E and F are sets of real numbers defined as follows.
E={v I v≤v3}
F={v I v>6}
Write E∪F and E∩F using interval notation.
If the set is empty, write ∅.

Answer:

Below in bold.

Step-by-step explanation:

7x - 2 + 9x - 2 + 2(5x) = 2(5x + 5) + 2(4x)

7x + 9x + 10x - 4 = 10x + 10 + 8x

7x + 9x + 10x - 10x - 8x = 10 + 4

8x = 14

x = 14/8 = 7/4

So, ST = 5*7/4 + 5

           = 55/4

           = 13 3/4

Answer:

ST = 13.75

Step-by-step explanation:

The perimeter of a trapezium is calculated with the following formula:

P = a + b + c + d (a, b: bases, c, d: sides)

The perimeter of a rectangle is calculated with the following formula:

P= 2(a + b) (a: base, b: side)

we will write the following equation to find the length of ST

7x - 2 + 9x - 2 + 5x + 5x = 2(5x + 5 + 4x) first do the inside the parenthesis

2(9x + 5) = 18x + 10

Now,

7x - 2 + 9x - 2 + 5x + 5x = 18x + 10 add like terms on the left side of the equation

26x - 4 = 18x + 10 transfer like terms to the same side of the equation

26x - 18x = 10 + 4 add/subtract

8x = 14 divide both sides by 8

x = 1.75 replace x with this to calculate the lentgh of ST

5x + 5 = 5*(1.75) + 5 and ST = 13.75

Answer:

70 feet

Step-by-step explanation:

Depth

200 + 370 - 500 = 70 feet

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (2x - y)⁴ is expanded as 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴.

The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

The total number of terms in the expansion of (x+y)ⁿ are (n+1).

The sum of exponents of x and y is always n.

nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ

The binomial coefficients which are equidistant from the beginning and from the ending are equal.

i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.

Let the function be (2x - y)⁴

By using binomial expansion theorem, we get

(2x - y)⁴ = 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴

(2x - y)⁴ is expanded as 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴

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Answer:

x < 2

Step-by-step explanation:

3(x- 17) = 3x - 51

9(1-3x) = 9 - 27x

3x - 51 < 9 - 27x

30x - 51 < 9

30x < 60

X < 2

Denote by x the number of cones sold or produced.

Denote by C(x) the total cost.

Denote by R(x) the revenue made.

Denote by P(x) the net profit accumulated.

[tex]C_{T}(x)=C_{fixed}+C_{variable} \: \\ C_{T}(x)=36+0.52x[/tex]

[tex]R_{T}(x)=selling \: price \: x \\ R_{T}(x)=1.4x[/tex]

[tex]P(x)=R_{T}(x)-C_{T}(x) \\ P(x)=1.4x-(36 + 0.52x) \\ P(x)=1.4x - 36 - 0.52x \\ P(x)=0.88x - 36[/tex]

If there exists profit, then P(x) has to be positive.

[tex]P(x) > 0 \\ 0.88x - 36 > 0 \\ 0.88x > 36 \\ x > \frac{36}{0.88} \\ x > 40.90909 \\ x = 41[/tex]

The weight of the kitten will be no less than the weight of the puppy in 1.4 + 1.2x ≥ 2.8 + 0.5x week.

Statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

A puppy weighs 2.8 pounds at birth and gained about 0.5 pounds per week.

A kitten weighs 1.4 pounds at birth and gains about 1.2 pounds per week.

puppy: 2.8 + 0.5x

Kitten: 1.4 + 1.2x

As, kitten is no less than puppy.

Kitten ≥ puppy

1.4 + 1.2x ≥ 2.8 + 0.5x

hence, the weight of the kitten will be no less than the weight of the puppy in 1.4 + 1.2x ≥ 2.8 + 0.5x week.

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2.4012 is the value of x after solving equation  [tex]e^{x+1}[/tex] = 30 using natural logarithms

We have been asked to solve [tex]e^{x+1}[/tex] = 30 using natural logarithms

⇒   [tex]e^{x+1}[/tex] = 30

⇒ x + 1 = ㏑ 30

⇒ x =  ㏑ 30 - 1

       ≈ 2.4012

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

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Use natural logarithms to solve each equation.

 [tex]e^{x+1}[/tex] = 30

The radius is 169 inches.

As per the known fact, the radius and area of circle are related by the formula -

Area = πr²

So, rewriting the expression in equation -

r=√(A/π)²

As mentioned, r is the radius and A is the area of the circle and π is constant

Keep the value of A in the above mentioned rewritten equation to find the value of radius of circle.

r = √(169π/π)²

On solving the above equation we get the new equation, which is as follows -

r = 169π/π

Cancelling π as it is common in both numerator and denominator

r = 169 inches

Hence, the radius of circle is 169 inches.

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Answer:

6

Step-by-step explanation:

2,4,6,8,10

6,12,18,24

The least number that is on both lists is 6

Answer:

7.5 × 10[tex] {}^{2} [/tex] (scientific notation)

Step-by-step explanation:

➟ 750 = 7.5 × 10[tex] {}^{2} [/tex] (scientific notation)

Answer: (5,-4)

Step-by-step explanation:

start at zero and go right five because of the adding of five

Then go down 4 because of the minus of zero.

Answer:

36

Step-by-step explanation:

3/4x = 18  multiply both sides by 4/3

(4/3)(3/4)x = (18/1) (4/3)

x = 24  There are 24 boys in the class.

2/3x = 24  Multiply both sides by 3/2

(3/2)(2/3)x = (24/1)(3/2)

x = 36

By solving a linear equation , we get the total number of students in the class are 36

An linear equation is a mathematical statement consists of expressions of only one variable that too with power 1 and constants and  compares two such expressions by equating them.

Standard form of  linear equation in one variable : ax +b = c

x = (c-b)/a

Let the total number of students in the class are  x

Given that 2/3 of the students in a class are boys

∴ The number of boys = 2/3(x) =(2x)/3

Then given that 3/4 of the boys are right handed and there are 18 right-handed boys

∴ 3/4( no of boys ) =18

⇒3/4 *(2x/3) =18

⇒(3*2x)/(4*3) =18

⇒x/2 =18

Multiplying both sides by 2

⇒x = 2*18 = 36

Therefore, the total number of students in the class are 36

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Start off with %70 of 150

0.7 • 150 = 105

To find their total donation amount,

105 • £1 = £105

Then we know the rest of the parents account for the last %30 of the attendees

We can find this out by either,

150 - 105

or

0.3 • 150

Either way we end up with 45

45 • £2 = £90

%70 (105) of the parents donated £105

%30 (45) of the parents donated £90

The parents, in total, donated £195

Answer:

7/2z +4

Step-by-step explanation:

z(4-1/2)+4

=7/2z +4

Answer:

7.5

Step-by-step explanation:

Remove parentheses; z=4-1/2+4

Add the 4s: -1/2+8

convert to fraction: 8*2/2-1/2

combine fractions:8*2-1/2

8*2-1=15

15/2

now convert 15/2 to a decimal, boom, 7.5

The equation for red graph is y= f(x-1)

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Given:

y = f(x)

Here if look at the graph with black with function f(x) = x

Now, if we look at the graph closely to shift the black graph to red.

There is shifting the graph in the right hand side which which gives the function y= f(x-1)

Hence, the equation for red graph is y= f(x-1)

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Answer:

I'm pretty sure it is -3x+7

The measure of the angle of their turn on to University Blvd is; 80°

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.

Thus, from the given diagram when we apply the concept of corresponding angles, we can say that;

17x + 15 = 19x + 5

19x - 17x = 15 - 5

2x = 10

x = 5

Thus;

19x + 5 = 19(5) + 5 = 100°

Now, the sum of the angles on a straight line is 180 degrees. Thus, the measure of the angle of their turn on to University Blvd is;

180 - 100 = 80°

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Answer:

T=x(T*2) where X=660

Step-by-step explanation:

If it has been 2 hours than t=2

plug in 2 for t and you get x*4

The percent increase or decrease of the starting and ending quantities below are:

The percent increase can be found by the formula:

= (End - Start) / Start x 100%

The percent increase of these quantities are:

= (10 - 3) / 3 x 100%

= 7 / 3 x 100%

= 2.3333 x 100%

= 233%

= (20 - 9) / 9 X 100%

= 11/9 x 100%

= 1.222 x 100%

= 122%

= (85 - 100) / 100 x 100%

= -15 / 100 x 100%

= -15%

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Answer: GCF = 6

Step-by-step explanation:

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54

Then the greatest common factor is 6.

For the given square pool the relationship between the line segment will be BD = BC + CD and AB + BC = CD + BC and it will go to proves that AC = BD.

A line section that can connect two places is referred to as a segment.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Given that,

AB = CD

By segment addition postulate

AC = AB + BC

Again by segment addition postulate

BD = BC + CD

In addition property of equality

AB + BC = CD + BC

So,

AC = BD

Hence "BD = BC + CD and AB + BC = CD + BC will proves that AC = BD".

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Answer: 2

Step-by-step explanation:

Answer:

28/5

Step-by-step explanation:

7 x 4/5 = 28/5

use keep, change, flip

Answer:

28/5

Step-by-step explanation:

just did it on khan academy.

The proof that at least three of any 25 days chosen must fall in the same month of the year holds true because; there are twelve months in a year.

This proof required for the statement in the task content follows from the fact that, there are 12 months in a year.

Hence, the proof that at least three of any twenty-five, 25 days chosen must fall in the same month of the year is because, there are 12 months in a years and after choosing two days from each month, amounting to 24 days, the 25th day would fall into a month and hence, such month has 3 days already.

Ultimately, the statement that at least three of any 25 days chosen must fall in the same month of the year holds true because there are 12 months in a year.

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(a) The expression to represent the difference between the elevations is 5764 - ( - 9).

(b) The answer will be a positive integer.

(c) The difference between the highest and lowest point is 5773 feet.

The elevation of a county is 5764 feet above sea level.

The elevation of the county is 9 feet below sea level at the lowest point.

(a) The highest point = 5764 feet

The lowest point = 9 feet

Then the difference between the highest and the lowest point will be:

difference = Highest - lowest

difference = 5764 - ( - 9)

(b) The answer will be written as a positive integer.

(c) The difference between the highest and lowest points of the county will be:

difference = Highest - lowest

difference = 5764 - ( - 9)

difference = 5764 + 9

difference = 5773 feet

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The complete question is mentioned below:

At its highest point, the elevation of a county is 5764 feet above sea level. At its lowest point, the elevation of the county is 9 feet below sea level. Answer parts (a) through (c).

a. Write an expression using integers to represent the difference between the elevations.

b. Will the answer be written as a positive or negative integer?

c. What is the difference between the highest and lowest points of the county?

[tex]a = \pi \: r {}^{2} \\ r {}^{2} = \frac{a}{\pi} \\ r = \sqrt{ \frac{a}{\pi} } [/tex]

Answer to this question is:

Domain of given function is (-∞,∞),{x|x∈R}

Range of given function is [0,∞),{y|y≥0}

Inverse of given function is -√x+7,√x+7

The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.

Interval Notation:(-∞,∞)

Set-Builder Notation:{x|x∈R}

The set of all valid y values constitutes the range.

Interval Notation:[0,∞)

Set-Builder Notation:{y|y≥0}

For calculation of inverse:

∴Domain of given function is (-∞,∞),{x|x∈R}

Range of given function is [0,∞),{y|y≥0}

Inverse of given function is -√x+7,√x+7

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Answer:

1/4

Step-by-step explanation:

or 90/360