Which expression is equivalent to (4 7i)(3 4i)? â€""16 37i 12 â€"" 28i 16 â€"" 37i 37 16i.

Answer:

xy(5-6xy)/4

Step-by-step explanation:

Here, we want to evaluate the expression given

We have this as ;

(5xy - 6x^2y^2)/4

= xy(5-6xy)/4

The equivalent cosine function is f(x) = 3 cos (2x - 60°).

To rewrite a sine function as a cosine function, we use the identities given below:

cosθ = sin (90° - θ)sinθ = cos (90° - θ)

In other words, we replace the θ in sin θ with (90° - θ) to get the equivalent cosine function and vice versa. Let's consider an example. Let's say we have the sine function

f(x) = 3 sin (2x + 30°) and we want to rewrite it as a cosine function.

The first step is to find the equivalent cosine function using the identity:

cosθ = sin (90° - θ)cos (2x + 60°) = sin (90° - (2x + 60°))cos (2x + 60°) = sin (30° - 2x)

The next step is to simplify the cosine function by using the identity:

sinθ = cos (90° - θ)cos (2x + 60°) = cos (90° - (30° - 2x))cos (2x + 60°) = cos (2x - 60°)

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Answer:

No

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

For a Triangle to be a Right-Angled Triangle, should follow the Pythagoras Theorem which states that

If a is the larger side and b , c are the lengths of the other two sides

Then \(a^{2} =b^{2} +c^{2}\)

Here a=30  , Then \(a^{2}=30^{2} =900\)

and b=20 , c=25  , Then \(b^{2} +c^{2} =20^{2} +25^{2} =1025\)

Since \(a^{2} \neq b^{2} +c^{2}\)

Then the Triangle is not Right Triangle

Answer:

  b²√(30b)

Step-by-step explanation:

The number 30 has factors 2, 3, 5, so there are no squares.

The square root of the 5th power of b is b^(5/2) = (b^2)(b^(1/2)). That is, the square of b^2 can be removed.

  \(\sqrt{30b^5}=\sqrt{b^4\cdot30b}=\boxed{b^2\sqrt{30b}}\)

Answer:

R 1,440

Step-by-step explanation:

To increase R1,200 by 20%, you can follow these steps:

Step 1: Calculate the 20% of R1,200.

20% of R1,200 = (20/100) * R1,200 = 0.2 * R1,200 = R240.

Step 2: Add the calculated 20% to the original amount.

Increased amount = R1,200 + R240 = R1,440.

Therefore, by increasing R1,200 by 20%, you get R1,440.

I hoped this helped, have a good day

Answer:

when x = -12:

\(\implies y=\dfrac13(-12)-2\)

\(\implies y=-\dfrac{12}{3}-2\)

\(\implies y=-4-2\)

\(\implies y=-6\)

when x = 0:

\(\implies y=\dfrac13(0)-2\)

\(\implies y=0-2\)

\(\implies y=-2\)

Using the given equation, the prediction for the number of cups of lemonade Lin might sell on a day where the high temperature is 74 degrees is 59 cups

Given that a computer program found that the line c = 2t - 89 is a good fit for the data and we need to use this equation to predict the number of cups of lemonade Lin might sell on a day where the high temperature is 74 degrees.The given equation is:c = 2t - 89Here, t is the temperature and c is the number of cups of lemonade Lin might sell. We need to substitute t = 74 into the equation to predict the number of cups of lemonade Lin might sell on a day where the high temperature is 74 degrees.

Substituting t = 74 in the given equation, we get:c = 2(74) - 89c = 148 - 89c = 59Therefore, the prediction for the number of cups of lemonade Lin might sell on a day where the high temperature is 74 degrees is 59 cups.Using the given equation, we know that c = 2t - 89Substituting t = 74, we get:c = 2(74) - 89= 148 - 89= 59Therefore, the prediction for the number of cups of lemonade Lin might sell on a day where the high temperature is 74 degrees is 59 cups.

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Answer:

It would be the graph that has point (0,12) and is decreasing to the right.

The amount that an investor with 55 shares of this stock have earned in dividends will make in one year is A. $108.35.

It should be noted that the dividend for the year will simply be calculated by adding the dividend in each quarter.

Therefore, the amount that an investor with 55 shares of this stock have earned in dividends will make in one year will be:

= $27.50 + $19.25 + $34.10 + $27.50

= $108.35

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Answer:

9 dollars per pound of salmon

The probability distribution of the number of goals scored by Stat113 FC in a single game is a discrete distribution, but the specific distribution (such as Poisson or Negative Binomial) is unknown without more information. The probability of Stat113 FC scoring exactly 4 goals or the probability of scoring 4 goals in one half of a game cannot be determined without additional details. However, the expected number of goals is given as 2.4 per game, while the variance cannot be calculated without more specific information about the distribution or data.

(a) The probability distribution of X, the number of goals scored by Stat113 FC in a single game, is a discrete distribution since goals can only be counted as whole numbers. To determine the specific distribution, more information is needed. However, based on the given context, it is reasonable to assume that the distribution could follow a Poisson distribution or a Negative Binomial distribution.

(b) To compute Pr(X = 4), the probability that Stat113 FC scores exactly 4 goals in a game, we need additional information about the specific distribution. Without that information, it is not possible to calculate the probability.

(c) Similarly, without additional information about the distribution, it is not possible to determine the probability of Stat113 FC scoring exactly 4 goals in one half of a game.

(d) The expected number of goals, E(X), represents the average number of goals Stat113 FC is expected to score in a game. The given information states that on average, Stat113 FC scores 2.4 goals per game. Therefore, E(X) = 2.4.

The variance, Var(X), quantifies the variability or spread of the goal-scoring distribution. Without specific information about the distribution, it is not possible to calculate the variance. Additional details about the distribution or data are required to compute Var(X).

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a) The volume of the box (in cubic inches) when the cutout length is 0.8 inches can be represented using function notation as f(0.8).

b) The volume of the box (in cubic inches) when the cutout length is 1.2 inches can be represented using function notation as f(1.2).

c) The change in volume of the box (in cubic inches) when the cutout length increases from 0.8 inches to 1.2 inches can be represented using function notation as f(1.2) - f(0.8).

d) The change in volume of the box (in cubic inches) when the cutout length increases from 5.6 inches to 5.7 inches can be represented using function notation as f(5.7) - f(5.6).

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Answer:

y=2x-3

Step-by-step explanation:

Answer:

Y=-2x+2

OR

Y=2-2x

Both equations are the same

Step-by-step explanation:

Y intercept formula is

Y=Mx+b

Y is a random Y coordinate

M is slope

X is a random X coordinate

B is y intercept

Now we want to isolate the Y

So first we subtract the 8x on both sides which will give

4y=8-8x

Now we get ri of the 4 to isolate the Y completely

y=2-2x

there you go

Or you can write it in addition

y=-2x+2

The solution to the system of inequalities is (-1, 4).

To graph the system of inequalities and identify the point that represents a solution, we will plot the lines corresponding to the inequalities and shade the regions that satisfy the given conditions.

The first inequality is x > -2, which represents a vertical line passing through x = -2 but does not include the line itself since it's "greater than." Therefore, we draw a dashed vertical line at x = -2.

The second inequality is y ≤ 2x + 7, which represents a line with a slope of 2 and a y-intercept of 7.

To graph this line, we can plot two points and draw a solid line through them.

Now let's plot the points (-1, 6), (1, 11), (-1, 4), and (-3, -1) to see which one lies within the shaded region and satisfies both inequalities.

The graph is attached.

The dashed vertical line represents x > -2, and the solid line represents y ≤ 2x + 7. The shaded region below the solid line and to the right of the dashed line satisfies both inequalities.

By observing the graph, we can see that the point (-1, 4) lies within the shaded region and satisfies both inequalities.

Therefore, the solution to the system of inequalities is (-1, 4).

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a) The slope of the line is given as follows: 0.5.

b) The meaning of the slope is that the volume increases by 0.5 gallons per minute.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

From the graph, when x increases by 8, y increases by 4, hence the slope m is obtained as follows:

m = 4/8 = 0.5.

As x is the time in minutes and y is the volume in gallons, the meaning of the slope is that the volume increases by 0.5 gallons per minute.

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4ft = 48in or 4 feet is equivalent to 48 inches.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

The sentence states an equality between units of length: feet and inches.

From there, we can say that we are asked how many inches are there in 4 feet

Converting feet to inches, we must use the conversion

1 foot = 12 inches

4ft = 4 (12 inches)

4ft = 48in

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

450 / 1000 will give the fraction

450 / 1000 in its simplest form is taken by dividing both with a common factor that is 50

then the ans is

9/20

Answer:He used 6 plots of land.

explanation:

total no. of plots =10 (land was divided in 10 equal parts)

used plots = 3/5 of 10 =3/5*10 =6

Step-by-step explanation:

Answer:

this should be the answer 4x^3 & 2x^2

Answer:

The triangles can be congruent.

Step-by-step explanation:

They are congruent if proven by SSS: 2 sides are clearly stated that they are congruent due to the marks they have.

The last side can be congruent if the diagonals are congruent in length by proving.

They can also be congeuent due to SAS because there is gonna be alternate interior angles due to the transversal.

a) The height of the frisbee each second it is in the air are 5, 29, 45, 53, 53, 45, 29, 5, -27 and -67.

b) The frisbee is in the air for a total of 8 seconds.

To find the height of the frisbee each second it is in the air, we need to substitute different values of t into the equation \(h = -16t^2 + 40t + 5\) and calculate the corresponding height.

a) Let's substitute t = 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 into the equation:

When t = 0: \(h = -16(0)^2 + 40(0) + 5 = 5\)

When t = 1: \(h = -16(1)^2 + 40(1) + 5 = 29\)

When t = 2: \(h = -16(2)^2 + 40(2) + 5 = 45\)

When t = 3: \(h = -16(3)^2 + 40(3) + 5 = 53\)

When t = 4: \(h = -16(4)^2 + 40(4) + 5 = 53\)

When t = 5: h = \(-16(5)^2 + 40(5) + 5 = 45\)

When t = 6: h = \(-16(6)^2 + 40(6) + 5 = 29\)

When t = 7: h = \(-16(7)^2 + 40(7) + 5 = 5\)

When t = 8: h = \(-16(8)^2 + 40(8) + 5 = -27\)

When t = 9: h =\(-16(9)^2 + 40(9) + 5 = -67\)

b) The frisbee is in the air as long as its height is greater than 0. From the calculations above, we can see that the frisbee is in the air from t = 0 to t = 7, inclusive.

Note: The table you provided shows the height of the frisbee at each second it is in the air, but it seems to be cut off. However, based on the calculations above, the height values at each second should be as follows:

0 seconds: 5 feet

1 second: 29 feet

2 seconds: 45 feet

3 seconds: 53 feet

4 seconds: 53 feet

5 seconds: 45 feet

6 seconds: 29 feet

7 seconds: 5 feet

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Answer:

(5 + 3y)(25 - 15y + 9y²)

Step-by-step explanation:

This is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²), thus

125 + 27y³

= 5³ + (3y)³ with a = 5 and b = 3y

= (5 + 3y)(5² - 5(3y) + (3y)² )

= (5 + 3y)(25 - 15y + 9y²)

Light bulbs is normally distributed with a variance of 625 and a mean lifetime of 520 hours, we need to calculate the cumulative probability up to 549 hours. The answer will be rounded to four decimal places.

Given a normally distributed lifetime with a mean of 520 hours and a variance of 625, we can determine the standard deviation (σ) by taking the square root of the variance, which gives us σ = √625 = 25.

To find the probability of a bulb lasting for at most 549 hours, we need to calculate the area under the normal distribution curve up to 549 hours. This can be done by evaluating the cumulative distribution function (CDF) of the normal distribution at the value 549, using the mean (520) and standard deviation (25).

The CDF will give us the probability that a bulb lasts up to a certain point. Rounding the result to four decimal places will provide the desired precision.

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The problem involves using normal distribution to find the probability of a given outcome. Using the Z-score, we can determine that the probability of a light bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%

Given the mean (µ) of the lifetime of a bulb is 520 hours. Also, the variance (σ²) is given as 625. Thus, the standard deviation (σ) is the square root of the variance, which is 25.

To find the probability of a bulb lasting for at most 549 hours, we first calculate the Z score. The Z-score formula is given as follows: Z = (X - µ) / σ, where X is the number of hours, which is 549. So substitute the given values into the formula. Z = (549 - 520) / 25, the Z value is 1.16.

We then look up the Z-table to find the probability associated with this Z-score (1.16), which is approximately 0.8770. Therefore, the probability of a bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%.

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