Acellus
If P = (3,2), find the image
of P under the following rotation.
180° counterclockwise about the origin
([?], []).
Enter the number that belongs in
the green box
Enter

Answer:

a) 1 : 4

b) 60 : 180 or 1 : 3

Step-by-step explanation:

Answer:

a. 1:4

b. 1:3

Step-by-step explanation:

Let’s start with a.

So the ratio 14:56 can be divided in two to 7:28 and they are both divisible by 7 we its most simplified form is 1:4 because 28/7 is 4 and 7/7 is 1.

Now for b.

So if 240 were sold in total and 180 of them were online them doing 240-180, 60 of them were sold in person so the ratio is 60:180 which can be simplified to 30:90 to 15:45 to 3:9 to 1:3.

Answer:

The answer is option A

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

From the question

Slope or m = 5

y intercept is ( 0 , - 3) which is - 3

So the equation of the line is

y = 5x - 3

Hope this helps you

Answer:

x = 0 , 3

Step-by-step explanation:

[tex]\frac{1}{x}=\frac{x+3}{2x^{2}}\\\\1*2x^{2}=x*(x+3)\\\\2x^{2}=x*x+x*3\\\\2x^{2}=x^{2}+3x\\\\2x^{2}-x^{2}-3x = 0\\\\x^{2}-3x =0\\\\x(x-3)=0[/tex]

x = 0 ;   x - 3 = 0

x = 0 ;      x = 3

Answer:

14.2cm

Step-by-step explanation:

The diagram representing the circle and its attributes has been attached to this response.

As shown in the diagram;

The circle is centered at o,

The length of radius OL = 6cm

The length of the arc LM = 6.3cm

The angle MON = 75°

The angle LOM = θ

Remember that;

The length, L, of an arc is given by;

L = (θ / 360) x (2πr)         -------------(i)

Where;

θ is the angle subtended by the arc

r = radius of the circle.

Using the formula in equation (i), let's calculate the angle θ subtended by arc LM as follows;

L = (θ / 360) x (2πr)  

Where;

L = length of arc LM = 6.3cm

r = radius of the circle = length of radius OL = 6cm

Substitute these values into the equation to get;

6.3 = (θ / 360) x (2 x π x 6)

6.3 = (θ / 360) x (12 x π)

6.3 = (θ / 30) x (π)              [Take π = 22/7]

6.3 = (θ / 30) x (22 / 7)

θ = [tex]\frac{6.3*30*7}{22}[/tex]

θ = 60.14°

Therefore, the angle subtended by arc LM is 60.14°

Now, from the diagram,

The angle subtended by arc LMN is;

θ + 75° = 60.14° + 75° =  135.14°

Let's now calculate the length of arc LMN using the same equation (i)

L = (θ / 360) x (2πr)  

Where;

L = length of arc LMN

θ = angle subtended by LMN = 135.14°

r = radius of the circle = length of radius OL = 6cm

Substitute these values into the equation;

L = (135.14° / 360°) x (2 x π x 6)             [Take π = 22/7]

L = 14.15cm

Therefore, the length of arc LMN is 14.2cm to the nearest tenth.

Answer:

14.2

Step-by-step explanation:

Edge

Answer:

t = 5 years

online readership will exceed physical sales in 5 years

Step-by-step explanation:

The number of physical readership can be represented by the equation;

P(t) = 120 - 6t

The number of Online readership can be represented by the equation;

K(t) = 60 + 8t

For online readership to exceed physical sales

K(t) > P(t)

60 + 8t > 120 - 6t

Collecting the like terms;

8t+6t > 120-60

14t>60

t > 60/14

t > 4.29

To the nearest year greater than 4.29.

t = 5 years

online readership will exceed physical sales in 5 years

Answer:

3/5 or 0.6

Step-by-step explanation:

Here, given the value of tan theta , we want to find the value of sine theta

Mathematically;

tan theta = 0pposite/adjacent

Sine theta = opposite/hypotenuse

Firstly we need the length of the hypotenuse

This can be obtained using the Pythagoras’ theorem which states that the square of the hypotenuse equals sum of the squares of the two other sides.

Let’s call the hypotenuse h

h^2 = 3^2 + 4^2

h^2 = 9 + 16

h^2 = 25

h = √(25)

h = 5

Now from the tan theta, we know that the opposite is 3

Thus, the value of the sine theta = 3/5 or simply 0.6

Answer:

$13,450

Step-by-step explanation:

The fixed costs of production, are the costs incurred that are independent from the production volume, that is, regardless of how many spinners the company produces, those costs will remain the same. If 'x' is the number of spinners produced, interpreting the cost function, we can see that it costs $1.28 to produce each spinner and that there is a cost that does not rely on production of $13,450. Therefore, the fixed cost of production is $13,450.

Answer:

-26

Step-by-step explanation:

-13 + 25 - 36 + -2

12 - 36 - 2

-24 - 2

-26

Answer:

-13 + 25 - 36 + -2

12 - 36 + -2

12 - 38

-26

Answer:

18

Step-by-step explanation:

Since, k + 9, 2k -1 and 2k + 7 are the consecutive terms of an A.P.

Therefore, their common differences would be same.

Hence,

(2k - 1) - (k + 9) = (2k + 7) - (2k - 1)

2k - 1 - k - 9 = 2k + 7 - 2k + 1

k - 10 = 8

k = 8 + 10

k = 18

Step-by-step explanation:

Equation 2: -[tex]x^{2}[/tex] + 3x - 6

Equation 2 should represent a parabola that opens down and has a negative y-intercept.

Parabola that opens down = a<0

Ax^2 + Bx + C

-[tex]x^{2}[/tex] + 3x - 6

Negative y-intercept: -(0)^2 +3(0) -6 = y= -6

Strategy to solve: Quadratic formula

Why? - This equation doesn't factor cleanly.

Show your work:

a= -1 b= 3 c= -6

Write the quadratic formula down ([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +

Show step, solve.

x​= 1.5 + 1.9365i

Equation 3:

Sorry, I can't do this.

Equation 4 :[tex]x^{2} -1[/tex]

You decide.

Alright, easy parabola.

1. Does parabola open up or down. UP

2. Is there a vertical stretch or compression? NO

3. What is the y-intercept- (0,-1)

[tex]x^{2} -1[/tex]

Strategy: Simple factoring patterns (Difference of squares) -

(x+1)(x-1)

x = + 1

Show work: x^2 is square of x,

Equation 5: [tex]x^{2} -3x+15[/tex]

x^2−3x+15

a=1 b= -3 c=15

([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +

Good luck! Sorry that I couldn't do equation 3, vertical stretches are not my thing.

Answer:

B: 3x+5

Step-by-step explanation:

You can solve this equation by doing the following steps:

6x2 + x - 15 is your polynomial. So take your polynomial and factor it down.

6x^2 + x - 15 = 6x^2 - 9x + 10x - 15 = 3x(2x - 3) + 5(2x - 3) = (3x+5)(2x - 3).

Check your answers again.

A) 3x - 5

Would this be possible considering our last answer? Which was (3x + 5)(2x - 3). No, it's not adding, so it's wrong.

B) 3x + 5

Could this be possible? Yes, it could because it has the first half of our answer. (3x + 5), keep this in mind.

C) 4x - 5

There was no 4 in the last part, so no. It's wrong. We're working with 2, 3, and 5 only. No 4.

D) 4x + 5

Again, no 4. Make sure to double-check your answers before clicking.

Answer:

D. The volume is the product of the area of the base, (2x - 1)(x - 3), and the height x + 4.

Step-by-step explanation:

Volume of a Rectangular Block: V = lwh

Since we are given variables l, w, and h, we simply plug them in:

V = (2x - 1)(x -3)(x + 4)

We can see that we would need to multiply all 3 to find our volume. Therefore, our answer is D.

Answer:

5^3

Step-by-step explanation:

5*5^2

We are multiplying when the bases are the same

5^1 * 5^2

Add the exponents

5^(1+2)

5^3

Answer:5^3

Step-by-step explanation:Its a fact

I hope this helps you

Step-by-step explanation:

By using cosine rules:

6/sin45° = b/sin90°

b = 6× sin45°/sin90°

b = 9.124(3d.p)

Also,

using Pythagoras theorm of right-triangle

b² = 6² + a²

9.124² = 6² + a²

83.247376 = 36 + a²

83.247376-36 = a²

47.247376 = a²

√47.247376 = a

6.874 = a

Step-by-step explanation:

Part A

A 3rd degree polynomial can have no more than 3 x-intercepts or zeros. Kelsey is correct. However, Ray stated it had 4 intercepts which can include 3 x-intercept and 1 y-intercept.

Graph the function g(x) = x3 − x2 − 4x + 4. See attached picture.

It has x-intercepts at (-2,0), (1,0) and (2,0). The y-intercept is (0,4). As x-> -∞ then y -> -∞. As x->∞, y->∞.

Part B

Use the quadratic function f(x) = -x^2 - 6x. The parabola faces downward with y -intercept (-3,9) and zeros (-6,0) and (0,0). See the attached graph.

The axis of symmetry will serve as a ladder through the coaster at x = -3.

Part C and D will use the math above to create the coaster and ad campaign.

Step-by-step explanation:

LOOK AT THE PICTURE

In ΔABC:

[tex]\sin\alpha=\dfrac{x}{y+p}\\\\\cos\alpha=\dfrac{q}{y+p}\\\\\tan\alpha=\dfrac{x}{q}[/tex]

In ΔADC

[tex]\sin\alpha=\dfrac{y}{x}\\\\\cos\alpha=\dfrac{z}{x}\\\\\tan\alpha=\dfrac{y}{z}[/tex]

In ΔBCD

[tex]\sin\alpha=\dfrac{z}{q}\\\\\cos\alpha=\dfrac{p}{q}\\\\\tan\alpha=\dfrac{z}{p}[/tex]

Answer:

See below.

Step-by-step explanation:

First, notice that this is a composition of functions. For instance, let's let [tex]f(x)=\sqrt{x}[/tex] and [tex]g(x)=7x^2+4x+1[/tex]. Then, the given equation is essentially [tex]f(g(x))=\sqrt{7x^2+4x+1}[/tex]. Thus, we can use the chain rule.

Recall the chain rule: [tex]\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)[/tex]. So, let's find the derivative of each function:

[tex]f(x)=\sqrt{x}=x^\frac{1}{2}[/tex]

We can use the Power Rule here:

[tex]f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2} })=\frac{1}{2\sqrt{x}}[/tex]

Now:

[tex]g(x)=7x^2+4x+1[/tex]

Again, use the Power Rule and Sum Rule

[tex]g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4[/tex]

Now, we can put them together:

[tex]y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)[/tex]

[tex]y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }[/tex]

Answer:

13

Step-by-step explanation:

Since a point on the line is (0, 13) we know that the y-intercept is 13. The answer is already written in slope-intercept form so the answer is 13.

Answer:

13

Step-by-step explanation:

Let the missing value be c.

y = -3x + c

Put x as 0, and y as 13.

13 = -3(0) + c

13 = 0 + c

13 = c

Answer: 21 books

Step-by-step explanation:

I am estimating $32.50 to $33.

Remaining amount= 204 - 33 = $171

$8.15 = $8

$171 ÷ $8 = 21.375

Estimated answer = 21 books.

By reading the question it feels like there are options to choose from for the final answer. If it is, then choose the one which seems as close as possible to what I have got above.

Hope this helps :)

A = old value = 3431

B = new value = 3732

C = percent change

C = [ (B-A)/A ] * 100%

C =  [ (3732-3431)/3431 ] * 100%

C = (301/3431) * 100%

C = 0.0877 * 100%

C = 8.77%

Note: if C was a negative value, then we'd have a percentage decrease

Answer:

See explanation below

Step-by-step explanation:

range = 2200 - 300 = 1900

To find standard deviation, we have:

standard deviation = range/4 = [tex] \frac{1900}{4} [/tex] = 475

The range rule of thumb estimate for the standard deviation is 475

Given:

Standard deviation,[tex] \sigma[/tex] = 475

Margin of Error, ME = 100

[tex] \alpha [/tex] = 1 - 0.90 = 0.10

Za/2 = Z0.05 = 1.64

Find sample size, n:

n ≥ [tex] [Z_\alpha_/_2 * (\frac{\sigma}{ME})]^2 [/tex]

n ≥ [tex][1.64 * (\frac{475}{100})]^2[/tex]

n ≥ 60.68

≈ 61

Minimun sample size,n = 61

Answer:

m⊥n

Step-by-step explanation:

the answer is n⊥m

Answer:

Width=8

Length=28

Step-by-step explanation:

Width=x

Length=3x+4

perimeter is 2 lengths and 2 widths

2x + 2(3x+4)=72

2x+6x+8=72

8x=72-8

8x=64

x=8, so the width is 8

the length Is 3(8)+4 = 28

Answer:

25 minutes

Step-by-step explanation:

10 ÷ 2 = 5

1 lap = 5 minutes

5/1 × 5 = 25

25 minutes

Hope this helped! :)

Answer:

25 minutes

Step-by-step explanation:

Let's set up a proportion using the following setup:

minutes/laps=minutes/laps

It takes 10 minutes to swim 2 laps.

10 minutes / 2 laps = minutes/laps

We don't know how long it will take to swim 5 laps. Therefore, we can say it takes x minutes to swim 5 laps.

10 minutes/ 2 laps= x minutes / 5 laps

10/2= x/5

We want to find out what x is. Therefore, we need to get x by itself.

x is being divided by 5. The inverse of division is multiplication. Multiply both sides by 5.

5*(10/2)=(x/5)*5

5*10/2=x

5*5=x

25=x

It takes 25 minutes to swim 5 laps.

Answer:

Step-by-step explanation:

the simple interest formula= principal* interest rate*time

simple interest : 100000*%2*2 years

simple interest= 4000 dollars

compound quarterly : A=principal(1+r/4)^t

since it is quarterly and have 4 quarters in a year, and 8 in two years.

compound quarterly: 100000(1+0.03/4)^8=106159.88

it is better to invest with compound interest because it add 6159 dollars in two years to the investment of 100000 dollars.

the difference between the interest: 6159.88-4000=2159.88

Answer:  I would use pennies. It is the lowest cost per unit of area.

The cost of the "penny carpet" would be about $ 5,319

Step-by-step explanation:

Each penny is 19.05mm or 1.905cm in diameter 100 centimeters per meter, so 100/1.905 = 52.493 pennies per meter in width, Squared to find number per square meter: 52.493² = 2755.5

The total area of the floor is 23 × 12 in the main area and 3×3 in the entrance,

184 m² + 9 m² = 193 m² .  Multiplied by the cost per square meter,   $27.56

Total cost: $5,919

The closest comparison would be the nickel. At 2.121 cm, it would take slightly  fewer coins per m² , about 2223, but at  $0.05 each, the cost per m² is about $111.15.  The nickel carpet would cost 4 times as much as the penny carpet.

Answer:

-3x + 19

Step-by-step explanation:

f(x) = -5² - 4

f(x) = 25 - 4

f(x) = 21

(f+g)(x) = f(x) + g(x)

21 + -3x - 2

-3x + 19

Answer:

1 and 3

Step-by-step explanation:

The equation can be arranged to form equations 1 and 3.

Hope this helps!!! Please mark brainliest and thanks!!

Answer:

[tex]\large \boxed{\sf \ \ \ (x+2)(x-\dfrac{1}{2}) \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's solve

[tex]x^2+\dfrac{3}{2}x-1=0\\\\<=> 2x^2+3x-2=0 \ \text{multiply by 2}\\\\\\[/tex]

[tex]\Delta=b^2-4ac=9+4*2*2=9+16=25[/tex]

There are two solutions

[tex]x_1=\dfrac{-3-\sqrt{25}}{4}\\\\x_1=\dfrac{-3-5}{4}\\\\x_1=\dfrac{-8}{4}\\\\\boxed{x_1=-2}[/tex]

And

[tex]x_2=\dfrac{-3+\sqrt{25}}{4}\\\\x_2=\dfrac{-3+5}{4}\\\\x_2=\dfrac{2}{4}\\\\\boxed{x_2=\dfrac{1}{2}}[/tex]

So we can write

[tex]x^2+\dfrac{3}{2}x-1\\\\=(x-x_1)(x-x_2)\\\\=(x+2)(x-\dfrac{1}{2})[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you