F(x) = 3x-1 and g(x)=2x^2

a. Find (f g) (x).


b. Find (f-g) (x).


c. Find f(g(x)).


d. Find g(f(x)).

Answer:

(x−4)² + (y−5)² = 36

Step-by-step explanation:

The equation of a circle is:

(x−h)² + (y−k)² = r²

where (h, k) is the center and r is the radius.

If the center is (4, 5) and the radius is 6, then the equation is:

(x−4)² + (y−5)² = 6²

(x−4)² + (y−5)² = 36

Answer:-(√3)/2, (√2)/2, -√3, and undefined

Step-by-step explanation:

There are two ways you can solve this.  One is with the Pythagorean identity:

sin²θ + cos²θ = 1

The other way is by knowing your unit circle.

1. From the unit circle, we know that cos θ = 1/2 at θ = π/3 and θ = 5π/3.  Since θ is in Quadrant IV, then θ = 5π/3.  sin (5π/3) = -(√3)/2.

We can check our answer using the Pythagorean identity:

sin²θ + cos²θ = 1

sin²θ + (1/2)² = 1

sin²θ + 1/4 = 1

sin²θ = 3/4

sin θ = ±(√3)/2

Since sine is negative in Quadrant IV, sin θ = -(√3)/2.

We can repeat these steps for the other questions.

2. sin θ = (√2)/2 at θ = π/4 and θ = 3π/4.  Since θ is in Quadrant I, θ = π/4.  Therefore, cos θ = (√2)/2.

3. cos θ = -1/2 at θ = 2π/3 and θ = 4π/3.  Since θ is in Quadrant II, θ = 2π/3.  Therefore, sin θ = (√3)/2, and tan θ = sin θ / cos θ = -√3.

4. sin θ = -1 at θ = 3π/2.  Therefore, cos θ = 0.  tan θ = sin θ / cos θ, so tan θ is undefined.

1. sinθ = √3/2, 2. cosθ = √2/2, 3. tanθ = -√3, 4. tanθ is undefined.

1. Given that cosθ=1/2 and θ terminates in Quadrant IV, we can use the Pythagorean identity sin^2θ + cos^2θ = 1 to find sinθ. Substitute the value of cosθ into the equation: sin^2θ + (1/2)^2 = 1. Solve for sinθ: sinθ = ± √(1 - (1/4)) = ± √(3/4) = ± √3/2. Since θ terminates in Quadrant IV, sinθ is positive. Therefore, sinθ = √3/2.

2. Given sinθ=(√2)/2 and θ terminates in Quadrant I, we can again use the Pythagorean identity sin^2θ + cos^2θ = 1 to find cosθ. Substitute the value of sinθ into the equation: (√2/2)^2 + cos^2θ = 1. Solve for cosθ: cosθ = ± √(1 - (1/2)). Since θ terminates in Quadrant I, cosθ is positive. Therefore, cosθ = √(1 - (1/2)) = √(1/2) = 1/√2 = √2/2.

3. Given cosθ=-1/2 and θ terminates in Quadrant II, we can find sinθ using the Pythagorean identity sin^2θ + cos^2θ = 1. Substitute the value of cosθ into the equation: sin^2θ + (-1/2)^2 = 1. Solve for sinθ: sinθ = ± √(1 - (1/4)) = ± √(3/4) = ± √3/2. Since θ terminates in Quadrant II, sinθ is positive. Therefore, sinθ = √3/2. Now, we can find tanθ using the relationship tanθ = sinθ / cosθ. Substitute the values of sinθ and cosθ into the equation: tanθ = (√3/2) / (-1/2) = -√3.

4. Given sinθ=-1 and 0≤θ<2π radians, we can find cosθ using the Pythagorean identity sin^2θ + cos^2θ = 1. Substitute the value of sinθ into the equation: (-1)^2 + cos^2θ = 1. Solve for cosθ: cos^2θ = 1 - 1 = 0. Since 0^2 = 0, cosθ = 0. Now, we can find tanθ using the relationship tanθ = sinθ / cosθ. Substitute the values of sinθ and cosθ into the equation: tanθ = -1 / 0 = undefined.

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Answer:

13.7 cm²

Step-by-step explanation:

area of yellow region = area of square - area of 4 quarter circles

area of square = 8² = 64

area of 4 congruent quarter circles = area of circle

area of circle with radius = 4

A = π × 4² = 16π

yellow region = 64 - 16π ≈ 13.7 cm²

Answer:

593.0 cm³

Step-by-step explanation:

The volume (V) of the prism is calculated as

V = area of triangular end face × length

A of Δ = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 10.2 and h = 10. 2

A of Δ = 0.5 × 10.2 × 10.2 = 52.02 cm², hence

V = 52.02 × 11.4 ≈ 593.0 cm³

Answer: the height would be 15

Step-by-step explanation:

v= pi*radius^2*height

1215pi mm= pi*9^2*height

1215pi mm= pi*81*height

(divide by pi on both sides, which isolates pi on both sides)

1215 mm= 81*height

(divide by 81 on both sides, which would isolate 81 on the right side of the equation)

1215/81= 15= height

The height of the cylinder is 15 mm.

To find the height of a cylinder, we can use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.

Given that the volume is 1215π mm and the radius is 9 mm, we can plug these values into the formula and solve for h.

1215π = π(9)²h

Simplifying the equation, we have:

1215 = 81h

Dividing both sides by 81, we find:

h = 15 mm

Therefore, the height of the cylinder is 15 mm.

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Answer:

Area of a kite = 34.3 ft^2

Step-by-step explanation:

a kite has diagonals 9.8 ft and 7 ft

WE are given with the diagonals of the kite

Area of a kite = diagonal 1 * diagonal 2 /2

diagonal 1= 9.8 ft

diagonal 2 = 7ft

Area of a kite =  [tex]\frac{9.8 * 7}{2}[/tex]

Area of a kite= 34.3 square feet

Answer:

D

Step-by-step explanation:

When a number is listed outside the function it is a vertical movement. So negative is down, positive is up!

Inside the function would be left/right. This would have been found in your exponent.

D. The graph of [tex]f(x)[/tex]  is shifted three units down from the graph of g(x).

f(x) = [tex]-4^{5x} -3[/tex] and g(x) = [tex]-4^{5x}[/tex]

In general, replacing x with x – h in a mathematical sentence translates its graph h units horizontally. Similarly, replacing y with y – k in a sentence translates its graph k units vertically.

For example, your sketch of Group B should show that the graph of y = x2 + 3 is 3 units above the graph of y = x2.

Using the slope-intercept form, the slope is 4 . All lines that are parallel to y=4x−6 y = 4 x - 6 have the same slope of 4 .

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Answer:

She needs to buy 8 packages.

Step-by-step explanation:

Divide 44 (cookies) by 6 (cookies in package) to get 7.33 (packages). Since you can't buy 7.33 packages, you will have to buy 8. Hope this helps!

[tex]\bf sin(A)=\cfrac{\stackrel{opposite}{12}}{\stackrel{hypotenuse}{20}}[/tex]             Check the picture below.

Answer:

18 pieces

Step-by-step explanation:

Divide the 3 yd string by 1/6:

[tex]\frac{3}{\frac{1}{6} }[/tex]

Rewrite that to look a little more manageable:

[tex]\frac{3}{1}[/tex]÷[tex]\frac{1}{6}[/tex]

And of course you know that if you want to divide fractions, you flip the one on the bottom upside down and change the sign to multiplication:

[tex]\frac{3}{1}[/tex]×[tex]\frac{6}{1}[/tex]

Do that multiplication and you get 18 pieces.

Answer:

18

Step-by-step explanation:

Answer: C. 4

Step-by-step explanation:

The amount of money that can be saved without having a negative actual net income is: $170 can be saved resulting in an actual net income of $0.

Predict how much money can be saved without having a negative actual net income.

Monthly Budget  (is an itemized list of expected income and expenses that helps you to plan how the money will be spent or saved and track of spending habits.)

Budgeted Amount  (is an itemized allotment of funds, time for a given period)

Actual Amount  (is the particular year in which the amount is spent)

Income  (business receives in exchange to provide a good /service /through investing capital )

Wages  (is monetary compensation paid by  employer to employee in exchange for work done)

Savings Interest  (is money the you earn in return for holding your savings in an account.)

$1150

$25

$900

$25

Expenses

Rent

Utilities

Food

Cell Phone

Savings

$400

$100

$250

$75

$200

$400

$80

$200

$75

$____

Net Income

$150

$____

How much money can be saved without having a negative actual net income?

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Answer:

$170 can be saved resulting in an actual net income of $0.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula of a volume of a cylinder:

[tex]V=\pi r^2H[/tex]

We have

[tex]r=6cm,\ V=904.78\ cm^3[/tex]

Substitute:

[tex]\pi(6^2)H=904.78\\\\36\pi H=904.78\qquad\text{use}\ \pi\approx3.14\\\\(36)(3.14)H=904.78\\\\113.04H=904.78\qquad\text{divide both sides by}\ 113.04\\\\H\approx8\ cm[/tex]

Answer:

$140

Step-by-step explanation:

4 pairs of shoes = $80

( ÷ 4 to get the price of one pair of shoes)

1 pair of shoes = $20

( × 7 to get the price of 7 pairs of shoes )

7 pairs of shoes = $140

Answer:

  225 cm²

Step-by-step explanation:

The ratio of areas is the square of the scale factor.

  area UVW = (5/2)²·area RST = (25/4)(36 cm²) = 225 cm²

I hope this diagram explains it and helps you :)

Answer:

Angle D = arc tangent (72 / 21)

Angle D = arc tangent (3.4285714286)

Angle D = 73.74 Degrees

and to the nearest degree it's 74

Step-by-step explanation:

C=2πr

C=πd

A=πr^2

r=C/2π

r=1/2 d

By the way all you do to solve r is:

C=2πr

C/2π=2πr/2π

C/2π=r

r=C/2π

Hope this helps:)

ANSWER

20 units.

EXPLANATION

We want to find the distance between (-8,-8) and (4,8).

We use the distance formula:

[tex]d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]

We substitute the points into the formula to get:

[tex]d = \sqrt{ {(4 - - 8)}^{2} + {(8 - - 8)}^{2} } [/tex]

We simplify to get;

[tex]d = \sqrt{ {(12)}^{2} + {(16)}^{2} } [/tex]

[tex]d = \sqrt{144+ 256} [/tex]

[tex]d = \sqrt{400} [/tex]

[tex]d = 20[/tex]

The distance between the two points is 20 units.

Answer:

Distance = 20 units

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between give 2 points

Here (x1, y1) = (-8, -8)  and (x2, y2) = (4, 8)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(4 - -8)² + (8 - -8)²]

 = √[(4 + 8)² + (8 + 8)²]

 = √[12² + 16²] =  √[144 + 256)

  =  √400 = 20

Therefore distance = 20 units

Answer:

Jordan will save $16.25 each month by choosing financing through the dealership.

Step-by-step explanation:

The EMI formula is :

[tex]\frac{p\times r\times(1+r)^{n}}{(1+r)^{n}-1}[/tex]

Case 1:

p = 17500

r = [tex]6.9/12/100=0.00575[/tex]

n = [tex]5\times12=60[/tex]

Putting the values in formula;

[tex]\frac{17500\times0.00575\times(1+0.00575)^{60}}{(1+0.00575)^{60}-1}[/tex]

=> [tex]\frac{17500\times0.00575\times(1.00575)^{60}}{(1.00575)^{60}-1}[/tex]

EMI = $345.70

Case 2:

p = 17500

r = [tex]4.9/12/100=0.004083[/tex]

n = [tex]5\times12=60[/tex]

Putting the values in formula;

[tex]\frac{17500\times0.004083\times(1+0.004083)^{60}}{(1+0.004083)^{60}-1}[/tex]

=> [tex]\frac{17500\times0.004083\times(1.004083)^{60}}{(1.004083)^{60}-1}[/tex]

EMI = $329.45

So, difference per month in payments will be :

[tex]345.70-329.45=16.25[/tex] dollars

Hence, Jordan will save $16.25 each month by choosing financing through the dealership.

A: 5.50/p

B: 4.20/p

total 602.10

ratio 1:4 =5

602.10 ÷ 5 =120.42

A= 120.42

(B= 120.42×4= 481.86)

120.42÷ 5.50= 21.8945.....

Answer: 27 pounds

Step-by-step explanation:

We know that Coffee A costs $5.50 per pound, Coffee B costs $4.20 per pound and that this month the total cost was $602.10, then:

[tex]5.50A+4.20B=602.10[/tex]  (2)

We know that this month were used used four times as many pounds of type B coffee as type A, then:

[tex]B=4A[/tex]  (1)

So, you need to substitute (1) into (2) and solve for A:

[tex]5.50A+4.20(4A)=602.10\\22.3A=602.10\\A=27[/tex]

Answer:

Part 1) The value of w is 13.3 units

Part 2) The value of x is 10.3 units

The answer is the option

w=13.3, x=10.3

Step-by-step explanation:

see the attached figure with letters to better understand the problem

Part 1) Find the value of w

we know that

In the right triangle ABD

tan(42°)=12/w

Solve for w

w=12/tan(42°)=13.3 units

Part 2) Find the value of x

In the right triangle ABC

tan(27°)=12/(w+x)

(w+x)=12/tan(27°)=23.6 units

(w+x)=23.6 units

Solve for x

x=23.6-w

substitute the value of w

x=23.6-13.3=10.3 units

The measure of side lengths w and w are 13.3 and 10.3 units respectively.

The correct option is A) w = 13.3; x = 10.3

The figures in the image are those of two right triangles.

To solve for the measure of side length w and x, we use the trigonometric ratio:

First, we solve for side length w:

Angle θ = 42 degrees

Opposite to angle θ = 12

Adjacent to angle θ = w

tan(θ) = opposite / adjacent

tan( 42 ) = 12 / w

w = 12 / tan( 42 )

w = 13.3

Now we solve for side length x:

Angle θ = 27 degrees

Opposite to angle θ = 12

Adjacent to angle θ = ( w + x )

tan(θ) = opposite / adjacent

tan( 27 ) = 12 / ( w + x )

( w + x ) = 12 / tan( 27 )

( w + x ) = 23.55

Plug in w = 13.3

13.3 + x = 23.55

x = 23.55 - 13.3

x = 10.3

Therefore, the value of x is 10.3 units

Option A) w = 13.3 and x = 10.3 is the correct answer.

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Answer:

Answer is B

Step-by-step explanation:

A number that cannot be expressed as a fraction ,where p and q are integers and q is not equal to zero

Answer:

a number that cannot be expressed as a fraction, , where p and q are integers and q is not equal to zero

Answer:

Other answer.

Step-by-step explanation:

[tex]f(x) = 3(x-1)^4\\ f(-x) = 3(-x-1)^4 = 3\big(-(x+1)\big)^4 = 3(x+1)^4 \\ \\ f(-x)\neq f(x) \\ f(-x)\neq -f(x)\\ \\ \Rightarrow \text{The function is neither odd or even}[/tex]

Answer:

The function is neither even nor odd.    

Step-by-step explanation:

Given : Function [tex]f(x)=3(x-1)^4[/tex]

To find : Determine whether the function is even or odd ?

Solution :

Rules to determine the function is even or odd :

If f(x)=f(-x) then the function is even.

If f(x)=-f(x) then the function is odd.

Now, Test for even function

[tex]f(x)=3(x-1)^4[/tex]

[tex]f(-x)=3(-x-1)^4[/tex]

[tex]f(-x)=3(-(x+1)^4[/tex]

[tex]f(-x)=3(x+1)^4[/tex]

[tex]f(x)\neq f(-x)[/tex] so function is not even.

Test for odd function,

[tex]f(x)=3(x-1)^4[/tex]

[tex]-f(x)=-3(x-1)^4[/tex]

[tex]f(x)\neq -f(x)[/tex] so function is not odd.

So, The function is neither even nor odd.

Answer:

The correct answer option is B. 0.21.

Step-by-step explanation:

We are to find the value of [tex]cos \theta[/tex] using the law of cosines.

We know that the formula of the cosine rule is given by:

[tex] c ^ 2 = a ^ 2 + b ^ 2 - 2 a b cos C [/tex]

So substituting the given values in the above formula:

[tex] 10.9 ^ 2 = 5.8 ^ 2 + 10.5 ^ 2 - 2 (5.8) (10.5) cos C [/tex]

[tex]118.81=33.64+110.25-121.8cosC[/tex]

[tex]118.81 - (33.64+110.25) = -121.8cosC[/tex]

[tex]118.81-143.86=-121.8cosC[/tex]

[tex]cosC=\frac{-25.05}{-121.8}[/tex]

cos C = 0.21

Answer:

B. 0.21

Step-by-step explanation:

Answer:

c(x) = –8x^2 + 3x – 5 is a quadratic

Step-by-step explanation:

A quadratic function involves the 2nd power of x:  x^2, and may (or may not) involve the 1st and zeroth power of x.

a(x) = -2x^3 is not a quadratic because of that exponent 3; in a quadratic, the highest power is always 2.

b(x) = 5x^3 + 8x^2 + 3 is not a quadratic for the same reason that a(x) is not a quadratic.

c(x) = –8x^2 + 3x – 5 is a quadratic:  the highest power of x is x^2, the other powers are x^1 and x^0.

Answer:

The surface area is [tex]SA=1,108\ in^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the composite figure is equal to

The lateral area of the rectangular prism plus the area of the base of the rectangular prism plus the area of the two triangular faces of triangular prism plus the area of two rectangular faces of the triangular prism

so

[tex]SA=2(12+20)(5)+(12)(20)+2[\frac{1}{2}(12)(9)]+2(20)(11)[/tex]

[tex]SA=320+240+108+440[/tex]

[tex]SA=1,108\ in^{2}[/tex]

Answer:

1,108in~2

Step-by-step explanation:

Trust us! Acellus 2022

Answer:

c

Step-by-step explanation:

Given the roots are x = - 1 + 4i and x = - 1 - 4i then the factors are

(x - (- 1 + 4i))(x - (- 1 - 4i))

= (x + 1- 4i )(x + 1 + 4i )

= (x + 1)² - 16i² → [ i² = - 1 ]

Expand and simplify

= x² + 2x + 1 + 16

Hence

x² + 2x + 17 = 0 → c

Answer:

Step-by-step explanation:

Recall that we use the first derivative to discover where a function is increasing or decreasing; it's increasing where the first derivative is + and decreasing where the first derivative is -.

The derivative of y = x^4 - 8x^2 + 16 is  dy/dx = 4x^3 - 16x, or 4x(x^2 - 4).

This can be factored further:  4x(x - 2)(x + 2).

Set this equal to zero and solve for the three critical values:

{-2, 0, 2}.

Set up a total of four intervals:  (-∞, -2), (-2, 0), (0, 2), (2, ∞).

Now choose a test point within each interval:  {-3, -1, 1, 3}.

Evaluate the first derivative, dy/dx, at each of these four test points.  Rule:  if the first derivative is +, we know the function is increasing on that interval; if -, the function is decreasing.

At x = -3, dy/dx = 4x(x - 2)(x + 2) becomes (-)(-)(-), which is -, so we know that the function is decreasing on interval (∞, -2).

At x = -1, dy/dx is (-)(-)(+), which is +, so we know that the function is increasing on (-2, 0).

At x = 1, dy/dx is (+)(-)(+), which is -, so we know that the function is decreasing on (0, 2).

Finally:  at x = 3, dy/dx is (+)(+)(+), so we know that the function is increasing on (2, ∞ ).

Answer:

[tex]\$16.64[/tex]

Step-by-step explanation:

we know that

The exponential function while the player is still active is equal to

[tex]y=3(1.07)^{x}[/tex]

where

y ----> is the value of the baseball card

x ----> the time in years

Find the value of y for x=7 years (7 years still active)

[tex]y=3(1.07)^{7}=\$4.82[/tex]

After 20 years

x=20-7=13 years (13 years retired player)

The initial value is [tex]\$4.82[/tex]

The new equation is equal to

[tex]y=\$4.82(1.1)^{x}[/tex]

substitute

x=13 years

[tex]y=\$4.82(1.1)^{13}=\$16.64[/tex]

All of the right triangles are similar by AA similarity, so corresponding side lengths are proportional. The ratio of the long leg to the short leg is the same for the two smaller triangles, for example:

  CP/AP = MP/CP

  CP/9 = 16/CP . . . . . fill in the given numbers

  CP² = 9·16 . . . . . . . multiply by 9·CP

  CP = 3·4 = 12 . . . . . take the square root

Now, you can use the Pythagorean theorem to find AC and/or CM.

  AC = √(9² +12²) = √225 = 15

  CM = √(12² +16²) = √400 = 20

In summary, CP = 12, AC = 15, CM = 20.

_____

Once you have CM, you can see these are 3-4-5 right triangles, so you can determine the other lengths by using these side ratios.

  3:4:5 = 9:12:15 = 12:16:20

_____

The altitude CP is called the "geometric mean" of AP and MP. It is the square root of their product. This is true for any right triangle, not just one with sides in the ratio 3:4:5. If you know this, you can write down your answers almost immediately. Above, we had to derive this fact using similarity.