Using a number line, find both the intersection and the union of the following
intervals:
(-∞,2) and [0,∞)

Therefore the product of two conjugates is a difference of two squares.

When two binomials have the same terms but different arithmetic operators in the center of these related words, they are said to be conjugate. For instance, the conjugate of p + q is p - q.

An integer known as a binomial number is produced by evaluating a homogeneous polynomial with two terms, also known as a binomial.

This statement is true.

The conjugates of a complex number are two complex numbers that differ only in their signs. They are of the form a + bi and a - bi.

When two conjugates are multiplied, the product is (a + bi)(a - bi) = a^2 + (bi)^2 = a^2 - b^2 + (2abi) = (a^2 - b^2) + (2ab)i.

which is in the form (a^2 - b^2) + (2ab)i = (a^2 - b^2) + (2ab)i = (a+b)(a-b)

So the product of two conjugates is a difference of two squares.

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54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.

A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.

given

To find P P, divide P

P by the total number of participants (students and chaperones), which is 81.

Seventh graders totaling 81 - 7 =

74 participated in the field trip.

54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.

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The coordinate points of the point P is (-3.5, 2.3).

What is a coordinate plane?

Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line.

The ratio in which the point 'P' divides the line segment RQ is -

a:b = 5:1

The coordinates of the end-points of line segment RQ are -

R(4, -1)  and  Q(-5, 3).

The coordinates of the point H are obtained when a point H divides a line segment with end points (p, q) and (s, t) in the ratio a:b -

H = [(as + bp)/(a + b)], [(at + bq)/(a + b)]

H = [(5*-5 + 1*4)/(5 + 1)], [(5*3 + 1*-1)/(5 + 1)]

H = (-21/6, 14/6)

H = (-3.5, 2.3)

Therefore, the coordinate points are obtained as H = (-3.5, 2.3).

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The class has a 45-minute, or 0.75-hour, climb to the summit planned to observe a nearby monument. The bus driver intended to travel at a steady 40 mph. Accordingly, the average speed is 0.888.

The time required to travel 20 miles at 40 mph is 30 minutes, and the time required to go 40 miles is 60 minutes. The journey of 60 miles will therefore take 90 minutes. In most cases, an hour's worth of time, this will tell you the average speed.

As a result, Ben's average speed was 50 miles per hour when he covered 150 miles in 3 hours. 40m in an hour. 12 hour to cover 20 miles. In fifteen minutes, ten miles. It is determined by dividing something's total travel distance by its total journey time. Take the earlier automobile, for instance. The average speed of the vehicle would be 70 / 2 = 35 miles per hour if it covered 70 miles in two hours.

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Complete question is: Hassan's history class is taking a field trip to the state capitol building. The capitol building is 50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to view a local monument. The bus driver plans to drive at an average speed of 40 miles per hour. Which equation can you use to find how many hours, x, the second part of the trip will take?

Answer:

Using the cosines law

Step-by-step explanation:

So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC

The distance from point A to point B is 781.5 ft.

Since the angle of elevation from point A to the lighthouse is 15 degrees, use the tangent function to find the height of the lighthouse. Let x be the height of the lighthouse,

tan(15°) = x / 862

Solve for x.

x = 862 (tan(15°))

Similarly, let y be the distance from point B to the lighthouse,

tan(8°) = x / y

Solve for y.

tan(8°) = 862 (tan(15°)) / y

y = 862 (tan(15°)) / tan(8°)

y = 1643.45 feet

Subtract 862 from 1643.45 to get the distance from point A to point B.

distance from point A to point B = 1643.45 - 862 = 781.45 ft = 781.5 ft

Therefore, the distance from point A to point B is 781.5 ft.

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On solving the provided question, we can say that - the slope of the following will be slope, m = [tex]4-6/4-2 = -2/2 = -1[/tex]

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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On solving the provided question, we can say that - the slope of the following will be slope, m = -1

what is slope?

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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Logarithmic Functions

In mathematics, the logarithmic function is an inverse function to exponentiation

Domain and range of logarithmic functions

We know that is defined only when >0. So the domain is the set of all positive real numbers. We can see that can be either a positive or negative real number (or) it can be zero as well. Thus,  can take the value of any real number.

Note:

The domain of function = is >0 (or) (0,∞).

The range of any log function is the set of all real numbers ().

Logarithmic graph

We know that exponentials and functions are inversely proportional to each other, and so their graphs are symmetric concerning the line =. Also, note that =0 when =0 as =(1)=0 for any . Thus, all such functions have an -intercept of (1,0).  A logarithmic function doesn’t have a -intercept as 0 is not defined.

Properties of logarithmic graph

>0 and ≠1.

The logarithmic graph increases when >1 and decreases when 0<<1.

The domain is obtained by setting the argument of the function greater than 0.

The range is the set of all real numbers.

Graphing logarithmic functions

Before plotting the log function, just have an idea of whether you get an increasing curve or decreasing curve as the answer. If the >1 then the curve is increasing, and if 0<<1, then the curve is decreasing.

Here are the steps for graphing logarithmic functions:

Find the domain and range.

Find the vertical asymptote by setting the argument equal to 0. Note that a  function doesn’t have any horizontal asymptote.

Substitute some value that makes the argument equal to 1 and use the property (1)=0. This gives us the -intercept.

Substitute some value that makes the argument equal to the base and use the property ()=1 This would give us a point on the graph.

Connect the two points (from the last two steps) and extend the curve on both sides relative to the vertical asymptote.

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The solution to w in the equation 9(w - 4) - 7w = 5(3w - 2) is w = -2.

Now, According to the question:

The given Equation:

9(w-4)-7w=5(3w-2)

To solve for w we first need to simplify our equation, removing any brackets and adding together similar terms. This gives us:

9(w-4)-7w=5(3w-2)

9w - 36 -7w = 15w - 10

2w - 36 = 15w - 10

Next, we subtract 2w from both sides to have all the variables on one side of our equation, then we add 10 to both sides to move the numerical values to one side.

2w - 36 = 15w - 10

2w -2w - 36 = 15w - 2w - 10

-36 = 13w - 10

-36 + 10 = 13w - 10 + 10

-26 = 13w

Finally, we divide both sides by 13 to find the value of w.

w = -2

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The complete question is this :

What is the solution to the equation of 9(w - 4) - 7w = 5(3w - 2).

Answer:

The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Answer:

aida:$7500

Bernardo:$6000

Christiano :$4500

b.i $10500

b.ii 13/60

b.iii $13000

c. 24%

Answer:

139⁰

Step-by-step explanation:

since g and h are parallel

then n= 139⁰ (corresponding angles)

The probability that a car chosen at random will need no​ repairs = 72%; no more than one​ repair = 91%;  some​ repairs = 9%

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.

28% of all vehicles will require some sort of repair; of these, 19% will require one repair, 7% will require two repairs, and 2% will require more than two repairs.

The number of vehicles that would not require any form of repairs is equal to the entire number of vehicles less the proportion that requires repairs; for example, 100% - 28% = 72%. The total number of automobiles minus the percentage that require more than one repair equals the percentage of vehicles that will require no repairs or just one

; hence, 100% - (7% + 2%) = 91%. The total number of vehicles in need of repairs is equal to the product of those with two repairs and those with three or more.

the probability that a car chosen at random will need no​ repairs = 72%; no more than one​ repair = 91%;  some​ repairs = 9%

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The population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours.

Given that,

P_t = P_0 * 2^(t/d) , which refers to the formula for the calculation of the number of bacterial cell in a population.

In the given formula, P_t is the population after t hours, P_0 is the initial population, t is the time in hours and d is the doubling time in hours,

Therefore,

P_0 = 7100

d = 2

t = 15

so,

P_15 = 7100 * 2^(15/2) = 7100 * 181.019= 1285234.9 which is nearly equal to 1285235

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours, the population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235

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The graph C. represents the polynomial with zeros of -3, 0 and 2.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information about the graph's x-intercepts for the polynomial.

Alternately, we might state that the zeros of the polynomial are the x-intercept of its graph. Thus, the needed function is represented by the graph with the coordinates -3, 0, and 2.

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The complete question is as follows:

Select the correct answer.

Which graph best represents a function with zeros of -3, 0, and 2?

The perimeter of the rectangle is 13x+7 feet

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: The width of a rectangle is 5x-1.5 feet and the length is 1.5x+5 feet. Therefore the perimeter of the rectangle is given by

= 2(5x-1.5+1.5x+5)

=2(6.5x+3.5)

= 13x+7

Hence, The perimeter of the rectangle is 13x+7 feet

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Answer:

6n-5

Step-by-step explanation:

let 'n' equal 'a number'

the equation above means you are multiplying 6 and that number, then reducing it by 5

Answer:

9

Step-by-step explanation:

6 1/3 yards of material is 19/3 yards total. 6 yards broken into thirds is 18/3. 18 divided by 2 is 9. There are 9 total pieces to cut, and an extra 1/3 left over

Answer:

The fraction 480/840 can be reduced to its lowest terms by dividing the numerator and denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd). This results in a reduced fraction of 4/7.

Step-by-step explanation:

All points in Quadrant IV have a positive x-coordinate and a negative y-coordinate.

The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant. The x-axis in this quadrant has positive values, whereas the y-axis has negative numbers.

A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from first to fourth.

A quarter of a circle; a 90° arc. the region enclosed by an arc and two radii are drawn one to each extreme. As a mechanical component, anything is shaped like a quarter of a circle.

All Quadrant I points have two positive coordinates.

Quadrant II points all have a negative x-coordinate and a positive y-coordinate.

All Quadrant III locations have two negative coordinates.

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Answer:

|5-2x|<_11

=5+2x<11

=2x=11-5

2x=6

=X<-3

On solving the provided question, we can say that the equation will be 1.8x=7200 => x=4000

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

the equation will be

1.8x=7200

x=7200/1.8

x=4000

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Answer:

C is the correct answer

From the graph we can see that at the given interval [-6,0] the graph decreases from left to right.

Initially the y-values is a little over 3 and then it decreases to about 0.5 at the end of the interval.

Thus, the graph of the function over the interval [-6,0] is decreasing.

The Two steps equation in mathematics are the equations that can be solved within exactly two steps.

What is a Two Step Equation ?

The Two Step Equation are the algebraic problems that  just take two steps to solve. It is a linear equation in one variable.

When solving the two step equation, we have to perform operation on both sides of the equation .

For Example : Solve [tex]2x+6=12[/tex] ;

Step1 : we Subtract -6 from both sides to isolate variable x.

⇒ [tex]2x + 6 - 6 = 12 - 6[/tex]

⇒ [tex]2x = 6[/tex]

Step2 : We Divide both the sides of equation by 2 and solve for x.

⇒ [tex]\frac{2x}{2} =\frac{6}{2}[/tex]

⇒ [tex]x = 3[/tex] ;

Therefore , the equation is solved in two steps .

The given question is incomplete , the complete question is

What is the two step equation in math ?

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The length of the triangle ΔABC will be √7 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

In triangle ΔABC, AC = BC, the CD is perpendicular to AB with D belonging to AB, AB = 4 inches, and CD = √(3) inches.

The CD is half of the length AB. Then we have

CD = AB / 2

CD = 4 / 2

CD = 2 inches

Then the length of AC is calculated as,

h² = (√3)² + (2)²

h² = 3 + 4

h= √7 inches

The length of the triangle ΔABC will be √7 inches.

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Answer:

a. 1.6

b. 16

c. 0.16

d. 1.6

On solving the provided question, we can say that - the value of the linear equation is 2y+8x = 140

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, we have 2y + 8x

and x = 10 ; y = 15

2y + 8x

20 + 120 = 140

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Answer:

  $16,755

Step-by-step explanation:

You want the difference in interest earned on $66,000 after 19 years between an account earning 6 3/8% compounded annually, and one earning 5 3/4% compounded continuously.

The formula for the account value multiplier when interest is compounded annually is ...

  k = (1 +r)^t . . . . . . compounded annually at rate r for t years

When interest is compounded continuously, the multiplier is ...

  k = e^(rt)

The difference in account values between the two rates is ...

  ∆value = $66,000·(1 +0.06375)^19 -e^(0.0575·19))

  ∆value ≈ $16,754.70

Benjamin will have about $16,755 more than Christian after 19 years.

The 3 different polynomial equations are linear polynomial equations, quadratic polynomial equations, and cubic polynomial equations.

A polynomial equation is one where a polynomial is set equal to zero. i.e., it is an equation created with variables, non-negative integer exponents, and coefficients together with operations and an equal sign.

A polynomial equation is always like "polynomial = 0". Algebraically, it is of the form p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₁ x¹ + a₀x⁰ = 0, where

aₙ, aₙ₋₁, ...., a₁, a₀ are coefficients and all these numbers are real numbers.

'x' is the variable.

p(x) means "polynomial in terms of variable x"

'n' is a non-negative integer, it is the degree of p(x).

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The probability is 5/32.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

To roll exactly 4 odds out of 5 rolls is [tex](\frac{1}{2} )^{4}\frac{1}{2}[/tex]  where the odds are 1, 3, and 5 for 3/6=1/2 and the other 1/2 is the probability of rolling an even since we want exactly 4 odds.

Since there are 5 dice being rolled there are 5 ways to order them.

So the probability is 5/32.

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