sketch the graph of f(x)=((x^(3)-1)/(x^(2)-1))​

Answer:

[tex] \boxed{\bf \cfrac{\boxed{c}}{\boxed{a }+ b}} [/tex]

Step-by-step explanation:

Given:

[tex] \tt (x_1,y_1) : A (0,0)[/tex]

[tex]\tt (x_2,y_2) : C (a+b, c) [/tex]

[tex]\boxed{\tt Slope= \cfrac{y_2,y_1}{x_2,x_1}} [/tex]

[tex]\tt \cfrac{c - 0}{a + b - 0} [/tex]

Add zero (Anything plus zero gives itself).

[tex] \tt \cfrac{c}{a + b + 0} [/tex]

[tex]\tt \cfrac{c}{a + b} [/tex]

▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎

Answer:

456_487= 57,548 that it try it and lete know

The coordinates plane is illustrated below.

A coordinate plane simply means the graphing system for points and lines.

Based on the information given, the area of teb triangle will be:

= 1/2 × b × h

= 1/2 × 11 × 20

= 110

Other information are attached.

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Answer:

4.5

Hope it helps

Answer:

only the first one

Step-by-step explanation:

all the others sign to at least one x value 2 different y values. and that violates the definition of a function.

Answer:

     A = b(h/2)

Step-by-step explanation:

Any rewrite of the equation can make use of the commutative and associative properties of multiplication.

The commutative property of multiplication lets you change the order of the operands. The given equation can have any of 6 different orders of operands:

  A = (1/2)bh = (1/2)hb = b(1/2)h = bh(1/2) = h(1/2)b = hb(1/2)

The associative property of multiplication lets you change the grouping of the operands:

  A = ((1/2)b)h = (1/2)(bh)

These ways of grouping operands can apply to any of the 6 different orders of operands, so there are 12 ways to write the equation.

One way to write the equation is ...

  A = b(h/2)

__

Additional comment

Please note that the way we have written the equation helps you see that the area of a triangle is equivalent to the area of a rectangle that has half the height. This can sometimes be useful when computing the areas of composite figures.

Answer:

[tex] A = \dfrac{bh}{2} [/tex]

Step-by-step explanation:

[tex]A = \dfrac{1}{2}b \cdot h[/tex]

[tex] A = \dfrac{bh}{2} [/tex]

Answer:

Step-by-step explanation:

let he drives at 21 m/hr=x gallons

gas used at 18 m/hr=15.5-x

21x+18(15.5-x)=300

divide by 3

7x+6(15.5-x)=100

7x+93-6x=100

x=100-93=7 gallons

gas used in city=15.5-7=8.5 gallons

distance travelled in city=18×8.5=153 miles

Answer:

Average rate of change = 4/3

Step-by-step explanation:

We have to calculate the average rate of change of the graph at x = 2 to x = 5.

From the graph attached,

At x = 2,

f(2) = 3

At x = 5,

f(5) = 7

Since, average rate of change of the function between x = a and x = b is defined by,

Average rate of change = f (b)-f (a) / b - a
                                         

Therefore, average rate of change of the function represented by the graph will be =7-3/5-2

          = 4/3

The factored inequality is  [tex]x^2-3x+6\geq 0[/tex]

The given inequality is:

[tex]-x^2+3x-6\leq 0[/tex]

This can be further simplified as:

[tex]-(x^2-3x+6)\leq 0[/tex]

The inequality can be re-written as:

[tex]x^2-3x+6\geq 0[/tex]

Since the question does not state that we should solve the inequality, the simplest we can get after factoring is [tex]x^2-3x+6\geq 0[/tex]

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The angular speed of the turntable is = 4.7 rad/sec.

Angular speed can be defined as the rate at which angular displacement changes with respect to time.

Speed can be defined as the distance traveled by an object at a particular time interval.

The rate of rotation of the turntable = 45 rotations per minute.

That is, the time taken to complete one rotation in seconds = 1/45 ×60sec = 1.34secs

This is taken to be the period of rotation (T)

Therefore, the angular speed is calculated using the formula, 2π/T

= 2×3.14/1.34 = 4.7 rad/sec.

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Answer:

Step-by-step explanation:

The original selling price is $847.10

The given parameters are:

Discount price = $720

Discount = 15%

The original selling price is calculated as:

Discount price = Original selling price * (1 - Discount)

This gives

720 = Original selling price * (1 - 15%)

Evaluate the difference

720 = Original selling price * 0.85

Divide by 0.85

Original selling price = 847.10

Hence, the original selling price is $847.10

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Answer:

diameter =7 cm

Step-by-step explanation:

circum=2pi×r

[tex]2\pi \times r[/tex]

2×pi×r=22

2×22÷7×r=22

r=22×7÷44

r=7÷2

r=3.5

d=2×r=2×3.5=7

The distance from the second destination back to Dallas is 918 miles

A triangle has points Dallas, destination 1, and destination 2.

The distance from Dallas to destination 1 is 720 miles

The distance from destination 1 and destination 2 is 290 miles

the angle formed between Dallas, destination 1, and destination 2 is 125 degrees.

He moves from destination 1 to Dallas then destination 2

We could use cosine law to find the distance

The Law of cosines or cosine law means the relation between the length of sides of a triangle with respect to the cosine of its angle. It is also called the cosine rule

[tex]b^{2}=a^2+c^2-2ac*cosB[/tex]

=[tex]290^2+720^2-2*720*290*cos125[/tex]

=84100+518400-417600 cos 125

=602500-417600*(-0.5735)

=602500+239493.6

=841993.6

b=917.6 miles

≅918 miles

The distance is 918 miles  he will fly from the second destination back to Dallas

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Answer:

918 miles

Step-by-step explanation:

got it right on edge

Answer:

it's-3

Step-by-step explanation:

please mark me as brainlist

The quotient of the division operation is [tex]\frac{5}{9}[/tex]

From the question, we are to find the quotient of the division operation

The given division operation is

[tex]\frac{2}{3} \div \frac{6}{5}[/tex]

1. The divided is [tex]\frac{2}{3}[/tex]

2. The divisor is [tex]\frac{6}{5}[/tex]

3. The reciprocal of the divisor is [tex]\frac{5}{6}[/tex]

4. The equivalent multiplication of the division problem is

[tex]\frac{2}{3} \times \frac{5}{6}[/tex]

5. The multiplication gives

[tex]\frac{2}{3} \times \frac{5}{6}=\frac{10}{18}[/tex]

6. Simplifying the quotient, we get

[tex]\frac{10}{18}=\frac{5}{9}[/tex]

Hence, the quotient of the division operation is [tex]\frac{5}{9}[/tex]

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Answer:

120870

Step-by-step explanation:

Your answer choices are not correct. The least common denominator of 34, 45, and 237 would be 120870.

LCD(1/34, 1/45, 1/237) = LCM(34, 45, 237) = 2×32×5×17×79 = 120870

1/34= 3555/120870

1/45= 2686/120870

1/237= 510/120870

HOPE THIS HELPS!!

Answer:

1.  Vertical shrink by a factor of ¹/₅

2.  Right 5

3.  Up 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Identify the transformations that take the parent function to the given function.

Question 1

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=\dfrac{1}{5}x^3[/tex]

Comparing the parent function with the given function, we can see that the parent function has been multiplied by ¹/₅.

Therefore, the transformation is:

[tex]y=\dfrac{1}{5}\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:\dfrac{1}{5}[/tex]

As 0 < a < 1, the transformation visually is a compression in the y-direction, so we can also say:  Vertical shrink by a factor of ¹/₅

Question 2

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(x-5)^3[/tex]

Comparing the parent function with the given function, we can see that 5 has been subtracted from the x-value of the parent function.

Therefore, the transformation is:

[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]

Question 3

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=x^3+5[/tex]

Comparing the parent function with the given function, we can see that  5 has been added to the parent function.

Therefore, the transformation is:

[tex]f(x)+5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units up}[/tex]

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Answer:

1) Vertical shrink by a factor of 1/5

2) Right 5

3) Up 5

Explanation:

Given main function: f(x) = x³

1.) f(x) = 1/5 (x³)

Comparing with a(f(x)) which gives vertical stretch or compression.

Here the function f(x) has been shrinked vertically by a factor of 1/5

2.) f(x) = (x - 5)³

Comparing with f(x - c) which gives horizontal translation c units right.

Here the function f(x) has been shifted 5 units to the right.

3.) f(x)= x³ + 5​

Comparing it with f(x) + d which gives vertical translation d units up.

Here the function f(x) has been moved 5 units up.

See below for the changes when the exponential function is transformed

The exponential functions are given as:

[tex]y = \sqrt x[/tex]

[tex]y = 5\sqrt x[/tex]

[tex]y = 14\sqrt{x[/tex]

[tex]y = -2\sqrt{x[/tex]

An exponential function of the above form is represented as:

[tex]y = a\sqrt{x[/tex]

See attachment for the graph of the four functions.

When a is large

This is represented by [tex]y = 14\sqrt{x[/tex]

In this case, the curve of the base form [tex]y = \sqrt x[/tex] is vertically stretched and it moves closer to the y-axis

When a is small

This is represented by [tex]y = 5\sqrt x[/tex]

In this case, the curve of the base form [tex]y = \sqrt x[/tex] is vertically stretched and it moves away from the x-axis

When a is negative

This is represented by [tex]y = -2\sqrt{x[/tex]

In this case, the curve of the base form [tex]y = \sqrt x[/tex] is vertically stretched and is reflected across the y-axis.

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The given trig equation is obtained by solving for the critical points of [tex]f[/tex], which is done by differentiating [tex]f[/tex] and setting the derivative equal to zero.

We have

[tex]18 \sin(x) \cos(x) - 9 \sin(x) = 0[/tex]

[tex]9 \sin(x) (2 \cos(x) - 1) = 0[/tex]

[tex]9 \sin(x) = 0 \text{ or } 2 \cos(x)  - 1 = 0[/tex]

[tex]\sin(x) = 0 \text{ or } \cos(x) = \dfrac12[/tex]

In the interval [tex]0\le x< 2\pi[/tex], we have

[tex]\sin(x) = 0 \implies x = 0 \text{ or } x = \pi[/tex]

and

[tex]\cos(x) = \dfrac12 \implies x = \dfrac\pi3 \text{ or } x = \dfrac{5\pi}3[/tex]

In order from smallest to largest, that's

[tex]x = 0 \text{ or } x = \dfrac\pi3 \text{ or } x = \pi \text{ or } x = \dfrac{5\pi}3[/tex]

The solution to the Trigonometric equation is given as below.

A trigonometric equation is one that involves one or more unknown trigonometric ratios. It is represented in terms of sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles.

The provided trigonometric equation is produced by determining the critical points of f by differentiating and setting the derivative to zero.

Thus,

18 sin (x) cos (x) - 9 sin (x) = 0

8 sin(x) = 0 or 2 cos (x) - 1 = 0

Sin (x) = 0 or Cos (x) = 1/2

Given the interval of 0 ≤ x ≤ 2π

→ Sin (x) = 0 → x = 0 or x = π

and

Cos (x) = 1/2

→ x = π/3 or x = 5π/3

Arranging the values from the smallest to the largest, we have:

x = 0 or x = π/3

x = π or x = 5π/3

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Answer:

mark on day three can use up to 4 cans of blue paint and 5 cans of yellow paint

Step-by-step explanation:

given--started with 14 cans of blue paint

given--started with 20 cans of yellow paint

given--used 10 cans of blue paint and 15 cans of yellow paint in total

by subtracting the blue paint he used with the amount he started with you get an answer of 4 blue paint cans--- vice verse--20 yellow paint cans minus 15 yellow paint cans equal 5 yellow paint cans.

According to the internet it states, The median of a triangle is a line segment joining the vertex of the triangle to the mid-point of its opposite side.

It bisects the opposite side, dividing it into two equal parts.

The median of a triangle further divides the triangle into two triangles having the same area

Answer:

B

Step-by-step explanation:

Convert everything to inches first

The floor is 120 inches by 144 inches

The floor can be covered with (120/6) * (144/8) tiles

(120/6) * (144/8) = 20*18=360 tiles, hence b.

The moving average of the stock for the end of day 7 is 53

Note that

Average = Day 1 + Day 2 + Day3 + Day 4 = Day 5 + Day 6 + Day 7/ 7

We have

Average = 32 + 56 + 50 + 60 + 59 + 55 + 59 /7

Average = 371/ 7

Average = 53

Therefore, the moving average of the stock for the end of day 7 is 53

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la longitud del jardín del amigo de Carmen es 18 m 22 cm.

Una ecuación es un enunciado matemático que se forma cuando una expresión algebraica se iguala mediante un signo igual a otra expresión algebraica o una constante.

Se da que la longitud de Carme

Se sabe que la longitud del jardín de Carmen es de 15 m 24 cm.

y el largo del jardín de su amigo es 2 m 98 cm más largo que el de Carmen.

Sea La longitud del jardín de Carmen es x m

Entonces la ecuación se convierte en

La longitud del jardín de su amigo = x + 2m 98 cm

ahora ,

x = 15m 24cm

Sustituyendo los valores en la ecuación

La longitud del jardín de su amigo = 15m 24cm + 2m 98 cm

1m = 100cm

La longitud del jardín de su amigo = 17 m 122 cm

as 100 cm = 1m

122 cm = 1 m 22 cm

so ,

La longitud del jardín de su amigo = 18 m 22 cm.

Por lo tanto, la longitud del jardín del amigo de Carmen es 18 m 22 cm.

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Answer:

  7/9

Step-by-step explanation:

In order to write the fraction without any units (as a pure number), we must have units in the numerator and denominator that are the same. Then the units cancel.

We are given the conversion ...

  4 quarts = 1 gallon

Multiplying by 7, we see ...

  28 quarts = 7 gallons

This lets us write the desired fraction as ...

  (28 quarts)/(9 gallons) = (7 gallons)/(9 gallons) = 7/9

The ratio in simplest form is 7/9.

By using Geogebra online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Given the following system of inequalities:

3y > 2x + 12  ⇒ 3y - 2x > 12

2x + y ≤ -5

By using Geogebra online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

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Answer:

sin=-3/5
cos=4/5

tan-3/4

csc=5/-3

sec=5/4

cot=4/-3

Step-by-step explanation:

you draw a right triangle in the fourth quadrant and then use pythagoreas theorem to find the length of the hypotenuse(2 sides are -3 and 4, hypotenuse is 5), and then just use the sides to find all 6 trigonometric functions.

The value f x when y= 5 is 2

Let the given equation be y = k/x

where k is the constant

if y = 2 when x= 5, then;

k = xy

k= 2(5)

k = 10

In order to determine the value of x when y = 5

x = k/y

x = 10/5

x = 2

Hence the value f x when y= 5 is 2

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