Topic : Composition of Functions - Worksheet 2 Using f(x) = 5x + 4 and g(x) = x - 3,find: 1. f(g(6)) 2. g(f(-7)) 3. f(f(8)) 4. g(f(x))

Answer:

Step-by-step explanation:

I'm a little confused by your question. But I solved the question this way.

y+12+2y-18+2y+16=180

Why 180° you ask? Because the angle sum interior of a triangle always measures 180°.

(y+2y+2y)+(12+−18+16)=180

5y+10=180

Subtract

5y+10−10=180−10

5y=170

divide

5y/5=170/5

y=34

Answer: 9

Step-by-step explanation:

Answer:

7/2

Step-by-step explanation:

Answer:

101.76

Step-by-step explanation:

Answer:

(12.9 - 3.1) i'm in middle school so if i can do it you can

Step-by-step explanation:

Answer:

the answer is 0.3%

Step-by-step explanation:

12 divided by 40 is 0.3

Answer:

30%

Step-by-step explanation:

Write a proportion.

12 / 40 = x / 100

Cross multiply.

40x = 1200

Solve for x.

x = 30

She ate 30% of the chips.

Answer:

1/2

Step-by-step explanation:

Answer: 224

Step-by-step explanation:

Answer:500

Step-by-step explanation:500 +7++U+U++UU+

Answer:

rage we are not doing ur homework

Step-by-step explanation:

14236.53

Step-by-step explanation:

I lookedd it up I'm not smart. ;)

Answer:

What two consecutive odd integers have a sum of 88? x + x + 2 = 88 • 2x + 2 = 88 • 2x = 86 • x = 43, x + 2 = 45 • 43 + 45 = 88 • Ans: 43, 45 • They equal 88 and are both odd.

*the graph of Function W and table of values of Function Z are in the diagram attached below.

Answer:

B. The slope of Function W is greater than the slope of Function Z.

F. The y-intercept of Function W is greater than the y-intercept of Function Z.

Step-by-step explanation:

To determine which of the statements compare both functions correctly, let's find the slope (m) and the y-intercept (b) of each function given.

✍️Function W:

Slope of Function B, using two points on the line, (0, -1) and (2, 0):

[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 -(-1)}{2 - 0} = \frac{1}{2} = 0.5 [/tex]

✅Slope = 0.5.

y-intercept is the point at which the line intercepts the y-axis. Therefore, the y-intercept, b = -1. The line cuts the y-axis at y = -1. At this point, x = 0.

✅y-intercept = -1.

✍️Function Z:

Slope of Function Z, using two pairs of values from the table of values for function Z, (0, -2) and (2, -1.5):

[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1.5 -(-2)}{2 - 0} = \frac{0.5}{2} = 0.25 [/tex]

✅Slope = 0.25.

y-intercept is the value of y when x = 0. It is at this point the line of the function of X intercepts the y-axis. From the table given, we can see that when x = 0, y = -2. Therefore:

✅y-intercept = -2.

Thus, the following statements that compares both functions are TRUE:

B. The slope of Function W is greater than the slope of Function Z.

✔️This is TRUE because 0.5 is greater than 0.25.

F. The y-intercept of Function W is greater than the y-intercept of Function Z.

✔️This is TRUE because -1 is greater than -2.

Answer: B and F

Step-by-step explanation:

Answer:

[tex]\log _b\left(\sqrt{\frac{57}{74}}\right)[/tex] is equivalent to  [tex]\frac{1}{2}\left(\log \:_b\left(57\right)-\log \:_b\left(74\right)\right)[/tex].

Hence, option 'c' is true.

Step-by-step explanation:

Given the expression

[tex]\log _b\left(\sqrt{\frac{57}{74}}\right)[/tex]

Rewrite as

[tex]=\log _b\left(\left(\frac{57}{74}\right)^{\frac{1}{2}}\right)[/tex]

[tex]\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0[/tex]

[tex]=\frac{1}{2}\log _b\left(\frac{57}{74}\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _c\left(\frac{a}{b}\right)=\log _c\left(a\right)-\log _c\left(b\right)[/tex]

[tex]=\frac{1}{2}\left(\log _b\left(57\right)-\log _b\left(74\right)\right)[/tex]     ∵ [tex]\log _b\left(\frac{57}{74}\right)=\log _b\left(57\right)-\log _b\left(74\right)[/tex]

Therefore,

[tex]\log _b\left(\sqrt{\frac{57}{74}}\right)[/tex] is equivalent to  [tex]\frac{1}{2}\left(\log \:_b\left(57\right)-\log \:_b\left(74\right)\right)[/tex].

Hence, option 'c' is true.

Answer: well it's correct-

Step-by-step explanation: it shows that e equals to 6-x, x would be 3 so then the problem would still be correct (3=|3|) and |3| just equals, well, 3.

Answer:

565

Step-by-step explanation:

77

Answer:

30km/hr

Step-by-step explanation:

18km/hr +12km/hr

The man rides 86.4 km distance.

Speed tells us how slow or fast an object moves. It describes the distance travelled divided by the time taken to cover the distance.

Speed is directly Proportional to Distance and inversely proportional to Time.

Speed = Distance/Time

Given,

Speed of man way to the village = 18km/hour

Speed of man when returns from the village = 12km/hour

Time for double journey = 6 hour

Let going time is x and returning time is y

x + y = 6   -------(a)

⇒ x = 6 - y

Distance for going = distance for returning

18x = 12y

Putting value of x in terms of y

18(6 - y) = 12y

108 - 18y = 12y

30y = 108

y = 108/30

y = 3.6 hours

Putting value of y in equation (a)

x + 3.6 = 6

x = 6 - 3.6

x = 2.4

Returning time = 3.6 hours

Returning distance = returning time × returning speed = 3.6 × 12

Returning distance = 43.2 km

Going distance = Returning distance = 43.2

Total ride distance = 43.2 + 43.2 = 86.4 km

Hence, 86.4 km is the distance of ride by the man.

Learn more about speed here:

https://brainly.com/question/28224010

#SPJ2

Answer:

D

Step-by-step explanation:

since her test average for the first 8 tests is 80, the sum of all the scores for the first 8 tests is 640. Since her 9th test is 71, we do 640+71=711. To find the average of all 9 tests, we do 711/9 = 79

D

Answer:

Its d i took the class

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

6 * 1.5 = 9

Answer:

1.3

Step-by-step explanation:

[tex]\sqrt[6]{9}[/tex]  = 9 divided by 6, 6 goes into 9, 1 time. Remainder of 3, 1.3 is the answer.

Answer:

1/2

Step-by-step explanation:

Answer:

The longest side length b is approximately 13.172 cm

Step-by-step explanation:

The given parameters are;

The area of the triangle = 22.4 cm²

The given angles of the triangle = ∠97°

The given side of the triangle = 3.7 cm

The formula for the area of a triangle, A = 1/2 × a × b × sin(C)

Where;

a, and b are the side legs forming the angle C

Therefore,  we have;

A = 22.4 = 1/2 × 3.7 × a × sin(97°)

a =  22.4/(1/2 × 3.7 × sin(97°)) ≈ 12.199

a ≈ 12.199 cm

Therefore, by cosine rule, we have;

b² = a² + c² - 2 × a × c × Cos(B)

Substituting the values, gives;

b² = 12.199² + 3.7² - 2 × 12.199 × 3.7 × Cos(97°)

b² ≈ 173.507

∴ b ≈ √173.507 ≈ 13.172

b ≈ 13.172 cm

Answer:

3x-8y=32

Step-by-step explanation:

Answer:

5 letters

Step-by-step explanation:

Let x = the number of letters engraved.

For the first store, the cost can be written as (18.50 + 0.15x).

For the second store, the cost can be written as (18 + 0.25x).

For the cost and value of x to be the same, let them equal eachother and evaluate x:

18.5 + 0.15x = 18 + 0.25

0.1x = 0.5

∴x=5

Answer:

I think that it is y= -2x +9

Step-by-step explanation:

I am sure about the slope but the y-intercept (9) might be wrong.

Try using the pythagorean theorem i think?

Answer:

The Base is Greater than the height

Step-by-step explanation:

So the answer has to be greater than eight.

Answer:

The expression for the area of the given triangle is 5x^4+4x^3units

Step-by-step explanation:

Answer:

The coordinates of Point D are: (-5,-8)

Step-by-step explanation:

The formula for mid-point is given by:

[tex]M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})[/tex]

For the point (x1,y1) and (x2,y2)

Given that

M = (-3, -6)

C = (-1, -4) => (x1,y1)

Putting the values of given points in the formula for mid-point

[tex](-3,-6) = (\frac{-1+x_2}{2} , \frac{-4+y_2}{2})[/tex]

Putting respective coordinates equal

[tex]-3 = \frac{-1+x_2}{2}\\-6 =-1+x_2\\x_2=-6+1\\x_2 = -5\\AND\\-6 = \frac{-4+y_2}{2}\\-12 = -4+y_2\\y_2 = -12+4\\y_2 = -8[/tex]

Hence,

The coordinates of Point D are: (-5,-8)