Which of the following similarity statements about the traiangles in the figure is true

Answers

Answer 1

Answer: the second one I hope I am correct

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Unknown g (x) = ax + b and g (g (x)) = 16x - 15. Calculate the value of a and b.

Answers

g(g(x))=16x-15
means that when you subsituted g(x) for x in g(x), you got 16x-15

a(ax+b)+b=16x-15
distribute
xa^2+ab+b=16x-15d
we look at the x terms
therefor
xa^2=16x
a^2=16
a=-4 or 4
we will find out

look a constant terms
ab+b=-15
undistribute b
b(a+1)=-15

if a is -4 then
b(-4+1)=-15
b(-3)=-15
b=5

if a=4 then
b(4+1)=-15
b(5)=-15
b=-3

so
g(x)=-4x+5 or
g(x)=4x-3

if a=-4, b=5
if a=4, b=-3

Find the inverse of each function1) g (x)= 3+(x-1)^3
4) f (x)=x^3+2
5) f (n)= 5 square root of (-n+1/2)

Answers

to find the inverse
1. replace f(x) or g(x) or f(n) with y
2. switch places of x and y
3. solve for y
4. replace y with f⁻¹(x) or g⁻¹(x) or f⁻¹(n)

1.
g(x)=3+(x-1)^3
replace
y=3+(x-1)^3
switch
x=3+(y-1)^3
solve
x=3+(y-1)^3
subtract 3
x-3=(y-1)^3
cube root both sides
$\sqrt[3]{x-3}$ =y-1
add 1
$\sqrt[3]{x-3}$ +1=y
switch y with g⁻¹(x)
g⁻¹(x)= $\sqrt[3]{x-3}$ +1

4. f(x)=x^3+2
replace with y
y=x^3+2
switch x and y
x=y^3+2
solve for y
x=y^3+2
subtract 2
x-2=y^3
cube roo both sides
$\sqrt[3]{x-2}$ =y
replace with f⁻¹(x)
f⁻¹(x)= $\sqrt[3]{x-2}$

5.
f(n)=5 $√(-n+1/2)$
replace
y=5 $√(-n+1/2)$
switch n and y
n=5 $√(-y+1/2)$
solve for y
n=5 $√(-y+1/2)$
divide both sides by 5
n/5=n= $√(-y+1/2)$
square both sides
$(n^2)/(25)$ =-y+1/2
subtract 1/2 from both sides
$(n^2)/(25)$ - $(1)/(2)$ =-y
multiply both sides by -1
- $(n^2)/(25)$ + $(1)/(2)$ =y
replace with f⁻¹(n)
f⁻¹(n)=- $(n^2)/(25)$ + $(1)/(2)$

1. g⁻¹(x)= $\sqrt[3]{x-3}$ +1
4. f⁻¹(x)= $\sqrt[3]{x-2}$
5. f⁻¹(n)=- $(n^2)/(25)$ + $(1)/(2)$

PLEASE HELP ill Mark BRAINLIEST 31 points too

Answers

Answer:(-1,7)

Step-by-step explanation:

Raymond purchases concert tickets online for $43.50. There is a 3% processing fee. What is the total cost of the tickets? Round to the nearest cent. The actual answer is not 44.80 it’s 44.81 thanks anyway I guess I got it wrong though :(

Answers

Answer:

$44.81

Step-by-step explanation:

43.50 * 0.03 = 1.305

$43.50 + 1.305 = 44.805 = $44.81

Triangle P=27,Q=40,P=33 law of sines round measures to the nearest tenth

Answers

For the law of sines, you would apply it in this particular problem like so:
Since P is 27, its angle is 33 and Q's length is 40; you would set it up like this
40/SinQ = 27/Sin33, multiply 40 with Sin33, then it would be 40Sin33, then divide it by 27. The result should be 40Sin33/27 = X

Find the slope between the two points: (9,9) and (12,15)

Answers

The slope formula is $(Y2-Y1)/(X2-X1)$ . For the two points, $(x,y)$ . You can pick any of the Y and X from these two points, but only once. $(9-15)/(9-12)$ = $(-6)/(-3)$ = 2 or $(15-9)/(12-9)$ = $(6)/(3)$ = 2 and both will equal to. The answer for the slope is 2.

Slope = Change in y / Change in x

Between (9, 9) and (12, 15).

We would use the coordinates from the second point minus that from the first point.

1st point = (9, 9), 2nd point = (12, 15)

Slope = (15 - 9) / (12 - 9)

= 6 / 3

= 2

Slope = 2