Solve for x.
2(x - 6) - 3x ≥ - 3
Simplify your answer

Answer:188

Step-by-step explanation:

first multiply the seven in 47 by the 4, you would get 28.Drop the 8 carry the the 2.4 times 4 is 16 and the 2 to the 6 and get 18 then put the 8 from before following.

The largest value τ can have for a given value of a = 1/2\(\left| a \right|\). Where the said value is described as τmax.

To arrive at the above conclusion, let:

r(t) = (a cos t) i + (a sin t)j + btk, a, b ≥ 0

⇒ τ = b/(a² + b²)

Given the value of τ above, we have to find τmax for given values of a, so that a is constant.

Hence:

dτ/db = [(a² + b²) * 1 - b (2b)]/ (a² + b²)² = 0

a² + b² - 2b² = 0

a² + b² = 0

a² - b² = 0

a² = b²

Hence, τmax = b/a² + b² = \(\left| a \right|\)/2a²

= 1/ 2\(\left| a \right|\)

Thus, τmax = 1/2\(\left| a \right|\)

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Full Question:

Show That The Torsion Of The Helix

r(T) = (A Cos t)Ii + (A Sin T) J + Btk, A, B ≥ 0

Is τ = B/(A2 + B2).

What Is The Largest Value τ can have for a given value of a?

The water pipe sometimes bursts in winter because of the flowing water getting transformed into freezing water due to drop in temperature and the volume increases creating more pressure on the wall pipes.

Bursting of Water Pipes During a Very Cold Winter

The straightforward explanation is that during very cold winters, as water freezes into ice, it expands, causing solid ice to fill a larger volume than the liquid that was previously flowing through the pipes.

As we know that, the pressure P increases with increase in volume, V, the increased volume of frozen water leads to increase in the pressure inside the pipe.

The pressure that the ice builds up inside the pipes could rupture the pipe walls.

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After 15 hours there will be 1.875 grams of the radioactive tellurium.

We know that the half-life of a radioactive kind of tellurium is 3 hours.

This means that for any quantity A of that radioinuclei, after 3 hours we will have half of that amount.

Then we can write the exponential equation:

M(x) = A*(1/2)^(x/3h)

Here we start with A= 60 grams, and after 15 hours we will have:

M(15h) = 60g*(1/2)^(15h/3h)

M(15h) = 60g*(1/2)^(5) = 1.875 g

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Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

▪︎▪︎▪︎▪︎▪︎▪︎

The two variables are expected to vary together in both correlation and regression. the correct option is - Both.

Correlation and regression are two closely related topics in statistics. Correlation refers to the Pearson product-moment correlation coefficient (r), and regression is with one predictor variable only (often referred to as simple regression).

Can tell you whether one variable (such as smoking) causes another (such as cancer) - Neither Provides a way to predict a specific value of one variable (such as weight) from the value of another variable (such as height) - Regression Requires a measure of how the two variables vary together - Both  Correlation can indicate the degree of association between two variables, but it doesn't imply causation.

Regression can help predict a particular value of one variable based on the value of another variable.

The two variables are expected to vary together in both correlation and regression. Therefore, the correct option is - Both.

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Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'

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The solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.

The equation 4x^2 - 20x + 25 = 10 can be rewritten as 4x^2 - 20x + 15 = 0. To find the solutions to this equation, we can factor it or use the quadratic formula.

The equation factors as (2x - 5)(2x - 3) = 0. Setting each factor equal to zero, we get 2x - 5 = 0 and 2x - 3 = 0. Solving these equations, we find x = 5/2 and x = 3/2.

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± sqrt(b^2 - 4ac)) / 2a, we can determine the solutions.

In this case, a = 4, b = -20, and c = 15. Substituting these values into the quadratic formula, we get x = (-(-20) ± sqrt((-20)^2 - 4 * 4 * 15)) / (2 * 4), which simplifies to x = (20 ± sqrt(400 - 240)) / 8.

Simplifying further, we have x = (20 ± sqrt(160)) / 8, which becomes x = (20 ± 4sqrt(10)) / 8. Finally, simplifying again, we obtain x = 5/2 ± sqrt(10)/2, which gives us the same solutions as before: x = 5/2 and x = 3/2.

Therefore, the solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.

To find the solutions to the equation, we can either factor it or use the quadratic formula. In this case, factoring and using the quadratic formula both yield the same solutions: x = 5/2 and x = 3/2. These values of x satisfy the equation 4x^2 - 20x + 25 = 10 when substituted back into the equation.

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The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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Answer:

Step-by-step explanation:

The fraction of the female birds is:

Answer:

159.25 ft²

I hope this helps! :)

Step-by-step explanation:

Formulas:

For the Rectangle... bh = a

For the Semicircle... 1/2 × πr²

Step 1:

Solve the area for the rectangle:

bh = a

10 × 12 = 120

a = 120 ft²

Step 2:

Solve the Area for the Semicircle:

1/2 × πr²

1/2 × 3.14 = 1.57

Radius = Diameter ÷ 2

10 ÷ 2 = 5

Radius = 5

1.57 × 5²

1.57 × 5 × 5

= 39.25 ft²

Step 3:

Add the two areas together:

120 + 39.25 = 159.25 ft²

Answer:

\(y=\frac{1}{2}x\)

Step-by-step explanation:

Slope-intercept form: y = mx + b

Slope formula: \(\frac{y2-y1}{x2-x1}\)

Given points: (2, 1), (-4, -2)

(2, 1) = (x1, y1)

(-4, -2) = (x2, y2)

To write the equation in slope-intercept form we need to find the slope(m) and the y-intercept(b) of the equation.

First, let's find the slope. To do this, input the given points into the formula used to find slope:

\(\frac{-2-1}{-4-2}\)

Simplify:

-2 - 1 = -3

-4 - 2 = -6

\(\frac{-3}{-6} =\frac{1}{2}\)

The slope is \(\frac{1}{2}\). We can input the slope and one of the given points (in this example I'll use point (2, 1)) into the equation to find b:

\(1= \frac{1}{2}(2)+b\)

1 = 1 + b

0 = b

The y-intercept is 0. Now that we know the slope and the y-intercept, we can write the equation:

\(y = \frac{1}{2}x+0\)

\(y=\frac{1}{2}x\)

Using the tables to answer the question, the correct option is D.

Only table B represents a function

A relation/table will represent a function if each value of x is attached to a unique value of y.

That is, no value of x must be mapped to more than one value of y.

By considering the tables represented

Set A = {(-5, 2), (-8, 5), (-5, 8)}

As clearly shown above, when x = -5, y = 2 and 8. This means that there are more than 1 value of y for a single value of x, therefore, table A does not represent a function.

Set B = {(-5, 2), (-8, 5), (-11, 2)}

As shown above, all values of x have different values of y. Therefore, table B represents a function.

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Answer:

It is False

Hey bro Good Luck for exams!

Step-by-step explanation:

I think it's answer is false

Answer:

3.32 g

Step-by-step explanation:

1.10

2.22  

---------

3.32

(As both the numbers, have the same number of digits, you just need to add them like you do normal addition)

Answered by Guathmath

Answer:

#1

Factoring the function:

f(x) = x3 + 7x2 + 14x + 8

f(x) = (x + 4) (x + 1) (x + 2)

From the options, (x + 2) is the factor

#2

f(x) / g(x) = (6x3 - 19x2 + 16x - 4) / (x - 2)

This can be solved by factoring the numerator, by synthetic division or using the remainder theorem.

The result is:

6x^2 - 7x + 2 or (x - 2/3)(x - 1/2)

#3 same with #2

#4

(x3 - 5x2 + 2x + 5) / (x - 2)

Again, this can be solved by a number of methods, the result is:

x2 -3x - 4 - (3/x-2)

Step-by-step explanation:

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Since 7 is larger than 3, the point (1, -4) and every other point below the line satisfy the inequality. 

A relationship between two values, expressions, or variables that shows one to be larger than, less than, or not equal to the other is known as an inequality in mathematics. The characters "" (less than), ">" (greater than), "=" (less than or equal to), "> and "!=" can be used to denote an inequality (not equal to). For instance, the inequality "y = 10" denotes that the number y is less than or equal to 10. Inequalities are frequently used in algebra, athm, and other disciplines of mathematics to describe relationships between various mathematical objects, to set requirements for the correctness of particular solutions or functions, as well as to solve issues in a variety of fields including

given

A faint line on the graph has a y-intercept of -3 and a slope of 3. This indicates that the value of y decreases by 3 for every unit increase in x.

Any point on one side of the line can now be plugged into the inequality to determine whether it meets it.

Selecting the spot (1, -4), which is below the line, shall be done.

When we enter the condition 3x - y > 3 with the values x=1 and y=-4, we get:

3(1) - (-4) > 3

3 + 4 > 3

7 > 3

Since 7 is larger than 3, the point (1, -4) and every other point below the line satisfy the inequality. Consequently, the graph's representation of the right inequality is 3x - y > 3.

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Answer:

the ratio would be 6:2 or 6/2. Yes, the ratio of sugar to flour change when I compare the single batch to the double batch.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Pie (π) is an infinite decimal where it goes on forever, and numbers do not repeat in a pattern.

For these reasons, you cannot get all the numbers of pie.

EXTRA

I can provide to you with some of the digits.

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006

Here you go!! :)

Answer:

137,257

Step-by-step explanation:

Answer:

137,527

Step-by-step explanation:

Looking at the plot, we can see that the stems range from 60 to 89, with each stem representing a group of ten pounds. The leaves represent the remaining single digits, indicating the exact weight of each tuna. There are 4 tuna that weigh less than 90 pounds

Based on the stem-and-leaf plot of the weights of yellowfin tuna caught during a fishing contest, we can count the number of tuna that weigh less than 90 pounds.

To determine the number of tuna that weigh less than 90 pounds, we need to look at the stems that are less than 9. This includes stems 6, 7, and 8. The leaves associated with these stems show the weights of the tuna that are less than 90 pounds. We can count the number of leaves associated with these stems to determine the number of tuna that weigh less than 90 pounds.

In this case, there are 4 tuna that weigh less than 90 pounds. Two of them weigh 88 pounds and the other two weigh 87 pounds. Therefore, we can conclude that there are 4 tuna that weigh less than 90 pounds in the fishing contest based on the stem-and-leaf plot.

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Answer:

18.4 if it is in square root

Step-by-step explanation:

it may help you to understand.

The solution to the inequality is: n < -9.

Given the inequality statement, 4n - 6 (n + 1) > 12, to solve for the value of n, we would isolate the n to one side of the inequality as shown below:

4n - 6 (n + 1) > 12

Distribute

4n - 6n - 6 > 12

Combine like terms

-2n - 6 > 12

-2n - 6 + 6 > 12 + 6

-2n > 18

Divide both sides by -2

-2n/-2 < 18/-2

n < -9

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

The number of hours in a week a student played basketball is \(11\frac{3}{8}\).

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.

Also given that 1/4 of the exercise of a student came from playing basketball.

Therefore, Time playing basketball is one-fourth of the total time exercised which is,

= (3 + 1/4)×(1/4).

= (13/4)×(1/4).

= (13/8).

Therefore, In a week the student played (13/8)×7.

= 91/8.

= \(11\frac{3}{8}\).

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Answer:

The answer is the last option.

Step-by-step explanation: