Operations with Complex Numbers

Answer:

B) The potential energy of the rock is transformed into kinetic energy.

Step-by-step explanation:

Our understanding of Physics tells you the potential energy due to the rock's position in the gravitational field is transformed into kinetic energy as the rock gains speed (and loses height).

_____

Comment on the problem

There are additional effects not accounted for by this simplified answer, including thermal effects, radiation effects, and sound effects. (In this new age, there can also be energetic effects in dimensions we're not accustomed to considering, including emotional or other effects on—or due to—consciousness.)

Answer B)it goes from being still to moving

Answer:71.4

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

so just plug 1 in and you wil get it

Answer:

16

Step-by-step explanation:

6(2)+4

6 x 2=12

12+4=16

Answer:

5/12

Step-by-step explanation: find common denominator

Check the picture below.

The length of the missing side (the other leg) is approximately 6.47 units.

To find the measure of the missing side of a right triangle when you know the hypotenuse and one of the other sides, you can use the Pythagorean Theorem. The theorem states:

a² + b² = c²

Where:

- a and b are the lengths of the two shorter sides (legs) of the right triangle.

- c is the length of the hypotenuse.

In this case, you know the hypotenuse (c) is 7.4 and one of the legs (height, let's call it 'a') is 3.6. You want to find the length of the other leg (b).

Plug the values into the Pythagorean Theorem:

3.6² + b² = 7.4²

Solve for b:

b² = 7.4² - 3.6²

b² = 54.76 - 12.96

b² = 41.8

To find b, take the square root of both sides:

b = √41.8

b ≈ 6.47 (rounded to two decimal places)

So, the length of the missing side (the other leg) is approximately 6.47 units.

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Answer:

r = 4b + 3

Step-by-step explanation:

As b is the independent variable, r must be the dependent variable which should be on the left by itself in function notation.

Rearranging 16b = 4r - 12

4r = 16b + 12

r = 4b + 3

Answer:

r = 4b + 3

Step-by-step explanation:

given equation 16b = 4r - 12

in function notation, dependent variable should be on the right n independent variable appears on the left

16b + 12 = 4r - 12 +12

16b + 12 = 4r

flip left n right

4r = 16b + 12

divide by 4

r= 4b + 3

Answer:

[tex]\begin{array}{cccc}&\text{ Like fruit }&\text{ Do not like fruit }&\text{ Total }\\\text{Like vegetables}&11&1023&1034\\\text{Do not like vegetables}&44&33&77\\\text{Total}&55&1056&1111\end{array}[/tex]

Step-by-step explanation:

You are given such information:

Then 55 - 44 = 11 members like fruit and vegetables. Thus,

1111 - 55 - 33 = 1023 members like vegetables but not like fruit.

A two-way frequency table will take look

[tex]\begin{array}{cccc}&\text{ Like fruit }&\text{ Do not like fruit }&\text{ Total }\\\text{Like vegetables}&11&1023&1034\\\text{Do not like vegetables}&44&33&77\\\text{Total}&55&1056&1111\end{array}[/tex]

Nikita can organize her data into a two-way frequency table showing members' preferences for fruit and vegetables. The table identifies how many members like only fruit, only vegetables, both, or neither accordingly.

Nikita has the following data about her food club consisting of 1111 members:

We can organize this information into a two-way frequency table. Here are the steps:

Calculate the number of members who like both fruit and vegetables. Since 55 members like fruit, 44 like only fruit, and 33 like neither, we subtract the 44 members who like only fruit from the total 55 fruit-likers to find those who like both: 55 - 44 = 11.

Calculate the number of members who like vegetables only. The number of members who like either fruit or vegetables or both can be found by subtracting those who like neither from the total number of members: 1111 - 33 = 1078. We already know 55 like fruit, so those who like vegetables only: 1078 - 55 = 1023 (1111 total members - 33 neither - 55 fruit).

The two-way frequency table looks like this:

                           Fruit   No Fruit Total

Vegetables       11 1023 1034

No Vegetables 44 33          77

Total                 55 1056 1111

Answer:

81

Step-by-step explanation:

9girls x 9 boys to play each other

A. d = 5 − 15t; d = 18t

Derrick's distance from home is initially 5 miles and is decreasing at the rate of 15 miles per hour. His distance from home can be modeled by ...

... d = 5 - 15t . . . . . . d in miles; t in hours

Mark's distance from home is initially zero and is increasing at the rate of 18 miles per hour. His distance from home can be modeled by ...

... d = 18t . . . . . . . . . d in miles; t in hours

Together, these equations form the pair ...

_____

Comment on the equations

There is nothing in the problem statement or definition of the variables to suggest that one distance is measured in the same direction as the other, or that one value of d has any relationship to the other.

Usually, a "system of equations" expresses relationships among variables that all have the same definition with respect to some problem statement. Here, both values of d are "distance from home", but they don't necessarily have any relationship to each other. Their being the same value doesn't mean the boys have met, for example.

Answer:

The equation would be y = -1/2x + 8

Step-by-step explanation:

To find the equation of the line, we start by find the slope. Perpendicular slopes have opposite and reciprocal slopes. since the original slope is 2, then the perpendicular slope is -1/2.

Now, using the point and the slope in point-slope form, we can find the equation.

y - y1 = m(x - x1)

y - 6 = -1/2(x - 4)

y - 6 = -1/2x + 2

y = -1/2x + 8

The equations that is perpendicular to y = 2x + 5 and passes through the point (4 , 6) is y = - 1/2 x + 8

For an equation to be perpendicular to the another line equation the product of there slope will be negative one. Therefore,

Therefore, the slope of  y = 2x + 5  is 2. The equation should have the following slope:

2m₂ = - 1

m₂ = -1 / 2

A linear equation is represented as follows:

m = slope

b = y-intercept

Therefore,

let use the point  (4 , 6) to find b

6 = - 1/2 (4) + b

6 = -2 + b

b = 6 + 2

b = 8

The equation will be as follows:

y = - 1/2 x + 8

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Answer:

Axis of symmetry are lines x=-6 and y=-4, center  (-6,-4)

Step-by-step explanation:

Consideer the equation [tex]x^2+y^2+12x+8y=48.[/tex]

First, complete perfect squares:

[tex](x^2+12x)+(y^2+8y)=48,\\ \\(x^2+12x+36-36)+(y^2+8y+16-16)=48,\\ \\(x+6)^2+(y+4)^2-36-16=48,\\ \\(x+6)^2+(y+4)^2=100.[/tex]

This equation represents a circle with center at point (-6,-4) and radius r=10.

Axis of symmetry are lines x=-6 and y=-4 (vertical and horizontal lines passing through the center).

4/5

The question is asking you to find the ratio of Wednesday's time (2/3) to Tuesday's time (5/6). To do that, you divide the fractions:

... Wednesday / Tuesday = (2/3) / (5/6)

There are a couple of different methods you can use to divide fractions.

1. Invert the denominator and multiply.

When we invert 5/6, it becomes 6/5. So our division problem is now a multiplication problem:

... (2/3) × (6/5) = (2×6)/(3×5) = 12/15

This result can be reduced by removing a factor of 3 from numerator and denominator:

... Wednesday/Tuesday = 4/5

___

2. Make both fractions have the same denominator, then drop the denominators.

The denominators of the fractions in our ratio are 3 and 6. If we multiply 3 by 2, it becomes 6, so we can rewrite the numerator fraction as ...

... 2/3 = (2/3)×(2/2) = 4/6

Now, it has a denominator of 6 and our division problem is

... (2/3) / (5/6) = (4/6) / (5/6)

Dropping the (same) denominators gives ...

... Wednesday/Tuesday = 4/5

Answer:

C) 1/2(15 +23)(9)

Step-by-step explanation:

The formula for the area of a trapezoid in terms of base lengths b1 and b2 and height h is ...

... A = 1/2(b1 +b2)h

Substituting the values shown in the figure, this becomes ...

... A = 1/2(15 +23)(9) . . . . . matches selection C

Answer:

5 x-intercepts at most.

Step-by-step explanation:

Polynomial function with degree of 5

End behavior: falls to the left and rises to the  right OR falls to the right and rises to the left .

Can have 0,1,2,3 or 4 turning points; can have

0,1,2,3,4 or 5 x-intercepts

A quintic polynomial, which is of degree 5, can have at most 5 x-intercepts as per the Fundamental Theorem of Algebra.

A quintic polynomial is a polynomial of degree 5. According to the Fundamental Theorem of Algebra, a polynomial of degree n will have exactly n roots, or solutions. However, not all roots necessarily represent x-intercepts, as some might be complex roots.

On a graph, x-intercepts are points where the polynomial touches or crosses the x-axis, corresponding to the real roots of the polynomial equation. So, in general, a quintic polynomial will have at most 5 x-intercepts. This is because a polynomial of degree n can intersect the x-axis at most n times.

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Answer:

8.3%

Step-by-step explanation:

[tex]a-digit\ of\ tens\\b-digit\ of\ ones\\10a+b-the\ number\\10b+a-the\ number\ with\ reversed\ digits\\\\\left\{\begin{array}{ccc}a+b=12&\to b=12-a\\10b+a=15(10a+b)\end{array}\right\\\\\text{Substitute}\\\\10(12-a)+a=15(10a+12-a)\\10(12-a)+a=15(9a+12)\qquad\text{use distributive property}\\(10)(12)+(10)(-a)+a=(15)(9a)+(15)(12)\\120-10a+a=135a+180\\120-9a=135a+180\qquad\text{subtract 120 from both sides}\\-9a=135a+60\qquad\text{subtract 135a from both sides}\\-144a=60\qquad\text{divide both sides by (-144)}\\\\a=-\dfrac{60}{144}[/tex]

a is negative and it's not a digit.

The sale price was 30% off the original price, which means it was on sale for 70% of the original cost ( 100% - 30% = 70%)

To find the original cost, divide the sale price by the percent of the original cost:

21 / 0.70 = 30

The original price was $30

check:

30 x 0.3 = 9 ( amount of discount)

30 - 9 = 21 ( sale price)

Final answer:

To find the original price of the sweatshirt that Zoe found, which was sold at a 30% discount, we use the sale price of $21 to calculate that the original price was $30 by dividing by 0.70. An example with sales tax involves an $85 jacket with 7.5% tax, where sales tax is rounded to $6.38 and added to the original price for a total of $91.38.

Explanation:

To determine the original cost of the sweatshirt that Zoe found, which was discounted by 30%, we need to work backwards from the sale price. The sale price represents 70% of the original cost since the item is 30% off. If the sale price is $21, we can set up the equation 0.70 * original price = $21 to find the original price.

Dividing both sides of the equation by 0.70 gives us the original price. Therefore, original price = $21 / 0.70. After performing this calculation, we find that the original cost of the sweatshirt was $30

Emily bought a jacket for $85. If the sales tax is 7.5%, the amount of sales tax would be calculated as 0.075 * $85, which equals $6.375. To get the total cost, we would round $6.375 to the nearest penny to get $6.38, and then add it to the original price of the jacket. The total cost is $85 + $6.38 = $91.38.

Add all the hours together:

1 3/4 + 1 1/4 = 3 + 1 1/2  = 4 1/2 + 1 1/5

To add fractions with different denominators, find the common denominator and rewrite the fractions

Common denominator of 2 and 5 is 10

1/2 becomes 5/10

1/5 becomes 2/10

now you have 4 5/10 + 1 2/10 = 5 7/10 + 2 = 7 7/10

Now subtract that from 12:

12 - 7 7/10 = 4 3/10 hours

Answer:

0.45

Step-by-step explanation:

9/20=0.45

Travis spent 9/20, which in decimal form is 0.45, of his 20-minute preparation time eating breakfast, which is equivalent to 9 minutes.

Travis spent a total of 20 minutes getting ready for school. Out of this time, he spent 9/20 of it eating breakfast. To express this fraction of time as a decimal, we simply perform division: 9 divided by 20.

9 / 20 = 0.45

Therefore, Travis spent 0.45 of the 20 minutes, or 45% of his preparation time, eating breakfast. When converting this to minutes, 0.45 * 20 minutes equals 9 minutes. Thus, Travis spent 9 minutes eating breakfast.

Answer:

Option d) 115 degrees

Step-by-step explanation:

We are given a trapezium ABDE in the picture.  AB and ED are the parallel sides.

F is the mid point of AE and C the midpoint of BD.  FC is joined.

We are also given that angle of AED = 65 degrees.

To find the measure of angle BAE.

Since sides AB and ED are parallel sides we find that AE is the transvesal intersecting the two parallel lines.

Hence by parallel lines axiom, the two interior angles namely Angle AED and BAE are supplementary.

i.e. 65 +angle BAE=180

Hence angle BAE = 115 degrees.

Option d is the answer.

19.5 inches

Let r represent the length of one of the sections of rope (in inches). Then the total length of the original rope is ...

... 8r +28.9 = 184.9

... 8r = 156 . . . . . . . . . . . . subtract 28.9; next, divide by 8

... 156/8 = r = 19.5

The length of each of the sections is 19.5 inches.

Answer:

When she mixes the clay she now had 3/2 and 3/4 added would be 6/4 and 3/4 so she has 9/4 pounds of clay. If each student needs 1/8 and she had 18/8 that means she can make 18 students finish.

Please mark brainliest as that would help alot/

Step-by-step explanation:

Answer:

none shown

Step-by-step explanation:

1/x^3 = x^(-3) has a negative exponent. It does not match the requirement that exponents be a non-negative integer. Therefore, any expression containing 1/x^3 will not be a polynomial.

Answer:

More students take French than take Spanish.

Step-by-step explanation:

Effectively, out of every 39 students taking French and/or Spanish, 19 of them take Spanish and 20 of them take French. The number of French students in that group is higher. (20 is more than 19)

$6.00

A fairly easy way to do the mental calculation of a 15% tip is to realize that ...

... 15% = 10% + (1/2)·10%

Of course, you can compute 10% by moving the decimal point 1 place left, so ...

... 10% of $40.00 = $4.00

Half that is $2.00, so the 15% tip is $4.00 +2.00 = $6.00.

To calculate the total bill including sales tax and tip, convert the percentages to decimals and multiply by the meal cost. Add the computed sales tax and tip to the original meal cost to get the total payable amount. In the example provided, the total comes to $58.90, including sales tax and tip.

The question involves calculating the total bill for a dinner, which includes the meal cost, sales tax, and tip. To solve this problem, one must perform a series of calculations:

Firstly, figure out the sales tax by converting the percentage to a decimal and multiplying it by the total cost of the meal.

Next, decide on the tip percentage, convert it to a decimal, and again multiply by the cost of the meal.

Add both the sales tax and the tip to the original cost of the meal to get the total amount to be paid at the register.

Using the provided example, if the meal cost is $47.50 and the sales tax is 6%, you would calculate the tax as follows:

0.06  x47.50 = $2.85 (sales tax)

And if they decide to leave an 18% tip:

0.18 x $47.50 = $8.55 (tip)

Finally, you add the meal cost, sales tax, and tip:

$47.50 + $2.85 + $8.55 = $58.90

The total amount to be paid at the register with a credit card is $58.90, which includes the meal cost, sales tax, and tip.

D. 8.2

ST = SD + DT . . . . . segment addition theorem

11.1 = 2.9 + DT . . . . substitute the given lengths

8.2 = DT . . . . . . . . subtract 2.9

The length of segment DT is 8.2 units.

Answer:8.2

Step-by-step explanation:

I got it right on edginuity

Answer:

x=5

y=10

Step-by-step explanation:

Answer:

3:5

Step-by-step explanation:

We are looking for the ratio of baskets made to baskets attempted

made: attempted

9:15

We can divide each number by 3

9/3: 15/3

3:5

The ratio of baskets made: attempted  is 3:5

The ratio that describes the number of baskets made to the number of baskets attempted by the basketball player is 9 to 15, which simplifies to 3 to 5.

The question pertains to the ratio of successful basket attempts to total attempts made by a basketball player in a game.

In this case, the player successfully made 9 baskets out of 15 attempts.

To express this as a ratio, we simply compare the number of made baskets to the total attempts,

thus the ratio is 9 to 15, which can also be simplified by dividing both numbers by their greatest common divisor, which is 3, resulting in a simplified ratio of 3 to 5.

Check the picture below.

make sure your calculator is in Degree mode.