A, B, C and D form the vertices of a
quadrilateral. Calculate the area of the
quadrilateral rounded to 1 DP.

\( - 1 - 5x + 6 - 30x \leqslant - 65\)

\( - 35x + 5 \leqslant - 65\)

Factoring -5

\( - 5(7x - 1) \leqslant - 65\)

Divided sides by -5

##############################

Point :

If the sides of an inequality are multiplied by or divided by a negative number, the direction of the inequality changes and returns.

##############################

\( \frac{ - 5}{ - 5}(7x - 1) \geqslant \frac{ - 65}{ - 5} \\ \)

\(7x - 1 \geqslant 13\)

Plus sides 1

\(7x - 1 + 1 \geqslant 13 + 1\)

\(7x \geqslant 14\)

Divided sides by 7

\( \frac{7}{7}x \geqslant \frac{14}{7} \\ \)

\(x \geqslant 2\)

Done ♥️♥️♥️♥️♥️

No, the nature of the relations (function or non-function) cannot be determined without the specific relations provided.

Without the specific relations mentioned in the question, it is not possible to determine whether they are functions or not. The nature of a relation as a function depends on the mapping of inputs to outputs, where each input value corresponds to exactly one output value. Without this information, we cannot make a conclusive determination.

To break the code mentioned in the question, the product of the odd problems and the product of the even problems would need to be calculated, followed by finding the difference between the two products. However, without the actual relations and their corresponding values, we cannot proceed with the code-breaking process.

It is important to have the specific relations in order to analyze whether they meet the criteria for functions, and then proceed with the code-breaking instructions as mentioned.

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Answer:

18

Step-by-step explanation:

70^2 = 4900 < 5607 < 6400 = 80^2

so sqrt(5607) is a two-digit number with tenth-digit 7

71^2 = 5041, 72^2 = 5184, 73^2 = 5329, 74^2 = 5476, 75^2 = 5625

so the smallest square bigger than 5607 is 75^2, which is 5625

so the number should ne 5625 - 5607 = 18

Answer:

12

Step-by-step explanation:

50% of 8 is 4 therefor it would be 8+4 to get the total witch is 12

The value of c is approximately 1.1476.

To find the value of c for which the average value of the function f(x) = (9π/x^2)(cos(π/x)) on the interval (1,c) is -0.09, we need to calculate the average value of the function and solve for c.

The average value of a function f(x) on an interval [a, b] is given by:

Average value = (1 / (b - a)) * ∫[a, b] f(x) dx

In this case, we have the interval (1, c) and want the average value to be -0.09. So we can set up the equation:

-0.09 = (1 / (c - 1)) * ∫[1, c] [(9π/x^2) * cos(π/x)] dx

To solve this equation, we first evaluate the integral on the right side. The integral of the given function can be quite challenging to evaluate analytically. Therefore, we can use numerical methods or software to approximate the value of the integral.

Once we have the numerical approximation for the integral, we can solve for c by rearranging the equation:

(c - 1) = (1 / -0.09) * ∫[1, c] [(9π/x^2) * cos(π/x)] dx

(c - 1) = -1 / 0.09 * Approximated value of the integral

Finally, we can solve for c by adding 1 to both sides of the equation:

c = 1 + (-1 / 0.09) * Approximated value of the integral

Using numerical methods or software, we can compute the value of the integral and substitute it into the equation to find the approximate value of c, which is approximately 1.1476.

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The correct option is C. Randomization.What is randomization? Randomization is a process that randomly assigns subjects to either a control or an experimental group to reduce bias in scientific research.

Randomization can be done by using various methods such as random number tables, coin flip, and so on.The main objective of randomization is to avoid subjective biases, confounding variables, and statistical outliers in an experiment, to establish cause and effect relationships in a research study.

For instance, in a clinical trial to test the efficacy of a new drug on hypertension, randomization can be performed by dividing the participants into two groups randomly, one group receives the new drug (treatment group), while the other group receives a placebo (control group).The advantage of randomization is that it ensures that known and unknown confounding variables are distributed evenly between the two groups.

Thus, the chances of drawing incorrect conclusions from the research are minimized. It also increases the generalizability and reproducibility of the results obtained.

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From the computation done, it can be denoted that the total price that will be paid will be $12.90.

1 Krispy Kosmos at $2.89 = $2.89

2 Chewy Chocos at $3.19 each = 2 × $3.19 = $6.38

1 Gooey Globs at $2.99 = $2.99

Total = $2.89 + $6.38 + $2.99 = $12.26

We'll then add the sales tax of 5.2%, therefore, the total value will be:

= $12.26 + (5.2% × $12.26)

= $12.26 + $0.638

= $12.90

In conclusion, the correct option is $12.90.

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Answer:

C

Step-by-step explanation:

Edg 2022

We want to find the slope of the line that connects points C' and D'. We will find that the slope is -3/7.

First, we start with the points:

Now we create points C' and D' by translating points C and D to the left by 6 units, this means that we need to subtract 6 in the x-value of each point, so we will have:

And we know that if a line passes through points (x₁, y₁) and (x₂, y₂) the slope is given by:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

Then the slope that connects points C' and D' is:

\(a = \frac{5 - 8}{2 - (-5)} = \frac{-3}{7}\)

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Population in the year 2000= 198.85million

From the question, we get to know that the population in 2009 was 191.5 million.

And we have to find the population of the year 2000 which is 3.7%more than the 2009 population.

So let us take the population of the year 2000 to be x.

From the above, we can form an equation:

(population of year 2000 * ( 100-3.7 /100) = (population of year 2009)

i.e., x * 100-3.7/ 100 = 191.5

x * 96.3 = 191.5

x = 198.85

So 198.85 is the population of 2000.

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The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.

What is algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants .

From the given expression ,

y = 2.5 x + 10

So, we have to find the length of line segment from x = 0 to x = 16.

so when x = 0 ,

y = 0+10

y = 10

and when x=1

y = 2.5*1+10

y=12.5

and similarly

when x = 2

y = 2.5* 2 + 10

y = 15

So, like this the sequence will be goin on y = 10 , 12.5 , 15 , 17.5 and etc .

Hence, The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.

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An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products.

An algebraic statement with parentheses is known as a factored form. A factored form is essentially a sum of products. or a sum of sums plus their products. A factored form can represent any logic function, and every factored form represents some logic function.

1a)The length given as words is "3 more than 7 times x"

The width given as words is "4 times x minus 2"

The expression for length would be 7x + 3

The expression for width would be 4x - 2

1b)Area = length × width

To estimate the algebraic expressions for length and width

Area = (7x + 3)(4x - 2) = 28x² - 14x + 12x - 6 = 28x² - 2x - 6

Area = 28x² - 2x - 6

Given x = 10,

Let the equation be 28 x² - 2x - 6

substitute the value of x, in the above equation, we get

= 28(10)² - 2(10) - 6

= 2774

Area = 2774 sq . m

2. We can group the first two terms and next two terms:

xy - 4y + 7x - 28 = (xy - 4y) + (7x - 28)

simplifying the above equation, we get

y(x - 4) + 7(x - 4) = (x - 4)(y + 7)

Therefore, the equation is in factored form.

The complete question is:

1.) You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow change. The college conducts a lottery, and whichever number is drawn, represents the x value. Your plot has a length that is three more than seven times x and the width is four times x minus 2.a.) What are the dimensions of your mowing plot? (2 points)

Length: ______________________________________

Width: ______________________________________

b.) What is the area of your plot (remember area = length x width)? (2 points)

Area: _________________________________________

c.) If x = 10 meters, how many square meters is your plot? (show steps)(2 points)

Area: _________________________________________

2.) Factor by grouping: (4 points)

xy − 4y + 7x − 28

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To find the length of side T in simplest radical form with a rational denominator,

you'll need to apply the Pythagorean theorem or another relevant geometric formula depending on the shape of the figure.

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

Please provide more information or a diagram about the shape and given measurements,

so I can help you solve for the length of side T.

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Answer:

3

Step-by-step explanation:

It is 3 because fi you multiply 5 by 3 you get 15, and if you multiply 10 by 3 you get 30. Subtract 30 by 6 and get 24. And finally, if you multiply 2 by 3 it gives you 9. 9+12= 21.

The value of x, considering the intersecting chords in the circle, is given as follows:

x = 11.

A chord of a circle is a straight line segment that connects two points on the circle. Specifically, it is a line segment whose endpoints are on the circle. A chord is often denoted by drawing a line segment between the two endpoints, with the segment passing through the interior of the circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Then the value of x is obtained as follows:

4(-1 + x) = 5(x - 3)

4x - 4 = 5x - 15

x = 11.

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Answer:

x is 46.67

y is 28.4°

Step-by-step explanation:

To solve for x we use sine

sin ∅ = opposite / hypotenuse

AC is the opposite

x is the hypotenuse

so we have

sin 59° = 40 / x

x sin 59 = 40

Divide both sides by sin 59

x = 40/sin 59

x = 46.67

To solve for y we also use sine

sin y = 30/ 63

y = sin^-1(30/63)

y = 28.4°

Hope this helps you

DOES ANYONE NOW About THE Incas?

The value of CPI will be 178.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Now,

Since, In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Hence, The value of CPI will be;

CPI = 118.10 × 100 / 66.35

      = 11810 / 66.35

       = 178

Thus, The value of CPI will be 178.

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Answer:

32472

Step-by-step explanation:

You basically do 9×3608 which equals 32472

The equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0) is y = 0.

To find the equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0), we need to find the slope of the tangent line at that point.

The derivative of y = ln(x^2 - 5x + 1) is:

y' = (2x - 5)/(x^2 - 5x + 1)

At the point (5,0), we have:

y' = (2(5) - 5)/(5^2 - 5(5) + 1) = 0

So the slope of the tangent line at (5,0) is 0.

The equation of the tangent line can be written as:

y - y1 = m(x - x1)

where (x1, y1) is the point of tangency and m is the slope.

Since the slope is 0, we have:

y - 0 = 0(x - 5)

which simplifies to:

y = 0

Therefore, the equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0) is y = 0.

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Answer: Option (4)

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.

Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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Answer:

1) Yes

2) No

3) Yes

4) No

5) No

6) Yes

7) Yes

8) No

Step-by-step explanation:

Each equation must be increasing or decreasing by a constant amount in order for it to be linear. Graphing these equations, you can see that the linear equations will be a straight line.

Answer: y=18, x=30

Step-by-step explanation:

A. The fundamental matrix for the homogeneous system is given by:Φ(t) = [1 e^(-t) cos(√3t), 1 e^(-t) sin(√3t);-1+i√3, -1-i√3] / 2.

B. The inverse is Φ^(-1)(t) = (1/ie^(t/2)(√3e^(√3t) + 1))[(-1-i√3)/2, 1/2;1+i√3, -1-i√3]/e^t.

C. y(t) = Φ(t)c(t) = ∫Φ(t)Φ^(-1)(t)g(t) dt - ∫Φ(t)Φ^(-1)(t)Φ'(t)∫Φ^(-1)(t)g(t) dt dt

D. y(t) = [(√3e^(-t) + 1)(-3c^(-1) - e^(-t));(-3c^(-1) - e^(-t))(-1-i√3)/2 + (1/2)e^(-t)sin(√3t)] + [∫0^t (1/2) e^(-s) sin(√3s) (-3c^(-1) - e^(-s)) ds; ∫0^t (1/2) e^(-s) sin(√3s) (-1-i√3)/2 + (1/2)e^(-s)sin(√3s) (-3c^(-1) - e^(-s)) ds]

To write a fundamental matrix for the associated homogeneous system.

The homogeneous system of the given non-homogeneous system is obtained by removing the constant term from the non-homogeneous system.

That is, the homogeneous system for this non-homogeneous system is given by: y' = Ay.

Here, A is the matrix obtained by removing the constant terms from the non-homogeneous matrix.

Thus, the matrix A is: A = [2 2; -5 -4]..

Now, the fundamental matrix for this system is given by the formula: Φ(t) = [v1 e^(λ1 t), v2 e^(λ2 t)], where λ1 and λ2 are the eigenvalues of matrix A, and v1 and v2 are the corresponding eigenvectors.

To find the eigenvalues of matrix A, we solve the characteristic equation det(A-λI) = 0, where I is the identity matrix.

This yields: det(A-λI) = (2-λ)(-4-λ) + 10 = λ^2 + 2λ + 2 = 0.

Using the quadratic formula, we obtain:λ1,2 = -1 ± i√3.

Thus, the eigenvalues are complex. To find the eigenvectors, we solve the equation (A-λI)v = 0, where v is the eigenvector.

This yields two eigenvectors:v1 = [1, -1+i√3]t, v2 = [1, -1-i√3]t.

Therefore, the fundamental matrix for the homogeneous system is given by:Φ(t) = [1 e^(-t) cos(√3t), 1 e^(-t) sin(√3t);-1+i√3, -1-i√3] / 2

B. Compute the inverse.

To compute the inverse of Φ(t), we first find its determinant:

det(Φ(t)) = (1 e^(-t) cos(√3t))(1 e^(-t) sin(√3t) + (1 e^(-t) cos(√3t))(-1-i√3)/2

= (e^(-t)/2)(2i√3e^(√3t) + 2i)e^(-t)

= ie^(t/2)(√3e^(√3t) + 1)

Thus, the inverse of Φ(t) is given by:Φ^(-1)(t) = (1/det(Φ(t))) adj(Φ(t)), where adj(Φ(t)) is the adjugate of Φ(t), which is the transpose of the matrix of cofactors of Φ(t).

Thus, we have:Φ^(-1)(t) = (1/ie^(t/2)(√3e^(√3t) + 1))[(-1-i√3)/2, 1/2;1+i√3, -1-i√3]/e^t.

C. Multiply by g⃗ g→ and integrate.

Now, we need to find the particular solution to the non-homogeneous system: y' = Ay + g.

We can use the method of variation of parameters to find the particular solution.

The method involves assuming that the solution has the form: y(t) = Φ(t)c(t), where c(t) is a vector of unknown coefficients.

Substituting this into the equation, we get:

Φ'(t)c(t) + Φ(t)c'(t) = AΦ(t)c(t) + g(t)Φ'(t)c(t)

= g(t) - Φ(t)c'(t)

Multiplying both sides by Φ^(-1)(t), we obtain: c'(t) = -Φ^(-1)(t)Φ'(t)c(t) + Φ^(-1)(t)g(t).

Thus, to find c(t), we need to integrate both sides of this equation.

That is, we have: c(t) = ∫(Φ^(-1)(t)g(t) - Φ^(-1)(t)Φ'(t)c(t)) dt.

Multiplying both sides by Φ(t), we obtain: y(t) = Φ(t)c(t) = ∫Φ(t)Φ^(-1)(t)g(t) dt - ∫Φ(t)Φ^(-1)(t)Φ'(t)∫Φ^(-1)(t)g(t) dt dt.

D. Give the solution to the system.

Now, we substitute the values of Φ(t), Φ^(-1)(t), and g(t) into the formula above to obtain the solution to the system:

y(t) = [(√3e^(-t) + 1)(-3c^(-1) - e^(-t));(-3c^(-1) - e^(-t))(-1-i√3)/2 + (1/2)e^(-t)sin(√3t)] + [∫0^t (1/2) e^(-s) sin(√3s) (-3c^(-1) - e^(-s)) ds; ∫0^t (1/2) e^(-s) sin(√3s) (-1-i√3)/2 + (1/2)e^(-s)sin(√3s) (-3c^(-1) - e^(-s)) ds]

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Let's break down the given information and solve the problem step by step:

Let's assume:

The cost of the burger is 'b' dollars.

The cost of the souvenir is 's' dollars.

The cost of the pass is 'p' dollars.

According to the given information:

The burger was 1/6 as much as the souvenir. This can be expressed as: b = (1/6) * s.

The souvenir cost 3/4 the cost of the pass. This can be expressed as: s = (3/4) * p.

Erica had $4.00 left over after buying these items. This can be expressed as: b + s + p + 4 = 30.25.

Now, let's solve these equations to find the cost of each item.

Substituting the value of 's' from equation 2 into equation 1:

b = (1/6) * ((3/4) * p)

b = (3/24) * p

b = (1/8) * p

Substituting the values of 'b' and 's' into equation 3:

(1/8) * p + ((3/4) * p) + p + 4 = 30.25

Multiply through by 8 to eliminate the fraction:

p + 6p + 8p + 32 = 242

15p + 32 = 242

15p = 210

p = 210 / 15

p = 14

Substituting the value of 'p' into equation 2 to find 's':

s = (3/4) * 14

s = 10.50

Substituting the value of 'p' into equation 1 to find 'b':

b = (1/8) * 14

b = 1.75

Therefore, the cost of the burger is $1.75, the cost of the souvenir is $10.50, and the cost of the pass is $14.0

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The value of x is x = 9/4. The equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4

The equation 2xc = d and 2x + 1 = 9 are similar in that they are both linear equations and involve the variable x.

However, they are different in that they have different constants and coefficients.

How to use 2xc = d to solve 2x + 1 = 9? To use 2xc = d to solve 2x + 1 = 9, you first need to rewrite 2x + 1 = 9 in the form 2xc = d.

To do this, you need to isolate x on one side of the equation. 2x + 1 = 9

Subtract 1 from both sides2x = 8. Divide both sides by 2x = 4Now, we can write 2x + 1 = 9 as 2x * 1/2 = 9/2.

Therefore, we can see that this equation is similar to 2xc = d, where c = 1/2 and d = 9/2.

We can use this relationship to solve for x in the equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4 Therefore, x = 9/4.

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Answer:

$57.99

Step-by-step explanation:

So, Maggie already had $28.33

Then her mom gave her $7.50 more dollars.

So we add $7.50 to $28.33

28.33 + 7.50 = $35.83

Now Maggie has $35.83

Then she was paid $22.16 more dollars.

So, we have to add $35.83 to $22.16

22.16 + 35.83 = $57.99

So Maggie has $57.99 now.

Hope I helped :)

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