Multiply the rational expressions: x²-x¸ x² −1
(x+1)²
X
A) X-1
X+1
B) (x-1)²
X+1
C) 1
X+1

None of the chosen pairs will be dependent as nothing is specified.

Independent events are those events whose occurrence does not have any effect on the events that may occur or occurred.

Dependent events are those vents whose occurrence either depends on some other event or has an effect on occurring or occurred vents.

Given, The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books.

As not mentioned that what kind of book he chooses first or types of book.

Also which shelf he chooses first choosing the first book is independent

and choosing the second book is also independent so none of the chosen pair will be dependent.

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Answer:

20

Step-by-step explanation:

Answer:

D 10

because 400=400

Step-by-step explanation:

N :700 - 30 (x)

L : 200 - 20 (x)

so the 1st week they'll both equal

N:670

L:220

we'll continue the subtraction process until they both hit and equal amount or hit zero

or the faster way, use the options of weeks were giving

lets try A

12th week

L: 12 x 30 = 360

700- 360 = 340

N: 12 x 20 = 240

200 + 240 = 440

340 < 440

we're a bit off from equal so next is B

N: 30 x 20 = 600

700 - 600 = 100

L: 20 x 20 = 400

200+ 400 = 600

100<600

this is incorrect as well which makes it incorrect which makes the user above incorrect  

c.

N; 15 x 30 = 450

700 - 450 = 250

L: 15 x 20 = 300

200 + 300 = 500

250 < 500

Incorrect

the last option might be correct but lets check

30 x 10 = 300

700-300 = 400

10 x 20 = 200

200+200 = 400!

400=400 D is correct

Answer:

39.5 divided by 4 is  9.875

Step-by-step explanation:

just divide 39.5 by 4

Step-by-step explanation:

area of rectangle (a1)=b×h

area of triangle=1/2 ×b×h

total area of arrow=a1+a2

Answer:

Step-by-step explanation:

You will find authentic some of the areas of 3 shapes, two of them are triangles, and one is rectangle.

The formula for calculating the area of right angle triangle is A= 1/2bh

The formula used to find the area of rectangle is A= W×L

A1+A2+A3

= 1/2b1h1+ 1/2b2h2+ W×L

1/2(10inches)(30inches)+ 1/2 (10 inches)(30 inches)+ (30 inches)(20 inches)

=150 inches²+ 150 inches²+ 600inches²

=900 inch²

The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.

From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.

Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:

[asy]

unitsize(1cm);

pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);

draw(O--N--A,Arrow);

draw(O--S--B,Arrow);

\(label("$52^\circ$", N + 0.3*dir(52), NE);\)

\(label("$134^\circ$", S + 0.3*dir(134), SE);\)

draw(O--A--B--cycle,dashed);

\(label("$x$", (N+A)/2, W);\)

\(label("$y$", (S+B)/2, E);\)

[/asy]

We can use the tangent function to find x and y, since we have the angle and opposite side.

From the north observation point, we have:

\($$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$\)

From the south observation point, we have:

\($$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$\)

Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

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Recall that for two vector x and y making an angle θ with each,

x • y = ||x|| ||y|| cos(θ)

If we replace y with x, we see that

x • x = ||x|| ||x|| cos(0) = ||x||²   ⇒   ||x|| = √(x • x)

Using the last identity, the magnitude of w is

||w|| = √(w • w)

but since w = u + v, we have

w • w = (u + v) • (u + v)

The dot product distributes over sums and is commutative, so

w • w = (u • u) + (u • v) + (v • u) + (v • v)

… = ||u||² + 2 (u • v) + ||v||²

… = ||u||² + 2 ||u|| ||v|| cos(θ) + ||v||²

If u has a direction of 45° with the positive x-axis, v has a direction of 150°, then the angle between u and v is |45° - 150°| = 105°. So,

||w|| = √(||u||² + 2 ||u|| ||v|| cos(150°) + ||v||²)

… = √(10² + 2 • 10 • 13 cos(150°) + 13²)

… ≈ 14.2

Using the parallelogram rule for vector addition (see attached sketch), the sum of the angle between w and u and 45° is equal to the direction of w.

If φ is the angle between w and u, then

w • u = ||w|| ||u|| cos(φ)

… = 14.2 • 10 • cos(φ)

but we also have

w • u = (u + v) • u

… = (u • u) + (v • u)

… = ||u||² + ||u|| ||v|| cos(105°)

… = 10² + 10 • 13 • cos(105°)

… ≈ 66.4

Then

14.2 • 10 • cos(φ) ≈ 66.4

cos(φ) ≈ 0.467

φ ≈ 62.1°

and so the direction of w is 62.1° + 45° ≈ 107.1°.

Answer:

\(V(x)=4x^3-112x^2+720x\)

Step-by-step explanation:

\((36-2x)(20-2x)x\)

\((720-72x-40x+4x^2)x\)

\((4x^2-112x+720)x\)

\(4x^3-112x^2+720x\)

Therefore, the resulting volume would be \(V(x)=4x^3-112x^2+720x\)

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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Answer:

-3x -12

Step-by-step explanation:

-6x +3x = -3x

-3-9 = -12

To find the unit rate, we have to use the slope formula.

Let's replace the points (7, 14) and (8,16).

Answer:

23

Step-by-step explanation:

Answer

\( | \sqrt \frac{3v}{\pi \: h} | = r\)

The given formula for the volume of cone can be written as \(\sqrt{\frac{2V}{\pi h} }\) in terms of V and h for r.

To bring a term from one side of an equation to the other, with corresponding change in sign or by doing opposite operations is called transposing a term in an expression.

According to the given question.

We have a formula for the volume of cone

\(V = \frac{1}{2} \pi r^{2} h\)

To solve the the above formula for r we use transpose method.

Therefore,

\(V = \frac{1}{2} \pi r^{2} h\)

⇒ \(2V = \pi r^{2}h\)           (multiplying by 2 both the sides)

⇒ \(\frac{2V}{\pi h} =r^{2}\)                (dividing both the sides by πh)

⇒ \(r=\sqrt{\frac{2V}{\pi h} }\)

Hence, the given formula for the volume of cone can be written as \(\sqrt{\frac{2V}{\pi h} }\) in terms of V and h for r.

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A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.

Here, we have

Given:

Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C

After 14 days, the percentage οf the mοοn is zerο

A = (max-min)/2 = 50/2 = 25

The periοd = 28 days

P = Acοs(BT = t) + c

B = 2π/periοd = 2π/28 = π/14

c = min + A = 0 + 25 = 25

We get,

P = 25cοs(π/14t) + 25,

Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.

Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

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Answer:

the answer would be twenty

Step-by-step explanation:

20x2=40 +9=49

49=49

Answer:

Number one is D/12.5

Step-by-step explanation:

correct me if im wrong plz

A more modern explanation would be, "Parallel lines are two lines within a given plane that never intersect."

Two lines on a sphere are an illustration that defies the notion of parallel lines. Meridians are the name given to longitude lines on spheres like the Earth.

Meridians are lines that run parallel to one another from the North Pole to the South Pole. However, if we take into account two meridian lines, they will cross at the North and South Poles. Two lines that are originally parallel will, therefore, eventually intersect at the poles on a sphere, defying the notion of parallel lines.

We can change the original definition of parallel lines to read, "Parallel lines are two lines that do not intersect within a given plane."

This adjustment accounts for the fact that lines can exist in many geometrical contexts, such as on a sphere or in three-dimensional space, where the idea of parallelism may be different. By including the phrase "within a given plane," we restrict the concept to the typical geometry seen in Euclidean geometry, where parallel lines do not meet.

A newer definition may therefore read, "Parallel lines are two lines within a given plane that never intersect." This updated definition makes clear that parallel lines must be taken into account inside a certain plane in order to maintain their validity, while also acknowledging the limitations of the idea.

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Answer:

\(P= 49.2m\), \(A=140.4m^2\)

Step-by-step explanation:

The diagonal splits the rectangle into two right triangles so we can use Pythagorean theorem to find the length of the missing side.

Pythagorean theorem states that a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides

So we can label our unknown side as x

x^2 + 9^2 = 18^2

x^2 + 81 = 324

Subtract 81 from both sides to isolate the x

x^2 = 243

Find the square root of both sides

√x^2 = √243

x ≈ 15.6

(The instruction said round to the nearest 10th).

So now we know

l = 15.6m and w = 9m

P= 2l + 2w

A= lw

P= 2(15.6) + 2(9)

P= 31.2 + 18

P= 49.2m

A=15.6(9)

A=140.4m^2

(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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The solution of the logarithmic expressions will be:-

19) 2logb4 - 2logb5

20) (1/2)logb (3)

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two expressions are logb 16/25 and logb √3.

The expressions will be solved as:-

E = logb 16/25

E = logb 16 - logb 25

E = logb 4² - logb 5²

E = 2logb 4 - 2logb 5

The second expression will be solved as:-

E =  logb √3.

E = ( 1 / 2 ) logb 3

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Check the picture below.

Make sure your calculator is in Degree mode.

\(\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}\)

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

All numbers less than 7 and greater than -7:

|x| < 7

Answer:

D.

Step-by-step explanation:

The answer is 117

Answer: The answer is not listed

Step-by-step explanation:

Answer: y = 2/9

..............................

y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2

m=-2

Now let us find the y intercept

-3=-2(4)+b

-3=-8+b

-3+8=b

5=b

Hence, y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

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Answer:

(a) = 60

(b) = 70

Step-by-step explanation:

(a) Sum of all the angles of a triangle is 180

This is an equilateral Triangle

which means all the sides are equal since all the sides are equal that means all the angles are equal

\(x + x + x = 180 \\ 3x = 180 \\ x = \frac{180}{3} \\ x = 60\)

(b) this is an isosceles triangle with two equal sides that means the two opposite angles are equal

\(40 + x + x = 180 \\ 40 + 2x = 180 \\ 2x = 180 - 40 \\ 2x = 140 \\ x = 70\)

As a result, there must be an x value such that the inequality is no longer true, and the parabola and the circle must intersect as a result.

The circle is centered at the origin on a coordinate grid, and the vertex of an upward-opening parabola is located at (0, 9). If the circle has a radius less than 9, the parabola and the circle must intersect.Let's suppose that the upward-opening parabola is y = ax² + 9. Since its vertex is (0, 9), this implies that a > 0, and therefore the parabola opens upwards. Since the circle is centered at the origin and has a radius less than 9, its equation is x² + y² < 81.We can substitute y with ax² + 9 in the inequality x² + y² < 81 and obtain:x² + (ax² + 9)² < 81This simplifies to:(a² + 1) x^4 + 18a² x² + 64 < 0Since the left-hand side of the inequality must be less than zero, it must be negative. Since x² is always non-negative, it follows that a² + 1 > 0. Thus, (a² + 1) x^4 + 18a² x² + 64 < 0 cannot be true for all x

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Answer:

  (x, y) = (1120, 700)

Step-by-step explanation:

You want the number of discount (x) and premium (y) tickets to be sold so that a total of 1820 tickets are sold for $40 and $45, respectively, and they generate revenue of $76,300.

The equations reflect the relationships stated in the problem:

  x + y = 1820 . . . . . . the total number of tickets sold is 1820

  40x +45y = 76,300 . . . . . total sales must be $76,300

It usually works well to substitute for the variable representing the lower-price tickets:

  40(1820 -y) +45y = 76300 . . . . . . substitute for x using the first equation

  5y = 3500 . . . . . . . . . . . . . . subtract 72800, simplify

  y = 700 . . . . . . . . . . . . divide by 5

  x = 1820 -700 = 1120

The numbers of tickets of each type sold are (x, y) = (1120, 700).