−4x+4≥2(6−x) step-by-step explanation please and thank you

Answer:

15 = 12 +3   or   5x = 4x + 3.

Hope that helps. x

Answer:

X+7 < 40 is the answer

x can equal anything less than 33

Step-by-step explanation:

Answer:

domain: 4, -4, 2, 3, 10

range: 9,3,-5

FUNCTION

Step-by-step explanation:

(a) Concerning the coefficients of the equation for the volume of the eggplant ( \(V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}\)), the units of the coefficients with values \(3.53 \times 10^{-2}\) and 2 are cubic feet and \(\frac{1}{h^{2}}\), respectively.

(b) Regarding the determination of the coefficients by linear regression, the scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.

(c) After the solicitation of the European distributor of the film, the new formula is \(V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}\), where volume is in cubic meters and time is in seconds.

Note - The statement reports typing mistakes. We present the correct statement below:

The climatic moment in the film "The Eggplant that Ate New Jersey" comes when the brilliant young scientist announces his discovery of the equation for the volume of the eggplant: \(V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}\), where \(t\) is the time in hours from the moment the vampire injected the eggplant with a solution prepared from the blood of the beautiful dental hygienist.

(a) What are the units of \(3.53\times 10^{-2}\) and \(2\)?

(b) The scientist obtained the formula by measuring \(V\) and \(t\) and determining the coefficients by linear regression. What would he have plotted versus what on what kind of coordinates? What would he have obtained as the slope and intercept of his plot?

(c) The European distributor of the film insists that the formula must be given for the volume in cubic meters (\(m^{3}\)) as a function of time, in seconds. Derive the formula.

(a) In this exercise, we must make use of principles for dimensional analysis. We know that the equation for the volume of the eggplant is represented by:

\(V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}\) (1)

Dimensionally speaking, we have the following case:

\([L]^{3} = [A]\cdot e^{[B]\cdot [t]^{2}}\) (2)

By direct inspection and some algebraic handling, we conclude that:

\([A] = [L]^{3}\)

\([B] = [t]^{-2}\)

Therefore, the units of \(3.53 \times 10^{-2}\) and 2 are cubic feet and \(\frac{1}{h^{2}}\), respectively.

(b) The curve fit for the exponential expression used by the scientist is of the form:

\(V = A\cdot e^{B\cdot t^{2}}\) (3)

If we apply logarithms on both sides of the expression above, then we have the following form:

\(\ln V = \ln A\cdot e^{B\cdot t^{2}}\)

\(\ln V = \ln A + B\cdot t^{2}\) (4)

The scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.

(c) An hour equals 3600 seconds and a cubic feet equals 0.028 cubic meters. Hence, we can adapt (1) to fulfill the requirements of the European film distributor by using the following conversions:

\(t' = 3600\cdot t\) (5)

\(V' = 0.028\cdot V\) (6)

Where:

By applying (5) and (6) in (1), we have the resulting formula:

\(V' = 0.028\cdot [3.53\times 10^{-2}\cdot e^{2\cdot \left(\frac{t'}{3600} \right)^{2}}]\)

\(V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}\)

The new formula is \(V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}\), where volume is in cubic meters and time is in seconds.

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After a small online search, I've found that the volume equation is:

\(V[ft^3] = 3.53 \cdot10^{-2} \cdot exp(2 \cdot t^2)\)

a) We want to see what are the units of the first factor:

\(3.53 \cdot10^{-2}\)

You can see that the volume is in cube feet, and the only part in the equation that can have units is this one, so the units of this factor should be cube feet.

b) On the vertical coordinate he would see the volume and on the horizontal coordinate he would see the time.

The graph of this function is an increasing exponential function, that grows slow at the beginning and then grows faster.

c) Remember that the term with the units is:

\(3.53 \cdot10^{-2}\)

So we should write this as:

\(3.53 \cdot10^{-2} ft^3\)

Now we know that:

\(1m^3 = 35.3 ft^3\\\\1 = \frac{1 m^3}{35.3 ft^3}\)

Now we can multiply our measure by this to get:

\(3.53 \cdot10^{-2} ft^3 = ( \frac{1 m^3}{35.3 ft^3})*(3.53 \cdot10^{-2} ft^3) = 0.1 m^3\)

Then the equation is:

\(V = 0.1m^3\cdot exp(2 \cdot t^2)\)

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Answer:

Find the 40th term for the arithmetic sequence in which

a8=60 and a12=48 .

Substitute 60 for a8 and 48 for a12 in the formula

an=a1+(n−1)d  to obtain a system of linear equations in terms of a1 and d .

a8=a1+(8−1)d→60=a1+7da12=a1+(12−1)d→48=a1+11d

Subtract the second equation from the first equation and solve for d .

12=−4d−3=d

Then 60=a1+7(−3) .  Solve for a .

60=a1−2181=a1

Now use the formula to find a40 .

a40=81+39(−3)=81−117=−36 .  

Step-by-step explanation:

The rule for the nth term of the given arithmetic sequence is given by aₙ = 41-7n

An arithmetic sequence is a list of numbers with a definite pattern.

Given is the 8th and 17th term of an arithmetic sequence, which are -15 and -78

We know that, nth term of an arithmetic sequence, is given by =

aₙ = a₁ + (n-1)d

Where n is the number of terms and d is the common difference,

Therefore,

a₈ = a₁ + (8-1)d

-15 = a₁+7d

a₁ = -7d-15...(i)

a₁₇ = a₁ + (17-1)d

-78 = a₁+16d

a₁ = -78-16d...(ii)

Solving equations 1 and 2,

-78-16d = -7d-15

9d = -63

d = -7

a₁ = = -78-16(-7)

a₁ = 34

Therefore, nth term =

aₙ = a₁ + (n-1)d

aₙ = 34+(n-1)(-7)

aₙ = 34-7n+7

aₙ = 41-7n

Hence, the rule for the nth term of the given arithmetic sequence is given by aₙ = 41-7n

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Using the given ratio 3:4, Zali has 3 marbles and Muthu has 4 marbles.

If Muthu gives half of his marbles to Zali, Muthu would have 2 marbles (4/2 = 2) and Zali would have 5 ( 3+2 = 5). The ratio would now be 5:2

Answer: 5:2

The smaller angle formed by the hands of a clock at the following time.

1:25 is 42.5 degrees and 107.5 degrees

360 degrees

We need to find the angles of clock at 1:25

At 1:25, the hour hand has moved 85 out of 720 possible times from the top of the clock. 85 times 0.5 degrees is 42.5 degrees.

At 1:25, the minute hand has moved 25 out of 60 possible times from the top of the clock. 25 times 6 degrees is 150 degrees.

150 - 42.5 = 107.5 degrees

Therefore the smaller angle formed by the hands of a clock at the  time 1:25 is 42.5 degrees and 107.5 degrees

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Answer:

okay i'll keep this in mind

Step-by-step explanation:

Answer:

use the quadratic formula, factor it

By graph, the solution of the system of equations is (- 1, - 3).

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The system of equations are,

⇒ y - 2x - 1

⇒ y = - 3x - 6

Now, We can draw the graph of given system of equations.

The red line shows the graph of y = 2x - 1 and blue line shows the graph of y = - 3x - 6.

So, By graph;

Both equations are cut into at point (- 1 , - 3).

Hence, By graph, the solution of the system of equations is (- 1, - 3).

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The false statement from the stem-and-leaf plot is given as follows:

b. The data for Paul’s group has two modes.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The mode of a data-set is the data-set that appears the most times in a data-set.

Hence, for Paul's group, the mode is given as follows:

44.

As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.

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Answer:

50 items were sold for $75

35 items were sold for $90

Step-by-step explanation:

75 x 50 = 3750

90 x 35 = 3150

3750 +3150 = 6,900

Answer:

Step-by-step explanation:

Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.

Answer:

Step-by-step explanation:

Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.

Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

Answer: 3/4 is greater than 1/2  

                                   >

Step-by-step explanation:

Using the t-distribution, it is found that the proportion in a t-distribution less than −1.4 if the samples have sizes n1=30 and n2=40 is of 0.083.

The proportion is found using a calculator, with three inputs:

In this problem, we have a left-tailed proportion, as we want the proportion that is less than a value, with test statistic t = -1.4 and 30 + 40 - 2 = 68 df, hence the proportion is of 0.083.

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Answer:

Step-by-step explanation:                                                                                                              

ZXVCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

Answer:

x = 20

Step-by-step explanation:

The two angles inside the triangle added together equals the one other angle that's outside the triangle. Its called an exterior angle.

42° + 5x + 4 = 7x + 6

combine like terms

5x + 46 = 7x + 6

subtract 5x

46 = 2x + 6

subtract 6

40 = 2x

divide by 2

20 = x

To solve the system of equations:

We need to choose two sets of two equations and eliminate the same variable from those to get a 2 by 2 system that we can solve. If we choose the first and second equation and multiply the first one by -6 we get:

Now we add the equation to get:

Now we choose the second and third equation and change the sign of the second equations, then we get:

Adding them we have:

Now we have the system:

To solve it we mutiply the first equation by 7 and the second one by -13, then we have:

Adding this equation we have:

Now that we have the value of x we plug it in the second equation for the 2 by 2 system to get y:

Finally to find z we plug the value of x and y in the first equation of the original 3 by 3 system, then:

Therefore the solution of the system is:

The number of Jim's model car is 48

From the question, we have the following parameters that can be used in our computation:

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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To create a spider plot showing the effect on profit of varying the availability of resources, follow these steps:

1. Start by setting up your base-case values for each resource. This will be the starting point for your spider plot.

2. Next, create a series of data points for each resource by varying its availability between 90% and 110% of the base-case value in 2% increments. For example, if the base-case value for a resource is 100, you would create data points at 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, and 110.

3. Plot these data points on a spider plot, with the base-case value at the center and the varying values radiating outwards. Each resource should have its own line or "spider leg" on the plot.

4. Finally, add labels and a legend to your spider plot to make it easy to understand which resource is represented by each line and what the varying values mean.

By following these steps, you can create a spider plot that clearly shows the effect on profit of varying the availability of resources.

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Answer:

x = 49

Step-by-step explanation:

Since the line is parallel, the value of 2x - 8 is equal to 90.

=> 2x - 8 = 90

=> 2x = 98

=> x = 49

Answer:

x = 49

Step-by-step explanation:

2x - 8 and the right angle are corresponding angles and are congruent , then

2x - 8 = 90 ( add 8 to both sides )

2x = 98 ( divide both sides by 2 )

x = 49

The angle A for the given triangle will be 65°.

What is a triangle's definition?

In geometry, triangles have three sides and three vertices. This two-dimensional figure has three straight sides. A triangle is a three-sided polygon. The total of three triangle angles equals 180°. The triangle is enclosed by only one plane. Triangles are classified into three different categories based on their sides.

Scalene Triangle - The length of each side varies.

Isosceles Triangle - A triangle having two equal-length sides and one that is not.

Equilateral Triangle - A triangle with three sides of equal length.

Now,

let the right angle is at B

then AC=hypotenuse and AB=Base

then cos A=B/H=8/19

cosA=0.4210

∠A=65°

hence,

          The angle A for the given triangle will be 65°.

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The correct options are \(x^{2}\) – 4 = 0 and 4 \(x^{2}\)  = 16.

What is Algebraic expression ?

An algebraic expression is a mathematical expression that contains one or more variables, as well as numbers and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. It represents a mathematical relationship or rule and can be used to describe or represent quantities that can vary.

The equations that are true for x = -2 and x = 2 are:

\(x^{2}\)  – 4 = 0

This equation becomes (-2)2 - 4 = 0, which simplifies to 4 - 4 = 0, and it is true.

4 \(x^{2}\)  = 16

This equation becomes 4(-2)2 = 16, which simplifies to 4(4) = 16, and it is also true.

So, the correct options are:

\(x^{2}\)  – 4 = 0

4 \(x^{2}\)  = 16

Note: The other options are not true for x = -2 and x = 2. For example, x2 = -4 is not true for real numbers since the square of a real number cannot be negative. 3x2 + 12 = 0 is not true for x = -2 and x = 2, as it becomes 3(-2)2 + 12 = 0 which simplifies to 12 + 12 = 0, which is false. And 2(x - 2)2 = 0 is not true for x = 2, as it becomes 2(2 - 2)2 = 0, which simplifies to 0 = 0, and it is true, but it is not true for x = -2.

So, the correct options are  \(x^{2}\)  – 4 = 0 and 4 \(x^{2}\)  = 16.

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The cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

To find the cost of one hosta and one geranium, we can set up a system of equations based on the given information.

Let's assume the cost of one hosta is represented by 'h' and the cost of one geranium is represented by 'g'.

From the information given, we can set up the following equations:

Eugene's spending:

18h + 6g = $150

Jessica's spending:

7h + 16g = $113

We can now solve this system of equations to find the values of 'h' and 'g'.

Multiplying the first equation by 2 and the second equation by 3 to eliminate 'g', we get:

36h + 12g = $300

21h + 48g = $339

Now, we can subtract the second equation from the first to eliminate 'h':

(36h + 12g) - (21h + 48g) = $300 - $339

36h - 21h + 12g - 48g = -$39

15h - 36g = -$39

Simplifying further, we have:

15h - 36g = -$39

Now we can solve this equation for 'h' and substitute the value back into any of the original equations to find 'g'.

Let's solve for 'h':

15h = 36g - $39

h = (36g - $39) / 15

Substituting this value of 'h' into Eugene's equation:

18[(36g - $39) / 15] + 6g = $150

(648g - $702) / 15 + 6g = $150

648g - $702 + 90g = $150 * 15

738g - $702 = $2250

738g = $2250 + $702

738g = $2952

g = $2952 / 738

g ≈ $4

Now, substituting the value of 'g' back into Eugene's equation:

18h + 6($4) = $150

18h + $24 = $150

18h = $150 - $24

18h = $126

h = $126 / 18

h ≈ $7

Therefore, the cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

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Therefore, in response to the given query, we can state that R(-1)'s inequality possible spectrum is thus: [0, 10]

A connection between two expressions or numbers that is not equivalent in mathematics is referred to as an inequality. Thus, disparity results from inequity. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and disparity are not the same. Use the not equal sign most frequently when two numbers are not identical. (). Values of any size can be contrasted using a variety of disparities. By changing the two sides until only the factors are left, many straightforward inequalities can be answered. However, a number of factors support inequality: Both parts' negative numbers are divided or added. Exchange the left and the right.

The equation can be used to describe the candle's length, R(t):

R(t) = 11 - 1.1t

where t represents how long the light has been burning, in hours.

We must determine t in terms of R in order to determine the negative of R(t):

R = 11 - 1.1 t = (11 - R)/1.1 t = (11 - R)

R(t)'s inverse function is thus:

\(R^{(-1)}(R) = (11 - R)/1.1\)

0 ≤ R ≤ 11

So, R(-1)'s scope is as follows:

[0, 11]

0 ≤ R ≤ 11

Inputting these limits into the equation for R(-1) yields the following results:

\(R^{(-1)}(0) = 11/1.1 = 10\\R^{(-1)}(11) = 0/1.1 = 0\)

R(-1)'s possible spectrum is thus:

[0, 10]

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