graph (-3,2)(1,2)(8,2)(12,4)​

If we start with the parent function f(x) = cot(x), the transformation needed to go from this function to cot(x + π/6) is expressed as:

That is, we need to make a shift of π/6 units to the left, beginning with the cot(x) graph. The graph of cot(x + π/6) is:

Answer: y = -3/2x - 1

Step-by-step explanation:

y = mx + b

1. m is the slope so substitute -3/2 for m. ( y = -3/2x + b)

2. b is the y intercept so substitute -1 in for b. ( y = -3/2x - 1)

Jenna bought a coat on sale for $120

The price of the coat is the 2/3of the original price

Let the original price is $x

So, the equation will be :

2/3 of x =120

So, The original price of the coat is $180

Top left: Yes, each input corresponds to only one output.

Top right: Yes, each input corresponds to only one output.

Bottom left: Yes, each input corresponds to only one output.

Bottom right: No, the input of -1 corresponds to three different outputs.

In order to simplify an equation we want to add all the terms with the same unkowns.

In the equation

4 - 2y + (-8y) + 7.3

we can see that there are terms with y and numbers alone.

We combine like terms:

Terms with y: -2y,

The general form of a quadratic equation is given by the expression:

A quadratic equation having a maximum value or point is one that has its value of a to be lesser than zero

(a < 0). Such a graph opens downwards

Therefore, any quadratic equation that has the a-value to be lesser than zero has a maximum point

Mathematically expressed as:

The factor by which the current changes if the resistance increases 10% is; 90.9% reduction

Ohm's law states that the electrical current (I) flowing in a circuit is directly proportional to the voltage (V) and inversely proportional to the resistance(R). Therefore, if the voltage is increased, the current will increase provided the resistance of the circuit does not change. Thus;

I = V/R

Now, we are told that the resistance increases by 10%.

Thus, New value of resistance = 1.1R

Thus, new current/old current = 1/1.1 = 0.909 = 90.9%

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Formula for the trigonometry is y = b sin ( πx/2 - π/2) + 4

y = A sin( ωx + δ) + b

period: t = 4

ω = 2π/t = 2π/4 = π/2

A = 10 -(-2)/ 2

  = 6

b = (10-2)/2

  = 4

y = b sin (πx/2 + δ) + 4

x = 0, y = bsinδ + 4 = -2

sinδ = -1   => δ = -π/2

y = b sin( πx/2 - π/2) + 4

Therefore the formula for the trigonometry function is y = b sin(πx/2 - π/2) + 4.

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Select all expressions that are equivalent to (2n + 6)(n + 3)

we have

(2n + 6)(n + 3)

apply distributive property

2n^2+6n+6n+18

2n^2+12n+18

Verify each option

option A

2(n^2 + 6n +9)=2n^2+12n+18 -------> is ok

option B

is not correct

option C

is correct

option D

is not correct

option E

2(n + 3)(n + 3)= (2n + 6)(n + 3) ------> is correct

option F

2(n + 3)^2=2(n^2+6n+9)=2n^2+12n+18 -----> is ok

therefore

Using the Fundamental Counting Theorem, the number of length-n sequences that have at least one pair of adjacent LEDs that light up with the same color is:

[tex]N = 4 - 4 \times 3^{n - 1}[/tex]

It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In the context of this problem, there are n LEDs, each with 4 possible colors, hence he total number of sequences is:

[tex]T = 4^n[/tex]

For sequences with no repeating LEDs, we have that:

Hence the number is:

[tex]T_n = 4 \times 3^{n-1}[/tex]

(n - 1) as the first LED is not included on those with 3 possibilities.

Having at least one repeating and no repeating are complementary events, hence the number of sequences is:

[tex]N = 4 - 4 \times 3^{n - 1}[/tex]

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There are two shiftments, 1 to the side along the x-axis and 1 vertical along the y-axis

Horizontal shifts:

Vertical shifts

Since the x is substracted 4 units, it means that the graph is translated 4 units to the right.

Since the function is completely added 1 unit its means that all the graph is shifted 1 unit up.

Answer: y = -2x + 5

Step-by-step explanation:

y = _x + 5

(5,0) (3,4)

(y2 - y1) / (x2 - x1)

(4 - 0 ) / (3 -5)

4 / -2

-2

y = -2x + 5

The coat of the dress based on the percentage is $66.

From the information, it was stated that Tonya spends 55% of her savings on a new dress and that she saved $120.

Let the cost of the dress be represented as x

Therefore, the appropriate information given I'll be expressed as:

= 55% × 120 = x

0.55 × 120 = x

Multiply

x = 66

The amount spent is $66.

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The average cost per minute which the shop runs is $1.50

To find the shop's cost per minute, we can write down equations and proceed to solve.

In the given question, 3 cupcakes cost $6.75 and 5 cupcakes cost $9.75.

But we were not given the average cost per cupcake.

To do that, let's write an equation for this.

[tex]y = mx + c[/tex]

Let's find the slope to this equation which determines the average cost per minute.

[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{9.75 - 6.75}{5 - 3} \\m = 1.50[/tex]

The shop's cost per minute was calculated to be $1.50.

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From the frequency bar graph, we can read the following information.

15 students got an A

6 students got a B

5 students got a C

10 students got a D

14 students got an F

a) As described above, 5 students got a C

b) Adding up the frequencies of the students who got C or higher:

5 + 6 + 15 = 26

26 students passed the course

c) Assuming the students who did not pass got any credits, then we add up the students with D and F: 10 + 14 = 24

24 students received no credit for the course

d) Total students in the course: 15 + 6 + 5 + 10 + 14 = 50

e) The mode is the letter grade that got the highest frequency:

Mode = A

A got 15

(4x -2) yd, 2x yd, 2(x + 7) yd, 2.5x yd. The triangle's perimeter is the same as the square's perimeter. The value of x=6

Given that,

The graphic displays the yards-long sides of a triangle and a square. The triangle's perimeter is the same as the square's perimeter.

We have to find the value of x in the given side.

In the picture we can see the triangle and square.

The perimeter of the triangle is sum of the three sides of the triangle.

The perimeter of the square is 4 times the side of the square.

4x-2+2x+2(x+7)=4×2.5x

4x-2+2x+2x+14=10x

8x+12=10x

10x-8x=12

2x=12

x=12/2

x=6

Therefore, the value of x=6

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Answer:

26 centilitres.

Explanation:

First, we start by recalling the standard conversion between millilitres and centilitres.

Let 260 milliliters = x centiliters

We express it as a ratio:

Cross multiply to solve for x:

Therefore, 260 millilitres is 26 centiliters.

Solution

- To divide by a fraction, you simply invert the fraction and instead multiply by the inverted fraction.

- Thus, we have:

Given the graph, we cam find f(-3)+g(-2) below.

Explanation

Answer: -2

Given -

Money deposited in an account = $3,100

Interest rate = 2.5% compounded quarterly

Time = 5 years

To Find -

The final amount of money =?

Step-by-Step Explanation -

As we know there are 4 quarters in a year.

So,

In five years, there are 20 quarters.

On applying the formula:

Final Amount =

Final Answer -

The final amount of money = $3511.4

If Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years

The interest rate = 4.6%

The final amount = $1610

The time period = 15 years

The compound interest

A = [tex]P(1+\frac{r}{100})^{t}[/tex]

Where A is the final amount

P is the principal amount

r = interest rate

t is the time period

Substitute the values in the equation

1610 = [tex]P(1+\frac{4.6}{100})^{15}[/tex]

1610 = P×1.96

P = 1610/1.96

P = $820.06

Hence, if Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years

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given: 100 cm = 1 meters

We need to convert 4 m to cm

so,

The measure of the fourth angle that is x and the value is 133°

A regular octagon will have all its sides equal in length. Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080°.

Let the 8 interior angles of the octagon be:

x-12, x-8, x-4, x, x+4, x+8, x+12, x+16.

Their sum = 8x+16 = 1080, or

this implies 8x = 1080–16 = 1064  

thus on further solving we get x = 133

Hence the sixth angle = x+8 =141 degrees.

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Answer:

L x W =   8.5 x 24    or     12 x 17

Step-by-step explanation:

x  (41 -2x) =204

-2x^2 + 41x -204 = 0      Use Quadratic Formula to find x = 8.5 or 12

(x-8.5)(x-12) = 0

         two sides = 8.5       and river/third side =  24

      or  two sides 12     and river/thirdside = 17

Hello!

First, let's rewrite the expression here:

We will have to find the coefficients a, b and c:

• a ,= -2;

• b ,= 12;

• c ,= -15;

As we can see, coefficient a is negative. It means that the parabola will face downwards and have a maximum value.

We can obtain this point by using the two formulas below to calculate the coordinates (x, y) of this point, look:

As we know the coefficients, let's replace the values in the formulas:

Xv:

Now let's find Yv:

Doing this, we obtained the coordinate of the maximum point (x, y) = (3, 3).

As it doesn't have any restrictions, the domain will be: [-∞, +∞].

The maximum value will be when y = 3, so the range is [-∞, 3].

Look at the graph of this function below:

Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The areas are 123.83 [tex]m^{2}[/tex] and[tex]209.07m^{2}[/tex]

The form having the greatest surface area for a given perimeter is a circle.

Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The orthogonal group O is the symmetry group of it (2,R). Circle group T is the collection of rotations alone.

A distinct circle can be found through any three locations that are not all on the same line. It is feasible to express explicitly equations for the coordinates of the circle's center and radius in terms of the coordinates of the three specified points in Cartesian coordinates.

Circumference= [tex]2\pi r[/tex]= 220 and 286

[tex]2\pi r[/tex]= 220

2*3.14*r=220

r= 220/35.03= 6.28

area=[tex]\pi r^{2}[/tex]

     = 3.14*6.28*6.28

     = 123.83[tex]m^{2}[/tex]

[tex]2\pi r[/tex]= 286

2*3.14*r= 286

r= 286/35.03 = 8.16

area= [tex]\pi r^{2}[/tex]

      = 209.07[tex]m^{2}[/tex]

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The expected value of the proposition is $22.6

The given parameters are

Represent the proportion as a fraction

So, we have

p = 359/449

The expected value is then calculated as

E(x) = p * Amount paid for making a throw - (1 - p) * Amount collected for losing a throw

Where p represents the proportion defined above

So, we have

E(x) = 359/449 * 39 - (1 - 359/449) * 43

Evaluate the difference

E(x) = 359/449 * 39 - 90/449 * 43

So, we have

E(x) = 22.6

Hence, the proposition has an expected value of $22.6

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Answer:

-1.09

The problem requires one to calculate the win payoff and win probability as well as the lose payoff and probability. You would then do a calculation like this:

[(Win Payoff) x (Win Probability)] + [(Lose Payoff) x (Lose Probability)]

y= 2x+4

Slope-intercept form

y=mx+b

Where:

m= slope

b= y-intercept

y=2x+4

Slope = m= 2

Perpendicular lines have negative reciprocal slopes.

So, the slope of the new line = -1/2

New equation:

y= -1/2x+b

Replace x,y by the point (4,2) and solve for b:

2 = -1/2(4)+b

2= -2 + b

2+2 = b

4 = b

New line equation:

y= -1/2x+4