Solve. Check for extraneous solutions. -∛x+3=0

Answer:

Hello,

Step-by-step explanation:

[tex]A=\begin{bmatrix}2 & 2 \\3 & 4 \end{bmatrix}\\\\\\B=\begin{bmatrix}0 & 4 \\2 & -3 \end{bmatrix}\\\\\\C=\begin{bmatrix}4 & 6 \\5 & 6 \end{bmatrix}\\\\\\(X-4B)*A=C\\\\X-4B=C*A^{-1}\\\\X=C*A^{-1}+4B\\[/tex]

[tex]\begin{array}{|cc|cc|}A&&A^{-1}&\\---&---&---&---\\2&2&1&0\\3&4&0&1\\---&---&---&---\\1&1&\frac{1}{2}&0\\0&1&\frac{-3}{2}&1\\---&---&---&---\\1&0&2&-1\\0&1&\frac{-3}{2}&1\\---&---&---&---\\\end {array}\\\\[/tex]

[tex]X=C*A^{-1}+4B=\begin{bmatrix}4 & 6 \\5 & 6 \end{bmatrix}*\begin{bmatrix}2&-1\\\frac{-3}{2}&1\end{bmatrix}+4*\begin{bmatrix}0 & 4 \\2 & -3 \end{bmatrix}[/tex]

[tex]X=\begin{bmatrix}-1 & 2 \\1 & 1 \end{bmatrix}+\begin{bmatrix}0 & 16 \\8 & -12 \end{bmatrix}\\\\\\X=\begin{bmatrix}-1 & 18 \\9 & -11 \end{bmatrix}\\[/tex]

Answer:

2 and 2/25 miles per hour.

Step-by-step explanation:

Harry's speed = distance / time

                        = 10 4/10 / 5

                        = 104/10 * 1/5

                         = 104/50

                          = 2 4/50

                          = 2 2/25

Answer:

Step-by-step explanation:

First term of the sequence is 10 and common difference is 3.

a

1

​

 = 10 and d = 3

Next term = a

2

​

=a

1

​

+d=10+3=13

a

3

​

=a

2

​

+d=13+3=16

Thus, first three terms of the sequence are 10, 13 and 16.

Let 100 be the nth term of the sequence.

a

n

​

=a

1

​

+(n−1)d

100=10+(n−1)3

90=(n−1)3

n−1=30

n=31, which is a whole number.

Therefore, 100 is the 31

st

 term of the sequence.

The diameter of the tank is 25.8 feet.

We are given the volume of water tank. Also, we are provided the formula relating volume and density.

Rewriting the formula -

V = 1/6×π×d³, where d represents the diameter. Taking the value of π as 3.14

Rewriting the formula according to diameter -

d³ = 6V/π

Keep the values in formula to find the value of diameter of water tank

d³ = 6×9000/3.14

Performing multiplication and division to find the value of diameter

d³ = 54000/3.14

Performing division to find the value of diameter of water tank

d³ = 17197.45

d = ∛17197.45

Taking square root to find the value of diameter of water tank

d = 25.8 feet

Hence, the diameter of tank is 25.8 feet.

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The correct answer of the question is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .

The given quadratic equation is 3 x²+ 9 x=27

To begin, we must transform the equation in the form

ax² + bx + c = 0, then apply the quadratic formula i.e.

x = {-b±√(b²- 4ac)}/ 2a .

Now,

3 x²+ 9 x=27

⇒ 3 x²+ 9 x - 27 = 0

⇒  3(x²+ 3 x - 9 )= 0

⇒  x²+ 3 x - 9 = 0

Here, a = 1, b = 3 and c = --9

Now, applying quadratic formula

{-b±√(b²- 4ac)}/ 2a

= {-3±√(3²- 4 × 1 × -9)}/ (2 × 1)

= {-3±√(9 + 36)}/ 2

= {-3±√45}/ 2

= {-3±3√5}/ 2

= 3{-1 ±√5}/ 2

= 3{-1+√5}/ 2 or 3{-1-√5}/ 2

Therefore, the ultimate answer to the given equation is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .

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After pumping all of container A into container B there will remain empty space in B = 78.5 ft³

The percentage for this empty space is of the entire volume is = 3.4 %

What is volume of cylinder?

Volume of cylinder is calculated as;

v = π r² h  

Since, Container A has a diameter of 18 feet and a height of 9 feet.

Then, Radius = 18/2 = 9 ft

Hence, Volume of Container A = π r² h  

                                                = 3.1416 * 9 * 9 * 9

                                                = 2,290.22 ft³

Since,  Container B has a diameter of 16 feet and a height of 11 feet.

Then, Radius = 16/2 = 8 ft

Hence, Volume of Container B = π r² h

                                               = 3.1416 * 8 * 8 * 11

                                               = 2,211.68 ft³

After pumping all of container A into container B there will remain empty space in B = 2,290.22 - 2,211.68 = 78.5 ft³

And, The percentage for this empty space is of the entire volume is,

78.5/2,290.22 = 0.03427 *100 = 3.4 %

So, After pumping all of container A into container B there will remain empty space in B = 78.5 ft³

The percentage for this empty space is of the entire volume is = 3.4 %

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Answer:

Step-by-step explanation: its 1.45-3.10 and then its =1.35

ez

have a good day

For one gallon of gas, it travels 85 miles.

Given a motorcycle travels 340 miles on 4 gallons of gas

We have to find the unit rate that means for one gallon of gas how much this travel.

This is known as the Unitary method.

Unitary method:

The unitary method is the method in which we need to solve the problem by first finding the value of a single unit, then we can multiply that single unit value by the necessary amount that we need.

So, given 340 miles on 4 gallons of gas per gallon, it should be

= 340/4

= 85 miles

Therefore, It travels 85 miles on one gallon of gas.

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The college bookstore paid $44.4 for the book

A college store marks up the price it pays the publisher for a book by 35%

The selling price of the book is $60.00

Therefore the amount paid by the bookstore can be calculated as follows

( 35/100 + 1) x = 60

0.35+1x= 60

1.35x= 60

Divide both sides by the coefficient of x which is 1.35

x= 60/1.35

x= 44.4

Hence the book store will pay $44.4 for the book

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The order of transformation which best describes how to sketch the graph of h(x) = ∛1 - x is: A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ y-axis.

Generally, there are different types of transformation and these include the following:

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In conclusion, we can reasonably and logically deduce that the order of transformation which best describes how the graph of h(x) = ∛1 - x should be sketched is to start by plotting the graph of the basic function y = ∛x, and then horizontally shift the graph of function y = ∛x to the left one​ unit, and then reflect the graph about the​ y-axis.

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Complete Question:

Which of the following order of transformations best describes how to sketch the graph of h(x) = ∛1 - x?

A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ y-axis.

B. Starting with the graph of the basic function y = ∛x, vertically shift the graph up one​ unit, and then reflect the graph about the​ y-axis.

C. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ x-axis.

D. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the right one​ unit, and then reflect the graph about the​ y-axis.

Answer:

AB has the slope of 4/3

CD has the slope of 3/2

Step-by-step explanation:

CD I chose the points (0,2) and (3,0)

[tex] \frac{y2 - y1}{x2 - x1} \\ \frac{0 - 2}{3 - 0} \\ m = \frac{ - 2}{3} [/tex]

AB I chose the points (0,6) and (8,0)

[tex] \frac{y2 - y1}{x2 - x1} \\ \frac{0 - 6}{8 - 0} \\ m = \frac{ - 3}{4} [/tex]

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

|-5|+|7|

|-5|=5

|7|=7

=5+7

=12

hope this helps u ; )

The earthquake in 1995 was 1.2 times than the 2001 earthquake .

It is given that in 1995, an earthquake in Mexico registered 8.0 on the Richter scale and earthquake of magnitude 6.8 in Washington state.

If [tex]I_1[/tex]and [tex]I_2[/tex] are the intensities of the Mexico and Washington earthquakes, then we are required to find [tex]\frac{I_1}{I_2}[/tex]. To relate this to the definition of magnitude, we divide numerator and denominator by S

   [tex]log(\frac{I_1}{I_2})=log\frac{\frac{I_1}{S} }{\frac{I_2}{S} }[/tex]

Using property of logarithm [tex]log\frac{a}{b} =loga-logb[/tex] , we get

  [tex]log(\frac{I_1}{I_2})=log{\frac{I_1}{S} -log{\frac{I_2}{S} \\\\\\[/tex]

  [tex]log(\frac{I_1}{I_2})=8.0-6.8\\\\log(\frac{I_1}{I_2})=1.2[/tex]

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Answer: (1/14, 10/7, -13/14)

Step-by-step explanation:

3x+2y−z=82x+2z=−4x+3y=4 ==> convert this to system of equations

3x+2y−z=4

82x+2z=4

−4x+3y=4

(3x+2y−z=4)*2

6x+4y−2z=8 ==> add this equation

82x+2z=4 ==> add this equation

88x+4y=12 ==> add the top 2 equations

(−4x+3y=4)*4

-16x+12y=16

(88x+4y=12)*3   ==> multiply by 3 to get 12y

264x+12y=36

-16x+12y=16

264x-(-16x)=36-16

264x+16x=20

280x=20

280x/280=20/280

x=1/14

−4x+3y=4

−4(1/14)+3y=4

-4/14 + 3y=4

-2/7 + 3y=4

(-2/7 + 3y=4)*7 ==> multiply equation by 7 to remove fractions

-2+21y=28

21y=30

y=30/21

y=10/7

3x+2y−z=4

3(1/14)+2(10/7)−z=4

3/14 + 20/7 - z=4

(3/14 + 20/7 - z=4)*14 ==> multiply equation by 14 to remove fractions

3 + 20*14/7 - 14z=56

3 + 280/7 - 14z=56

3+40-14z=56

43-14z=56

43-43-14z=56-43

-14z=13

z=-13/14

Answer: (1/14, 10/7, -13/14)

Step-by-step explanation:

y=3x

y=x-4

3x=x-4

2x=4

x=2

y=3*2

y=6

(2,6)

x=2

y=6

Step-by-step explanation:

so, if I understand you correctly and nothing was left out :

f(t) = t² + 8t + 9

d(t) = t² + 11t + 4

just by looking at the 2 functions, it is clear that d(t) creates larger functional values for higher values of t.

because t² = t², but 11t > 8t. and the constants in the end are irrelevant for larger numbers.

so the pool will drain.

a.

w(t) = f(t) - d(t) = t² + 8t + 9 - t² - 11t - 4 = -3t + 5

b.

yes, it will completely drain, as -3t will drive it to 0, and if it was physically possible into the negative ask the way to -infinity.

c.

-3t + 5 = 0

5 = 3t

t = 5/3

it will be completely drained after

1 2/3 hours = 1 hour 40 minutes.

d.

to intersect they need to create the same result for a value of t :

t² + 8t + 9 = t² + 11t + 4

8t + 9 = 11t + 4

-3t + 5 = 0

t = 5/3 or 1 hour 40 minutes.

that means that the filling and the draining are only equal, when there is no water in the pool.

that also means that f(t) is actually calculating how much water there is in the pool, if there would not be no drain, with a starting value of 9.

e.

the domain is the interval or set of all valid input values (here for t).

negative t (hours) don't make any sense for any of the 3 functions.

but f(t) can go on theoretically forever. but usually it's limited by the size of the pool (once it reaches the top, there is no more filling). we just don't know anything about that.

so, the domain for f(t) is

0 <= t < +infinity

d(t) could go on and on as well, as long as there is water in the pool.

so, the domain for d(t) is also

0 <= t < +infinity

but w(t) based on its meaning and definition makes only sense between the start (t = 0) and until the water is fully drained by the combination of f(t) and d(t).

so, the domain of w(t) is

0 <= t <= 5/3

we could define w(t) as segmented function

w(t) = -3t + 5 0 <= t <= 5/3

= 0 t > 5/3

THEN the domain would be again

0 <= t < +infinity

The value of x in the equation x² - 2 x + 5 = 2 is 1 ± i √2.

We are given the equation:

x² - 2 x + 5 = 2

We need to solve the equation to find the value of x.

For this, we will first subtract 2 from both the sides:

x² - 2 x + 5 - 2 = 2 - 2

x² - 2 x + 3 = 0

Now, we will solve for the value of x:

D = b² - 4 ac

D = (- 2)² - 4 (3)(1)

D = 4 - 12

D = - 8

√D = 2 i √2

Now putting it in quadratic formula, we get that:

x = (- b ± √D) / 2 a

x = (2 ± 2 i √2) / 2 (1)

x = 1 ± i √2

Therefore, the value of x in the equation x² - 2 x + 5 = 2 is 1 ± i √2.

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Your question is incomplete. Please refer the content below:

What is the solution to the equation for x:

x² - 2 x + 5 = 2

It should be noted that in order to measure the value, the measurement has to be in the same unit.

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.

Measurement is crucial in establishing connections across different branches of mathematics. For instance, it gives the use of math abilities and spatial concepts a rich and meaningful context. Measurement also establishes connections between mathematics and other academic disciplines.

From the information, it was illustrated that the boys all had measurements of trees taken. Therefore, it should be noted that since they are in different units, it cannot be done.

In this case, the reason is that in order to measure the value, the measurement has to be in the same unit. This will make it easier to do the calculation.

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1. The y-intercept is: 12.

2. The y-intercept represent the initial cost that excluding the cost per DVD.

3. Your friend is incorrect. A dozen DVD's is gotten for $84.

4. 50 DVD's from the website would cost: $312.

The y-intercept is the value of the y-coordinate of the point where the line intercepts the y-axis.

The y-intercept is referred to as the starting value or initial value. At this point, x = 0.

1. First, find the slope (m) of the line using two points, (1, 18) and (2, 24):

Slope (m) = change in y/change in x = (24 - 18)/(2 - 1) = 6/1

Slope (m) = 6

Substitute m = 6 and (x, y) = (1, 18) into y = mx + b to find the y-intercept, b:

18 = 6(1) + b

18 - 6 = b

b = 12 (y-intercept)

Substitute m = 6 and b = 12 into y = mx + b:

y = 6x + 12

The y-intercept that connects all the data points is: 12.

2. The y-intercept in this context represents the initial cost that excludes the charge for each DVD.

3. Substitute x = 12 into y = 6x + 12 and solve to see if y equals 90:

y = 6(12) + 12

y = 84 [not equal to $90)]

Thus, your friend is incorrect. a dozen DVD's can be gotten for $84.

4. Substitute x = 50 into y = 6x + 12:

y = 6(50) + 12

y = 312

It would cost $312 to get 50 DVD's from the website.

The graph for the points (1, 18), (2, 24) , and (3, 33) is shown below.

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The sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.

The continuous compounding formula is as follows:

So,

According to the first point, we know that atr = 0.02,  and t = 1.

Thus for advantage > 1$ we need is as follows:

According to the second point, we got that:

Then,

Now we hold that r > 0.04439:

According to the third point, we got to know that:

Now 2nd equation holds t > 4.621.

Therefore, the sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.

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Answer:

It looks like the chart says time and hours.

Step-by-step explanation:

Using the axis title we found that the time is the measurement represented on the x- axis  and and time is measured in hours

The axis title is a title in the form of words or numbers that describes the  entire axis . The title that describes that what quantity varies along x-axis is called x-axis title and the title which describes what quantity varies along y- axis is called y- axis title.

Some times units of the quantities measured along the respective axis  is also mentioned in the title of the axis in a bracket.

From the Given graph in the question we can see that a Distance vs Time graph is given

And the title of the x- axis is Time (hours )

Therefore , the measurement along the x- axis is of time and unit of time is hours.

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The solution for x in the compound inequality is 18 < x ≤ 3

The compound inequality is given as

6x − 10 ≤ 8 or 1/3x + 6 > 12

Add or subtract the constant to both sides of the compound inequality

So, we have

6x ≤ 18 or 1/3x > 6

Divide both sides of the compound inequality by the coefficient of x

So, we have

x ≤ 3 or x > 18

Rewrite as

x > 18 or x ≤ 3

Combine both inequalities

18 < x ≤ 3

Hence, the solution for x in the compound inequality is 18 < x ≤ 3

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Cinematic layout lead, Technical Assistant, Game Artist, 2D Artist, and Game Producer are the best anime jobs that use geometry.

There are many opportunities for animators to get anime jobs that use geometry as well. In order to demonstrate how an object is rotated or shifted to be made larger or smaller—for the process of producing movement—animators must comprehend the geometrical characteristics of figures and apply linear algebra.

Due to their work with moving and changing objects, animators frequently use a number of mathematical techniques, including geometry, linear algebra, and others. The ability to utilize linear algebra to demonstrate how a certain figure or object is shifted or rotated with the intention of making it smaller or larger is crucial for animators. Movement is produced by this mechanism.

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.

Answer: hello frawn

Step-by-step explanation:

free point dootie head

The transformation rules for the given figure are as follows:

A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

From Triangle TUV to Triangle T'U'V', the complete rule is given by:

(x,y) -> (y, x).

The rule for a reflection over the y-axis is:

(x,y) -> (-x,y).

Hence the rotation rule was given by:

(x,y) -> (-y, x).

Hence the rules are:

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Answer:

10812

Step-by-step explanation:

books sold=106

number of pages=102

106 × 102=10812

Answer:

106^102

Step-by-step explanation:

Because there are 106 copies of the book and each book has 102 pages

to get the equation of any straight line, we simply need two points off of it, hmmm let's take a peek at the y-intercept of the line above

[tex]y = 5x \stackrel{\stackrel{b}{\downarrow }}{+2} \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies \stackrel{y-intercept}{(0~~,~~2)}[/tex]

so we're really looking for the equation of a line that passes through (2 , -3) and (0 , 2)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{2}}} \implies \cfrac{2 +3}{-2} \implies -\cfrac{ 5 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-\cfrac{ 5 }{ 2 }}(x-\stackrel{x_1}{2}) \implies y +3= -\cfrac{ 5 }{ 2 } (x -2)[/tex]

The mapping of T'U'V'W' onto TUVW is translated as follows:

The backward translation of the mapping T'U'V'W' onto TUVW is the mapping TUVW onto TUVW.

Reversing the mapping involves the steps listed below.

Therefore, the mapping of T'U'V'W' onto TUVW is translated as follows:

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The complete question is given below:
The translation (x,y)(x+3,y-3) maps TUVW onto T'U'V'W. What translation maps T'U'V'W onto TUVW?

(x,y)(x+3,y-7)

(x,y)(x-7,y+3)

(x,y)(x+7,y-3)

(x,y)(x-3,y+7)

Answer:1,816

2,013 minus 197 equals 1,816