Suppose vector d = vector a - vector b where vector vector a has components ax = 4, ay = 5 and vector vector b has components bx = -4, by = -4

Answer: [tex]x^{2}[/tex]+2x-5

Step-by-step explanation:

(g+f)(x) = g(x)+f(x)

g(x) = 2x-2

f(x) = [tex]x^{2}[/tex]-3

g(x)+f(x) = (2x-2) + ([tex]x^{2}[/tex]-3)

g(x)+f(x) =  [tex]x^{2}[/tex]+2x-5

The answer is value of x when y=25 are 8.33.

The missing variable y varies directly with x, which means that y = kx, where k is a constant.

We can use this equation to find the value of k and then use it to find the value of x when y=25.

First, let's find the value of k:
y = kx
75 = k*25
k = 75/25
k = 3

Now that we know the value of k, we can use it to find the value of x when y=25:
y = kx
25 = 3x
x = 25/3
x = 8.33

Therefore, the value of x when y=25 is 8.33.

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Height of a trapezoid with Pythagorean theorem is = √{Hypotenuse ^2 - Base ^2}

Trapezoid has two parallel sides and two non parallel sides. The length of the parallel sides are unequal but the length of the non parallel sides are equal.

Thus the trapezoid can be divided into three parts where one is rectangle ( which has length equal to the shortest length of the parallel sides) and two triangles which are equal ( having equal base, height and hypotenuse).

The Pythagoras theorem on the triangular part of the trapezoid can be stated as ,

Hypotenuse ^2 = Base ^2 + Height ^2

⇒ Height ^2 = Hypotenuse ^2 - Base ^2

⇒ Height = √{ Hypotenuse ^2 - Base ^2}

where, Height of the triangle is equal to that of the trapezoid it belongs to;

Hypotenuse of the triangle is the non parallel but equal side of the trapezoid;

Base of the triangle is = {(length of the longest side of parallel sides of trapezoid) -   (length of the shortest side of parallel sides of trapezoid) }/2

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The polynomial is  4x^3 - 18x^2 + 2x + 12

A polynomial of degree 3 that satisfies, we need to use the fact that if a polynomial has a zero at x = a, then (x - a) is a factor of the polynomial. So, for the given zeroes, we have the factors (x + 1/2), (x - 2), and (x - 3).

Multiplying these factors together, we get:

(x + 1/2)(x - 2)(x - 3) = (x^2 - (3/2)x - 1)(x - 3) = x^3 - (9/2)x^2 + (1/2)x + 3

To get a constant coefficient of 12, we need to multiply this polynomial by a constant. Since the current constant coefficient is 3, we need to multiply by 4:

4(x^3 - (9/2)x^2 + (1/2)x + 3) = 4x^3 - 18x^2 + 2x + 12

So, the polynomial that satisfies the given conditions is:

P(x) = 4x^3 - 18x^2 + 2x + 12

The polynomial is  4x^3 - 18x^2 + 2x + 12

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Therefore , the solution of the given problem of probability comes out to be  the likelihood of obtaining a sum of 4 is about 8.3%.

Calculating the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Chance can be represented by any number between 0 and 1, at which 1 usually represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

There are a total of 6 x 6 = 36 results when the spinner is spun twice because there are six sections on it, each with a number from 1 to 6.

We can make a list of every result and determine how many times the sum is 4:

=> 1, 3

=> 2, 2

=> 3, 1

There are three results, and their total is 4. As a result, 3/36 = 1/12 is the chance of receiving a sum of 4. We can multiply this by 100 and tenth it to represent it as a percentage:

=> 1/12 x 100 ≈ 8.3

In other words, the likelihood of obtaining a sum of 4 is about 8.3%.

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Answer:

When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:

.        __________

0.85 | 9.00

        8.50    (0.85 goes into 9.00 one time)

      -----

        1.50    (subtract 8.50 from 9.00)

        1.27    (0.85 goes into 1.50 one time)

      -----

        0.23    (subtract 0.85 from 1.50)

When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:

sql

Copy code

.        __________

0.85 | 9.00

        8.50    (0.85 goes into 9.00 one time)

      -----

        1.50    (subtract 8.50 from 9.00)

        1.27    (0.85 goes into 1.50 one time)

      -----

        0.23    (subtract 0.85 from 1.50)

The quotient is the number above the division line, which is 10 with a remainder of 23/100. Therefore:

9 / 0.85 = 10 with a remainder of 23/100, or 10.5882 (rounded to four decimal places)

So, 9 divided by 0.85 is approximately 10.5882.

The polynomial  3x³ - 4x² + 9x - 12 as a product of binomials is (3x - 4)(x² + 3).

To rewrite the polynomial 3x³ - 4x² + 9x - 12 as a product of binomials, we need to factor the polynomial. One method to do this is by grouping. Here are the steps:

1. Group the first two terms and the last two terms: (3x³ - 4x²) + (9x - 12)
2. Factor out the common factor from each group: x²(3x - 4) + 3(3x - 4)
3. Notice that (3x - 4) is a common factor in both groups, so we can factor it out: (3x - 4)(x² + 3)
4. Now we have the polynomial rewritten as a product of binomials: (3x - 4)(x² + 3)

Therefore, the polynomial 3x³ - 4x² + 9x - 12 can be rewritten as (3x - 4)(x² + 3).

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No, this relation does not define y as a function of x.

A function is a relation in which each input (x-value) is paired with exactly one output (y-value). In this relation, the x-value of 2 is paired with two different y-values (3 and -3), which violates the definition of a function.

Therefore, this relation does not define y as a function of x.

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Answer:

Gradient of A:    [tex]2[/tex]

Gradient of B :  [tex]- 1[/tex]

Step-by-step explanation:

Gradient of a line is the slope of the line

Slope = rise/run

rise = difference in y values between any two points on the line

run = difference in x values between the corresponding points

Line A

Take points (0, 1) and (3,7)
rise = 7 - 1 = 6
run = 3 - 0 = 3

slope = gradient = 6/3 = 2

Gradient of a line which goes diagonally up from left to right is positive

Line B

Take points (0,5) and (5, 0)

rise = 0 - 5  = - 5

run = 5 - 0 = 5

slope = gradient = -5/5 = - 1

Gradient of a line which goes diagonally down from left to right is negative

Answer:

The notation f⁻¹(-3) refers to the value(s) of x for which f(x) = -3.

However, the function f is not given in the prompt. Therefore, we cannot determine the value(s) of x for which f(x) = -3 or find f⁻¹(-3) without knowing the definition of f.

Step-by-step explanation:

Answer:

27+X=42

X=15

Step-by-step explanation:

interior opposite angle are equal.

To find a unit vector with a positive first component that is orthogonal to all three of the given vectors, we need to find a vector x = (x1, x2, x3, x4) that satisfies the following equations:

= 0
= 0
= 0

This means that:

x1 - x2 + 7x3 = 0
8x1 + x2 + x4 = 0
x1 + 6x3 + x4 = 0

We can solve this system of equations to find x. One possible solution is x = (1, -1, 0, 1). However, this is not a unit vector, so we need to divide each component by the length of the vector to get a unit vector:

x = (1, -1, 0, 1) / ||(1, -1, 0, 1)|| = (1/sqrt(3), -1/sqrt(3), 0, 1/sqrt(3))

So, the unit vector with a positive first component that is orthogonal to all three of the given vectors is (1/sqrt(3), -1/sqrt(3), 0, 1/sqrt(3)).

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Answer:

420mm^3

Step-by-step explanation:

10mm×10.5mm=105mm

105mm×8mm=840mm^3

840mm^3÷2=420mm^3

The volume of this prism is calculated by this equation:

V = (area of a triangle)(height)

So plugging in the numbers it looks something like this

V = (10 x 10.5 x 1/2)(8)

V = (105 x 1/2)(8)

V = (52.5)(8)

V = 420 mm^3

The samples randomly and independently.

True. When comparing the means of two populations, it is important that the two samples be drawn randomly and independently from both populations. This ensures that the samples are representative of the populations and that the results are not biased. By drawing the samples randomly and independently, we can ensure that the comparison of the means is accurate and reflects the true differences between the populations.

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Answer:

Just help your mother to wash your dise

The probability that more than 91,000 cars will pass through the M50 toll is 0.2227, or 22.27% to 4 decimal places.

The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The probability mass function of the Poisson distribution is given by:

P(X = x) = (lambda^x * e^-lambda) / x!

Where lambda is the mean rate of occurrence and x is the number of occurrences. In this case, lambda = 90,000 and we want to find the probability that X > 91,000. We can use the cumulative distribution function (CDF) of the Poisson distribution to find this probability:

P(X > 91,000) = 1 - P(X <= 91,000)

Using the CDF of the Poisson distribution, we can calculate P(X <= 91,000) as follows:

P(X <= 91,000) = e^-lambda * sum_{i=0}^{91,000} (lambda^i / i!)

Using a calculator, we can find that P(X <= 91,000) = 0.7773. Therefore, the probability that more than 91,000 cars will pass through the M50 toll is:

P(X > 91,000) = 1 - 0.7773 = 0.2227

So the probability that more than 91,000 cars will pass through the M50 toll is 0.2227, or 22.27% to 4 decimal places.

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The area is 893/15.

The area can be calculated by evaluating the given expression at the limits of integration and subtracting the two values.

we will evaluate the expression at the upper limit of integration, t = 7:
[(7)/(3)(7)^((3)/(2))-(1)/(5)(7)^((5)/(2))] = [(7)/(3)(7^(3/2))-(1)/(5)(7^(5/2))] = [(7)/(3)(49)-(1)/(5)(16807/49)] = [(343/3)-(33614/245)] = [(343/3)-(274/5)] = [(1715/15)-(822/15)] = 893/15

we will evaluate the expression at the lower limit of integration, t = 0:
[(7)/(3)(0)^((3)/(2))-(1)/(5)(0)^((5)/(2))] = [(7)/(3)(0)-(1)/(5)(0)] = 0

we will subtract the two values to find the area:
893/15 - 0 = 893/15

Therefore, the area is 893/15.

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The two integers are 5 and 6.

To solve this problem, we need to set up an algebraic equation based on the information given.

Let's call the first integer x and the second integer y. According to the problem, an integer (x) is 14 less than 4 times another (y).

This can be written as: x = 4y - 14

We are also told that the product of the two integers is 30. This can be written as:

xy = 30

Now we can substitute the first equation into the second equation to solve for one of the variables.

Let's solve for y:

(4y - 14)y = 30

4y^2 - 14y = 30

4y^2 - 14y - 30 = 0

Using the quadratic formula, we can solve for y:

y = (-(-14) ± √((-14)^2 - 4(4)(-30)))/(2(4))

y = (14 ± √(196 + 480))/8

y = (14 ± √676)/8

y = (14 ± 26)/8

y = 5 or y = -1.5

Now we can plug these values of y back into the first equation to find the corresponding values of x:

x = 4(5) - 14 = 6

x = 4(-1.5) - 14 = -20

So the two integers are either 5 and 6, or -1.5 and -20. However, since the problem asks for integers, we can eliminate the second solution.

Therefore, the two integers are 5 and 6.

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The unit rate of running 2.3 km in 7 minutes is 5.48 metres per second.

Unit rate can be defined as a measure used to represent how many units of one type of quantity corresponds to one unit of anther type of quantity.

Here the distance is given in kilometres (km) which can be converted into metres by multiplying by 1000 as,

2.3 km = 2.3*1000 metres

= 2300 metres

Here the time taken to cover 2.3 km is 7 minutes which can be converted ito seconds by multiplying by 60 as,

7 minutes= 7*60 seconds

= 420 seconds

Hence the unit rate of running 2.3 km in 7 minutes expressed in metre per second is calculated as = 2300 metres / 420 seconds

= 5.4761 metres per second

= 5.48 metres per second (approximately)

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To find the total surface area of a cross-section solid, it is necessary to identify all the faces or surfaces of the solid, find the area of each individual face or surface, and then add them all together.

After finding the area of each individual face or surface, the final step is to add them all together to get the total surface area of the cross-section solid. This can be expressed mathematically as:

Total Surface Area = Area of Face 1 + Area of Face 2 + ... + Area of Face n

Where n represents the total number of faces or surfaces of the solid.

Pythagoras theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed mathematically as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

By using Pythagoras theorem to find the length of an unknown side, it is then possible to use the appropriate formula to find the area of the face or surface and then add it to the total surface area of the cross-section solid.

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The simplest form of the given expression x will be 42.

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial.

When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

Here we assume that no of suitcases be x

So, 7/24 = x/144

24x = 1008

x = 42.

Hence the simplest form of the given expression x will be 42.

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To find a linear function h(x) given two points, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
Where m is the slope, (x1, y1) and (x2, y2) are the two points.

In this case, the two points are (-3, -4) and (-9, -5). Plugging in the values into the formula, we get:
m = (-5 - (-4)) / (-9 - (-3))
m = (-1) / (-6)
m = 1/6
Now that we have the slope, we can use the point-slope form of a linear equation to find the function h(x):
y - y1 = m(x - x1)
Plugging in the slope and one of the points, we get:
y - (-4) = (1/6)(x - (-3))
y + 4 = (1/6)(x + 3)
y = (1/6)x + 3/6 - 4
y = (1/6)x - 21/6

Simplifying the equation, we get:
y = (1/6)x - 7/2

Therefore, the linear function h(x) is:
h(x) = (1/6)x - 7/2

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okay i will answer it for you yes

Answer:

1369.1

Step-by-step explanation:

Answer:

1369.1 feet

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf 116\ in.\²}[/tex]

Step-by-step explanation:

The composite figure is made up of two shapes.

= Length × Width

Where L = 13 in., W = 7 in.

= 13 × 7

= 91 in.²

[tex]\displaystyle =\frac{\pi r^2}{2} \\\\\underline{Where \ r:}\\\\= \frac{13-5}{2} \\\\= \frac{8}{2} \\\\= 4 \ in.\\\\So,\ the \ above\ equation \ becomes\\\\= \frac{(3.14)(4)^2}{2} \\\\= \frac{(3.14)(16)}{2} \\\\= (3.14)(8)\\\\= 25.13 \ in.^2[/tex]

= Area of rectangle + Area of semi-circle

= 91 + 25.13

= 116.13 in.²

[tex]\rule[225]{225}{2}[/tex]

The requested functions are:

a. (f+g)(x) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = (3x+5)/(x−3)

c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)

Given the functions f(x)=3x+5 and g(x)=1/(x−3), we can find the requested functions by applying the corresponding operations to the functions.

a. (f+g)(x) = f(x) + g(x) = (3x+5) + (1/(x−3)) = (3x(x−3)+5(x−3)+1)/(x−3) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = f(x) ∙ g(x) = (3x+5) ∙ (1/(x−3)) = (3x+5)/(x−3)

c. (2f+3g)(x) = 2f(x) + 3g(x) = 2(3x+5) + 3(1/(x−3)) = (6x+10+3/(x−3)) = (6x(x−3)+10(x−3)+3)/(x−3) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = 3g(x) - 4f(x) = 3(1/(x−3)) - 4(3x+5) = (3-4(3x+5)(x−3))/(x−3) = (-12x^2+8x+57)/(x−3)

Therefore, the requested functions are:

a. (f+g)(x) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = (3x+5)/(x−3)

c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)

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(1) The polynomial x^2 − 2 can be factored into (x + 5)(x − 5) in Z7[x].
(2) The polynomials x^3 − k, where k = 0, 1, 2, 3, 4, 5, 6, are all irreducible in Z7[x].

(3) The polynomial x^4 − 1 can be factored into (x − 1)(x + 1)(x^2 + 1) in Z7[x].

This is because 5 and −5 are both roots of the polynomial, since 5^2 ≡ 2 (mod 7) and (−5)^2 ≡ 2 (mod 7).

This is because none of them have any roots in Z7, which means they cannot be factored into lower degree polynomials.

For example, x^3 − 0 has no roots in Z7, since there is no integer x such that x^3 ≡ 0 (mod 7). Similarly, x^3 − 1 has no roots in Z7, since there is no integer x such that x^3 ≡ 1 (mod 7), and so on for the other values of k.

This is because 1, −1, and ±i are all roots of the polynomial, since 1^4 ≡ 1 (mod 7), (−1)^4 ≡ 1 (mod 7), and (±i)^4 ≡ 1 (mod 7). Therefore, x^4 − 1 = (x − 1)(x + 1)(x^2 + 1) in Z7[x].

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