If this net where folded into a cube,which number would be opposite the number 1

The coordinates of the figure following the composite transformation, which includes a translation and dilation transformation are;

A''(6, 24)

B''(6, 12)

C''(-12, 18)

A composite transformation consists of performing two or more transformation on a geometric figure, such as a translation and a dilation.

The coordinates of the figure are; A(-3, 3), B(-1, 1), C(-4, 2)

The transformation are; Translation <2, 1>, and a dilation of K = 6, (About the origin)

Therefore, we get the following transformation;

Translation <2, 1>

A(-3, 3) ⇒ A'(-3 + 2, 3  + 1) = A'(-1, 4)

B(-1, 1) ⇒ B'(-1 + 2, 1 + 1) = B'(1, 2)

C(-4, 2) ⇒ C'(-4 + 2, 2 + 1) = C'(-2, 3)

Dilation by a scale factor of 6;

A'(-1, 4) ⇒ A''6 × (-1, 4) = A''(-6, 24

B'(1, 2) ⇒ B'' 6 × (1, 2) = B''(6, 12)

C'(-2, 3) ⇒ C'' 6 × (-2, 3) = C''(-12, 18)

Therefore, the coordinates of the image of the figure, following the translation and dilation are; A''(-6, 24), B''(6, 12), C''(-12, 18)

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The roots of the equation \((x^2 + 1)(x^3 + 2x)(x^2 - 64)\) = 0 are x = ±i, ±√(-2), 0, 8, -8.

To find the roots of the equation \((x^2 + 1)(x^3 + 2x)(x^2 - 64)\) = 0, we can use the zero-product property, which states that if a product of factors equals zero, then at least one of the factors must be equal to zero.

So, we'll set each factor equal to zero and solve for 'x':

1. \(x^2 + 1\) = 0

  Subtracting 1 from both sides:

 \(x^2\) = -1

  Taking the square root of both sides:

  x = ±√(-1)

  Since the square root of a negative number is not defined in the real number system, the solutions to this equation are complex numbers.

  Therefore, the roots for this factor are:

  x = ±i (where i represents the imaginary unit)

2. \(x^3 + 2x\) = 0

  Factoring out 'x':

\(x(x^2 + 2)\) = 0

  Applying the zero-product property:

  x = 0 (one root)

  Also, \(x^2 + 2\) = 0

  Subtracting 2 from both sides:

  \(x^2\) = -2

  Taking the square root of both sides:

  x = ±√(-2)

  Again, the solutions to this equation are complex numbers.

  Therefore, the roots for this factor are:

  x = ±√(-2)

3.\(x^2 - 64\) = 0

  This is a quadratic equation, so we can solve it by factoring:

  (x - 8)(x + 8) = 0

  Applying the zero-product property:

  x - 8 = 0  or  x + 8 = 0

  x = 8  or  x = -8

Combining all the roots from each factor, we have:

x = ±i, √(-2), 0, 8, -8

The solutions to the equation \((x^2 + 1)(x^3 + 2x)(x^2 - 64)\) = 0, including all real and complex numbers are x = ±i, √(-2), 0, 8, -8.

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Answer:

A) Decreasing

Step-by-step explanation:

By graphing the logarithmic equation, we can see that as the x value increases, the y value decreases. Therefore, we say that the graph is decreasing.

Answer:

decreasing

Step-by-step explanation:

Answer:

(2x- 3)(X+3)

Step-by-step explanation:

For a polynomial of the form ax2+bx+c a x 2 + b x + c , rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅−9=−18 a ⋅ c = 2 ⋅ - 9 = - 18 and whose sum is b=3 . Factor 3 3 out of 3x 3 x . Factor out the greatest common factor from each group. Group the first two terms and the last two terms.

Answer:

1: (0,3)

2: (-4,-2)

3: (-1,-5)

4: (4,0)

Step-by-step explanation:

An initial investment of $5,951.71 is needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly.

To determine the amount of money needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly, we need to use the formula for compound interest.

The formula is A = P(1+r/n)^(nt), where A is the final amount, P is the initial investment, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

Using the given information, we can plug in the values and solve for P. A = $7,000, r = 0.025, n = 4, and t = 4.

A = P(1+r/n)^(nt)

A = P(1+0.025)^4
$7,000 = P(1+0.025/4)^(4*4)
$7,000 = P(1.00625)^16
P = $5,951.71
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Answer:

3787000

Step-by-step explanation:

360*1/9=40 - skilled workers

360-40=320- the quantity of unskilled

6*13500=81000- wage for six unskilled

(320-6)*9000= 314*9000= 2826000- wage for the rest of unskilled

2826000+81000= 2907000- wage for unskilled

40/2=20 - the half on skilled

20*19500= 390000- Payment for a half

20*24500= 490000- Payment for ANOTHER HALF OF SKILLED WORKERS

2907000+390000+490000= 3787000

Answer:

Verified

Explanation:

Given the identity:

We apply the following identity:

Therefore:

Thus, the identity is verified since both sides of the identity are equal.

When the area in the first quadrant bordered by x=0, y=1, x=y4, and y=10 is rotated about the line y=10, the solid's volume is 11π/3

We using,

V = π ∫|(f(x) - d) 2 - (g (x) - d) 2|dx Integrating from a to b

For this case, a = 0, b = 1, g(x) = 1, f(x) = x1/4

Simplifying the equation,

V = π∫|(x1/4 - 10) 2 - (1 - 10) 2dx = π∫|x1/2 - 20x1/4 + 100 - 81|dx

= π[(2/3) x 3/2 - 20(4/5) x 5/4 + 19x] evaluated from at 1 and 0

= π|(2/3 -16 +19) = 11π/3

The complete question is?

find the volume of the solid obtained by rotating the region in the first quadrant bounded by x=0, y=1, x=y^4 about the line y=10

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The following results by product rule and quotient rule are listed below:

The following results by chain rule are listed below:

In this part we must apply the following rules to calculate the derivatives:

\(\frac{d}{dx}[f(x)\cdot g(x)] = f'(x) \cdot g(x) + f(x) \cdot g'(x)\)   (1)

\(\frac{d}{dx}\left[\frac{f(x)}{g(x)} \right] = \frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{[g(x)]^{2}}\)   (2)

Now we proceed to obtain each expression:

1) \(f'(x) = 3\cdot x\cdot (x-6)+3\cdot x-9\)

\(f'(x) = 3\cdot x^{2}-15\cdot x - 9\) \(\blacksquare\)

2) \(f'(x) = \left(\frac{9}{4}\cdot x^{2}-4\cdot x+\frac{1}{4}\right)\cdot (2\cdot x^{2}-2\cdot x + 4) + \left(\frac{3}{4}\cdot x^{3}-2\cdot x^{2}+\frac{x}{4}-6\right)\cdot (4\cdot x-2)\)

\(f'(x) = \frac{9}{2}\cdot x^{4}-8\cdot x^{3}+\frac{1}{2}\cdot x^{2}-\frac{9}{2}\cdot x^{3}+8\cdot x^{2}-\frac{x}{2}+9\cdot x^{2}-16\cdot x+1 +3\cdot x^{4}-8\cdot x^{3}+x^{2}-24\cdot x-\frac{3}{2}\cdot x^{3}+4\cdot x^{2}-\frac{x}{2} +12\)

\(f'(x) = \left(\frac{9}{2}+3 \right)\cdot x^{4}+\left(-8-\frac{9}{2}+8-\frac{3}{2} \right)\cdot x^{3} + \left(\frac{1}{2}+8+9+1+4 \right)\cdot x^{2} + \left(-16-24-\frac{1}{2} \right)\cdot x + \left(1+12\right)\)

\(f'(x) = \frac{15}{2} \cdot x^{4}-6\cdot x^{3}+\frac{45}{2}\cdot x^{2}-\frac{81}{2} \cdot x +13\)   \(\blacksquare\)

3) \(f'(x) = \frac{-9\cdot (5\cdot x^{2}-8)-(-9\cdot x+4)\cdot (10\cdot x)}{(5\cdot x^{2}-8)^{2}}\)

\(f'(x) = \frac{-45\cdot x^{2}+72+90\cdot x^{2}-40\cdot x}{25\cdot x^{4}-80\cdot x^{2}+64}\)

\(f'(x) = \frac{90\cdot x^{2}-45\cdot x^{2}-40\cdot x +72}{25\cdot x^{4}-80\cdot x^{2}+64}\)   \(\blacksquare\)

4) \(f'(x) = \frac{\left(9\cdot x^{2}-18\cdot x-6\right)\cdot \left(\frac{x^{2}}{2}+7\cdot x-8 \right)-\left(3\cdot x^{3}-9\cdot x^{2}-6\cdot x +1 \right)\cdot \left(\frac{2}{3}\cdot x+7 \right)}{\left(\frac{x^{2}}{2}+7\cdot x-8 \right)^{2}}\)   \(\blacksquare\)

Let be a function of the form \(f[u(x)]\), the derivative of this function is defined by the following rule:

\(\frac{d}{dx}[f[u(x)]] = \frac{df}{du}\cdot \frac{du}{dx}\)

Now we proceed to present the following results:

1) \(f'(x) = 3\cdot (2\cdot x^{2}-2\cdot x +1)^{2}\cdot (4\cdot x-2)\)   \(\blacksquare\)

2) \(f'(x) = \frac{15\cdot x^{2}-16\cdot x+9}{2\cdot \sqrt{5\cdot x^{3}-8\cdot x^{2}+9\cdot x-6}}\)   \(\blacksquare\)

3) \(f'(x) = \frac{2}{3}\cdot \left(3\cdot x^{2}-\frac{2}{3}\cdot x+x^{-4} \right)^{-\frac{1}{3} } \cdot \left(6\cdot x-\frac{2}{3} -4\cdot x^{-5} \right)\)   \(\blacksquare\)

\(f'(x) = \frac{2\cdot \left(6\cdot x-\frac{2}{3}-4\cdot x^{-5} \right)}{3\cdot \sqrt[3]{3\cdot x^{2}-\frac{2}{3}\cdot x +x^{-4} } }\)   \(\blacksquare\)

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Let's recall that:

1 kilometer/hour = 0.2778 meters/second

Therefore,

100 kilometers/hour = 0.2778 * 100

100 kilometers/hour = 27.78 meters/second

Answer:

value preferred stock for $65,250 cash

The inverse of the function f(x) = x + 4 is given as f⁻¹(x) = x - 4

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, the function given is f(x) = x + 4;

We can find the inverse of the function as;

y = x + 4;

Let's switch the variables by replacing x as y and y as x;

x = y + 4

Solving for y;

y = x - 4

f⁻¹(x) = x - 4

The graph of the function is attached below

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Answer:

The answer is "\(\bold{\frac{1}{4}<k\leq 2+\sqrt{3}}\)"

Step-by-step explanation:

Given:

\(\ S_1 = k \\\\ S_{n+1} = \sqrt{4S_n -1}\)   \(_{where} \ \ n \geq 1\)

In the above-given value, \(S_n\) is required for the monotone decreasing so, \(S_2 :\)

\(\to \sqrt{4k-1} \leq \ k=S_1\\\\\)

square the above value:

\(\to k^2-4k+1 \leq 0\\\\\to k \leq 2+\sqrt{3} \ \ \ \ \ and \ \ 4k+1 >0\\\\\)

\(\bold{\boxed{\frac{1}{4}<k\leq 2+\sqrt{3}}}\)

So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

The slope of the line passing through points A and B can be calculated as follows:

slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1

The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

To find the y-intercept, we can use point A (0,0) and substitute the slope value.

y = mx + b

0 = 1(0) + b

b = 0

Therefore, the equation of the line passing through points A and B is:

y = 1x + 0

Simplifying, we get:

y = x

So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:

y - 0 = 1(x - 0)

y = x

This confirms our earlier answer.

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Answer: 4

This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.

4/5 ÷ 1/5

Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:

4/5 x 5

To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.

You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.

Hope this helps!

Answer:

B) in the modern art section of an art museum

Step-by-step explanation:

Hope it helps! =D

He have to calculate the Probability of Two Consecutive Events Occurring Together:

We know that:

Probability of event 1 - P1 (being nominated): 40% or 40/100 = 4/10

Probability of event 2 - P2 (being chosen): 70% or 70/100 = 7/10

To calcule the Probability of Two Consecutive Events Occurring Together:

The probability that a student is nominated for the Posse AND chosen to interview is 28%.

Answer:

-2x+10x^2 > -x-2

Step-by-step explanation:

All you are doing is combining like terms to simplify your answer.

The graph of the linear equation can be seen at the end of the answer.

Here we just need to find two points on the line, and then connect them with a line.

The equation is:

y = -x

To find the two points, we can evaluate in two values of x. I will use x = 0 and x = 2.

when x = 0:

y = -0 = 0

So we have the point (0, 0).

When x = 2:

y = -2

Then we have the point (2, -2).

Now we can just graph these two points and connect them with a line. The graph of the linear equation can be seen below:

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=>−5x+3y+−3y=5+−3y

=>−5x=−3y+5

\( \sf \: = > \dfrac{ - 5x}{ - 5} = \dfrac{ - 3y + 5}{ - 5} \)

x=3/5 y - 1

\( \frac{3}{5} y - 1\)

Answer:

x = \(\frac{3}{5}\) y - 1

Step-by-step explanation:

3y - 5x = 5 ( subtract 3y from both sides )

- 5x = - 3y + 5 ( divide through by - 5 )

x = \(\frac{3}{5}\) y - 1

Answer:

1780.43

Step-by-step explanation:

Given:

P = 800

r = 10% or 0.1

t = 8

The value of tan 2π/3 without calculator is -√3.

The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;

the value of π = 180 degrees

So we can replace the value of π in the function with 180 degrees as follows;

tan ( 2π / 3) = tan (2 x 180 / 3)

tan (2 x 180 / 3) = tan (2 x 60)

tan (2 x 60) = tan (120)

tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.

tan (120) = - tan (180 - 120)

= - tan (60)

= -√3

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Answer:

50 days

Step-by-step explanation:

So she gets 5,000 for five days.  

Let's count up from 5 thousand until 50 thousand.

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

50,000

This means 5,000x10=50,000

10x5=50

The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

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

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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Answer:

B

Step-by-step explanation:

perimeter is adding all sides. 4 sides. So option B.

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Deductive Reasoning.

What's the difference between inductive and deductive reasoning?

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down. Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

Examples-

Inductive Reasoning: The first lipstick I pulled from my bag is red. The second lipstick I pulled from my bag is red. Therefore, all the lipsticks in my bag are red.

Deductive Reasoning: The first lipstick I pulled from my bag is red.

A deductive approach involves the learners being given a general rule, which is then applied to specific language examples and honed through practice exercises. An inductive approach involves the learners detecting, or noticing, patterns and working out a 'rule' for themselves before they practise the language.

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

Thus ,I know I'll have to work a double shift today because I have a migraine and every time I have a migraine I get stuck pulling a double is and example of Deductive reasoning . Because a  deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

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Answer:

15 and -20

Step-by-step explanation:

The zeros/ roots are the x intercepts of the graph