If f(x) = 2x + 6 and g(x) = x^3 ,what is (gºf)(0)?

Answer:

b

Step-by-step explanation:

Answer:

A. (1, -2)

Step-by-step explanation:

We can substitute the variables of x and y into the inequality of [tex]y < -|x|[/tex].

Let's start with A, -2 being y and 1 being x.

[tex]-2 < - |1|[/tex]

The absolute value of 1 is 1, and negating that gets us -1.

[tex]-2 < -1[/tex]

Indeed, -2 is less than -1! So A is a solution to the inequality.

Let's test the rest of them, just in case.

For B:

[tex]-1 < -|1|[/tex]

Absolute value of 1 is 1, negating it is -1.

[tex]-1<-1[/tex]

-1 is EQUAL to -1, not less than it, so is not a solution to the inequality.

Let's try C.

[tex]0 < -|1|[/tex]

Absolute value of 1 is 1, negating it is -1.

[tex]0 < -1[/tex]

0 is GREATER than -1, so that is not a solution to the inequality.

Hope this helped!

Answer:

9 in.

Step-by-step explanation:

Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.

As such, the ratio of the sides would give the same results.

Hence,

4/6 = 10/(6 + x)

cross multiplying

4(6 + x) = 60

Dividing both sides by 4

6 + x = 15

collecting like terms

x = 15 - 6

= 9

Answer:

Step-by-step explanation:

Given the following complex values Z₁=2(cos(π/5)+i Sin(πi/5)) And Z₂=8(cos(7π/6)+i Sin(7π/6)). We are to calculate the following complex numbers;

a) Z₁Z₂ = 2(cos(π/5)+i Sin(πi/5)) * 8(cos(7π/6)+i Sin(7π/6))

Z₁Z₂ = 18 {(cos(π/5)+i Sin(π/5))*(cos(7π/6)+i Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)+i²Sin(π/5)Sin(7π/6)) }

since i² = -1

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)-Sin(π/5)Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) -Sin(π/5)Sin(7π/6) + i(cos(π/5)sin(7π/6)+ Sin(π/5)cos(7π/6)) }

From trigonometry identity, cos(A+B) = cosAcosB - sinAsinB and  sin(A+B) = sinAcosB + cosAsinB

The equation becomes

= 18{cos(π/5+7π/6) + isin(π/5+7π/6)) }

= 18{cos((6π+35π)/30) + isin(6π+35π)/30)) }

= 18{cos((41π)/30) + isin(41π)/30)) }

b) z2 value has already been given in polar form and it is equivalent to 8(cos(7pi/6)+i Sin(7pi/6))

c) for z1/z2 = 2(cos(pi/5)+i Sin(pi/5))/8(cos(7pi/6)+i Sin(7pi/6))

let A = pi/5 and B = 7pi/6

z1/z2 = 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B))

On rationalizing we will have;

= 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B)) * 8(cos(B)-i Sin(B))/8(cos(B)-i Sin(B))

= 16{cosAcosB-icosAsinB+isinAcosB-sinAsinB}/64{cos²B+sin²B}

= 16{cosAcosB-sinAsinB-i(cosAsinB-sinAcosB)}/64{cos²B+sin²B}

From trigonometry identity; cos²B+sin²B = 1

= 16{cos(A+ B)-i(sin(A+B)}/64

=  16{cos(pi/5+ 7pi/6)-i(sin(pi/5+7pi/6)}/64

= 16{ (cos 41π/30)-isin(41π/30)}/64

Z1/Z2 = (cos 41π/30)-isin(41π/30)/4

Answer:

13. 16(cos(41 π/30)+ isin(41 π/30))

14. Mine asked for z2 magnitude so I got 8 (magnitude is the same as modulus which is r)

15. 1/8 (cos(29 π/30)+ isin(29 π/30))

Step-by-step explanation:

13. Since we’re multiplying z1, and z2, use De Moivre’s theorem by multiplying the r values (2 and 8) and adding the theta values (π/5 and 7π/6). Adding the angle values should lead you to have 41 π/30, and the rest is self-explanatory.

14. Explanation is in the answer, just take the r value from z2 for magnitude (at least that’s what’s on my practice assignment)

15. Use De Moivre’s theorem again, this time with division, so you will divide the r values (2 divided by 8) and subtract the theta values (π/5 minus 7π/6). 2/8 simplifies to 1/8 and when subtracting with 6π/30 - 35π/30 (finding common denominators) you should get 29π/30.

Answer:

Yes.

Step-by-step explanation:

1+1=2

3+5=8

7+1=8

9+23=32

5+13=18

An odd number is an even number plus 1, and 1 plus 1 is an even number. even numbers added together are also always even numbers, so two even numbers (in the second example it'd be 2+1 & 4+1, so 2 and 4) plus an even number(1+1=2) must be an even number.

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have

[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]

Substitute:

[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]

The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:

[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]

We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:

[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]

[tex]=\dfrac{14}{7}=2[/tex]

The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!

Answer: 0.476

Step-by-step explanation:

Let A = Event of choosing an even number ball.

B = Event of choosing an 8 .

Given, A lottery game has balls numbered 1 through 21.

Sample space: S= {1,2,3,4,5,6,7,8,...., 21}

n(S) = 21

Then, A= {2,4,6,8, 10,...(20)}

i.e. n(A)= 10

B= {8}

n(B) = 1

A∪B = {2,4,6,8, 10,...(20)} = A

n(A∪B)=10

Now, the probability of selecting an even numbered ball or an 8 is

[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]=\dfrac{10}{21}\approx0.476[/tex]

Hence, the required probability =0.476

Answer:

Largest integer in the interval [−∞, 31] is 31.

Step-by-step explanation:

Given the interval: [−∞, 31]

To find: The largest integer in this interval.

Solution:

First of all, let us learn about the representation of intervals.

Two kind of brackets can be used to represent the intervals. i.e. () and [].

Round bracket means not included in the interval and square bracket means included in the interval.

Also, any combination can also be used.

Let us discuss one by one.

1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.

Smallest p

Largest q

2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.

Smallest value just greater than p.

Largest value just smaller than q.

3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.

Smallest value p.

Largest value just smaller than q.

4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.

Smallest value just greater than p.

Largest value q.

As per above explanation, we can clearly observe that:

The largest integer which belongs to the following interval: [−∞, 31] is 31.

Answer:

15.9degrees

Step-by-step explanation:

in photo above

Answer:

[tex]\boxed{15.95\°}[/tex]

Step-by-step explanation:

The angle can be found by using trigonometric functions.

tan (θ) = [tex]\frac{opposite}{adjacent}[/tex]

tan (θ) = [tex]\frac{4}{14}[/tex]

θ = [tex]tan^{-1} \frac{4}{14}[/tex]

θ = 15.9453959

θ ≈ 15.95

Answer:

Perimeter= 40 units

Step-by-step explanation:

Ok

We are asked to look for the perimeter.

We have some clue given.

All at right angle and some sides are given it's full length.

We have the bae to be 11 unit

The height to be 7 unit.

What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.

Let's go for the other side of the height.

Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.

So we have 7+7+11

But it's not complete yet.

We are given a dimension 2.

And the 2 is in two places so it's total 2*2= 4

The two is for a small base .

The base is actually an extra to the 11 of the other base.

So summing up

We have 2*11 + 2*7 + 2*2

Perimeter= 22+14+4

Perimeter= 40 units

Answer:

Volume: 112 m³.

Surface area: 172 m².

Step-by-step explanation:

The volume is the base times height times length. So, the volume will be 2 * 8 * 7 = 16 * 7 = 112 m³.

The surface area is 2lw + 2lh + 2wh. l = 8; w = 7; h = 2.

2(8)(7) + 2(8)(2) + 2(7)(2) = 2 * 56 + 2 * 16 + 2 * 14 = 112 + 32 + 28 = 112 + 60 = 172 m².

Hope this helps!

Answer:

outside the circle i think

Step-by-step explanation:

Answer:

inside the circle

Step-by-step explanation:

Answer:

  16x^3 +64x^2 -40x

Step-by-step explanation:

Use the distributive property. The factor outside parentheses multiplies each term inside parentheses:

  8x(2x^2 +8x -5) = (8x)(2x^2) +(8x)(8x) +(8x)(-5)

  = 16x^3 +64x^2 -40x

Answer:

3 is not a solution

Step-by-step explanation:

6x – 7 = 12?

Substitute 3 in for x and see if the equation is true

6*3 - 7 = 12

18-7 = 12

11 =12

This is false so 3 is not a solution

Answer: Pi multiplied by the diameter of the circle

Step-by-step explanation:

Answer:

The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].

Step-by-step explanation:

Formula for compound interest is given by

[tex]A = P(1 + R) ^{n} [/tex]

Where

A is the amount at the end of the period

P is the principal

R is the rate

n is the period

The interest = A - P

From the question

P = $ 3200

n = 3 years

R = 40%

So we have

[tex]A = 3200 \times 2.744[/tex]

A = $ 8780.80

The interest is

$ 8780.80 - $3200

Hope this helps you

Answer:

  19.9 days

Step-by-step explanation:

The amount remaining after d days is ...

  a = (1/2)^(d/7)

We want to find d when a = 0.14

  log(a) = (d/7)log(1/2)

  d = 7·log(0.14)/log(1/2) ≈ 19.855 ≈ 19.9

The farmers need to wait about 19.9 days for it to be safe.

Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k

parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t

Step-by-step explanation: The vector equation is a line of the form:

r = [tex]r_{0}[/tex] + t.v

where

[tex]r_{0}[/tex] is the position vector;

v is the vector;

For point (7,4,5):

[tex]r_{0}[/tex] = 7i + 4j + 5k

Then, the equation is:

r = 7i + 4j + 5k + t(3i + 2j - k)

r = (7 + 3t)i + (4 + 2t)j + (5 - 5t)k

The parametric equations of the line are of the form:

x = [tex]x_{0}[/tex] + at

y = [tex]y_{0}[/tex] + bt

z = [tex]z_{0}[/tex] + ct

So, the parametric equations are:

x = 7 + 3t

y = 4 + 2t

z = 5 - 5t

Answer:16.1%

Step-by-step explanation:

Answer:

The investment needs the rate of growth to be approximately 16.1%.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

The length of this triangle is 3x+1 and the width is x.

The perimeter P is:

P= 2(3x+1)+2*x

P= 6x+2+2x

P= 8x+2

Let's evaluate it when x=1/2

●1/2 =0.5

P= 8*0.5+2 =4+2= 6 ft

●●●●●●●●●●●●●●●●●●●●●●●●

The area A is:

A = (3x+1)*x

A= 3x^2 +x

Let's evaluate it when x=0.5 feet

A= 3*0.5^2 +0.5

A= 3*0.25+0.5

A= 0.75 +0.5

A= 1.25 ft^2

Answer:

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Step-by-step explanation:

To express the given product (108 X 125) as a product of prime factors

Step 1: Express each of the numbers as a product of its prime factors.

[tex]108=2^2 \times 3^3\\125=5^3[/tex]

Step 2: Write the product together, and combine any like terms if any

Therefore,

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )

AB × cos54° = 39 ( divide both sides by cos54° )

AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B

Answer:

the solutions to the inequality ys-x+1 are shaded on the graph. which point is B. (3 ,-2)

Answer:

Arrow from 0 to 4.7 and from 4.7 to 2.4

Step-by-step explanation:

4.7 is also 0+4.7

arrow from 0 to 4.7.

-2.3 from 4.7 is 4.7-2.3=2.4

arrow from 4.7 to 2.4.

Answer:

Use the interactive number line to find the difference.

4.7 - 2.3 = 4.7 + (-2.3) =

✔ 2.4

Step-by-step explanation:

Answer:

200.52 in^2

Step-by-step explanation:

to find the area of a circle, you square 6 and multiply it by pi in this case 3.14.

that gives you 113.04 but because this is only a half circle, it is 56.52 in^2.

Next, you need to find the rectangle. multiply 12(length) by 12(Width) to get 144 add 144 to 56.52 to get 200.52.

Hope this helped if it did please give me brainliest it helps me a lot. :)

Have a good day!

Answer:

D. 4 real roots and 0 complex roots

Step-by-step explanation:

If I assume that the function you are saying is

[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]

There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.

[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]

There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.

Answer:

8.1% decrease

Step by step

To find precentage decrease we use formula:

Percent decrease= original amount-new amount/original amount(100%)

percent decrease= 7,400-6,800/7,400(100%)=300/37=8.1%

Answer:

N(n+1) = N(n)^2 - 1, n>=0, N(0) = 2

or equivalently

N(n) = N(n-1)^2 - 1, n>0, N(0) = 2

Step-by-step explanation:

Year 0 = 2 trees

year 1 = 2^2-1 = 3

year 2 = 3^2-1 =8

year 2 = 8^2-1 =63

...

Recursive formula

Let

n = integer year number

N(n) = number of trees to plant in year n

N(n+1) = N(n)^2-1, n>=0, N(0) = 2

or equivalently

N(n) = N(n-1)^2, n>0, N(0) = 2

Whats the options???

Answer:

Rs. 32,000

Step-by-step explanation:

height = 4m

let length = x m

breadth = x/3 m

Area of the 4 walls = 2(length × height) + 2(breadth × height)

Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3

Area = (32x)/3 m²

1 m² = Rs. 5

The cost for an area that is (32x)/3 m²=  (32x)/3  × 5 Rs.

The cost of plastering 4 walls at Rs.5 per m² = 640

(32x)/3  × 5  = 640

(160x)/3 = 640

x = length = 12

Area =  (32x)/3 m² = (32×12)/3 = 128m²

The cost of carpeting its floor at the rate of Rs. 250/m²:

= 128m² × Rs. 250/m² = 32,000

The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000

Answer:

Part A- 6

Part B- 3

Part C- 3/22100

Step-by-step explanation:

Part A-

Use the permutation formula and plug in 3 for n and 2 for k.

nPr=n!/(n-k)!

3P2=3!/(3-2)!

Simplify.

3P2=3!/1!

3P2=6

Part B-

Use the combination formula and plug in 3 for n and 2 for k.

nCk=n!/k!(n-k)!

3C2=3!/2!(3-2)!

Simplify.

3C2=3!/2!(1!)

3C2=3

Part C-

It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.

I believe the answer is 3/22100

I honestly suck at probability but I tried my best.