what is the simplified expression for -3(2x-y)+2y+2(x+y)?
A. 8x+y
B. y-4x
C. 7y-4x
D. -4x-y

Answer:

D,

Step-by-step explanation:

that's because you only factorise when you have a common factor, ax-3b cannot be factorised because they have nothing in common so it is wrong to use x to factorise it. If you want to be sure that it is not factorisable, try expanding it and you'll see that you will not get the same answer.

Using the concept of fraction and percentage, the percentage increase of the baby at 12 months is 177.7 percent

Percentage increase is a mathematical concept that refers to the increase in a particular value over its initial amount. It is usually expressed as a percentage and is calculated by dividing the increase in the value by the original amount, then multiplying by 100.

In this problem, the data given are;

The percentage increase at 12 months old can be calculated as

percentage increase = [(mass at 12 months - Initial mass) / Initial mass] * 100

percentage increase = [(10 - 3.6) / 3.6] * 100

percentage increase = 1.7 * 100

Percentage increase = 177.7%

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Answer: A

Step-by-step explanation:

Nothing you a bum

Answer:

nx∧(-3)

Step-by-step explanation:

Since it contains one term with the variable

9514 1404 393

Answer:

  ≈ (3.578, 5.789)

Step-by-step explanation:

We can substitute for y and solve for x.

  (x -h)^2 +(y -k)^2 = r^2 . . . equation of a circle with center (h, k), radius r

  x^2 +(y -4)^2 = 4^2 . . . . . . the equation of the given circle

  x^2 +((0.5x +4) -4)^2 = 16

  (5/4)x^2 = 16

  x = 8/5√5 . . . . multiply by 4/5 and take the square root

  y = 0.5x +4

  y = 4/5√5 +4

The point of intersection is (8/5√5, 4+4/5√5), approximately (3.578, 5.789).

The signal f(t) = cos(6t) + sin(8t) + e(j2t) is not periodic.

To determine if a signal is periodic, we need to check if there exists a fundamental period T₀ such that f(t + T₀) = f(t) for all t.

Let's analyze each component separately:

1. cos(6t): The fundamental period of cos(6t) is 2π/6 = π/3. This means that cos(6t + π/3) = cos(6t) for all t. Therefore, the fundamental frequency ω₀ for cos(6t) is 6.

2. sin(8t): The fundamental period of sin(8t) is 2π/8 = π/4. This implies that sin(8t + π/4) = sin(8t) for all t. Hence, the fundamental frequency ω₀ for sin(8t) is 8.

3. e(j2t): The exponential term e(j2t) has a frequency of ω = 2. However, it does not have a fundamental period since e(j2(t + T₀)) ≠ e(j2t) for any T₀.

Since the three components have different fundamental periods, there is no common fundamental period T₀ that satisfies f(t + T₀) = f(t) for all t. Hence , it is not periodic.

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Answer:

28.4 miles/gallon

Step-by-step explanation:

to find the answer, you need to find the constant by dividing the miles drove by the amount of gasoline (or the other way around in terms of wording if it is not correct grammar) So you need to do 35.5/1.25 .  FYI I converted the fraction to decimal. The answer is 28.4 miles/gallon.

Hope this helped!! :)

a. Value of f(-2) is -15. b. Value of g(2) is 4. c. Value of x when f(x)=0 is 3.

The above values are obtained using substitution.

When in place of a variable, we substitute a value in the function, it is known as substitution.

a. We are given f(x)= 3x-9

So, for finding f(-2), we need to put x=-2

Thus, we get,

f(-2)= 3(-2)-9

f(-2)= -6-9

f(-2)= -15

b. We are given g(x)= x^2

So, for finding g(2), we need to put x=2

Thus, we get,

g(2)= 2^2

g(2)=4

c. Now, we are given that f(x)=0.

In order to find the value of x, we need to put f(x)=0

Thus, we get,

3x-9=0

3x=9

x=3

Hence the values of f(-2), g(2) and x when f(x)=0 are -15, 4 and 3 respectively.

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The approximate effective annual interest rate of the account is 1.21%.

Interest rate is calculated as a percentage of the loan amount, and is usually applied on an annual basis.

This is the result of the compounding of the interest rate at the end of each quarter. To calculate this, the formula for effective annual rate (EAR) is used:

EAR = (1 + i/n)ⁿ-1

Where i is the quarterly interest rate of 1.2%, and n is the number of compounding periods per year (4).

EAR = (1 + 0.012/4)⁴-1

EAR = (1.003)⁴-1

EAR = 1.012 - 1

EAR = 0.0121 or 1.21%

Finally, when rounded to the nearest hundredth of a percent, the approximate effective annual interest rate of the account is 1.21%.

This calculation is based on the assumption that the interest earned each quarter is left in the account and is compounded at the end of each quarter.

Therefore, the effective annual rate of the account is a result of the compounding of the interest rate at the end of each quarter.

This allows the principal to earn interest on the interest, increasing the potential return of the original investment.

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7.54 and 0.46 are the solutions to the given quadratic equations

Given the quadratic equation below:

x^2-18x+8=0

We need to determine the solutions to the given quadratic expression. Using the general formula below:

x = -b±√b²-4ac/2a

From the equation

a = 1

b = -18

c = 8

Substitute

x = 18±√18²-4(1)(8)/2(1)
x= 18±√324-32/2

x =18± 17.08/2

x = 35.08/2 and 0.92/2

x = 17.54 and 0.46

Hence the two solutions to the given quadratic equation are 17.54 and 0.46

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Given:

A new four way intersection is being constructed in New York Hyde park through point P(-3,-15).

Equation of line of one road : \(y=-\dfrac{3}{4}x+7\).

New road that will run perpendicular to the first road

To find:

The equation of line for the new road.

Solution:

The slope intercept form of a line is

\(y=mx+b\)

where, m is slope and b is y-intercept.

We have,

\(y=-\dfrac{3}{4}x+7\)

Slope of this line is \(-\dfrac{3}{4}\) and y-intercept is 7.

Product of slopes of two perpendicular line is -1.

\(m_1\times m_2=-1\)

\(-\dfrac{3}{4}\times m_2=-1\)

\(m_2=\dfrac{4}{3}\)

The point slope form of a line is

\(y-y_1=m(x-x_1)\)

where, m is slope.

The slope of new line is \(\dfrac{4}{3}\) and it passes through P(-3,-15). So, the equation of line of new road is

\(y-(-15)=\dfrac{4}{3}(x-(-3))\)

\(y+15=\dfrac{4}{3}(x+3)\)

\(y+15=\dfrac{4}{3}x+4\)

Subtract 15 from both sides.

\(y=\dfrac{4}{3}x+4-15\)

\(y=\dfrac{4}{3}x-11\)

Therefore, the equation of the line representing the new road is \(y=\dfrac{4}{3}x-11\).

Answer:

answer is d please follow me I hope it will help you

The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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if the volume is known, you can calculate the radius using the formula and the given values and it is =1.7853

To find the radius (r) of a right cylinder with a given height (h) of 10 and an unknown volume (V), additional information is needed to solve the problem. Without knowing the value of the volume, it is not possible to determine the exact value of the radius. The volume of a right cylinder is calculated using the formula V = \(\pi r^{2h}\), where π is a constant value approximately equal to 3.14159.

However, if you have the value of the volume (V), you can rearrange the formula to solve for the radius (r). For example, if the volume is given as V = 100 cubic units, you can use the formula V = πr^2h and substitute the known values to find the radius. Rearranging the formula, we get r = √(V / (πh)), where √ denotes the square root.

By plugging in the values of V = 100 and h = 10 into the formula, we can calculate the radius as r = √(100 / (π × 10)). Simplifying further, r ≈ √(10 / π) ≈ √(10 / 3.14159) ≈ √(3.1831) ≈ 1.7853

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Answer:

−7k^4−11k^2+6

Step-by-step explanation:

−4k^4+14+3k^2−3k^4−14k^2−8

(−4k^4+−3k^4)+(3k^2+−14k^2)+(14+−8)

−7k^4−11k^2+6

...

The length of SR to the nearest hundredth is approximately 13.12 units.

What is Pythagoras theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can use the Pythagorean theorem to find the length of QR, which is the hypotenuse of right triangle PQR:

PQ² + QR² = PR²

Substituting in the given values:

(9+x)²+ QS² = 16²

We know that QS is the altitude from Q to PR, which means it is also the height of triangle PQR. We can use the area of triangle PQR to find the length of QS:

area of PQR = (1/2) * PQ * QS = (1/2) * 9 * QS

area of PQR = (1/2) * QR * QS = (1/2) * 16 * QS

Since the area of PQR is the same, we can set these two equations equal to each other and solve for QS:

(1/2) * 9 * QS = (1/2) * 16 * QS

9QS = 16QS

QS = (16/9) * x

Substituting this value for QS into the equation we set up earlier:

(9+x)²+ [(16/9)*x]²= 16²

Simplifying and solving for x:

81 + 18x + x²+ 256x²/81 = 256

x²+ 18x + 81 + 256x²/81 - 256 = 0

81x² + 1458x + 6561 + 20736x² - 20736(81) = 0

2889x² + 1458x - 127008 = 0

Using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 2889, b = 1458, and c = -127008

x = (-1458 ± sqrt(1458² - 4(2889)(-127008))) / 2(2889)

x = (-1458 ± sqrt(5872034)) / 5778

x ≈ 13.12 or x ≈ -21.89

Since x represents a length, we take the positive value as our answer:

x ≈ 13.12

Therefore, the length of SR to the nearest hundredth is approximately 13.12units.

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Answer:

She answers 3 questions per minute!!

Step-by-step explanation:

I know this because 3x10 = 30 and if she solves 30 questions in 10 minutes,  that means in 1 minute she solves 3 questions.

Answer:

-135, -134, -133

Step-by-step explanation:

Hi there!

Let x be equal to the first integer in the set of three consecutive integers.

Let x+1 and x+2 be the consecutive integers.

We're given that they have a sum of -402.

We can construct an equation:

\((x)+(x+1)+(x+2)=-402\)

Combine like terms:

\(x+x+1+x+2=-402\\x+x+x+1+2=-402\\3x+3=-402\\3x=-405\\x=-135\)

Therefore the first integer is -135.

The next two consecutive integers after -135 is -134 and -133.

Therefore, the three consecutive integers are -135, -134 and -133.

I hope this helps!

Answer:

D. 8.053 x 10^4

Step-by-step explanation:

Given :

7.17 x 10^4 and 8.17 10^5

The number in between the two Given numbers should be greater Than 7.17*10^4 but less than 8.17*10^5

A. 6.92 x 10^4 - this is less than 7.17 * 10^4 ; hence doesn't fit in

B. 7.2 x10^9 - this is greater than both values, hence, doesn't fit in

C. 7.57 x 10^3 - this is less than 7.17*10^4 ; hence does not fit in

D. 8.053 x 10^4 - this fits in as it is greater than 7.17*10^4 and less than 8.17*10^5 ; hence, it is the correct answer.

x+(3x+10-4)+(3x+ 10)=72

Quit parenthesis:

x+3x+10-4+3x+10=72

Combine like terms:

x+3x+3x+10-4+10=72

7x +16 =72

Subtract 16 from both sides of the equation:

7x+16-16 = 72-16

7x= 56

Finally divide both sides by 7:

7x/7 =56/7

x= 8

Answer: C

Step-by-step explanation:

For our unknown value x, the opposite side = 10 and the adjacent side = 18, using this information you can use SOH CAH TOA.

TOA refers to opposite over adjacent, which would be

tan x = 10/18.

Hope this helps!

Answer: 6x+18

Step-by-step explanation: you just have to distribute so you multiply the six with whatever is inside so 6 times x is 6x + 6 times 3 is 18 so the answer is 6x+18 we cant simplify anymore

For the ratio of the average flux for e > 45 degrees to the omnidirectional flux, we divide the flux per solid angle for the directional case by the flux per solid angle for the omnidirectional case.

To find the ratio of the average flux for e > 45 degrees to the omnidirectional flux in a pancake distribution of sin(a) where a = 0, we need to calculate the directional flux, omnidirectional flux, directional solid angle, and omnidirectional solid angle.

Directional Flux:

The directional flux is the flux within a specific direction or range of angles. In this case, we are interested in e > 45 degrees.

Omnidirectional Flux:

The omnidirectional flux is the total flux in all directions or over the entire solid angle.

Directional Solid Angle:

The directional solid angle is the solid angle subtended by the specified direction or range of angles. In this case, it would be the solid angle corresponding to e > 45 degrees.

Omnidirectional Solid Angle:

The omnidirectional solid angle is the total solid angle subtended by all possible directions or over the entire sphere.

To find the flux per solid angle for both the directional and omnidirectional cases, we can use the formula:

Flux per Solid Angle = Total Flux / Solid Angle

Finally, to find the ratio of the average flux for e > 45 degrees to the omnidirectional flux, we divide the flux per solid angle for the directional case by the flux per solid angle for the omnidirectional case.

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Step-by-step explanation:

f + g and f - g are very simple concepts.

(f+g)(x) = f(x) + g(x)

and

(f-g)(x) = f(x) - g(x)

and so. ..

(f-g)(x) = 2x³ + 7x² - 4x - 5 - 3x - -2 = 2x³ + 7x² - 7x - 3

The series converges.

To determine the convergence or divergence of the given series, we can use the limit comparison test.

Let's consider the series:

∑(11n^2 - 4n^4)/(3n)

We can simplify the series by dividing both numerator and denominator by n^3, which gives:

∑(11/n - 4/n^3)

Now we can use the limit comparison test by comparing this series to the series ∑(1/n^2).

We have:

lim n→∞ (11/n - 4/n^3)/(1/n^2)

= lim n→∞ (11n^2 - 4)/(n^2)

= 11

Since the limit is finite and positive, and the series ∑(1/n^2) is a known convergent p-series with p=2, by the limit comparison test, the given series also converges.

Therefore, the main answer is that the series converges.

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Answer:

the correct answer is $269

Step-by-step explanation:

Answer:

$269

Step-by-step explanation: