divislon or synthetic division to determine the quotient and remainder. (x^(2)+4x-20)-:(x-4)

The distance between the hunter and the bird is 5.39

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below.

distance = √( (x₂ - x₁)² + (y₂ - y₁)²)

The hunter is at (0, 0) and shoots at (2, 5), so we can plug those values ​​into the formula for the distance:

distance = √( (2 - 9)² + (5 - 0)²)

distance = √( (2 )² + (5 )²)

distance = √( 4 + 25) = 5.39

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The solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3.

To solve the trigonometric equation sin 2x=−√3/2 on the interval [0,2π), we need to find the values of x that satisfy the equation. We can do this by using the inverse sine function and the periodicity of the sine function.

First, let's find the general solution of the equation:
sin 2x=−√3/2
2x= sin⁻¹(−√3/2) + 2πn or 2x= π - sin⁻¹(−√3/2) + 2πn, where n is an integer
2x= -π/3 + 2πn or 2x= 4π/3 + 2πn
x= -π/6 + πn or x= 2π/3 + πn

Now, we need to find the values of x that are in the interval [0,2π). We can do this by plugging in different values of n until we find all the solutions in the interval.

For x= -π/6 + πn:
When n=0, x= -π/6 (not in the interval)
When n=1, x= 5π/6 (in the interval)
When n=2, x= 11π/6 (in the interval)
When n=3, x= 17π/6 (not in the interval)

For x= 2π/3 + πn:
When n=0, x= 2π/3 (in the interval)
When n=1, x= 5π/3 (in the interval)
When n=2, x= 8π/3 (not in the interval)

Therefore, the solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3. These are the exact form answers. If we want to round them to two decimal places, we get x= 2.62, 5.24, 1.05, and 3.14.

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The amount of money in the account after 9 years is $2549.68.

The formula A=P(1+(r)/(n))^(nt) is used to calculate the amount of money in an account after a certain amount of time, given the principal amount (P), the interest rate (r), the number of times interest is compounded per year (n), and the number of years (t).

To find A when P=2000, r=3%, n=12, and t=9, we can plug these values into the formula and simplify:

A = 2000(1+(0.03)/(12))^(12*9)

A = 2000(1+0.0025)^(108)

A = 2000(1.0025)^(108)

A = 2000(1.2748)

A = 2549.68

Therefore, $2549.68 is the amount of money in the account after 9 years.

"

Correct question

Ulas and Applications:

If A=P(1+(r)/(n))^(nt)

Find A when P=2000,r=3%,n=12, and t=9.

"

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The solution to the equation is x=3, which means that when x is equal to 3, the equation is true.

The solution of an equation is the value of the variable that satisfies the equation.

In this case, the solution is x=3, which means that when x is substituted with 3, the equation is true.

We can say that the solution is unique, as there is only one value of x that satisfies the equation. It is also a real solution, as the value of x is a real number.

Additionally, we can say that the solution is finite, as there is a specific value for x that satisfies the equation.

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Answer:

35%

Step-by-step explanation:

26/40 = 0.65
1-0.65=35

Let ((2) = ve- 4 and g(2) = 12 11r + 30. Then f(1) = i√3, g(1) = 21, Domain of f(x) = [4, ∞) and  Domain of g(x) = (-∞, ∞)

First, let's find f(1) and g(1). To do this, we simply substitute x = 1 into the equations for f(x) and g(x):

f(1) = √(1 - 4) = √(-3) = i√3

g(1) = 2(1) - 11(1) + 30 = 2 - 11 + 30 = 21

Now, let's find the domains of f(x) and g(x). The domain of a function is the set of all values of x for which the function is defined.

For f(x) = √(x - 4), the expression inside the square root must be greater than or equal to 0 in order for the function to be defined. This means that:

x - 4 ≥ 0

x ≥ 4

So the domain of f(x) is [4, ∞).

For g(x) = 2x - 11x + 30, there are no restrictions on the domain, so the domain of g(x) is (-∞, ∞).

So the final answers are:

f(1) = i√3

g(1) = 21

Domain of f(x) = [4, ∞)

Domain of g(x) = (-∞, ∞)

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(5z+2)/(z) is the possible rational expression.

To subtract the two rational expressions, we can combine the numerators and keep the common denominator. The subtraction of the two rational expressions is shown below:

(19z+6)/(3z) - (4z)/(3z) = (19z+6-4z)/(3z)

Simplifying the numerator gives:

(15z+6)/(3z)

We can further simplify the expression by factoring out a common factor of 3 from the numerator:

3(5z+2)/(3z)

The 3 in the numerator and denominator cancel out, leaving us with the final simplified expression:

(5z+2)/(z)

Therefore, the answer is (5z+2)/(z).

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The final simplified expression is (3x+1)(5x+2)/(3x-2).

The given expression is (15x^(2)+13x+2)/(3x-2). We can try to simplify this expression by factoring the numerator and denominator, and then canceling out any common factors.

First, let's factor the numerator:

15x^(2)+13x+2 = (3x+1)(5x+2)

Now, let's factor the denominator:

3x-2 = (3x-2)

There are no common factors between the numerator and denominator, so we cannot simplify the expression any further.

Therefore, the simplified expression is:

(15x^(2)+13x+2)/(3x-2) = (3x+1)(5x+2)/(3x-2)

Since x!=(2)/(3), we do not need to worry about any undefined values.

So, the final simplified expression is:

(3x+1)(5x+2)/(3x-2)

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The linear equation in the given graph is.

y = 40x

We know that the general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept, these two values are constants, and the variables are x and y.

First, notice that the line intercepts the y-axis at the point (0, 0), then b = 0.

So we can write:

y = a*x

Also notice that the line passes through the point (1, 40), then:

40 = a*1

40/1 = a

The linear equation is.

y = 40x

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Answer:

-3 < y < -1

Step-by-step explanation:

|4y+8| < 4                                   |4y+8| > -4

4y + 8 < 4                                   4y + 8 > -4

4y < -4                                         4y > -12

y < -1                                             y > -3

So, the answer is -3 < y < -1

Answer: 0.00003396739

Step-by-step explanation:

hope this helps

Yes, the expression 49-64y^(2) is a difference of squares.

A difference of squares is an expression that can be written in the form a^(2) - b^(2), where a and b are any expressions. In this case, 49 can be written as 7^(2) and 64y^(2) can be written as (8y)^(2). Therefore, the expression can be rewritten as 7^(2) - (8y)^(2), which is in the form of a difference of squares.

It is important to note that a difference of squares can be factored into the product of two binomials, (a+b)(a-b), but the question specifically asks not to factor the expression.

In conclusion, yes, the expression 49-64y^(2) is a difference of squares.

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The slope of line A is -1/2 and the slope of line B is -3/5. The slope of line A is greater than the slope of line B.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

First, let's rewrite the equation of line A in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept -

y - 1 = - 1/2(x + 10)

y = 1/2(x + 10) + 1

y = 1/2x + 6

So, the slope of line A is - 1/2.

For line B, we can use the formula for finding the slope of a line given two points (m = (y2 - y1) / (x2 - x1)).

Let's use the first and last points to find the slope -

m = (-3 - 6) / (-10 - 5) = -9 / -15 = 3/5

So, the slope of line B is 3/5.

Therefore, the slope of line B is smaller as compared to slope of line A.

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P is rational number from the given equation P=2(2x+5)+2x.

Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).

The given equation is P=2(2x+5)+2x.

Here, P=2(2x+5)+2x

P=4x+10+2x

P=6x+10

Given that, x=1.5, 3 and 1.2

Substitute, x=1.5 in P=6x+10, we get

P=6×1.5+10

P=9+10

P=19

So, 19 is rational number

Substitute, x=3 in P=6x+10, we get

P=6×3+10

P=18+10

P=28

So, 28 is rational number

Substitute, x=1.2 in P=6x+10, we get

P=6×1.2+10

P=7.2+10

P=17.2

So, 17.2 is rational number

Therefore, P is rational number from the given equation P=2(2x+5)+2x.

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12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex].

The weight of 12 blue whales will be the product of the weight of a single blue whale and the number of blue whales. To find the product, we simply multiply the weight of a single blue whale by the number of blue whales.

So, the weight of 12 blue whales will be:

[tex]\( 1.8 \times 10^{6} \mathrm{~kg} \) × 12 = \( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Therefore, 12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Multiplication refers to binary operations in which different numerical sets are established. In mathematics the process of multiplication is elementary in several operations, it is also accompanied by addition, subtraction and division. Multiplication is the opposite of division.

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Answer:

75 dollars.

Step-by-step explanation:

Each person costs 25 dollars and p=3 we just put this into a equation.

25 × 3 = 75

C = 75

Therefore , the solution of the given problem of triangle comes out to be  the shape is 55 square miles.

Because a triangular has two or more extra sections, it is a polygon. It's shape is a simple rectangle. A triangular shape can only be distinguished from a parallelogram by its sides A, B, and C. A singular plane rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.

Here.

Two triangles with a base of 10 miles and heights of 7 miles and 4 miles can be formed from the composite design.

The following method can be used to determine a triangle's area:

A = (1/2)bh

where A represents area, B represents foundation, and H represents height.

We can calculate each triangle's area using the following formula:

=> Area of 1st triangle

=>  (1/2)(10)(7) = 35 square miles

=> Area of 2nd triangle

=>  (1/2)(10)(4) = 20 square miles

The two triangles' combined regions make up the composite shape's surface area.

55 square miles is the combined shape's area

=>  (35 + 20).

Consequently, the combined size of the two triangles in the shape is 55 square miles.

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Answer:

$1.65

Step-by-step explanation:

9.7%×(11.73+5.27)

0.097×(11.73+5.27)

=1.649

to 2d.p

=1.65

Jackie needs to pour 2/9of a quart of water from the first bottle to the second bottle to make them have the same amount of water.

Two or more expressions with an Equal sign is called as Equation.

Let us assume that we transfer an amount "x" from the first bottle to the second bottle.

This means that the first bottle will have 1-x quarts of water, while the second bottle will have 5/9 + x quarts of water.

Now, we want to find the value of "x" that makes both bottles have the same amount of water.

We can set up an equation:

1-x = 5/9 + x

We can then solve for "x" by adding "x" to both sides and subtracting 5/9 from both sides:

1 - 5/9 = 2x

4/9 = 2x

x = 2/9

Hence, Jackie needs to pour 2/9 of a quart of water from the first bottle to the second bottle to make them have the same amount of water.

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In the three-month period, the water level was 6.5 inches, 6.3 inches, and 6.7 inches, respectively. This is lower than the yearly average of 7.2 inches

Water level is a term used to describe the height of a body of water, usually in reference to an ocean, lake, river, or other body of water. It can also refer to the height of the water above sea level or other reference points.

The table indicates that the water level of the reservoir for the three-month period is lower than the yearly average. This can be seen by comparing the data in the table.

This could be due to a number of factors, including decreased precipitation and increased evaporation during the three-month period.

Ultimately, the data shows that the water level of the reservoir for the three-month period is lower than the yearly average. This could be a cause for concern in the long-term, as the water level of the reservoir could become too low to sustain local populations and ecosystems in the area.

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The value of x on the straight line is 43 degrees

From the question, we have the following parameters that can be used in our computation:

The straight line

The sum of angles on a straight line is 180 degrees

Using the above as a guide, we have the following equation

3x + 51 = 180

Evaluate

3x = 129

Divide by 3

x = 43

Hence, the value of x is 43 degrees

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Adam should purchase the long-range weather forecast for $1. By doing so, he will have the best chance of minimizing his total expected cost for the summer.

The expected value of the sample information (EVSI) is the expected cost if Adam does not purchase the forecast and goes with the meteorological records, which is $16.6 ($15 for the season pass plus an average of $1.6 per rainy day).

The expected value of perfect information (EVPI) is the expected cost if Adam purchases the forecast and uses it to make the decision, which is $15.6 ($15 for the season pass plus an average of $0.6 per rainy day).

Thus, purchasing the long-range weather forecast is the best decision for Adam, as it will save him $1 in expected costs and allow him to minimize his total expected cost for the summer.

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Using multiplicative property of equations, the solution to the equation is x = 32.

The multiplicative property of equations states that if you multiply both sides of an equation by the same number, the equation will still be true.

In this case, we can use the multiplicative property to solve for x by multiplying both sides of the equation by (4/3) to cancel out the fraction on the right side of the equation.

24 = (3/4)x

(4/3)(24) = (4/3)(3/4)x

32 = x

So the solution to this equation is x = 32.

No need to further simplify your answer since the solution is already in its simplest form.

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The numeric value of the composite function at x = 4 is given as follows:

|f(4) - 1|.

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

If g is the outer function, as is the case for this problem, we have that:

(g • f)(x) = g(f(x)).

At x = 4, the numeric value of the composite function is given as follows:

g(f(4)) = |f(4) - 1|.

The problem is incomplete, hence the composite function is given in general terms.

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The two bases B1 and B2 span the same subspace of R3.

Let B1 be the basis {(1,2,3),(2,−1,2)}={u1,u2} and B2 be the basis {(0,5,4),(1,−8,−5)}={v1,v2}. We want to show that these two bases span the same subspace of R3.

To do this, we need to show that any vector in the subspace spanned by B1 can also be written as a linear combination of vectors in B2, and vice versa.

Let x be a vector in the subspace spanned by B1. Then x = a*u1 + b*u2 for some scalars a and b. Substituting the values of u1 and u2, we get:

x = a*(1,2,3) + b*(2,−1,2)

= (a+2b, 2a-b, 3a+2b)

Now we want to express x as a linear combination of v1 and v2:

x = c*v1 + d*v2

= c*(0,5,4) + d*(1,−8,−5)

= (d, 5c-8d, 4c-5d)

Setting the two expressions for x equal to each other, we get the following system of equations:

a+2b = d

2a-b = 5c-8d

3a+2b = 4c-5d

Solving this system of equations, we can find values of c and d that satisfy the equations. This shows that any vector in the subspace spanned by B1 can also be written as a linear combination of vectors in B2.

Similarly, we can show that any vector in the subspace spanned by B2 can also be written as a linear combination of vectors in B1.

Therefore, the two bases B1 and B2 span the same subspace of R3.

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The size of angle ACB is approximately 50.66°.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

We are given that;

Angle ABC= Angle ACD + 31°

Now,

Since angle ABC is twice angle BAC, we can write:

angle BAC = x

angle ABC = 2x

angle ACB = 180° - (angle BAC + angle ABC)

Substituting these values into the equation for angle ACD, we get:

angle ACD = angle ABC + 31° = 2x + 31°

Since angles ACB and ACD form a straight line, we can write:

angle ACB + angle ACD = 180°

Substituting the values we know, we get:

(angle BAC + angle ABC) + (angle ABC + 31°) = 180°

3x + 31° = 180°

3x = 149°

x = 49.67°

Therefore, the angle of triangles answer will be 50.66°.

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The measure of the angle N to the nearest degree for the given triangle is 23 degrees.

Degree and radian both serve as angles' units of measurement in geometry. Two radians (in radians) or 360° can be used to symbolise one whole anticlockwise rotation (in degrees). As a result, degree and radian can be compared as follows:

2π = 360°

The given triangle is an right triangle.

Using the trigonometric functions we can write the relation between the segments as:

Sin (N) = 1.5 / 3.9 = opposite/hypotenuse

N = arcsin (1.5 / 3.9)

N = 22.61 = 23 degrees.

Hence, the measure of the angle N to the nearest degree for the given triangle is 23 degrees.

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Factorization of expression 16t³ + 10t is 2t (8t² + 5) .

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15

Given expression

16t³ + 10t

It can be written as

2 × 8 (t . t . t ) + 2 × 5 (t)

Factoring out common factors

2t (8t² + 5)

Hence, 2t (8t² + 5) is factorization of expression 16t³ + 10t

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The following o-fields are equal to each other because they both represent the Borel sigma field on the real line:
i. B= o({(-20,x); r < R})
ii. B2 = o({(-0,2); 2 € R})

Note that the Borel sigma field on the real line is the smallest sigma field containing all the open intervals on the real line. This means that any set that can be constructed from countable unions, intersections, and complements of open intervals is in the Borel sigma field.

In the first o-field, B= o({(-20,x); r < R}), the set {(-20,x); r < R} is an open interval on the real line, so it is in the Borel sigma field. Similarly, in the second o-field, B2 = o({(-0,2); 2 € R}), the set {(-0,2); 2 € R} is also an open interval on the real line, so it is also in the Borel sigma field.

Since both o-fields contain sets that are in the Borel sigma field, they are both equal to the Borel sigma field on the real line. Therefore, B= o({(-20,x); r < R}) = B2 = o({(-0,2); 2 € R}).

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