more answers

Help plzzzzz I’ll make you brainlest :)))))))

scZoUnD [109]

Answer:

first one my dear friend!

Step-by-step explanation:

can I get brainliest?? ;P

6 0

3 years ago

Read 2 more answers

Find the area of the shaded region in the figure below. 5in. 8in.

Fiesta28 [93]

Hi there!

<u>Answer:</u>

The area of the shaded region is 28 in²

<u>Step-by-step explanation:</u>

You will have to do 3 different steps in order to find the area of the shaded region.

First, you will need to find the total area of the rectangle using the values you have and the area formula for a rectangle, which is : A = Length × Width

"A" is the area, which is what we are looking for

The "Length" is equal here to 8 inches

The "Width" is equal here to 5 inches

A = <u>8 × 5</u>

A = 40 in²

Now that you have the area of the rectanlge, your second step is to find the area of the triangle using the values you have and the area formula for a triangle, which is : A = (Base × Height) ÷ 2

"A" is the area, which is what we are looking for

The "Base" is equal here to 8 inches

The "Height" is equal here to 3 inches

A = <u>(8 × 3)</u> ÷ 2

A = <u>24 ÷ 2</u>

A = 12 in²

Now that you have both the area of the rectangle and the area of the triangle, all you have to do for your third and final step is subtract the area of the triangle from the area of the rectangle so that you are left with the area of the shaded region :

Area shaded region = <u>40 in² - 12 in²</u>

Area shaded region = 28 in²

There you go! I really hope this helped, if there's anything just let me know! :)

6 0

3 years ago