Compute the average rate of change of f(x)=(x+4)/(x-3) over the interval [5,7].
A)4/3
B)7/8
C)-7/8
D)-4/3
(Image attached below)

Answer:

16.26°

Step-by-step explanation:

Start by labelling the given sides of a triangle as either adjacent, opposite or hypotenuse side.

• Adjacent side: side on which the right angle and angle of interest lie

• Opposite side: side facing the angle of interest

• Hypotenuse side: side facing the right angle

In this case, the side with '24' is the adjacent side while the side with '7' is the opposite side.

Given these two sides, we use tangent to find the unknown angle.

[tex]\boxed{ \tanθ = \frac{opp}{adj} }[/tex]

[tex] \tanθ = \frac{7}{24} [/tex]

Tasking the inverse of tangent on both sides:

[tex]θ = \tan^{ - 1} ( \frac{7}{24} ) [/tex]

θ= 16.260° (3 d.p.)

Thus, the second option is correct.

Notes:

[tex]\boxed{ \sinθ = \frac{opp}{hyp} }[/tex]

[tex]\boxed{ \cosθ = \frac{adj}{hyp} }[/tex]

[tex]\large\underline{\sf{Solution-}}[/tex]

We have to evaluate the given expression.

[tex] \rm = \sqrt{ \dfrac{1 - \sin(x) }{1 + \sin(x) } } [/tex]

If we multiple both numerator and denominator by 1 - sin(x), then the value remains same. Let's do that.

[tex] \rm = \sqrt{ \dfrac{[1 - \sin(x)][1 - \sin(x) ]}{[1 + \sin(x)][1 - \sin(x) ]} } [/tex]

[tex] \rm = \sqrt{ \dfrac{[1 - \sin(x)]^{2}}{1- \sin^{2} (x) } } [/tex]

We know that:

[tex] \rm \longmapsto { \sin}^{2}(x) + \cos^{2}(x) = 1[/tex]

[tex] \rm \longmapsto \cos^{2}(x) = 1 - { \sin}^{2}(x)[/tex]

Therefore, the expression becomes:

[tex] \rm = \sqrt{ \dfrac{[1 - \sin(x)]^{2}}{\cos^{2} (x)}} [/tex]

[tex] \rm = \dfrac{1 - \sin(x)}{\cos(x)}[/tex]

[tex] \rm = \dfrac{1}{\cos(x)} - \dfrac{ \sin(x) }{ \cos(x) } [/tex]

[tex] \rm = \sec(x) - \tan(x) [/tex]

[tex] \sqrt{ \frac{ \cos(n) }{1 + \: \sin(n) } } [/tex]

see the attachment!!

hope it helps

#carryolearning

Answer:

x=21, y= 35

Step-by-step explanation:

3x+7=5x-35

(subtract seven from -35)

3x=5x-42

(subtract 5 from 3)

-2x=-42

(-42/-2= positive number)

x=21

y+75=3y+5

(subtract 75 from 5)

y=3y-70

(subtract 3y from y)

-2y=-70

y=35

Answer: $42

Step-by-step explanation: 7 x 6 = 42

Answer:

$42

Step-by-step explanation:

7 times 6 is 42 so 6 movie tickets that cost $7 is $42 all together

Answer:

g = 6

Step-by-step explanation:

Step 1: Subtract 3.3g from both sides.

Step 2: Subtract 8 from both sides.

Step 3: Divide both sides by 2.

(hope this helps) :)

[tex]\tt5( x - 3 ) = 5x - 15 \\ \tt5x - 15 = 5x - 15 \\ \tt5x - 5x = - 15 + 15 \\ \tt\bcancel{5x} - \bcancel{5x} = \bcancel{- 15} + \bcancel{15} \\ \boxed{\tt0 = 0}[/tex]

Value of x (substitute 0 in the place of x).

[tex]\tt5( (0) - 3 ) = 5(0) - 15 \\ \tt0 - 15 = 0 - 15 \\ \tt \boxed{\tt -15 = -15}[/tex]

Answer:

[tex]s(u(2)) = 135[/tex]

Step-by-step explanation:

[tex]u(t) = 7t - 2 \\ u(2) = 7(2) - 2 \\ u(2) = 14 - 2 \\ u(2) = 12 \\ \\ s(t) = {t}^{2} - 9 \\ s(u(2)) = {(12)}^{2} - 9 \\ s(u(2)) = 144 - 9 \\ \\ s(u(2)) = 135[/tex]

I hope I helped you^_^

For the functions u(t) = 7t - 2 and s(t) = t² - 9. s(u(2)) = 135

A function is a mathematical equation that shows the relationship between two variables.

For the functions u(t) = 7t - 2 and s(t) = t² - 9.To find what is s(u(2)), we proceed as follows.

Since u(t) = 7t - 2. Then u(2) is evaluated when t = 2. So, we have that

u(t) = 7t - 2

u(2) = 7(2) - 2

u(2) = 14 - 2

u(2) = 12

Now, since u(2) = 12 and s(t) = t² - 9

s(u(2)) is evaluated as follows

s(t) = t² - 9

s(u(2)) = 12² - 9

s(u(2)) = 144 - 9

s(u(2)) = 135

So, s(u(2)) = 135

Learn more about function here:

https://brainly.com/question/29631554

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Answer:

1.8(3) (three is a repeating number)

Step-by-step explanation:

Divide the numerator from the denominator. Add the value of the integer part.

Answer:1.83

Step-by-step explanation:

so the  1 that's a whole number and 5 out of 6 should be around 82-85 but for real its 1.83 but its a repeating decimal so its like 1.83333

Answer:

p = w - cg

Step-by-step explanation:

w = p + cg ( isolate p by subtracting cg from both sides )

w - cg = p

Answer:

31/ 32

Step-by-step explanation:

Switch the fractions and multiply. This will work in place of division.

31/32 is already in the simplest form, you can't simplify it anymore.

-kiniwih426

Answer:

Answer:

2.5

Step-by-step explanation:

Answer:

1 7/8

Step-by-step explanation:

Exact Form 15/8

Decimal Form 1.875

Mixed Number 1 7/8

Answer:

B

Step-by-step explanation:

Perimeter is the sum of all the lengths of its sides.

Perimeter of the figure

= 9x +8x -2 +17x -6 +5x +1

= 9x +8x +17x +5x -2 -6 +1

= 39x -7

Thus, the correct answer is option B.

Answer:

C

Step-by-step explanation: C is the best equation

Answer:

Step-by-step explanation:

The graph is closer to a line:

According to above observation, the closest choice is C

Answer:

25. 7 months

26. Php 12500

27. a. 3x-4y=8

b. 4x+2y=0

c. _ graph yourself

d. Yes it does

28. A. Yes

B. Yes

C. No

The answer is the first option

The cost of one cherry pie (c) is $12 and one pumpkin pie (p) is $19 and the equation system will calculate the cost of one cherry 11c + 4p = 208  and 13c + 12p = 384 .

A linear equation is defined as an equation in which the highest power of the variable is always one.

Let the number of cherry pies be c,

And the number of pumpkin pies be p,

As per the given information, an equation system will calculate the cost of one cherry.

11c + 4p = 208    ...(i)

13c + 12p = 384  ...(ii)

Multiplying 12 by equation (i) and 4 by equation (ii), we get

132c + 48p = 2496 …(iii)

52c + 48p = 1536 …(iv)

Equation (iii) subtracts from (iv) and we get c = 12 then substitute the value of 'c’ into equation (i) and we get

11(12) + 4p = 208

4p = 208 - 132

4p = 76

p = 19

Thus, the cost of one cherry pie (c) is $12 and one pumpkin pie (p) is $19

Learn more about the Linear equations here:

https://brainly.com/question/13738061

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3.2128 is a rational number because you can not make it into a fraction/ratio

Answer:

where is the question???..............

Answer:

y = 0

Step-by-step explanation:

READ THE GRAPH. If X = 1, then Y = 0. have a nice day

Answer:

f(- 1) = 3

Step-by-step explanation:

locate x = - 1 on the x- axis, go vertically up to meet the graph at (- 1, 3 ) , so

when x = - 1, then y = 3 , that is

f(- 1) = 3

Answer:

1. 6

2. 8

3. 10

4. 12

5. 14

Step-by-step explanation:

just solve

Answer:

Step-by-step explanation:

the way to find how many participanted in the class voted, you need to look at the percentages and the number of students that voted for Vicky.

50% of students voted for Vicky and the question later explained that the total of the 50% was 30 students. This mean we know half of the student that participated. To find the total amount of students to make 100%, you need to multiple 30 by 2. which is 60.

Now that we know there were 60 students in total, we can find how many participated by using Iverson's percentage.

this is the formula that can help with any percentage math problem:

The percentage of something ÷ 100% = the number you are looking for ÷ the total

in our case:

40÷100 = x (because it is the unknown term)÷60

from here you cross multiple getting

2400÷100x

which equals

24

now we have to add Vicky's and Iverson's voter

24 + 30= 54

60-54=6

6 students did not participate

Answer:

24cm (piste 20characteristic pa bago masabi sagot)

Answer:

$39.20

Step-by-step explanation:

$49 * (1-.2) = $39.20

Answer: In ^3

Step-by-step explanation: V = (1/2) (4/3) π(d/2^3

Plug in  

d = 56.7 in

and get V in units of in^3.

Answer:

12

Step-by-step explanation:

-2x + 7=5

or, 7-5=2x

or, 2=2x

or, 2/2=x

or, 1=x

Then,

7x+5

=7×1+5

=7+5

=12

Answer:

x=1

Step-by-step explanation:

-7 both sides that will give you -2

-2x=-1 divide by -2 and u will get on i think that what you were asking

Answer:

y - 3 = - 1/4(x + 2)

Step-by-step explanation:

m = - 1/4

Point = (-2,3)

y-intercept = 3 - (- 1/4) (-2)

= 3 - 1/2 = 5/2

y = - 1/4x + 5/2

20.8 cm

so sorry if incorrect :(