9. Determine if triangle LMN and triangle OPQ are or are not similar, and, if they are, state how you know.

The questions are illustrations of Pythagoras theorem and trigonometry ratios.

Pythagoras theorem is used to determine the lengths of the legs of a right triangle.

It is represented as:

\(a^2 = b^2 + c^2\)

Where:

b & c are the legs of the triangle, while a is the hypotenuse

Question 16

Start by calculating the value of x, using the sine ratio

\(\sin(30) = \frac{x}{16\sqrt 3}\)

Evaluate sin(30)

\(0.5 = \frac{x}{16\sqrt 3}\)

Solve for x

\(x = 0.5 * 16\sqrt 3\)

\(x = 8\sqrt 3\)

Next, calculate the length (l) of the boundary between both triangles using Pythagoras theorem

\((16\sqrt 3)^2 = (8\sqrt 3)^2 +l^2\)

\(768 = 192 +l^2\)

Collect like terms

\(l^2 = 768 -192\)

\(l^2 = 576\)

Take the square root of both sides

\(l = 24\)

Given that the angle is 45 degrees, it means that:

\(z = y\)

So, we have:

\(z^2 + y^2 = 24^2\)

\(z^2 + z^2 = 24^2\)

\(2z^2 = 576\)

Divide through by 2

\(z^2 = 288\)

Take the square root of both sides

\(z= 12\sqrt 2\)

Hence, the values of x, y and z are:

\(x = 8\sqrt 3\)

\(y= 12\sqrt 2\)

\(z= 12\sqrt 2\)

Question 18

Start by calculating the value of z, using the sine ratio

\(\sin(45) = \frac{z}{20}\)

Evaluate sin(45)

\(\frac{\sqrt 2}{2} = \frac{z}{20}\)

Solve for z

\(z = \frac{\sqrt 2}{2} * 20\)

\(z = 10\sqrt 2\)

Next, calculate the value of y using tangent ratio

\(\tan(30) = \frac{y}{10\sqrt 2}\)

Solve for y

\(y = \tan(30) * 10\sqrt 2\)

Evaluate tan(30)

\(y = \frac{\sqrt 3}{3} * 10\sqrt 2\)

\(y = \frac{10\sqrt 6}{3}\)

Next, calculate the value of x using sine ratio

\(\sin(30) = \frac{10/3\sqrt 6}{x}\)

Solve for x

\(x = \frac{10/3\sqrt 6}{\sin(30)}\)

Evaluate sin(30)

\(x = \frac{10/3\sqrt 6}{1/2}\)

\(x = \frac{20\sqrt 6}{3}\)

Hence, the values of x, y and z are:

\(x = \frac{20\sqrt 6}{3}\)

\(y = \frac{10\sqrt 6}{3}\)

\(z = 10\sqrt 2\)

Question 20

Start by calculating the value of z, using the sine ratio

\(\sin(45) = \frac{z}{10\sqrt 6}\)

Evaluate sin(45)

\(\frac{\sqrt 2}{2} = \frac{z}{10\sqrt 6}\)

Solve for z

\(z = \frac{\sqrt 2}{2} * 10\sqrt 6\)

\(z = 5\sqrt {12\)

Simplify

\(z = 10\sqrt {3\)

Next, calculate the value of y using tangent ratio

\(\tan(30) = \frac{10\sqrt 3}{y}\)

Solve for y

\(y = \frac{10\sqrt 3}{\tan(30)}\)

Evaluate tan(30)

\(y = \frac{10\sqrt 3}{1/\sqrt 3}\)

Simplify

\(y = 10\sqrt 3 * \sqrt 3\)

\(y = 30\)

Next, calculate the value of x using sine ratio

\(\sin(30) = \frac{10\sqrt 3}{x}\)

Solve for x

\(x = \frac{10\sqrt 3}{\sin(30)}\)

Evaluate sin(30)

\(x = \frac{10\sqrt 3}{1/2}\)

\(x = 20\sqrt 3\)

Hence, the values of x, y and z are:

\(x = 20\sqrt 3\)

\(y = 30\)

\(z = 10\sqrt {3\)

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The perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

A rectangle is a quadrilateral with all four interior angles 90°.

Given that, the vertices of the rectangle are (-3.5,3), (3.5,3), (3.5,-3), and (-3.5,-3).

The length of the  rectangle is:

l = 3.5 - (-3.5)

l = 3.5 + 3.5

l = 7

The width of the rectangle is:

w = 3-(-3)

w = 3 + 3

w = 6

The perimeter of the rectangle is given by:

P = 2 (l +w)

P = 2(7 + 6)

P = 26

The area of the rectangle is:
A = l × w

A = 7 × 6

A = 42

Hence, the perimeter and the area of the rectangle are 26 units and 42 square units, respectively.

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Answer:

I think the answer will be the infinity sign=1 whole, 1/9

Answer:

a = B/(2R)

Step-by-step explanation:

2Ra = B

a = B / (2R)

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

Its so easysyyyy

Step-by-step explanation:

so obviously you need to get 4 dx[x+x+x20+ and get make it into the forth power then you make it into a fraction then multiply that fraciton by x -2=dx

answer= 42x

Answer:

Step-by-step explanation:

So f(-8) means that x=-8

so

x^2-3x=-8^2-3*-8

64+24

88

(plz give brainliest)

9514 1404 393

Answer:

  cone: 138.16 in²

  pyramid: 352 m²

Step-by-step explanation:

Use the appropriate formula from your list of area and volume formulas.

Area of a Cone

  A = πr(r +h) . . . . . where r is the radius and h is the slant height

The radius is half the diameter, so is 4 inches.

  A = π(4 in)(4 in + 7 in) = 44π in² ≈ 138.16 in²

__

Lateral Area of a Square Pyramid

  A = 2sh . . . . . where s is the side length of the base and h is the slant height

  A = 2(8 m)(22 m) = 352 m²

Answer:

126.5 cm^2

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

253\(cm^{2}\)

Step-by-step explanation:

11 times 23 =253\(cm^{2}\)

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.

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The length of the hypotenuse is 10.61 yd.

We have,

The sum of the angles in a triangle = 180

Now,

Two angles are 45.

This means,

The side opposite to angle 45 are equal.

So,

a = c

And,

a = 7.5 yd

Now,

Applying the Pythagorean theorem.

b² = a² + c²

b² = 7.5² + 7.5²

b² = 112.5

b = √112.5

b = 10.61

Thus,

The length of the hypotenuse is 10.61 yd.

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================================================

Work Shown for problem 1

P(pink, then violet) = P(pink)*P(violet given 1st was pink)

= (4/14)*(2/13)

= 8/182

= 4/91

------------------------------

Work Shown for problem 2

P(gray, then gray)

= P(gray)*P(gray given 1st was gray)

= (3/14)*(2/13)

= 6/182

= 3/91

-------------------------------

Work Shown for problem 3

P(not yellow, not yellow)

= P(not yellow)*P(not yellow given 1st was not yellow)

= (9/14)*(8/13)

= 72/182

= 36/91

-------------------------------

Work Shown for problem 4

P(yellow, not yellow)

= P(yellow)*P(not yellow given 1st was yellow)

= (5/14)*(9/13)

= 45/182

Answer:

2/3 = x

Step-by-step explanation:

- 7 ( x + 2 ) + 4x = 6 ( 2x - 4 )

First, solve the brackets.

-7x - 14 + 4x = 12x - 24

Combine like terms.

-3x - 14 = 12x - 24

Add 3x to both sides.

-14 = 12x + 3x - 24

-14 = 15x - 24

Add 24 to both sides.

-14 + 24 = 15x

10 = 15x

Divide both sides by 15.

10/15 = x

To simplify the answer divide numerator and denominator by 5.

2/3 = x

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

A C F G H J ARE THE FIGURES WHERE AB IS AN ALTITUDE

Answer:

x=3, y=-6

Step-by-step explanation:

As you know there are many ways to solve this question! First is Subsitutuion, Second is Elimination, and Third is Graphing!

Let’s begin with our detailed answer:

As you know subsitution is solving for a variable and then it can be used as a variable substitution to figure out x and y.

So in our system of equations:

\(\left \ {3x+2y=-3}} \atop {9x+4y=3}} \right.\)

I will just take one equation and solve for x but it actually dosent matter which variable you subsitutue and solve for.

\(\left \ {3x+2y=-3}} \atop {9x+4y=3}} \right.\)

To eliminate this question we can divide the top part by -3:

\(\left \ {-9x-6y=9}} \atop {9x+4y=3}} \right.\)

Let‘s sum these system of equation and we get: \(y=-6\)

We can now insert y as -6 and solve for x:

\(3x-12=-3\)

\(x=3\)

So, \(x=3, y = -6\)

Answer:

(3, - 6 )

Step-by-step explanation:

3x + 2y = - 3 → (1)

9x + 4y = 3 → (2)

Multiplying (1) by - 3 and adding to (2) will eliminate the x- term

- 9x - 6y = 9 → (3)

Add (2) and (3) term by term to eliminate x

0 - 2y = 12

- 2y = 12 ( divide both sides by - 2 )

y = - 6

Substitute y = - 6 into either of the 2 equations and solve for x

Substituting into (1)

3x + 2(- 6) = - 3

3x - 12 = - 3 ( add 12 to both sides )

3x = 9 ( divide both sides by 3 )

x = 3

solution is (3, - 6 )

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

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Explanation:

There are two approaches we can take.

The first approach is finding the amount we save, which is 5% of 15 = 0.05*15 = 0.75 dollars or 75 cents.

So the new price is 15 - 0.75 = 14.25 dollars

----------------

The second approach is to think of it like this: If you save 5%, then you still have to pay the remaining 95% (the two percentages add to 100%).

95% of 15 = 0.95*15 = 14.25

This second approach is handy if you want to chain multiple discounts together. So let's say there's a special 10% off sale on top of the 5% discount. We would multiply by 0.90 to further discount by 10% and get to 0.90*0.95*15 = 12.825 = 12.83. It also works in reverse too and we could chain percent increases along with percent decreases.

Answer:

-2/3 or -0.6666

Step-by-step explanation:

-3x + 6 = 4 -6x

Let's move the x to one side

-3x +6x=4-6

Combine like terms

3x = -2

Divide both sides by 3

-2/3=x

or -0.666666

The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1. The hypothesis can not be concluded.

The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1.

For the given problems, the Hypothesis mean is 4.5. The sample mean was 4.75 hours with a normal standard deviation of 2.0.

Now, calculating the z-score,

\(z = \dfrac{\bar x - \mu_o}{\dfrac{\sigma}{\sqrt n}}\\\\\\z = \dfrac{4.75-4.5}{\dfrac{2}{\sqrt{15}}}\\\\\\z = 0.48\)

Now, as per the standard normal table, the p-value is 0.6844. Since the p-value is greater than the significance level, the hypothesis can not be concluded.

Hence, The hypothesis can not be concluded.

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Answer:

sorry

Step-by-step explanation:

I don't know how to solve it

Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

For binary class classification, assumptions are necessary in a way:

Given that

From Boyer Naive classifier,

We evaluate (ai | vj) is given below

(ai | vj) = n(e) + m(p) / n + m

Here,

m = equivalent sample size

n(e) = number of training examples

for which v = vj and a = ai

n(i) = number of training example for which v = vj

P = a prior estimate for P(ai | vj)

Here, we calculate that

P(SUV | yes), P(Red | yes), P(Domestic | yes)

P(SUV | no), P(Red | no), P(Domestic | no)

We evaluating this value like

yes:

RED :                             SUV:                            DOMESTIC:

n = 5                              n = 5                             n = 5

n(c) = 3                          n(c) = 1                           n(c) = 2

P = 0.5                          P = 0.5                           P = 0.5

m = 3                              m = 3                            m = 3

Therefore, with the above calculation we can justify that the simplifying assumptions are necessary in a binary class classification.

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Answer:

just substitute each value of x into the function

Step-by-step explanation:

1. (x=-2) y= 4(-2)+2

2. (x=0) y= 4(0)+2

3. (x=2) y= 4(2)+2

4. (x=4) y= 4(4)+2

use the same steps but change the value of x. go ahead a use your calculator

Answer: the answer is 504!

Step-by-step explanation:

360*0.40=144

so they said 40% reggie collected main mor than 40% collected so you need to do add like 360+144=504