1. )Indicate the equation of the given line in standard form. Show all of your work for full credit.



The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0).



2. )Indicate the equation of the given line in standard form. Show all of your work for full credit.



The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).



3. ) Indicate the equation of the given line in standard form. Show all of your work for full credit.



The line containing the diagonal, BD, of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.

We have to find the value of  `(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)`

Let's find all trigonometric ratios:

We can say that:

\($$\tan \theta= \frac{opp}{adj}= \frac{-4}{3}$$$$\text\)

{Using the Pythagorean Theorem we can find the hypotenuse }

\($$$$\text{Hypotenuse = } \sqrt{(-4)^2+(3)^2}\)

\(= \sqrt{16+9}\)

= \(\sqrt{25}\)

=\(5$$$$\)

Substituting the values of sinθ, cosθ and tanθ in `

\(= \frac{\frac{3}{5} + \frac{-4}{5} - \frac{-4}{3}}{\frac{-4}{5} + \frac{5}{3} - \frac{-3}{4}}$$$$\)

\(=\frac{\frac{9}{15} + \frac{-12}{15} + \frac{20}{15}}{\frac{-16}{20} + \frac{25}{12} + \frac{3}{4}}$$$$\)

\(=\frac{\frac{17}{15}}{\frac{-14}{15}}$$$$\)

\(=-\frac{17}{14}$$\)

Therefore, \(`(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)\)` is equal to

`-17/14` when `tanθ=−43` (Quadrant II).

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Step-by-step explanation:

Nate - I can't fold my invitation at all. The parts won't match.

Hector - I can fold my invitation more than one way.

Daniel - I can fold my invitation along only a horizontal line.

Micheal - I can fold my invitation along only a vertical line.

Part a: The expression that represents the area of the rectangle is A = (3x + 5)(6x + 11). To calculate the area, we must multiply the two sides of the rectangle together. The length of the rectangle is 3x + 5 units and the width of the rectangle is 6x + 11 units. Therefore, the area is (3x + 5)(6x + 11).

Part b: The degree of the expression obtained in part a is 2 and the classification is a binomial.

Part c: The closure property for polynomials states that the result of combining two polynomials is also a polynomial. In part a, we combined two polynomials, 3x + 5 and 6x + 11, to form the expression (3x + 5)(6x + 11). This expression is also a polynomial, demonstrating the closure property for polynomials. The closure property for polynomials allows us to combine two polynomials and still have a polynomial as the result. This is important in mathematics because it allows us to simplify equations and solve problems more quickly and efficiently.

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The value of \(\sqrt{x^6}\) is -x³i as x<0.

A number or other mathematical object is factored (or factorised, see variants in spelling in English) or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.

Given:

We have the radical \(\sqrt{x^6}\)

First we have factorise the term which is under the root

\(x^6\)

= x. x . x . x . x . x

= (x . x ). (x . x ). (x . x )

and, we know in root the number which get pair comes out of the root then

\(\sqrt{x^6}\)

= √(x . x ). (x . x ). (x . x )

= x . x . x

= x³

But we have x<0 then it must contain "iota" because any number less than 0 is negative and √(-1)= i

So, the actual value will be \(\sqrt{x^6}\)=  x³i³ = -x³i

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The next tests to be done if the interaction between two factors is not significant are tests about the population means of factor A or factor B using two-way ANOVA without interaction. The correct option is C.

Tests about the population means of factor A or factor B using two-way ANOVA without interaction. If the interaction between two factors is not significant, then the next tests to be done are tests about the population means of factor A or factor B using two-way ANOVA without interaction.There are three types of interactions: no interaction, interaction, and crossover. When there is no interaction, the effect of factor A is the same for each level of factor B, or the effect of factor B is the same for each level of factor A. If there is an interaction, the effect of factor A depends on the level of factor B, or the effect of factor B depends on the level of factor A. If there is a crossover, the effect of factor A changes direction across the levels of factor B, or the effect of factor B changes direction across the levels of factor A.

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The critical points of the given plane autonomous system cannot be classified.

The given plane autonomous system is described by the equations x' = 2x - y^2 and y' = -y + xy. To classify the critical points, we need to find the points where both x' and y' are equal to zero.
Setting x' = 0 and y' = 0, we have the following system of equations:
2x - y^2 = 0
-y + xy = 0
To find the critical points, we solve this system of equations simultaneously. However, it is not possible to find specific values for x and y that satisfy both equations. The system does not have a unique solution.
Without specific values for x and y, we cannot determine the stability of the critical points. Stability analysis typically involves evaluating the Jacobian matrix and its eigenvalues at each critical point to determine the type of behavior (stable, unstable, spiral, saddle, etc.).
In this case, since the critical points cannot be determined, it is not possible to classify them as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point.

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Answer:

50

Step-by-step explanation:

hope it help

Answer:

b = 48 yards

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Step-by-step explanation:

Step 1: Define

Leg a = x

Leg b = 64

Hypotenuse c = 80

Step 2: Solve for x

Given the exponential function y = f(x), a is the initial value and it will fall to a value of B

An exponential function is given by:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

The value, y, of a car x years after it is purchased is modeled by the exponential function y = f(x), a is the initial value and it will fall to a value of B

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Answer: J

Step-by-step explanation: hope its correct

Hi!

The answer to your question would be J

Here's the math to prove it:

Step 1) You need to add all of the number of tiles together.

9+7+3+6=25

Step 2) You need to take each of your tile numbers and divide them by 25.

9/25=0.36 So F would be true

7/25=0.28 So G would be true

6/25=0.24 So H would be true

3/25=0.12 So J would be not true.

I hope this helps!

Have an amazing day/night!

God bless!

<33

The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.

An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.

Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).

The given interval is [1, 2]

The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'

The given statement is 'false'.

This is beacuse, an interval consists set of all the real values in between the two values given.

So, according to the definition, there are not only the end values but also many real values in between them.

Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.

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If the p-value less than the significance level then we have a type i error.

We know that if your P-value is less than the chosen significance level then you reject the null hypothesis i,e. accept that your sample gives reasonable evidence to support the alternative hypothesis.

Im statistics, a type i error means rejecting the null hypothesis when it's actually true, while type ii error means failing to reject the null hypothesis when it's actually false.

The chance that you commit type i errors is known as the type i error rate or significance level (p-value). This number is conventionally and arbitrarily set to o.o5 or 5%. Type ii errors are like "false negatives", an incorrect rejection that a variation in a test has made no statistically significant difference.

The probability of making a type i error is represented by alpha level, which is the p-value below which you reject the null hypothesis.

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Answer :

-7

Step-by-step Explanation :

To stop a 1200 kg car moving at 99 km/h in a straight path,

the work that must be done in Joules is 453750.

Step-by-step Given,

Mass of car, m = 1200 kg

Initial velocity, u = 99 km/h = 27.5 m/s

Final velocity, v = 0 m/s (as the car is brought to rest)

Initial kinetic energy, K.E1 = 1/2 m u²

Final kinetic energy, K.E2 = 1/2 m v²

Work done to bring the car to rest,

W = K.E1 - K.E2W

= 1/2 m u² - 1/2 m v²W

= 1/2 × 1200 × (27.5)² - 1/2 × 1200 × (0)²W

= 1/2 × 1200 × (27.5)²W

= 453750 J

Therefore, the work that must be done in Joules to stop the car is 453750.

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Answer:

4

Step-by-step explanation:

Notice each side was increased by 4 times

You can set up a ratio of

\(\frac{new}{old}\)

then reduce or divide

Vector equation: r(t) = <1, -1, 7> + t<6, 7, -6>

Parametric equations:

x(t) = 1 + 6t

y(t) = -1 + 7t

z(t) = 7 - 6t

The vector equation and parametric equations describe the line segment that joins the two points p and q.

The vector equation is given by r(t) = <1, -1, 7> + t<6, 7, -6>

Here, <1, -1, 7> is the vector that represents the point p, and <6, 7, -6> is the direction vector of the line segment.

The variable t is a scalar parameter that describes the position of any point on the line segment.

The parametric equations are x(t) = 1 + 6t, y(t) = -1 + 7t, z(t) = 7 - 6t.

These equations express the coordinates of any point on the line segment in terms of the parameter t. So we can substitute any value of t between 0 to 1 in this equation to get the coordinates of a point on the line segment.

For example, if we substitute t = 0, we get x(0) = 1, y(0) = -1, z(0) = 7

which gives us the coordinates of point p.

Similarly, if we substitute t = 1, we get x(1) = 7, y(1) = 6, z(1) = 1

which gives us the coordinates of point q.

So, the line segment is defined by the set of all points whose coordinates are given by these equations for values of t between 0 and 1.

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We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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Answer:

The price for each pound of tuna is not always the same.

Step-by-step explanation:

What we do is divide the price by the amount of tuna to find the price for each amount of tuna

For the 1st one, we have $8 for 2 tuna so we do 8/2

8/2 = 4

For the 2nd we have $16 for 4 so we do 16/4

16/4 = 4

For the 3rd, we have $27 for 9 so we do 27/9

27/9 = 3

Answer:

Quadratic

Step-by-step explanation:

Formula: ax^2+bx+c

The correlation between scores on two administrations of the same test at different times is an estimate of reliability.

Reliability refers to the degree to which a measure consistently produces the same results when measured multiple times. When a measure is reliable, it produces similar results each time it is used to measure the same thing. In psychological research, reliability is essential because it provides researchers with confidence in their findings.

There are many ways to estimate the reliability of a measure, one of which is the correlation between scores on two administrations of the same test at different times. This is known as test-retest reliability.

To estimate test-retest reliability, a group of participants take the same test twice, with a time interval in between. The scores from the first administration are then correlated with the scores from the second administration. The resulting correlation coefficient reflects the degree of consistency between the two sets of scores.

The higher the correlation, the more reliable the measure is considered to be.

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Answer:

25%

Step-by-step explanation:

Answer:

the cords are 4 -2

Step-by-step explanation:

Answer:

First pic (4, -2) second pic (-3, 2)

To calculate the realized income, we need to consider the hourly wage, the number of hours worked, and the deductions.

Hourly wage: $8.25

Hours worked per week: 35

Number of weeks: 3

Total earnings before deductions:

Total hours worked = 35 hours/week * 3 weeks = 105 hours

Total earnings = Hourly wage * Total hours worked = $8.25/hour * 105 hours = $863.25

Now, let's calculate the deductions:

FICA (7.65%):

FICA deduction = Total earnings * FICA rate = $863.25 * 7.65% = $66.14

Federal withholding (13%):

Federal withholding deduction = Total earnings * Federal withholding rate = $863.25 * 13% = $112.23

State withholding (9%):

State withholding deduction = Total earnings * State withholding rate = $863.25 * 9% = $77.69

To calculate the realized income, subtract the total deductions from the total earnings:

Realized income = Total earnings - (FICA deduction + Federal withholding deduction + State withholding deduction)

Realized income = $863.25 - ($66.14 + $112.23 + $77.69) = $607.19

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Answer:

115% increase.

Step-by-step explanation:

129 - 60 = 69 / 60 = 1.15

1.15 x 100 = 115

Answer:

difference = \(x^2-12x\)

Step-by-step explanation:

hope this helps :)

Using the Law of Cosihes,

\(b^2 = a^2 +c^2 -2ac \cos B \\ \\ b^2 = 43^2 + 19^2 - 2(43)(19)(\cos 35^{\circ}) \\ \\ b=\sqrt{43^2 + 19^2 - 2(43)(19)(\cos 35^{\circ}} \\ \\ b=\sqrt{2210-1634 \cos 35^{\circ}}

\)

Using the Law of Sines,

\(\frac{\sin A}{a}=\frac{\sin B}{b} \\ \\ \sin A=\frac{a \sin B}{b} \\ \\ \sin A=\frac{43 \sin 35^{\circ}}{\sqrt{2210-1634 \cos 35^{\circ}}} \\ \\ A=\sin^{-1}\left(\frac{43 \sin 35^{\circ}}{\sqrt{2210-1634 \cos 35^{\circ}}} \right), 180^{\circ}- \sin^{-1}\left(\frac{43 \sin 35^{\circ}}{\sqrt{2210-1634 \cos 35^{\circ}}} \right) \\ \\ \\ \implies \angle C=145-\sin^{-1}\left(\frac{43 \sin 35^{\circ}}{\sqrt{2210-1634 \cos 35^{\circ}}} \right), \sin^{-1}\left(\frac{43 \sin 35^{\circ}}{\sqrt{2210-1634 \cos 35^{\circ}}} \right)-35^{\circ}\)

Answer:

It will cost $21.25

Step-by-step explanation:

We can use ratios to solve

8.50          x

--------   = -----------

100 kg      250 kg

Using cross products

8.50 * 250 = 100 x

Divide each side by 100

8.50 * 250/100 = x

21.25 = x

It will cost $21.25

Answer:

(1.5,6)(15,33) slope=2

Step-by-step explanation:

Answer:

y-2x=3; A(1.5, 6) B(15,33) Slope = 2

Step-by-step explanation:

First thing, you add 2x on both sides and get y=2x+3. Since the equation y=mx+b states that m is the slope, the slope is 2.

2nd step is finding the missing coordinate for a. You plug in 6 as the y in the equation y=2x+3, and then get 2x+3=6. Now it is a simple algrebraic equation and you get x=3/2 or 1.5.

The final step is to solve for B. Using the equation y=2x+3, and substituting in x as 15, you get y=30+3 which equals 33.

I hope this gave you an in depth explanation on solving these problems!