Find The Sum or Difference
(-6x – 3) + (3x – 9)

Answer:

y < -4/3 or y > 4/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the function

f(x) = 2x3 − 6x2 − 18x − 4 on the interval [-10, 10]

At the end point x = -10

f(-10) = 2(-10)³ − 6(-10)² − 18(-10) − 4

f(-10) = 2(-1000)-6(100)+180-4

f(-10) = -2000-600+176

f(-10) = -1824

At the end point x = 10

f(10) = 2(10)³ − 6(10)² − 18(10) − 4

f(10) = 2(1000)-6(100)-180-4

f(10) = 2000-600-184

f(10) = 1400-184

f(10) = 1216

Hence the absolute minimum is at f(x) = -1824 and maximum is at f(x) = 1216

The solutions to the equation 1x² - 16x = 20 are x = 8 + 2√21 and x = 8 - 2√21.

To solve the quadratic equation 1x² - 16x = 20, we need to rearrange it into the standard form ax² + bx + c = 0. Let's simplify the equation step by step:

1x² - 16x = 20

First, move all terms to one side of the equation:

1x² - 16x - 20 = 0

Now we have a quadratic equation in the standard form. To solve it, we can use factoring, completing the square, or the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 1, b = -16, and c = -20. Substituting these values into the quadratic formula:

x = (-(-16) ± √((-16)² - 4(1)(-20))) / (2(1))

Simplifying further:

x = (16 ± √(256 + 80)) / 2

x = (16 ± √336) / 2

x = (16 ± √(16 * 21)) / 2

x = (16 ± 4√21) / 2

Simplifying:

x = 8 ± 2√21

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Answer:

i can't really see to clear ..

Step-by-step explanation:

Reflection is a rigid transformation in which the shape, the size, and the angles remain the same. Therefore, the reflection will be a figure of the same shape, but an image that will be symmetrical to the preimage.

Something like this:

Nikki can use modern portfolio theory to assess the risk and return behaviors associated with different combinations of assets X and Y.

Modern portfolio theory involves calculating the expected return and risk of a portfolio of assets by analyzing the correlations between the assets. It also looks at the diversification benefits of combining different assets and the impact of adding riskier assets to a portfolio. By quantifying the risk and return behaviors of different portfolios, Nikki can make informed decisions about which portfolios are most suitable for her.Modern portfolio theory is used to assess the risk and return behaviors of different combinations of assets X and Y. It considers correlations between the assets, the diversification benefits of combining them, and the impact of adding riskier assets. By quantifying the risk and return behaviors, Nikki can make informed decisions about which portfolios are most suitable for her.

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If the graph of \(f(x) = 4e^{0.1x}\) is blue, then the graph of \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is: C. red.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

For the rate of change of the blue exponential function \(f(x) = 4e^{0.1x}\), we have the following:

b = \(e^{0.1}\)

b = 1.11

For the rate of change of this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\), we have the following:

b = 1 + 0.1/0.5

b = 1.2

Therefore, this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is represented by the red line on the graph.

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When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

9/25

Step-by-step explanation:

3/10 * (6/7 + 12/35)

First put fractions in common denominators

3/10 * (30/35 + 12/35)

3/10 * 42/35   42/35 can be reduced to 6/5

3/10 * 6/5 = 18/50 = 9/25

Answer:

-17/12

Step-by-step explanation:

║5/6 - 7/12║- ║5/3║

= ║10/12 - 7/12║ - ║5/3║

= ║3/12║- ║5/3║

= 3/12 - 5/3

= 3/12 - 20/12

= -17/12

Answer:

$12=$60÷5. 12dollars is the answer

Answer:

Option A

Step-by-step explanation:

From the picture attached,

In the given triangles ABC and ADC,

m(∠B) = m(∠D) [Given]

AC ≅ CA [Reflexive property]

But in the absence of third property of congruence ΔABC and ΔADC can't be congruent.

Option A is the answer.

Answer: $80

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

i took the test

Answer:

\(\sqrt{72}\) or \(6\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{6}\times \sqrt{12}=\\\\\sqrt{6\times 12}= \\\\\sqrt{72}= \\\\6\sqrt{2}\)

Hope this helps!

Answer:

8.48 or 8.4

Step-by-step explanation:

the answer is 8.48528137424 but when you round it you get 8.48

You would need to deposit approximately $10,471.54.

To calculate the initial deposit needed to have $20,000 in an account after 20 years with continuous compounding at a 4.75% interest rate, we can use the formula for continuous compound interest:

\(A = P e^{(rt)\)

Where:

A = Final amount ($20,000 in this case)

P = Principal amount (initial deposit)

r = Interest rate (4.75% or 0.0475 as a decimal)

t = Time period in years (20 years in this case)

Rearranging the formula to solve for P:

\(P = A / e^{(rt)\)

Now we can substitute the given values and calculate the initial deposit:

\(P = $20,000 / e^{(0.0475\times20)\)

P = $20,000 / 1.9105 ≈ $10,471.54

Therefore, you would need to deposit approximately $10,471.54 into the account initially to have $20,000 after 20 years with continuous compounding at a 4.75% interest rate.

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Answer:

2.3 hours

Step-by-step explanation:

From 3:12 pm to 4:12 pm, one hour passes.

From 4:12 pm to 5:12 pm, another hour passes.

From 5:12 pm to 5:30 pm, there are 18 minutes that pass.

Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.

To convert this to a fraction, we can write:

2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours

So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.

Answer:

\(t = \frac{3sr}{2a \ + \ 5s}\)

Step-by-step explanation:

Given expression;

\(S = \frac{2at}{3r - 5t}\)

To make "t" the subject of the formula, cross and multiply;

\(S(3r - 5t) = 2at\\\\\)

open the bracket;

3sr - 5st = 2at

collect like terms together;

3sr = 2at + 5st

Factor out "t" on the right hand side;

3sr = t(2a + 5s)

Finally, make "t" the subject of the formula by dividing both sides by (2a + 5s).

\(t = \frac{3sr}{2a \ + \ 5s}\)

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Answer:

Data set 1

Step-by-step explanation:

Because for every x there is only one y

The data that are function are:

Data set 3 and Data set 1.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

A function can be one-to-one or onto.

This means,

one-to-one:

For every x value, there is only one y value.

Onto:

Every element in the range of the function corresponds to at least one element in the domain of the function.

Now,

Data set 2 is not a function because we have,

x = 1 have y = 6 and 4.

Since

Different x values can have the same y value.

So,

Data set 3 and Data set 1 is a functions.

Thus,

Data set 3 and Data set 1 is a functions.

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Answer: 2.15

Step-by-step explanation:

Consider the thousandths place being 0, because 0 is less than 5, you don't change the hundredths place. Therefore leaving 2.15.

8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

Answer:

We can write sin x in terms of tan x/2 using the formula:

⇒ sin x = (2 tan (x/2)) / (1 + tan2(x/2))

Therefore, using the above formula, we can find the values of tan x/2 by putting the value of sin x.

⇒ -4/5 = (2 tan (x/2)) / (1 + tan2(x/2))

Now, if we replace tan (x/2) by y, we get a quadratic equation:

⇒ 0.8y2 + 2y + 0.8 = 0

⇒ 2y2 + 5y + 2 = 0

By using the quadratic formula, we get y = -0.5, -2

Hence, the value of tan (x/2) = -0.5, -2

Now, we have two solutions of tan (x/2).

Now, let's check for the ideal solution using the formula tan x = (2 tan (x/2)) / (1 - tan2(x/2)).

For tan (x/2) = -0.5:

⇒ tan x = 2(-0.5) / 1 - (-0.5)2 = -4/3

It is also given that x lies in the third quadrant. We know that tan is positive in the third quadrant, and here we get tan x = -4/3 which is negative.

Hence, we can say that tan (x/2) = -0.5 is not a correct solution. Hence it is rejected.

Now let's check for tan (x/2) = -2.

⇒ tan x = 2(-2) / 1 - (-2)2 = 4/3

Here, we get tan x = 4/3 which is positive.

Hence, we can say that tan (x/2) = -2 is a correct solution.

Step-by-step explanation:

so, the 1 yard is split into 6 equal parts.

each small square has therefore an area of 1/6 × 1/6 yard² = 1/36 yard²

the shaded area is 4×3 = 12 small squares large.

is area is therefore

12 × 1/36 = 1/3 yard²

since 1 yard = 3 ft, 1 × 1 = 1 yard² = 3 × 3 ft² = 9 ft².

and 1/3 yard² = 1/3 × 9 ft² = 3 ft²

so, whatever dimension you need.

the area is

1/3 yard² = 3 ft²

Answer:

The logs do not form a right-angle triangle

Step-by-step explanation:

Given

\(Logs: 9ft, 11ft, 21ft\)

Required

Do the logs form a right-angled triangle

Applying Pythagoras theorem

\(a^2 = b^2 + c^2\)

Where a is the length of the longest log.

So, we have:

\(21^2 = 9^2 + 11^2\)

\(441 = 81 + 121\)

\(441 \ne 202\)

The above shows an inequality.

Hence, the logs do not form a right-angle triangle