Study the figure and find the effort.
Please help...

Answer:

(fog)(x) =x –14

(gof)(x) =x

Step-by-step explanation:

[tex](fog)(x) = f(g(x)) \\ = 8( \frac{x - 7}{8} ) - 7 \\ = x - 7 - 7 \\ = x - 14[/tex]

[tex](gof)(x) = g(f(x)) \\ = \frac{(8x - 7) + 7}{8} \\ \\ = \frac{8x}{8} \\ \\ = x[/tex]

We look for constants a and b such that

[tex]\displaystyle \frac{7x-8}{(2x-1)(x-2)} = \frac a{2x-1} + \frac b{x-2}[/tex]

Rewrite all terms with a common denominator and set the numerators equal:

[tex]\displaystyle \frac{7x-8}{(2x-1)(x-2)} = \frac{a(x-2)}{(2x-1)(x-2)} + \frac{b(2x-1)}{(x-2)(2x-1)} \\\\ \frac{7x-8}{(2x-1)(x-2)} = \frac{a(x-2)+b(2x-1)}{(2x-1)(x-2)} \\\\ \implies 7x-8 = a(x-2) + b(2x-1) = (a+2b)x - 2a - b[/tex]

Then

a + 2b = 7

-2a - b = -8

Solve for a and b. Using elimination: multiply the first equation by 2 and add it to the second equation:

2 (a + 2b) + (-2a - b) = 2(7) + (-8)

2a + 4b - 2a - b = 14 - 8

3b = 6

b = 2

Then

a + 2(2) = 7   ==>   a = 3

and so

[tex]\displaystyle \frac{7x-8}{(2x-1)(x-2)} = \frac 3{2x-1} + \frac 2{x-2}[/tex]

Answer:

a=3

b=2

Do whatever you want with that information^^

Answer:

1. PN

Step-by-step explanation:

Answer:

probability is 32/52 or about 0.615

Step-by-step explanation:

There are 12 face cards

of the remaining 52 - 12 = 40 cards, half of them are black

so 12 + 40/2 = 32 cards would be considered successful

Answer:

83°

.......................

Answer:

83

Step-by-step explanation:

9514 1404 393

Answer:

  p = 12

Step-by-step explanation:

The sines of the opposite angles are the same, so the lengths of the sides are the same.

  p = 12

_____

The law of sines tells you ...

  p/sin(P) = r/sin(R)

  p/0.2 = 12/0.2 . . . . . . substitute given values

Multiply by 0.2 to get ...

  p(0.2/0.2) = 12(0.2/0.2)

  p = 12

Answer:

r = 5

Step-by-step explanation:

the sine rules formula :

sin Q/q = sin R/r

=> r = q× sin R / sin Q

= 6× ⅓ / (2/5)

= 2 /(2/5)

= 2× 5/2

= 5

Answer:

r = 5

Step-by-step explanation:

Sine trigonometric ratio

[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]

where:

The sides of a triangle are opposite their angles.  Therefore, in ΔPQR:

⇒ side r is opposite angle R

⇒ side p is opposite angle P

⇒ side q is opposite angle Q

Using the given ratio of sin Q:

[tex]\sf \implies \sin Q=\dfrac{q}{H}=\dfrac{2}{5}[/tex]

Substitute the given value of q = 6 and solve for H:

[tex]\sf \implies \dfrac{6}{H}=\dfrac{2}{5}[/tex]

[tex]\sf \implies H=6 \cdot\dfrac{5}{2}[/tex]

[tex]\sf \implies H=15[/tex]

Using the given ratio of sin R:

[tex]\implies \sf \sin R=\dfrac{r}{H}=\dfrac{1}{3}[/tex]

Substitute the found value of H and solve for r:

[tex]\implies \sf \dfrac{r}{15}=\dfrac{1}{3}[/tex]

[tex]\implies \sf r=15 \cdot\dfrac{1}{3}[/tex]

[tex]\implies \sf r=5[/tex]

Learn more about trigonometric ratios here:

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Answer : 72

Step-by-step explanation:

It's above in the pic .

Answer:

m∠AKD = 46°

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

Measure of <AKG = 133°

So,

<AKG = <AKD + <DKG (As both together combine to form one <AKG as shown)

=> 133° = <AKD + 87°

=> <AKD = 133° - 87°

=> <AKD = 46° (Ans)

Answer: The highlighted digit 8 is in the tens place. The value of the 8 is 80

Step-by-step explanation:

The value of the 8 is 80 becuse it is in the tens place.

Answer:

C

Step-by-step explanation:

We want to simplify the expression:

[tex]\displaystyle 3 \sqrt{-28}[/tex]

Rewrite:

[tex]\displaystyle = 3 \sqrt{ 4\cdot 7 \cdot -1}[/tex]

Rewrite:

[tex]\displaystyle = 3 \cdot \sqrt{4} \cdot \sqrt{7} \cdot \sqrt{-1}[/tex]

Simplify. Let i = √(-1). Hence:

[tex]\displaystyle = 3 \cdot \left(2\right) \cdot \left(i\right) \cdot \sqrt{7}[/tex]

Multiply:

[tex]\displaystyle = 6i\sqrt{7}[/tex]

In conclusion, our answer is C.

Answer:

6.99 meters

Step-by-step explanation:

For this we have to use subtraction:

So if the second jump was .13 meters longer then the first and we know the second jump was 7.12 meters, we have to subtract 7.12 by .13 to get the length of his/her's first long jump. So our equation is 7.12-.13=length of first jump. So we end up getting 6.99=length of first jump.

Hope this helps! :D

294738917263748hehejshdhf

Answer:66.5 degrees

Step-by-step explanation:

Answer:

[tex]thank \: you[/tex]

Answer:

2-x^2-6x

Step-by-step explanation:

2-x(x+6)

2-x^2-6c

Answer:

y = 4x - 3

Step-by-step explanation:

Slope intercept form is made up of these components:

    The question gives you the slope and the y-intercept. Now all you need to do is substitute the values for the variables. Therefore, the equation is y = 4x - 3.

Answer:

The balloon is rising at a rate of 50π/3 feet per minute.

Step-by-step explanation:

A weather balloon is rising vertically while being observed from a point who is exactly 300 feet away from the spot directly beneath the ground.

This is represented in the diagram below.

We want to find the rate at which the balloon is rising (i.e. find dh/dt) when the angle between the ground and the observer is π/6 (i.e. when θ = π/6), and is increasing at a rate of π/24 radians per minute (i.e. when dθ/dt = π/24).

Write a ratio relating the variables:

[tex]\displaystyle \tan \theta = \frac{h}{300}[/tex]

Take the derivative of both sides with respect to t:

[tex]\displaystyle \frac{d}{dt}\left[ \tan\theta\right] = \frac{d}{dt}\left[ \frac{h}{300}\right][/tex]

Implicitly Differentiate:

[tex]\displaystyle \sec^2\theta \cdot \frac{d\theta}{dt} = \frac{1}{300} \frac{dh}{dt}[/tex]

Substitute in known values:

[tex]\displaystyle \sec^2 \left(\frac{\pi}{6}\right) \left(\frac{\pi}{24}\right) = \frac{1}{300} \frac{dh}{dt}[/tex]

Solve for dh/dt:

[tex]\displaystyle \begin{aligned} \frac{dh}{dt} &= 300\left(\sec^2\left(\frac{\pi}{6}\right)\left(\frac{\pi}{24}\right)\right) \\ \\ &= 300\left(\frac{4}{3}\right)\left(\frac{\pi}{24}\right) \\ \\ &= \frac{50\pi}{3} \text{ feet per minute}\end{aligned}[/tex]

In conclusion, the balloon is rising at a rate of 50π/3 feet per minute.

Answer:

2 5/16

Step-by-step explanation:

step by step instructions are in pic below

Answer:

56 chocolate chips will be used with 40 cookies.

Step-by-step explanation:

14 chocolate chips = 10 cookies

? chocolate chips = 40 cookies

Variable x = number of chocolate chips for 40 cookies

14/10 = x/40

Cross multiply:

14 × 40 = 10 × x

560 = 10x

56 = x

Answer:

-12z^2

Brainliest, please!

Step-by-step explanation:

-5z^2 - 7z^2 = -12z^2

Answer:

(-9/2,-1)

Step-by-step explanation:

Use the midpoint formula to find the midpoint of the line segment.

Answer:

3300

Step-by-step explanation:

P = 3/4n + 1800

P = 3/4(2000) + 1800

P = 3 × 500 + 1800

P = 1500 + 1800

P = 3300

Therefore, the cost of producing 2000 items is GHC 3,300.

cost of producing 2000 items =3300

Solution:-

P = 3/4n + 1800

P = 3/4(2000) + 1800

P = 3 × 500 + 1800

P = 1500 + 1800

P = 3300

Therefore, the cost of producing 2000 items is GHC 3,300.

Learn more about problems with cost here https://brainly.com/question/25109150

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Answer:

a) 28,770 ÷ 10 ^ 2  = 287.7

b) 28,770 ÷ 10 ^ 3  = 28.77

c) 28,770 ÷ 10 ^ 4  = 2.877

Answer:

(-7, 5)

Step-by-step explanation:

Answer:

(-7,5)

Step-by-step explanation:

have a nice day

9514 1404 393

Answer:

  a)  235 mi

  b)  259 mi

Step-by-step explanation:

The scale factor from the map to the real world is apparently ...

  (SA-H actual)/(SA-H map) = (188 mi)/(3 in) = 62 2/3 mi/in

Then the actual distance from Dallas to Houston is ...

  (3.75 in)(62 2/3 mi/in) = 235 mi

And from Dallas to San Antonio, the distance is ...

  (4.125 in)(62 2/3 mi/in) = 258.5 mi ≈ 259 mi

Answer:

x=4

Step-by-step explanation:

5+3x=17

-5        -5

3x=12

3       3

x=4

Answer:

x = 4

Step-by-step explanation:

[tex]5+3x=17\\\\3x=12\\\\x=4[/tex]