the width of a rectangle is 9yds less . The area is 36sq yards

a) Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.

b) The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].

According to theory of limits, a function f(x) exists for x = a if and only if [tex]\lim_{x\to a^{-}} f(x) = \lim_{x \to a^{+}} f(x)[/tex]. This criterion is commonly used to prove continuity of functions.

Rational functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following lateral limits:

[tex]\lim_{x \to -1^{-}} \frac{x}{x^{2}+x} = - \infty[/tex]

[tex]\lim_{x \to -1^{+}} \frac{x}{x^{2}+x} = + \infty[/tex]

Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.

In addition, we can simplify the function by algebra properties:

[tex]\frac{x}{x^{2}+ x} = \frac{x}{x\cdot (x + 1)} = \frac{1}{x + 1}[/tex]

[tex]g(x) = \frac{1}{x + 1}[/tex]

The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].

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Answer:

True. empty set is the subset of any set

Answer:

9 3/5

Step-by-step explanation:

2+6+-4 4/5 ÷ -3

PEMDAS! First is multiplicationSo, solve the bold

2+6+ -4  4/5 ÷ -3

So,

2+6+ 1 3/5

Next is Addition(IN ORDER OF THE EQUATION), So solve the bold,

2+6+ 1 3/5

So, the answer is

9 3/5

Answer:

It is necesary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator

Step-by-step explanation:

Based on the fact that Ram bought some pens and they cost Rs.90 but if he had paid Rs.1 less for each he would have 3 more pens, the number of pens he bought is 6 pens.

This can be represented as:

(x + 3) (y - 3) = 90

Where xy = 90

xy - 3x + 3y - 9 = xy

3y - 3x - 9 = 0

y - x - 3 = 0

x - y + 3 = 0

Solving further gives:

x - 90/ x + 3 = 0

x² + 3x - 90 = 0

Remembering that:

90 = 9 x 10

= 3 x 3 x 2 x 5

= 15 x -6

Going back to the formula:

x (x + 15) - 6 (x + 15)

(x + 15) (x - 6) = 0

x - 6 = 0

x = 6 pens

In conclusion, the number of pens bought was 6 pens.

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Using the inverse functions property:

Two functions f(x) and f⁻¹(x) are inverses if:

f( f⁻¹(x) ) = x

f⁻¹(f(x)) = x

We want to get:

f⁻¹(f(93)) = m

By using the above definition we get:

f⁻¹(f(93)) = m = 93

Now for the second one we want:

f(7) = n

If you look at the table, you can see that f(x) contains the point (7, -6), then:

f(7) = n = -6

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Answer:

67

Step-by-step explanation:

The interpretation of the slope is the price of an airline ticker per kilometer is 0.137

The regression equation is given as:

Price = 49 + 0.137 · (Distance)

A regression equation is represented as

y = b + mx

Where m represents the slope

By comparison, we have

m = 0.137

Slopes are used to represent average rates

This means that the interpretation of the slope is the price of an airline ticker per kilometer is 0.137

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Answer: (-4, 0)

Step-by-step explanation: I just took the quiz and got it correct!

The function is constant on the intervals: (-4, 0), (4, ∞), and (0, 4). Within these intervals, the function's output remains the same for all values of x in each interval.

To determine the interval in which the function is constant, we need to examine the given ordered pairs (x, y) and check if the function's output (y-values) remains the same within that interval.

Let's analyze each interval:

1. (-4, 0): This interval represents all x-values greater than -4 and less than 0. In this interval, the function takes the value 0 for all x-values in the interval. Therefore, the function is constant (equal to 0) within this interval.

2. (4, ∞): This interval represents all x-values greater than 4. In this interval, the function's output is given as "∞" (infinity) for all x-values in the interval. The function is constant (equal to infinity) within this interval.

3. (0, 4): This interval represents all x-values greater than 0 and less than 4. In this interval, the function takes the value 4 for all x-values in the interval. Therefore, the function is constant (equal to 4) within this interval.

4. (-∞, -4): This interval represents all x-values less than -4. In this interval, the function's output is not specified or may not be constant. The information provided does not give us the exact function to determine the output for all x-values in this interval.

The function is constant on the intervals: (-4, 0), (4, ∞), and (0, 4). Within these intervals, the function's output remains the same for all values of x in each interval. However, we don't have enough information to determine if the function is constant on the interval (-∞, -4).

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The value of AC = 23

According to the statement

Here we have given the values of tangent from the diagram

EC = 9, ED = 12, and BD = 20.

and we have to find the value of AC.

We know that the according to the given diagram the tangent

BE is always equal to the Tangent AE.

So, we generate a equation to find the AC then

BE = AE

Convert this into parts like

BD +DE = AC+CE

Substitute the values in it which are given in the statement

20+12 = AC + 9

32 = AC + 9

32 -9 = AC

AC = 23

So, The value of AC = 23

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The number of pounds of blueberries and grapes sold are 11 and 22.

According to the statement

we have given that the:

Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25.

And total money collected by selling pounds is $55

And total number of pounds sells = 33

And we have to find the Number of pounds of blueberries and grapes.

Let the number of pounds of blueberries is X

And Let the number of pounds of grapes is Y

So,

The equation becomes is:

X + Y = 33  -(1)

2.50X + 1.25Y = 55  -(2)

Now, From substitution method

From (1) equation

Y = 33 - X

put these in equation (2) then

2.50X + 1.25(33 - X ) = 55

2.50X + 41.25 - 1.25X = 55

1.25X = 13.75

X = 11

and the the value of Y becomes

Y = 33 - X

Y = 33 - 11

Y = 22.

So, The number of pounds of blueberries and grapes sold are 11 and 22.

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Answer:

connect the dots (0, -5) and (5, -10).

The scale factor Of the larger prism to the smaller prism is 0.9

The given parameters are

Large area = 441

Small area = 361

Divide the small area by the large area

Small/Large = 361/441

Take the square root to determine the scale factor k

[tex]k = \sqrt{\frac{361}{441}[/tex]

Evaluate

k = 0.9

Hence, the scale factor Of the larger prism to the smaller prism is 0.9

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Answer:

Step-by-step explanation:

(a). A = 5x( 7x - 2 ) - 3x( 2x + 4 )

(b). A = 35x² - 10x - 6x² - 12x = 29x² - 22x

A = 29x² - 22x

The speed of the driver is 200km/hr.

The information is incomplete and an overview will be given since the complete information wasn't found online.

It should be noted that speed is calculated as:

= Distance / Time

Let distance = 2000km

Let time = 10 hours.

Speed = Distance/Time

Speed = 2000/10

Speed = 200km/hr

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Answer:

Step-by-step explanation:

eq. of line x-3y-6=0

3y=x-6

y=1/3 x-6/3

or

y=1/3 x-2

its slope m1=1/3

y=2x+5

slope m2=2

if α is the angle between the lines then

[tex]tan~\alpha =|\frac{m1-m2}{1+m1m2} |=|\frac{\frac{1}{3} -2}{1+1/3\times 2}| =|\frac{1-3\times2}{3+2}| =5/5=1=tan 45\\\alpha =45^\circ\\[/tex]

Answer:

Current Cost = Rs 360000

24000 units sold at rs 20 per unit

Turnover = 24000 * 20 = Rs 480000

Present Profit = 480000 - 360000 = Rs 120000

Profit per unit = 120000/24000 = 5 rs per unit

cost increased for increasing 3000 Production

Direct Material cost increase = (120000/24000) * 3000 = Rs 15000

Direct Labour cost increase = (84000/24000) * 3000 = Rs  10500

Variable overhead increase = (48000/24000) * 3000 = Rs 6000

Semi variable cost increased = Rs 1000

Cost Increased = 15000 + 10500 + 6000 + 1000 = 32500

Price per unit = Rs 14

Turnover from 3000 units = 14 * 3000 = Rs 42000

Proposed Profit from 3000 units = 42000 -32500 = Rs 9500

Proposed Profit per unit = 9500/3000 =  Rs 3.17

Decision Depends upon management  as Profit is there in a new market but per unit profit is  lesser than current profit

Step-by-step explanation:

Got the answer from amitnrw

It would Gretchen 192 minutes to swim the entire 2 2/5 mile course.

What is speed?

Speed is distance divided by the time taken to cover the distance.

In this case, we can determine distance covered in a minute by dividing the speed by the distance, which is distance of 7/8 mile(i.e. 0.825 mile) over the time take to cover the distance.

speed per minute=0.825/70

speed per minute=0.0125 mile/minute

With this, we can determine the time in minutes it would take to cover 2.4 miles(2/5=0.4)

0.0125=2.4/time

0.0125*time=2.4

time=2.4/0.0125

time=192 minutes

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The solutions to the given quadratic equations are x = -25/16 and x = 1

From the question, we are to determine the solutions to the given quadratic equation

The given quadratic equation is

16x² + 9 = 25

The equation can be solved as follows

16x² + 9 = 25

16x² + 9 - 25 = 0

16x² -16x +25x -25 = 0

16x(x -1) +25(x -1) = 0

(16x +25)(x -1) = 0

16x + 25 = 0 OR x - 1 = 0

16x = -25 OR x = 1

x = -25/16 OR x = 1

Hence, the solutions to the given quadratic equations are x = -25/16 and x = 1

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Applying the law of sines, when the first lighting was made, the distance from the ship to the lighthouse was: 3.2 miles.

The law of sines is expressed by the equation, sin A/a = sin B/b = sin C/c.

Using the information we are provided with, the diagram that shows the ship and other information is drawn and shown in the image attached below, where:

m∠CAB = 65 + 30 = 95°

m∠BCA = 50 - 30 = 20°

m∠B = 180 - 95 - 20 = 65°

c =  the distance from the ship to the lighthouse

Considering triangle ABC, use the Law of Sines to find c:

sin B/b = sin C/c

B = 65°

b = 8.5 miles

C = 20°

Plug in the values

sin 65/8.5 = sin 20/c

Cross multiply

c(sin 65) = (8.5 × sin 200)

Divide both sides by sin 65

c(sin 65)/sin 65 = (8.5 × sin 200)/sin 65

c = (8.5 × sin 200)/sin 65

c ≈ 3.2 miles

Thus, when the first lighting was made, the distance from the ship to the lighthouse was: 3.2 miles.

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Answer:

x = -34

Step-by-step explanation:

-3x + 2x -34 = 0

sum the x

-3x + 2x = -x

replace -x in the equation

-x -34 = 0

move -34 to other side

-x = 34

divide the two sides by -1 to get x value

x = -34

now replace x value in the equation:

-3(-34) + 2(-34) -34 =

102 -68 -34 =

102 -102 = 0

Answer:

40

Step-by-step explanation:

angle 1 and 4 are vertical angles therefore they have the same measure of 40 degrees

Answer:

-6 is the answer for instance 6=-6 or +(-6)

Using an exponential function, it is found that f(7.5) = 45.5.

An exponential function is modeled by:

[tex]y = ab^x[/tex].

In which:

For this problem, we have that f(3.5) = 12, then:

[tex]y = ab^x[/tex]

[tex]12 = ab^{3.5}[/tex]

[tex]a = \frac{12}{b^{3.5}}[/tex]

We also have that f(9) = 75, then:

[tex]y = ab^x[/tex]

[tex]75 = ab^9[/tex]

Since [tex]a = \frac{12}{b^{3.5}}[/tex]:

[tex]75 = \frac{12}{b^{3.5}} \times b^9[/tex]

[tex]b^{5.5} = \frac{75}{12}[/tex]

[tex]\sqrt[5.5]{b^{5.5}} = \sqrt[5.5]{\frac{75}{12}}[/tex]

[tex]b = \left(\frac{75}{12}\right)^{\frac{1}{5.5}[/tex]

b = 1.39542165

Then:

[tex]75 = ab^9[/tex]

[tex]a = \frac{75}{1.39542165^9}[/tex]

a = 3.7386

Hence:

[tex]y = 3.7386(1.39542165)^x[/tex]

When x = 7.5, we have that:

[tex]y = 3.7386(1.39542165)^{7.5} = 45.5[/tex]

Hence f(7.5) = 45.5.

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Answer:

(6, 4)

{second option given}

Step-by-step explanation:

we know that point y is (3, 2)

If we dilate this point by a factor of 2, we will get (6, 4)

why?

when we "dilate" something, we multiply both numbers of that point by a scale factor, we can see that this factor is 2--so we can multiply both 3

(3 ·2 = 6)  and 2 (2 · 2 = 4) to get our new point, (6, 4)

hope this helps! have a lovely day :)

Answer:

0, -3

Step-by-step explanation:

Attachment.

In short, it is way easier to not graph it, however, if you really need to graph it, change it to the correct form, then do some plug and chug if the equation is not so friendly.

The number of pairs of angles formed are about 7 types.

In the image given, when transversal t crosses the two lines, a and b, 8 angles are formed.

The pairs of angles formed are:

Therefore, there are about 7 types of pairs of each type of angles formed.

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The surface area of the triangular prism is 93 squared feet.

The surface area of triangular prism is expressed as;

S.A = bh + ( s₁ + s₂ + s₃ )H

From the diagram;

We substitute our given values into the equation above.

S.A = bh + ( s₁ + s₂ + s₃ )H

S.A = (3ft × 2ft) + ( 3ft + 3ft + 3ft )10ft

S.A = 3ft² + ( 9ft )10ft

S.A = 3ft² + 90ft²

S.A = 93ft²

The surface area of the triangular prism is 93 squared feet.

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The number of color settings he can make is 20

The given parameters are

Colors, n = 6

Selected color, r = 3

The number of color setting is calculated as:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

This gives

[tex]^6C_3 = \frac{6!}{3!3!}[/tex]

Evaluate the expression

[tex]^6C_3 = 20[/tex]

Hence, the number of color settings he can make is 20

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