find the value of a and b in (a,2)=(2,b)​

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

For more question on expression

https://brainly.com/question/1859113

#SPJ8

Answer:

Step-by-step explanation:

Ar of circle

A= 49π

B=100π

C=169π

D=121π

Ar of circle A is less than Ar of circle D

Answer:

In the first section the steps are wrong because they ditributed the 2 wrong they 1 shpuld be a 2 in the second row of unbolded numbers

Answer:

180 minutes

Step-by-step explanation:

Because this is a Proportional Relationship, you can set up a proportion to solve for the unknown value. Change the 4.5 hours to minutes first.

\(\frac{2}{t}=\frac{3}{270}\)  ⇒  2×270 = 3t  ⇒  3t = 540  ⇒  t = 180

Answer:

29 degrees

Step-by-step explanation:

Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees

Answer:

\(6x^4y^8\sqrt{5x}\)

Step-by-step explanation:

\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)

\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)

\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)

\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)

\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)

\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)

\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)

\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)

\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)

\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)

\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)

\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(6 \sqrt{5x}\;x^4\;y^8\)

\(\textsf{Rearrange:}\)

\(6x^4y^8\sqrt{5x}\)

\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)

\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)

Answer:

Step-by-step explanation:

\(y = mx + b\\\)

We know that \(m\) is going to be 8

All that's left now is to find \(b\)

Let's make a system of equations where we plug in the known values of x and y for each coordinate

\(\left \{ {{-6 = 8(-1) + b} \atop {26 = 8(3) + b}} \right. \\\)

For this system of equations solution, please check the image that's annexed

Now that we know that \(b\) is 2, we can plug that into \(y = 8x+b\)  and get

\(y=8x+2\)

We can graphically verify this answer by using a graphing calculator (if you have one) or Desmos (check the other image that's annexed)

Good luck!

Answer:

11.11% repeating or 5% if it can be anything between 1 and 20

Points L. J and K are collinear

Mathematically, when a set of points are collinear, it means that they lie on a straight line

So, the set of points we need to have are the points that we need to lie on a staright line

Looking at the image, we have these set of points as LJK

The angle turns through 144 one-degree angles.

A circle is a two-dimensional shape that consists of a set of points that are equidistant from a single fixed point called the center. The distance between any point on the circle and its center is called the radius, which is the same length all around the circle.

A full circle has 360 degrees, so Noelle's circle also has 360 degrees.

If an angle turns through 2/5 of Noelle's circle, then it turns through:

(2/5) * 360 = 144 degrees

To find how many one-degree angles it turns through, we can divide 144 by 1:

144 ÷ 1 = 144

Therefore, the angle turns through 144 one-degree angles.

Each degree is a unit of measurement for angles. One degree is equivalent to 1/360th of a full circle or 1/180th of a straight angle. When we divide the total angle by one degree, we get the number of times the angle turns through one degree. In this case, the angle turns through 144 one-degree angles, which means it turns through 144 units of measurement of angles, each equivalent to one degree.

To know more about circle visit:

https://brainly.com/question/15525194

#SPJ1

Question:

Solution:

According to the diagram, we get the following equations:

Equation 1:

Equation 2:

the angle 3 is 112 degrees, so replacing this value into the previous equation, we get:

solving for angle 4, we get:

now, note that

Equation 3:

but the angle 4 is 68 degrees, so replacing this into the above equation, we get:

solving for angle 1, we get :

Finally, from equation 1, we get:

then,

we can conclude that the correct answer is:

Answer:

a

Step-by-step explanation:

The vertex of the function f(x) = x²+10 is (0,10). Correct option is (A).

Vertex form of equation is an alternate way of writing the equation of a parabola

The vertex form of an equation is
f(x)= a(x-h)²+k,

Here, h and k are constants

The given equation is,

f(x) = x²+10

To determine the vertex of the equation,

substitute x=0,

f(x)=0+10

f(x)=10

The vertex of the function f(x) is (0,10).

To learn more about Vertex form of equation on:

https://brainly.com/question/28938998

#SPJ2

Answer:

(x-3) is the correct expression

Step-by-step explanation:

To factor you split the expression apart -

x² + 2x – 15

This breaks up to (x+5)(x-3)

If you multiply (FOIL) these you get your expression x² + 2x – 15

Your answer choices do not include (x+5) so it must be (x-3)

I hope this helps!

The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

More can be learned about the area of a triangle at https://brainly.com/question/21735282

#SPJ1

Answer:

0.5 pounds is one game

2 pounds is one textbook

Step-by-step explanation:

g = games

t = textbooks

Let's start with how much a game weighs. We know that when Chad added two more games the weight of the box increased by one pound (it was previously 21 pounds and then went to 22 when the two games were added). This means one game equals half of a pound (or 0.5 lbs.)...

\(2g = 1\)

\(\frac{2g}{2} = \frac{1}{2}\)  -> if you divide one side by two, you must do the same to the other.

\(g = \frac{1}{2} = 0.5\)

Now that we know the weight of the games, we can figure out the weight of the textbooks.

\(6g + 9t = 21\) -> 6 games and 9 textbooks weigh 21 pounds.

Plugging in that each game is 0.5 pounds...

\(6(0.5) + 9t = 21\)

\(3 + 9t = 21\)

\(3 - 3 + 9t = 21 - 3\)

\(9t = 18\)

\(\frac{9t}{9} = \frac{18}{9}\)

\(t = 2\)

That means that each textbook equals 2 pounds.

I hope this helps!

Answer:

The 90th percentile for the distribution of the total contributions is $6,342,525.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of size n, the mean is \(\mu*n\) and the standard deviation is \(s = \sqrt{n}*\sigma\)

In this question:

\(n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250\)

The 90th percentile for the distribution of the total contributions

This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(1.28 = \frac{X - 6328125}{11250}\)

\(X - 6328125 = 1.28*11250\)

\(X = 6342525\)

The 90th percentile for the distribution of the total contributions is $6,342,525.

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

it will be d

Step-by-step explanation:

Answer:

f(x)=11x+12

Step-by-step explanation:

it shows that the intercept is around halfway between 0 and 20, and the plots are not exactly at the 10s marks, if you look- June is supposed to be 6, but it’s closer to 66. since 6*11=66, i’d say 11x+12 is the answer.

Answer:

A) would be the answer

Step-by-step explanation:

this is the answer because 2 groups with 10 blocked all together has to have 5 blocks each group, also 5+5=10

Answer:

39

Step-by-step explanation:

to find the area of the triangles use the equation

3(5)(.5)=7.5

since we have 4 triangles, multiply that by 4, which equals 30

Now find the area of the square

3(3)=9

Now add the area of the square and the area of the triangles

Answer:

39 km

Step-by-step explanation:

Surface area=area of square +area of triangles

=3*3 + 0.5*3*5*4

=39

(4 triangles)

My own multi-step combination problem is given below:

To solve this problem, Amanda  need to use the formula for combinations and it is:

nCr = n! / (r! x (n-r)!)

where:

n = total number of items to select from

r is the number of items to select.

First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:

5C3

=  5! / (3! x (5-3)!)

= 10

Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be

4C2

= 4! / (2! x  (4-2)!)

= 6

Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:

3C2

= 3! / (2! x  (3-2)!)

= 3

To have the total number of dinner menus, we have to multiply these three numbers together:

= 10 x 6 x 3

= 180

Therefore, one can say that Amanda have 180 different dinner menus that she can be create.

Learn more about multi-step combination from

https://brainly.com/question/2191693

#SPJ1

We can write the ratio of 8 megabytes to 13 megabytes as follows:

To reduce a fraction, we have to list the factors of the numerator and denominator and then divide both the numerator and denominator by the great common factor.

In this case, the factor of 8 are 1, 2, 4, 8 and the factors of 13 are 1, 13, since these numbers have not a common factor exept for one, we conclude that the fraction 8/13 can't be reduced further, then the answer is 8/13

Answer:

42

Step-by-step explanation:

divide the total by the cost of each invite

Answer:

45

Step-by-step explanation:

45

Answer:

x - 15 = 30

x = 45

Step-by-step explanation:

Answer:

D: 200

Step-by-step explanation:

1/5x-2/3 times 15=30

Simplify each term

x/5 -10=30

Move all terms not containing x to the right side of the equation

x/5=40

Multiply both sides of the equation by 5

5 times x/5=5 times 40

Simplify both sides of the equation

x=200

Hope this helped!

Answer:

7 is 50 , 8 is84, 9 is 45, 10 is 135, 11 is 155 and 12 is 80

Step-by-step explanation:

The surface area of the rectangular prism is 1476 square units

From the question, we have the following parameters that can be used in our computation:

30 mm by 12 mm by 9 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (30 * 12 + 30 * 9 + 12 * 9)

Evaluate

Area = 1476

Hence, the area is 1476 square units

Read more about surface area at

brainly.com/question/26403859

#SPJ9

Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5