93. Let f(x) = 3x - 1 and g(x) = x + 5. Evaluate the following limits. (a) lim x→3 f(g(x)] (b) lim x→3 g[f(x)]​

Answer:

Step-by-step explanation:

13) LCM of 20 , 5 is 20

Find equivalent fraction for 2/5 with denominator 20

[tex]\dfrac{2}{5}=\dfrac{2*4}{5*4}=\dfrac{8}{20}[/tex]

Now compare

[tex]\dfrac{7}{20} \ < \dfrac{8}{20}\\\\\dfrac{7}{20} \ < \dfrac{2}{5}[/tex]

14) Convert fraction to decimal

[tex]\dfrac{1}{8}= 0.125[/tex]

0.15  > 0.125

[tex]0.15 \ > \dfrac{1}{8}[/tex]

15) 0.5 , -1/7  , -0.2  ; 1/3

[tex]\dfrac{-1}{7}=-0.14\\\\\dfrac{1}{3}=0.3\\[/tex]

0.5, - 0.14 , -0.2  ; 0.3

Least to greatest:

-0.2 ;  - 0.14   ; 0.3  ; 0.5

Answer:

-0.2  ; [tex]\dfrac{-1}{7} \ ; \dfrac{1}{3} \ ; \ 0.5[/tex]

Answer:

f(g(25)) = -5

Step-by-step explanation:

You have to put 25 in place of x in g, and after, you take the result and put in place of x in f:

g(5) = √25 = 5

f(5) = 5^2 -6•5

f(5) = 25 -30

f(5) = -5

Answer:

[tex]than k\: you[/tex]

Answer:

[tex]\displaystyle \frac{\sqrt{3}}{3}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{2}{2\sqrt{3}} = \frac{1}{\sqrt{3}} = \boxed{\frac{\sqrt{3}}{3}}[/tex]

I am joyous to assist you at any time.

Answer:

Step-by-step explanation:

(1/2)(x+3)(2x+4)

= x^2 + 5x + 6

a=1

b=2

c=5

d=1

e=6

Scale factor used by Nancy for the model of an airplane = 1 : 14

Length of the tail of the airplane = 5.7 inches

Scale factor is defined by the expression,

Scale factor = [tex]\frac{\text{Dimension of the image}}{\text{Dimension of the original}}[/tex]

By substituting the dimension of the model in the expression,

[tex]\frac{1}{14}=\frac{5.7}{\text{Dimension of the original}}[/tex]

Dimension of the original plane = 14 × 5.7

                                                     = 79.80 inches

Therefore, length of the tail of the actual airplane will be 79.80 inches.

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Length of Actual airplane's tail is 79.8 inches or 6.65 ft

Given:

Scale model sample = 1 : 14

Length of model airplane's tail = 5.7 inches

Find:

Length of Actual airplane's tail

Computation:

Length of Actual airplane's tail = Length of model airplane's tail × Scale model sample

Length of Actual airplane's tail = 5.7 × 14

Length of Actual airplane's tail = 79.8 inches

Length of Actual airplane's tail = 79.8 inches or 6.65 ft

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Answer:19

Step-by-step explanation:

because if it added it becomes that

Answer:

the greatest common factor is 4a

Answer:

68/35

Step-by-step explanation:

Answer:

1.94285714286 (Rounded to): 1.943

Answer:

[tex] \frac{3 {a}^{3} \sqrt[3]{ {a}^{2} } }{ {b}^{3} } [/tex]

Step-by-step explanation:

[tex] \sqrt[3]{ \frac{243 {a}^{11} }{9 {b}^{9} } } = \sqrt[3]{ \frac{27 {a}^{11} }{ {b}^{9} } } [/tex]

➡️ [tex] \sqrt[3]{ \frac{27 {a}^{11} }{ \sqrt[3]{ {b}^{9} } } } = \sqrt[3]{ \frac{ {3}^{3} • {a}^{9} • {a}^{2} }{ \sqrt[3]{ {b}^{9} } } } [/tex]

➡️ [tex] \frac{ \sqrt[3]{ {3}^{3 }} • \sqrt[3]{ {a}^{9} } • \sqrt[3]{ {a}^{2} } }{ \sqrt[3]{ {b}^{9} } } [/tex]

➡️ [tex] = \frac{3 {a}^{3} \sqrt[3]{ {a}^{2} } }{ {b}^{3} } [/tex] ✅

Answer:

Step-by-step explanation:

Given sequence:

Rewrite as:

We observe the numerators: 1, 2, 3, 4 and denominators: 8, 7, 6, 5

The next two terms are:

or

Recreate

We can see

The denominator is decreasing by 1 and numerator is increasing by 1

So next term

Next term

Answer: 50%

Step-by-step explanation:

hope this helps !

Answer:

$600

Step-by-step explanation:

1800/300 = 6, so he got 6 'lots' of reward points

6 * 100 = $600

Answer:

He spent $600

Step-by-step explanation:

What you do is 1800/300= 6, so 100 × 6 = $600

Answer:

48 + 30m

Step-by-step explanation:

The perimeter of a hexagon is 6 times its side length.

6(8 + 5m)

= 48 + 30m (Distributive property)

Step-by-step explanation:

1)

[tex]\frac{2}{3} +\frac{4}{5} =\frac{10+12}{15}=\frac{22}{15} .[/tex]

2) the same value of the denominator of the fractions.

3) 4²*2²=16*4=64 or 4²*2²=(4*2)²=8²=64.

Megan's answer is correct.

4) if the given length is 2,25=9/4 (feet), then the length of each piece is 9/4 :3=3/4=0.75 (feet) or 3/4*12=9 (inches).

5) a. 4-6= -2; b. -4+6=2; c. -4-6= -10, so the required order is c<a<b.

6) A. -8+3= -5; B. -8*3= -24, so the greater value is (-5) - answer A.

7) if to calculate every option, then A. 2.3*6.5=14.95; B. 21.45-6.5=14.95; C. 8.32+6.63=14.95, - all of them are equal.

Answer:

450

Step-by-step explanation:

The total is 100 %

20% + 35% +15% = 70%

100-70 = 30

He saves 30%

1500 * 30%

1500 *.30

450

A man is paid $1500 salary. He spends 20% of the salary for his kids education, 35% for food, 15% for miscellaneous and he saves the rest. How much money does he save?

Total Income = $ 1500

According to the question,

He spends 20% to his kids education

He spends 35% for food

He spends 15% for miscellaneous

Out of total income he spends 20% on kids education

So, amount spent on kids education = 20% of $1500

Amount = 20/100 × $1500

Amount = $300

Hence, money spent on his kids education is $300

35% is spent on food

Money spent on food = 35% of $1500

Money spent = 35/100 × $1500

Money spent = $525

Hence, money spent on food is $525

15% is spent on miscellaneous

Money spent on miscellaneous = 15% of $1500

Money spent = 15/100 × $1500

Money spent = $225

Hence, money spent on miscellaneous is $225

Now, adding all the three we get

$300 + $525 + $225

$825 + $225

$1050

Total money spent = $1050

Remaining money = $1500 - $1050 = $450

Step-by-step explanation:

I hope this makes sense...and is visible..

:)

Answer:

164

Step-by-step explanation:

in standard form CLXIV IS 164

Answer:

3+ x • {2x} + 5 = 858

Step-by-step explanation:

<33 hoped this helped !!!

Answer:

one quarter is 0.25c

so q=0.25c

Answer:

percent of iron in alloy= 100-42 = 58%

weight of the iron = 55×58÷100= 31.9

weight of iron= 31.9 kg

weight of copper= 55-31.9=23.1

weight of copper = 23.1

Step-by-step explanation:

[ I'm not sure but I think this is right ]

Answer: copper = 23.1 kg

             iron = 31.9 kg

Step-by-step explanation:

copper = 42% of 55

             = 42/100 * 55

            = 42/20 * 11

           = 21/10 * 11

          = 231/10

          = 23.1 kg

  so iron = 100% - 42%

             = 58%

so

58% of 55

= 58/100 * 55

= 58/20 * 11

=31.9 kg

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.

[tex](3x + 4)(6 {x}^{2} - 5x + 7) \\ = 18 {x}^{3} - 15 {x}^{2} + 21x + 24 {x}^{2} - 20x + 28 \\ = 18 {x}^{3} + 9 {x}^{2} + x + 28[/tex]

I hope I helped you^_^

Answer:

In one month he earn €2,100

He worked whole year

1 year = 12 months

So,

George earning is 12 months = 12 × Earning of one month

=> 2100 × 12

=> 25200

Answer:

6x - 8

Step-by-step explanation:

2(3x – 4)

Distribute

2*3x - 2*4

6x - 8

Answer:

answer C

6x minus 8

use distributive property

Answer:

1

or,x+60°=180°(Being the sum of supplementry angle is equal to 180°)

or,x=180°-60°

:x=120°

2

or,y=120°(Being corresponding angle)