Simplify: 2 \left( 5 + 3 \mathrm{x} \right) + \left( \mathrm{x} + 10 \right)2(5+3x)+(x+10)

Proof by contradiction is a kind of proof that demonstrates the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction.

More broadly, proof by contradiction is a form of argument that shows a statement by arriving at a contradiction, even when the initial assumption is not the disproof of the statement to be proved. In general, proof by contradiction is also known as indirect proof.

A mathematical proof utilising proof by contradiction usually proceeds as follows:

1. The proposition to be proved is P.

2. We consider P to be false, i.e., we assume ¬P.

3. It is then shown that ¬P implies falsehood. This is typically accomplished by deriving two mutually contradictory assertions, Q and ¬Q, and appealing to the Law of noncontradiction.

4. Since assuming P to be false leads to a contradiction, it is concluded that P is, in fact, true.

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The height of the building is 36 ft.

Similar triangles have the same corresponding angle measures and proportional side lengths.

Given that, George places a mirror on the ground 45ft from the base of the building. He walks backward until he can see the top of the building in the middle of the mirror. At that point, George’s eyes are 6th above the ground, and he is 7.5ft from the mirror.

As we can see, this arrangement is creating similar triangles,

We know that, similar triangles have corresponding sides in equal ratios,

Therefore,  

x / 45 = 6 / 7.5

x = 6 / 7.5 × 45

x = 36

Hence, the height of the building is 36 ft.

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Algebraic expressions involving radicals are known as radical expressions.  The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both).

The main symbol attached to any algebraic expression is  x. Each radical expression consists of three separate components: first the "square root" sign itself serves as the radical sign.

The component of the expression inside the radical is known as the radicand

The degree outside the root indicates which root the radical refers to. Expressions without degree symbols have a degree of 2. A cube root is indicated by a degree of 3, a fourth root is shown by a degree of 4, and so on.

Now according to the above expression here, under the root can be any variable like,  2 , 28 , 25, or y7.

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No, the sides of a triangle cannot have lengths 8, 16, and 18.

What is known as a triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

This is because the length of any side of a triangle must be less than the sum of the other two sides and greater than the difference of the other two sides. This is called the triangle inequality theorem.

For a triangle with sides 8, 16, and 18, the side 8 is less than the sum of the other two sides 16+18=34, but greater than the difference of the other two sides 16-18=-2. Therefore, the sides of a triangle cannot have lengths 8, 16, and 18.

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Any complex number can be divided into four categories based on the characteristics of the real component and imaginary part:

Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).

The real and imaginary halves of a complex number are represented by the first and second values, respectively, of the complex data type in Python.

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-4,-3

Step-by-step explanation:

If you reflect over the y axis only the x #

Answer:

in what order are the sides in?

Answer:

No

Step-by-step explanation:

According to the triangle rule, the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side. Let's check this condition:

5 + 15 > 20 ? -> No

So such a triangle cannot exist. And the sides can't be that lengths.

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The time that it will take for them to complete the work is given as follows:

2 and 17/20 days.

To obtain the remaining time, we use the together rate, which is the sum of each of the separate rates.

The rates for this problem are given as follows:

Hence the together rate is obtained as follows:

1/x = 1/8 + 1/12

1/x = 5/24

5x = 24

x = 3.8 days.

Ann worked two days, meaning that only 6/8 = 75% of the document has to be completed, hence the time is of:

0.75 x 3.8 = 2.85 days = 2 and 17/20 days.

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Answer:

either the exponent is "negative" or else the base is between 0 and 1.

Step-by-step explanation:

Answer: Yes, but it's also exponential decay if the base if between 0 and 1.

Step-by-step explanation: I hope this helps!

Answer:

6.4166

Step-by-step explanation:

77/12 = 6.41666666667

Answer: 300

Step-by-step explanation: if ur dividing and you don’t know the divisible, you multiply the answer by the number you divide with, so 10(30) equals 300.

The side with length 5 cm is the hypotenuse.

The given lengths of the sides are 3 cm,4 cm and 5 cm

3²=3×3=9;

4² =4×4=16;

5² =5×5=25;

We found that

9+16=25

3²+4²+5²

Therefore, the triangle is a right-angled triangle.

Note : In any right-angled, triangle the hypotenuse happens to be the longest side.

In this example the side with length 5 cm is the hypotenuse.

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Answer: 16.6667

Step-by-step explanation:

(48 × p) / 100 = 8

((48 × p) / 100) × 100 = 8 × 100

48p = 800

48p / 48 = 800 / 48

p = 16.6666666666667

Percent Increase ≈ 16.6667

A polynomial equation is an equation that consists two or more algebraic terms including at least one variable and constants through the algebraic operation ( addition, substraction, and multiplication).

A polynomial is defined as an equation that has at least one algebraic term with at least one variable and all exponents are integers greater than or equal to 0. The polynomial equation is expressed in the form of aₙ(x), here a is the coefficient, x is the variable and n is the exponent and expanded form is ; F(x) = aₙxₙ + aₙ₋₁ xₙ₋₁ + …….. + a₁x +a₀ = 0

Types of Polynomial Equation : A polynomial equation has mainally four types;

Example of polynomial equations are the following: 1) 3y² + 5y + 20 = 0

2) 5x² - 6x + 9 = 0

3) x² - 3x + 2 = 0

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Step-by-step explanation:

1. Draw the diagonal BD of length 6 cm as base.

2. Draw perpendicular bisector of DB which intersects DB at O.

3. Take O as centre and draw an arc of 3 cm above and below the line segment BD.

4. Join A, B, C and D.

square.

see attachment....

Dilation is the process by which rectangle ABCD becomes another rectangle ABCD.

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The order of the numbers from least to greatest is given by 0.003,1/5³,3/8,4/7,√5

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.

Given here: The numbers are 1/5³ , 4/7,√5,3/8,0.003

To get a clarity of the magnitude of the numbers lets convert every number into decimal numbers.

Now we know To convert a fraction to a decimal, we'll just divide the numerator...by the denominator.

Thus 1/5³=1/125

              =0.008

4/7=0.5714

3/8=0.375

√5=2.2361

and 0.003

Now arranging the numbers from in ascending order we get

0.003,0.008,0.375,0.5714,2.2361

Hence, The order of the numbers from least to greatest is given by 0.003,1/5³,3/8,4/7,√5

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Using the percentage, the amount raised in the first three months is $840

How can I calculate the money raised in three months?

By the conclusion of the academic year, the Helping Hands Student Club hoped to have raised $3,000 for a project.

It has attained 28 percent of its objective after three months.

The following formula can be used to determine how much was raised within the first three months:

amount raised = 28% × 3000

amount raised = 28 / 100 × 3000

amount raised = 84000 / 100

Therefore,

the amount raised in the first three months = $840

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The height of the triangular prism is 22 meters, having a total surface area of 1192 square meters.

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let h represent the height of the triangular prism.

The base are right triangles with side lengths 12 meters, 15 meters, and 19 meters. Hence:

Total surface area = 2 * Area of base + sum of remaining area of surface

Total surface area = 2(1/2 * 15 * 12) + 12*h + 15*h + 19*h

The total surface area of the triangle prism is 1192 square meters. therefore:

1192 = 180 + 46h

46h = 1012

h = 22

The height is 22 meters

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Answer:

55%

Step-by-step explanation:

11/20=0.55

0.55 is the same as 55% since 55/100 is 0,55.

There are 11649 solutions for the given binomial series x¹ + x² + x³ + x⁴ + x⁵ = 21.

x¹ + x² + x³ + x⁴ + x⁵ = 21, where xi, i = 1, 2, 3, 4, 5, is a non-negative integer such that: 0≤ x1 ≤10 and x², x³, x⁴, x⁵ can range in between 0 to 21.

Now we have to choose the coefficient of x²¹ in the following expression

(1 + x + x² + x³.....+ x¹⁰) (1 + x + x² + x³.......+x²¹)(1 + x + x² + x³.....+ x²¹)(1 + x + x² + x³.....+ x²¹)(1 + x + x² + x³.....+ x²¹)

also we can extend term of x², x³, x⁴, x⁵ from x²¹ upto infinty because it didn't  change the value of x²¹ coefficient . 

(1 + x + x² + x³.....+ x¹⁰) (1 + x + x² + x³.......∞)(1+ x + x² + x³.....+ ∞)(1 + x + x² + x³.....+ ∞)(1 + x + x² + x³.....+ ∞)

(1 - x¹¹)/(1 - x)[1/(1 - x)⁴]

(1 - x¹¹) [1/(1 - x)⁵]

now we have to find only the coefficient of x²¹ for which we consider the coefficient of x²¹ and x¹⁰ in [tex]1-x^{-5}[/tex]

general term of the binomial coefficient is [tex]\binom{n+r-1}{r}[/tex]

[tex]\binom{5+21-1}{21}-\binom{5+10-1}{10}[/tex] = 12650-1001 = 11649

--The given question is incomplete; the complete question is

"How many solutions are there to the equation x¹ + x² + x³ + x⁴ + x⁵ = 21,

where xi, i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0≤ x¹≤ 10?"--

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Answer:no

Step-by-step explanation:

Let's start with the first method: converting the fractions to the same denominator. First, we'll set up 5/8 and 1/2 side by side so they are easier to see:

Converting Denominator

5

8

&

1

2

Our denominators are 8 and 2. What we need to do is find the lowest common denominator of the two numbers. This is the smallest number that can be divided by both 8 and 2. In this case, the lowest common denominator is 8.

If we multiply the first denominator (8) by 1 we will get 8. If we multiply the second denominator (2) by 4 we will also get 8. We also need to multiply the numerators above the line by the same amounts so that the fraction values are correct:

5 x 1

8 x 1

1 x 4

2 x 4

This is what 5/8 and 1/2 look like with the same denominator:

5

8

&

4

8

Now that these fractions have been converted to have the same denominator, we can clearly see by looking at the numerators that 5 is NOT less than 4 which also means that 5/8 is NOT less than 1/2.

[tex]\textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\\\\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log_2(x-3)+\log_4(x) \\\\[-0.35em] ~\dotfill\\\\ \log_4(x)\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_2(x)}{\log_2(4)}}\implies \cfrac{\log_2(x)}{\log_2(2^2)}\implies \cfrac{\log_2(x)}{2}\implies \cfrac{1}{2}\log_2(x) \\\\[-0.35em] ~\dotfill\\\\ \log_2(x-3)+\log_4(x)\implies \log_2(x-3)+\cfrac{1}{2}\log_2(x)\implies \log_2(x-3)+\log_2(x^{\frac{1}{2}}) \\\\\\ \log_2(x-3)+\log(\sqrt{x})\implies {\Large \begin{array}{llll} \log_2( ~~ \sqrt{x}(x-3) ~~ ) \end{array}}[/tex]

Answer:

1. The discount price of a T-shirt is  $14.40

2. The regular price of a hat is $22.50

3. The discount price is y = x(0.8)

Step-by-step explanation:

1.

20% = 0.2

18 times 0.2 = $3.60

18 - 3.60 = $14.40

So, the discount price of a T-shirt is $14.40

2.

100% - 20% = 80%

18 / 80 = 0.225

0.225 x 100 = $22.50

So, the regular price of a hat is $22.50

3.

Let's y represent the total cost

We have the equation

y = x(0.8)

Reason:

1/2 = 4/8

1/4 = 2/8

1/2+1/4+1/8 = 4/8+2/8+1/8 = (4+2+1)/8 = 7/8

The three cats eat a combined 7/8 of a box per day.

Over the course of 7 days, they eat 7*(7/8) = 49/8 = 6.125 boxes of cat food. This value is slightly larger than 6, which means Mr. Dungan did not buy enough cat food. He'll need to buy a 7th box.

Side note: 6.125 = 6 & 1/8 as a mixed number.

The provided line's slope and y-intercept are therefore 2, 3. We can use the details provided by the slope-intercept form to graph a linear equation.

For instance, the equation y=2x+3 reveals that the line's slope is 2 and that its y-intercept is located at (0,3).

Finding the value of y at x=0 on a graph will reveal the y-intercept. The graph's intersection with the y-axis occurs at this location.

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.

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Full Question = What is the slope and y-intercept of the line whose equation is y=2x+3?.

The probability that fewer than 58% of the residents in the sample enjoy riding roller coasters is b) 0.433.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

The mean value is 0.62

Z value formula is

z = (x' -mean)/([tex]\sqrt{n}[/tex])

Substituting the given values, we get -

sigma = Sqrt {[tex](x'-mean)^2[/tex]/n}

Sigma = sqrt { [tex](0.58-0.62)^2[/tex]/75} = 0.09

z = (0.58-0.62)/(0.09)

z = -0.433

Hence , The probability that fewer than 58% of the residents in the sample enjoy riding roller coasters is b) 0.433.

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The likelihood that less than 58% of the sample's residents enjoy going on roller coasters is 0.433.

Probability is the possibility that something will occur. The total number of conceivable outcomes.

The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

The average is 0.62.

The formula for the Z value is

Z = (x' – mean) ([tex]\sqrt{n}[/tex])

By substituting the provided values, we get -

Sigma Equals [tex]\sqrt{\frac{(x' - mean)^2}{n} }[/tex]

Sigma is equal to sqrt {[tex]{(0.58-062)^2/75[/tex]} = 0.09

z = (0.58-0.62)/(0.09) (0.09)

z = -0.433

Therefore, the likelihood that less than 58% of the sample's residents enjoy riding roller coasters is 0.433.

Option B is the proper response, thus.

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The length of each side of the triangle is 3 2/3 units

An equilateral triangle can be defined as a type of  triangle having all three sides of equal length.

It is also known as a regular triangle.

Unlike other triangles, an equilateral triangle is one having not only two sides equal like an isosceles triangle but all of its sides equal in length.

The formula for perimeter of an equilateral triangle is expressed as;

P = 3x

Where;

Substitute the values

12x + 33 = 3x

collect like terms

12x - 3x = 33

substract the like terms

9x = 33

Make 'x' the subject

x = 33/9

x = 3 2/3 units

Hence, the value is  3 2/3 units

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