Factor Method Lcm 20,25,30​

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

The reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.

For any function f(x), the reflection across the line y = x, gives the inverse of the function f(x).

In the question, we are asked for the equation, representing the reflection of f(x) = x⁴, across the line y = x.

The function can be shown as:

y = f(x) = x⁴,

or, x⁴ = y,

or, [tex]x = \pm\sqrt[4]{y}[/tex]

Changing the variables to general form, that is, y as the dependent variable and x as the independent variable, we get the inverse function as, [tex]y = F(x) = \pm \sqrt[4]x[/tex].

Thus, the reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.

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The complete question is:

"Which of the following equations represents F(x) = x⁴ reflected across the line y = x?

A. [tex]F(x)= \pm\sqrt[4]{x}[/tex]

B. [tex]F(x)= \sqrt[4]{x}[/tex]

C. [tex]F(x)= \pm x^4[/tex]

D. [tex]F(x)=- \sqrt[4]{x}[/tex] "

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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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:

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:

40

Step-by-step explanation:

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

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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All the angles required to complete each sentence are:

In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:

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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 total Stockholders’ Equity  is $4,367,000

Common Stock, $50 par $2,400,000

Paid-In Capital in Excess of Par—Common Stock $576,000

Paid-In Capital from Sale of Treasury Stock $48,000

Total paid in capital $3,024,000

Retained Earnings $1,368,000

Less Treasury stock  $25,000

Total Stockholders’ Equity $4,367,000

Therefore the total Stockholders’ Equity  is $4,367,000.

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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:

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]

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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A function which could represent the graph is: C. f(x) = x⁴(x - a)(x - b)².

The nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.

This ultimately implies that the polynomial graph has an even multiplicity at these three (3) points:

x⁴

x - a

(x - b)²

In conclusion, a function which could represent the graph is f(x) = x⁴(x - a)(x - b)².

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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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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 :)

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:

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.

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

Answer:

67

Step-by-step explanation:

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:

=

Step-by-step explanation:

{0}={} because 0 means that there is nothing and in null set too, there is no elements.

Hello,

5x² = 90/2

5x² = 45

x² = 45/5

x² = 9

x = √9 or x = -√9

x = 3 or x = -3

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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The pieces of information that is provided by the box plots are the median and first quartile.

The piece of information that is not provided by the box plots is the mean.

The interquartile range is 22.50.

An outlier would distort the values of the median and the quartiles.

A box plot is used to study the distribution and level of a set of scores. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median.  The third line on the box represents the upper (third) quartile. The difference between the quartiles is the interquartile range.

Interquartile range = 60 - 37.50 = 22.50

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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 inverse variation equation that relates x and y is x = 4032 / y.

if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable

The equation that represents inverse proportion : x = b/y

where b = constant of proportionality

112 = b /36

b = 36 x 112 = 4032

The equation : x = 4032 / y

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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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Answer:

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