6. The longest side of a 30° -60° - 90° triangle measures 8. What is the length of the
longer leg?

Answer:

See Explanation for proofs

Step-by-step explanation:

Given

See attachment for complete question

Solving (a):

\(\frac{\sqrt{2}}{2}\) is irrational

\(\sqrt{2} =1.41421356237.....\)

So, we have:

\(\frac{\sqrt{2}}{2} = \frac{1.41421356237.....}{2}\)

\(\frac{\sqrt{2}}{2} = 0.70710678118....\)

\(0.70710678118....\) can not be represented as a fraction of whole numbers.

Hence:

\(\frac{\sqrt{2}}{2}\) is irrational

Solving (b):

\(\sqrt{2} -2\) is irrational

\(\sqrt{2} =1.41421356237.....\)

So, we have:

\(\sqrt{2} -2 = 1.41421356237..... - 2\)

\(\sqrt{2} -2 = -0.58578643763.....\)

\(-0.58578643763.....\) can not be represented as a fraction of whole numbers.

Hence:

\(\sqrt{2} -2\) is irrational

Solving (c):

The sum of two positive irrational number is always irrational

Proof Below

If a is irrational and b is also irrational,

then

\(a + b = irrational\)

Take for instance:

\(a = \sqrt{2\)

\(b = \sqrt{8\)

\(a + b = \sqrt{2} + \sqrt{8\)

\(a + b = \sqrt{2} + \sqrt{4*2\)

\(a + b = \sqrt{2} + \sqrt{4}*\sqrt{2\)

\(a + b = \sqrt{2} + 2\sqrt{2\)

\(a + b = 3\sqrt{2\)

\(3\sqrt{2\) is irrational and this is true for the sum of every positive irrational numbers

Answer:

11*20!

Step-by-step explanation:

(20!+21!+22!)/44=

20!(1+21+21*22)/44=

20!(22+22*21)/44=

20!*22*22/44= 11*20!

The simplified expression of (20!+21!+22!)/44 is 20! * 11

The expression is given as:

(20!+21!+22!)/44

The factorial of a number n is:

n! = n * (n - 1)!

So, we start by expanding 22!

(20!+21!+22!)/44 = (20!+21!+22 * 21 * 20!)/44

Next, we expand 21!

(20!+21!+22!)/44 = (20!+21 * 20!+22 * 21 * 20!)/44

Factor out 20!

(20!+21!+22!)/44 = 20! * (1 + 21 + 22 * 21)/44

Evaluate the expression in the bracket

(20!+21!+22!)/44 = 20! * 484/44

Divide

(20!+21!+22!)/44 = 20! * 11

Hence, the simplified expression of (20!+21!+22!)/44 is 20! * 11

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The area of the border is 105.53 feet².

We have,

The swimming pool is a combination of two shapes.

Rectangle:

Length = 60 feet

Width = 30 feet

Area = 60 x 30 = 1800 feet²

Semicircle:

Diameter = 30 feet

Radius = 15 feet

Area = π/2 r² = 1/2 x 3.14 x 15 x 15 = 353.25 feet².

Now,

The area of the swimming pool.

= 1800 + 353.25

= 2153.25 feet²

Now,

Without the border.

Area of the swimming pool.

= rectangle area + semicircle area

= 60 x (30 - 1) + 1/2 x π x (15 - 1)²
= 60 x 29 + 1/2 x 3.14 x 14 x 14

= 1740 + 307.72

= 2047.72 feet²

Now,

The area of the border.

= 2153.25 - 2047.72

= 105.53 feet²

Thus,

The area of the border is 105.53 feet².

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Answer:

yes, it is a right triangle

Step-by-step explanation:

the other two angles are 35 and 55 degrees

Answer:

is NOT a right triangle

Step-by-step explanation:

is a right triangle if it checks the Pythagorean Th.

12² = 10² + 7²

144 = 100+49

144 = 149 False

Suppose \(f(x) =8^{3x\) and \(g(x) =8^{4x\), function operations that are correct include the following:

A. (f + g)(x) = \(8^{3x} + 8^{4x}\)

B. (f × g)(x) = \(8^{7x}\)

C. (f - g)(x) = \(8^{3x} - 8^{4x}\)

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = \(8^{3x+ 4x}=8^{7x}\)

(f ÷ g)(x) = \(8^{3x- 4x}=8^{-x}\)

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The perimeter of the rectangle is 62 square units.

The perimeter of a rectangle can be calculated using the formula:

P = 2(L + W)

Where:

L is the length of the rectangle

W is the width of the rectangle

We have:

L = 20 units

W = 11 units

Substituting into the formula:

P = 2(20 + 11)

P = 2(31)

P = 62 square units

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Question in English

What is the perimeter of a rectangle if it is 20 long and 11 wide?

Answer:

x = 7/15

Step-by-step explanation:

you can check by replacing the x with the number I gave you

Answer:

D. y=-1/2x+5

Step-by-step explanation:

Slope-Intercept Form: y=mx+b

Line passes through y-axis at (0,5) so the "b" part of the equation is positive 5 on the y-axis. Slope is -1/2 so "m" is -1/2.

Answer:

haha you are not going anywhere else to say it

Answer:

10 hours

Step-by-step explanation:

380 - 80 = 300

30 : 1 = 300 : x

x = 300 / 30

x = 10

Answer: it depends; if exam day, no

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

because 12 is the smallest number/angle

It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.

Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.


The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.

A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).

A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).

A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).

Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).

In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.

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The area of the square is given as 100 square unit

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

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Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

Answer:

(-1, 3)

Step-by-step explanation:

5x + 3y = 4

2x + y = 1 ⇒ y=1-2x

As per the concept of probability, If L is invited to speak on Friday, then the science fiction writer be invited on Monday and Wednesday

Probability:

In statistics, probability refers the possible and favorable outcome of the particular event.

Given,

Here we need to find if L is invited to speak on Friday, then on what days MUST a science fiction writer be invited.

Here we know that the writers of the same genre may not speak on consecutive nights.

And here we have the only five slots to fill, two of the three science fiction writers must speak on Monday and Friday

So, If both X and J are invited, then at least one will be forced to speak on Monday or Friday, which is not allowed.

Then, modification of the rules is actually just a bit of a red herring, since all of the answer choices except for the one regarding science fiction writers is true regardless.

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Answer:

7

Step-by-step explanation:

C= 2 pi r

14 pi= 2 pi r

7=r

The equation of the parabola that passes through the points (3,-10), (4,-11), and (5,-10) is y = 1/2(x - 4)^2 - 12.

To find the equation of the parabola that passes through the points (3,-10), (4,-11), and (5,-10), we can use the method of finite differences.

First, we need to find the average rate of change between the y-values at each pair of x-values.

Starting with x = 3 and x = 4:

(-11 - (-10)) / (4 - 3) = -1

Next, we use x = 4 and x = 5:

(-10 - (-11)) / (5 - 4) = 1

Since the two average rates of change are different, we know that the parabola is not a straight line.

Next, we need to find the equation of the parabola in vertex form, which is:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

To find the vertex, we average the x-coordinates and plug them into the equation, using the average rate of change we found above:

h = (3 + 4 + 5) / 3 = 4

k = -11 - (1)(4 - 3)^2 = -11 - 1 = -12

So the equation of the parabola is:

y = a(x - 4)^2 - 12

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Answer and Step-by-step explanation:

22ft = x (c)

20ft = y (b)

18ft = z (a)

Plug into equation.

\(22^{2} = 20^{2} + 18^{2} - 2(20)(18)cosC (X)\\\\484 = 724 - 720cosC\\\\-240 = -720cosC\\\\\frac{1}{3} = cosC\\\\cosx^{1} (\frac{1}{3} ) = C\\\\C = 70.5288\\\\\)

C ≈ 70.5 is the answer.

The base of the function given 2(4)ˣ+5 is 4ˣ

The base of an exponential function. If f(x) = ax, then we call a the base of the exponential function. The base must always be positive. Base 1. If f(x) is an exponential function whose base equals 1 – that is if f(x)=1x.

Given is a function, 2(4)ˣ+5, we need to find the base of the function,

With the multiplication of 4ˣ with 2, the rate at which f(x) changes is 2 times larger. Now it is added by 5, by adding 5 the value of f(x) is always 5 greater than the value of f(x).

This reverses the value of y for each corresponding value of x and increases the rate at which f(x) changes 8 times that of the original function.

Hence, the base of the function given 2(4)ˣ+5 is 4ˣ

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Answer:

la respuesta es 16vpor que aumenta 2

The value of x is 67. 3 degrees

To determine the value of the angle labelled x, we need to know that there are six different trigonometric identities.

These identities are listed as;

From the information given, we have that;

The angle = x

The opposite side = 43

The adjacent side = 18

Using the tangent identity, we have;

tan x = 43/18

Divide the values, we have;

tan x = 2. 3888

Find the tangent inverse, we get;

x = 67. 3 degrees

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Answer:

-3/2, -1 1/4, -3/4, -1/2, -3/8

Explanation:

I converted the denominator to 8, figured it out from there.

Hope that helps! :)

Answer:

Hi there!

Your answer is;

-2= x

Step-by-step explanation:

12= -5x +2

-2

10= -5x

/-5

-2 = x

Hope this helps

Answer: x = -2 give me brainliest

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

i used a calculator lol

The algebraic expression is 20b

The statement is given as:

$20 a ticket

This means that the cost of 1 ticket is $20.

So, the cost of b tickets is

Cost = 20 * b

Evaluate

Cost = 20b

Hence, the algebraic expression is 20b

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Answer:

\(\frac{30}{48}\) =\(\frac{x}{100}\)

the its 48x=30*100. solve for x.

48x=3000 then divide both sides by 48.

you get x=62.5. therefore, 30/48 converted into a percentage is 62.5

Looking at the graph, we can see that there is a point on the graph that lies on the vertical line x = 4 and has a corresponding y-value of 3. This point is the point (4, 3). So, the value of f(4) is 3.

In mathematics, a function is a relation between two sets of objects in which each element of the first set (called the domain) is associated with exactly one element of the second set (called the range).

To find f(4) from the given graph, we need to locate the point on the graph that corresponds to x = 4 and read off the corresponding value of y.

The graph shows that there is a point (4, 3) on the graph of the function y = f(x). This means that when x = 4, the value of y (or f(x)) is 3. Therefore, f(4) = 3.

In general, to evaluate a function at a given point, we need to substitute that point's value for the independent variable (in this case, x) in the function expression and simplify the resulting expression.

However, in this case, we are given the value of x and simply need to read off the value of y from the graph.

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The complete question is given below.