Given f(x)=5x+2 and g(x)=-3x-4, find the following: a. f(g(0))
b. f(f(3))
c. (g of)(0)
d. (g o g)(2)

Answer:

22/5

Step-by-step explanation:

4 [tex]\frac{2}{5}[/tex]

new numerator for improper fraction = (4 x 5) + 2 = 20 + 2 = 22  

=> 22/5

Answer:

[tex](f+g)(x)=x^2-x-3[/tex]

Step-by-step explanation:

We have [tex]f(x)=2x-1[/tex] and [tex]g(x)=x^2-3x-2[/tex]

Recall that [tex]f+g[/tex] is defined by [tex](f+g)(x)=f(x)+g(x)[/tex], therefore

[tex](f+g)(x)=f(x)+g(x)=2x-1+x^2-3x-2=x^2-x-3[/tex]

Recall some limit properties…

• limits distribute over sums:

[tex]\displaystyle \lim_{x\to c}(f(x)+g(x)) = \lim_{x\to c}f(x)+\lim_{x\to c}g(x)[/tex]

• limits distribute over products:

[tex]\displaystyle \lim_{x\to c}(f(x)\times g(x)) = \lim_{x\to c}f(x)\times\lim_{x\to c}g(x)[/tex]

• limits distribute over quotients, provided that the denominator doesn't approach 0 :

[tex]\displaystyle\lim_{x\to c}\frac{f(x)}{g(x)} = \frac{\displaystyle\lim_{x\to c}f(x)}{\displaystyle\lim_{x\to c}g(x)}[/tex]

• if f(x) is continuous at x = c, then the limit "passes through" a composition:

[tex]\displaystyle \lim_{x\to c}f(g(x)) = f\left(\lim_{x\to c}g(x)\right)[/tex]

# # #

(a) This limit is 2. At x = 2, we have f (2) = 1, but from either side of x = 2, we see f(x) approaching the point (2, 2). So

[tex]\displaystyle \lim_{x\to 2}(f(x)+g(x)) = \lim_{x\to2}f(x)+\lim_{x\to2}g(x) = 2+0 = 2[/tex]

(b) This limit does not exist. We would have

[tex]\displaystyle \lim_{x\to1}(2f(x)-3g(x)) = 2\lim_{x\to1}f(x)-3\lim_{x\to1}g(x)[/tex]

but g(x) approaches 2 from the left of x = 1, and g(x) approaches 1 from the right of x = 1. The one-sided limits don't match, so the two-sided limit doesn't exist.

(c) This limit is 0. It looks like f(x) passes through the origin, while g(x) ≈ 3/2 at x = 0. So

[tex]\displaystyle\lim_{x\to0}f(x)g(x) = \lim_{x\to0}f(x)\times\lim_{x\to0}g(x)=0\times\frac32 = 0[/tex]

(d) This limit does not exist since

[tex]\displaystyle \lim_{x\to-1}g(x)=0[/tex]

(e) This limit is 16. Nothing tricky here, just use the same property as in (c).

[tex]\displaystyle\lim_{x\to2}x^3f(x) = \lim_{x\to2}x^3\times\lim_{x\to2}f(x) = 8\times2=16[/tex]

(f) This limit is 1. f(x) is continuous at x = 1, while g(x) approaches 2 from the left.

[tex]\displaystyle\lim_{x\to1^-}f(g(x)) = f\left(\lim_{x\to1^-}g(x)\right) = f(2) = 1[/tex]

Answer: 8.EB and F: yes

9.DB and FC:no

10.AC and ED:yes

11.AE and DC:yes

12.F,A,B and C:yes

13.F,A,B and D:no

14.plane Q and EC:yes

15.FB and BD:yes

Step-by-step explanation:

hope this helps have a good day!

Answer:

[tex] \frac{1 - 2 \sqrt{x} + x }{1 - x} [/tex]

Step-by-step explanation:

[tex] \frac{1 - \sqrt{x} }{1 + \sqrt{x} } [/tex]

Rationalize the denominator by multiplying by it conjugate.

[tex] \frac{1 - \sqrt{x} }{1 + \sqrt{x} } \times \frac{1 - \sqrt{x} }{1 - \sqrt{x} } = \frac{1 - 2 \sqrt{x} + x}{1 - x} [/tex]

Answer:

ethethe

Step-by-step explanation:

thethetht

Answers:

The logarithmic function f(x) = ln(x) is the natural logarithmic function and has base  e  

=======================================

Explanation:

The ln(x) or Ln(x) is the natural log function. The order of L and n is backwards compared to "natural log", but you can think of it "log that is natural" or something along those lines.

The Ln(x) function is of the form [tex]\log_b(x)[/tex] where the base b is the special constant e = 2.718... (this constant is similar to pi = 3.14...)

Answer:

11

Step-by-step explanation:

Add:

26 + 19 + 43

^       ^

   45 + 43

       88

Divide:

88 / 8 = 11

So, each tank has 11 fish.

Hope this helped.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]6525\text{cm.}^3[/tex]

Keep in mind that this is APPROXIMATE.

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Volume of a Sphere Is:}}\\\\V = \frac{4}{3} \pi r^3\\----------------\\\rightarrow \text{We are given the radius of } 11.6\text{ cm.}\\----------------\\V = \frac{4}{3}(3.14) (11.6)^3\\\\V = \frac{4}{3}(3.14) 1560.896\\\\V \approx 6534.95125\text{cm.}^3\\\\\boxed{V \approx 6535\text{cm.}^3}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

common ratio=0.5, a1= 0.08

Step-by-step explanation:

r=a3/a2

r=a4/a3

compare both we get:

a3/a2=a4/a3

subtitute a2=0.04 and a4=1

a3/0.04=1/a3

(a3)^2=0.04*1

(a3)^2=0.04

taking square root in both sides

a3=0.02

For r, r=a3/a2

subtitute a3 and a2 above

r=0.02/0.04

r=0.5 common ratio

For a1

r=a2/a1

0.5=0.04/a1

a1=0.04/0.5

a1=0.08

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

The first term of the geometric sequence is 0.08.

The common ratio of the geometric sequence is 1/0.02.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

Geometric sequence:

The second term = 0.04

The fourth term = 1

In a geometric sequence the nth term is given as:

[tex]a_{n}[/tex] = [tex]a_1 r^{n-1}[/tex]

Second term = 0.04

[tex]a_2[/tex] = 0.04

[tex]a_1 r^1 = 0.04[/tex]

[tex]a_1r[/tex] = 0.04 _____(1)

Fourth term = 1

[tex]a_4 = 1[/tex]

[tex]a_1 r^3[/tex] = 1 _____(2)

From (1) and (2) we get,

0.04/r = 1/r³

r³ = r / 0.04

r² = 1/0.04

r = 1/0.02 ____(3)

Putting (3) in (1) we get

[tex]a_1[/tex] = 0.04 x 0.02 = 0.08

Thus,

The first term of the geometric sequence is 0.08.

The common ratio of the geometric sequence is 1/0.02.

Learn more about geometric sequence here:

https://brainly.com/question/2321576

#SPJ2

Answer:

672

Step-by-step explanation:

Given: 8 pizza hut's sold a total of 5,376 pizzas

Each pizza hut sold the same amount of pizzas

So number of pizzas sold from 1 pizza hut = 5376/8 = 672

The required simplified value of the given expression is 16x¹². Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
=(2x³)⁴

As we know that,
[xᵃ]ᵇ = xᵃˣᵇ

So,
(2x³)⁴ = 2⁴x³ˣ⁴
        = 16x¹²

Thus, the required simplified value of the given expression is 16x¹².

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2

168

this is the full process

Answer:

5x5= 25

Step-by-step explanation:

5+5+5+5+5= 25

Answer:

[tex]3 \times (4 + 7) =( 3 \times 4) + (3 \times 7) \\ thank \: you[/tex]

Answer:

[tex]{ \bf{ \bar {MN}} \: means \: length \: between \: M \: and \: N}[/tex]

MN means line joining point M to point N.

Answer:

30 caps can be bought

Step-by-step explanation:

[tex]{ \sf{Rs.800 = (10 \times 12) \: caps}} \\ { \sf{Rs.200 = ( \frac{200 \times 10 \times 12}{800}) \: caps}} \\ \\ { \sf{ = 30 \: caps}}[/tex]

Answer:

50¢

Step-by-step explanation:

$18.00=1800.

3*12=36

1800/36=50

Answer:

Step-by-step explanation:

the price of per inch is $2

Answer:

[tex]x^{14}[/tex]

Step-by-step explanation:

[tex]x^{5}[/tex] × [tex]x^{3}[/tex] × [tex]x^{6}[/tex]

[tex]x^{5+3+6}[/tex]

[tex]x^{14}[/tex]

Answer:

huh

Step-by-step explanation:

Answer:

402. 5

Step-by-step explanation:

This is your answer hope this helps

And also pls mark me brainliest

Answer:

a = 6

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

a^2 + 8^2 = 10 ^2

a^2 +64 = 100

a^2 = 100 -64

a^2 = 36

Take the square root of each side

sqrt(a^2) = sqrt(36)

a = 6

Step-by-step explanation:

that means the expression is the result of a multiplication with (x-0.5) being one factor.

so, we divide the whole expression by this and then deal with the remaining quadratic equation.

6x³ - 13x² + x + 2 / x - 0.5 = 6x² - 10x - 4

- 6x³ - 3x²

----------------------------

- 10x² + x + 2

- - 10x² + 5x

----------------------------

- 4x + 2

- - 4x + 2

----------------------------

finished. 0

so, the whole expression is also

P(x) = (x-0.5)×(6x² - 10x - 4)

now we need to find the 2 zero points of the quadratic part.

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 6

b = -10

c = -4

x = (10 ± sqrt(100 - 4×6×-4))/12 =

= (10 ± sqrt(100 + 96))/12 = (10 ± sqrt(196))/12 =

= (10 ± 14)/12

x1 = (10+14)/12 = 24/12 = 2

x2 = (10-14)/12 = -4/12 = -1/3

Answer:

Both of them drew the parallelogram right.

Step-by-step explanation:

In Raquel's drawing we can see that the parallelogram is shorter and smaller but both the opposite lines are congruent to each other and match the scale size to the original drawing. And it Felipe's drawing the parallelogram is longer and bigger than the original drawing but the opposite line are also congruent to each other and match the scale size to the original drawing!!

I hope you get it right! :)

Answer: no

Step-by-step explanation: