Find RS and QR in rectangle PQRS

The length of the rectangle = 2 - (1/3n) +(3/n²).

The formula for the area (taking this exists as a rectangle)

Area = length ⋅ width

where A exists the area of the rectangle

l exists the length of the rectangle and w exists the width of the rectangle.

If Area of the rectangle = length ⋅ width

then length of the rectangle = area/ width

Area = 6n² − n +9​

width = 3n²

Area = length [tex]*[/tex] width

length = area/ width

= (6n²  − n +9)/3n²

= 2 - (1/3n) +(3/n²).

The length of the rectangle = 2 - (1/3n) +(3/n²).

Therefore, the correct answer is option A. 2 - (1/3n) +(3/n²).

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Answer:

20 + 4y

Step-by-step explanation:

The 4 multiplies the 5 and the y, i.e., it distributes over the terms of the expression in ( ).

The bearing to take is 134 degrees and the shortest distance is 14.3 km

The attached diagram represents a labelled version of the ship movement

The angle at Q is

Q = 180 - 155 + 90 + 120 - 90

This gives

Q = 145

The distance PR is calculated as:

PR^2 =PQ^2 + QR^2 - 2 * PQ * QR * cos(Q)

This gives

PR^2 = 9^2 + 6^2 - 2 * 9 * 6 * cos(145)

Evaluate

PR^2 = 205.46

Take the square root

PR = 14.3 km

The angle at P is then calculated as:

QR/sin(P) = PR/sin(Q)

This gives

6/sin(P) = 14.3/sin(145)

Evaluate the quotient

6/sin(P) = 24.93

Make sin(P) the subject

sin(P) = 6/24.93

Divide

sin(P) = 0.2407

Take the arc sin of both sides

P = 14

The bearing is then calculated as:

Bearing = P + 120

This gives

Bearing = 14 + 120

Evaluate

Bearing = 134

Hence, the bearing to take is 134 degrees

In (a), we have

PR = 14.3 km

This represents the shortest distance

Hence, the shortest distance is 14.3 km

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Answer:

[tex]G(x) = x^{3} -1[/tex]

Step-by-step explanation:

The red graph is the blue graph translated 1 unit down, so the answer is A.

The factored expression of the polynomial is (x - 3)(x + 4)

The polynomial expression is given as;

x^2 + x - 12

Expand the expression

x^2 + 4x - 3x - 12

Factorize the expression

x(x + 4) -3(x + 4)

Factor out x + 4

(x - 3)(x + 4)

Hence, the factored expression of the polynomial is (x - 3)(x + 4)

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The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team

The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team.

The reason option B is the most biased is because members of a basketball team are typically taller than other people. We know that taller people generally have larger feet, and larger shoe sizes, than shorter people. Thus, choosing only people from this area would lead to a biased sample.

The missing options are;

A) every tenth boy on the school’s phone list

B) every member of the boys’ basketball team

C) every boy in a randomly selected ninth-, tenth-, eleventh-, and twelfth-grade gym class

D) every fifth boy who walks through the front doors of the school in the morning

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Answer:

B)

Step-by-step explanation:

Answer:

x = 90°

Step-by-step explanation:

Hello!

The sum of angles on a straight line is 180°.

To find the value of angle x°, we can subtract all the given angles form 180°.

The value of x is 90°.

Answer:

1000.

Step-by-step explanation:

We need 4 weights where 3 of them add up to

900, 1400, 1600 or 1800g.

Not sure of the method for doing this!

Lets assume that the answer is 1000 g.

Then the  3 that make 1800 could be

1000 500 and 300

- then to make 900 we need a 100g tomato giving:

1000 500 300 and 100 grams

So the 1400 will be the 1000, 300 and 100 tomato

and the 1600 will be 1000, 500 and 100.

That seems to fit !!

Answer:

Step-by-step explanation:

This function will have a minimum point only if f(x) has one.

Examples:  

y = x + 5:  straight line with no minimum

y = x^2 + 5:  parabola that opens up and has vertex at (0, 5); thus, the minimum is (0, 5)

What f(x) did you have in mind?  Please share it.

The number of angles that are alternate exterior with angle 5 is one, which is angle 11.

Alternate exterior angles are formed on the outside of the two parallel lines that are intersected by a transversal, each being located on the opposite side of the transversal.

The alternate exterior angle pairs are two angles that are supplementary. This means they add up to give a sum of 180 degrees.

Considering transversal s and parallel lines t and u, the angle that is an alternate angle to angle 5 is angle 11.

Angle 11 is the only angle that is alternate exterior angles with angle 5. therefore, we can conclude that, the number of angles that are alternate exterior with angle 5 is just 1, which is angle 11.

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Answer:

10

Step-by-step explanation:

Answer:

You have to complete around 49 assignments everyday to finish in one week.

Step-by-step explanation:

• First, we have to calculate the number of assignments left to do:

Assignments remaining = 419 - 79

                                        = 340

• There are 7 days in a week, which means 340 assignments need to be completed in 7 days.

7 days  ⇒  340 assignments

1 day    ⇒   340 ÷ 7

            =    48.6

            ≅ 49 assignments

∴ You have to complete around 49 assignments everyday to finish in one week.

Answer:

C) as x –> ∞, q(x) –> –∞, and as x –> -∞, q(x) –> –∞

Step-by-step explanation:

use the end behavior chart to figure out the end directions of the graph. remember these

   E   O

+|↑↑|↓↑

–|↓↓|↑↓

all you need to do is look at the first number of the equation and ask yourself:

1. Is the first number even or odd?

2. is the first number positive or negative?

find where the answers to both meet on the chart.

so, in this question, the first number is even and negative. when using the chart we see that they meet at the ↓↓ which means that the end behavior on both sides is going towards negative infinity.

Answer:

7

Step-by-step explanation:

we have 1008=2×2××2×3×3×3

The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.

Now 1008×7=2×2×2×2×3×3×7×7

7056=2×2×3×7

=84

Answer : 7

Answer:

1.   7

2.  square root is 84.

Step-by-step explanation:

First find the prime factors:

1008 =2*2*2*2*3*3*7

There's an even number of 2's and 3's but only one 7, so we multiply by 7

Smallest number = 7.

The square number is 1008 * 7

= 7056.

Its square root is  2*2*3*7 = 84.

The domain of the function f(x) is:

11 ≥ x

Here we have the function:

[tex]f(x) = \sqrt{11 - x}[/tex]

Now, remember that the argument of a square root can only be a number equal to or larger than zero, so the domain of our function is defined by:

11 - x ≥ 0

Then, solving this for x, we get:

11 ≥ x

Concluding, the domain of the function f(x) is:

11 ≥ x

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Step-by-step explanation:

324+x²=729

x²=405===> x=√405===> 9√5

The pythagorean theorem (leg 1)2 + (leg 2)² = (hypotenuse)² the values is about 8.5, -8.5.

The Pythagorean theorem is used to find the length of the sides of a right triangle, not for solving equations like x² = 72.

To solve the equation x² = 72,  to take the square root of both sides to find the value of x:

√(x²) = √(72)

Since the square root of x² is x (the absolute value of x), the equation simplifies to:

x = √(72)

Now, let's find the approximate value of √(72):

√(72) ≈ 8.49

So, the equation becomes:

x≈ 8.49

Now, remember that the absolute value of x is a positive value, so the equation gives two possible solutions for x:

x= 8.49 → x = 8.49

x = -8.49 → x = -8.49

Rounded to the nearest tenth, the solutions are:

x ≈ 8.5 and x ≈ -8.5

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Answer:

25,132.74 miles

Step-by-step explanation:

Hello!

We are basically asked to find the circumference of the Earth's cross-section.

Circumference: [tex]C = 2\pi r[/tex]

We can replace 2r with the diameter, because the diameter is 2 times the radius.

Multiply the Diameter by pi:

It is around 25,132.74 miles around.

Answer:

1/2

1/3

Step-by-step explanation:

x=1/2

x=-1/3

Answer:

[tex]x_{1} =-\frac{1}{3} \\x_{2} =\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]6x^{2} -x-1=0[/tex]

Factoring the equation:

[tex](3x+1)(2x-1)=0[/tex]

Extract the roots:

First factor

[tex]3x+1=0\\3x=-1\\x_{1} =-\frac{1}{3}[/tex]

Second factor

[tex]2x-1=0\\2x=1\\x_{2} =\frac{1}{2}[/tex]

Hope this helps

If the value of the sample standard deviation increases, the confidence interval becomes wider and is denoted as option A.

This term is used in statistics and refers to the probability that a population parameter will fall between two set values.

it has a direct relationship with standard deviation in which its increase will also lead to the set of values being wider thereby making it the most appropriate choice.

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The options are :

a. It becomes wider

b. It becomes more precise

c. It does not change

d. It narrows

La ecuación de la recta que contiene el punto (x, y) = (0, 6)  y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.

En esta pregunta tenemos que derivar una ecuación de la recta a partir de una recta y un punto. Dos rectas bajo forma implícita son paralelas si y solo si comparten los mismos coeficientes dependientes, entonces tenemos que el coeficiente independiente de la recta es:

2 · 0 + 3 · 6 + k = 0

18 + k = 0

k = - 18

Por tanto, la ecuación de la recta que contiene el punto (x, y) = (0, 6)  y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.

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Two ways to measure the relationship between the returns of two securities are correlation and covariance. That is options C and D.

Correlation can be defined as the measure of the difference between two variables in a statistical analysis.

Covariance can be defined as the measure of the relationship between two variables in statistical analysis.

Therefore, Two ways to measure the relationship between the returns of two securities are correlation and covariance.

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Answer:

-5

Step-by-step explanation:

Slope is rise over run. The graph decreases by 5 units every 1 unit to the right, so the slope is -5.

Answer:

2 face cards

Step-by-step explanation:

By definition, there are 12 face cards (Kings, queens, and jacks) and 36 numbered cards (2's through 10's) in a standard deck of 52 cards.  Aces are not considered face cards (no face on the card).

The ratio of face cards in a full deck is (12/52) or slightly over 23%.

The likelihood of a face card in a hand of 8 cards is:

(8 cards)*(12 face cards/52 cards) = 1.85 cards.  We need to round to the nearest whole card, so the expected number of face cards in a hand of 8 is 2 cards.  

Answer:

y^2 + 5y = 0

y(y + 5) = 0

y = 0, -5

The answer is y = 0 and y = -5.

The given question :

The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).

According to the question,

The circle with center at (-1,-4) that passes through the point (-4,0).

To find the radius of the circle:

Radius r = √[(-4 - (-1))² + (0- (-4))²]

=√(-4+1)² + (4)²

=√9+16

=√25

=5.

In order to find the standard equation of the circle is

(x - (-4))² + (y - (0))² = (5)²

(x + 4)² + (y )² = 25

x² + 8x + 16 + y² = 25

x² + y² + 8x + 16 = 25

x² + y² + 8x = 25 - 16

x² + y² + 8x = 9

x² + y² + 8x - 9 = 0

Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.

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Answer:

940

Step-by-step explanation:

Since there is a 5 in the ones spot we round the number is the tens spot up by 1: 935 --> 940

Answer:

D

Step-by-step explanation:

a quintic polynomial is a polynomial of degree 5

A is a polynomial of degree 4 (- [tex]x^{4}[/tex] term )

B is a polynomial of degree 3 (x³ term )

C is a polynomial of degree 2 ( x² term )

D is a polynomial of degree 5 ( 3[tex]x^{5}[/tex] term )

3.60

t = r√n − 2/1 − √r2

= 0.6√25 − 2/√1 − 0.62

= 3.5969 t or about 3.60 rounded to two decimal places.

Hypothesis Testing:

Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H0.

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The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.

A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).

The area of a rectangle = (length of rectangle)(width of rectangle).

Given the following parameters for the patio and the bench:

Area to be painted = area of rectangular patio - area of rectangular bench

Area of rectangular patio = (x + 20)(x + 10)

Area of rectangular bench = (6)(2) = 12

Area to be painted = (x + 20)(x + 10) - 12

The answer is: B. A = (x + 20)(x + 10) - 12.

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