Evaluate 4x^3 + 2 for x

Answer:

point E and F

Step-by-step explanation:

the only ones that make sense

The TV's width and height are approximately 36.61 inches and 20.55 inches respectively. The black bar's height is approximately 1.29 inches each. The movie covers almost 87.4% of the TV's screen area.

This question involves the use of ratios and some geometry. Your TV's aspect ratio of 16:9 essentially means the width is 16 parts and the height is 9 parts. And, the total diagonal is given 42 inches.

1. Using Pythagorean theorem a² + b² = c² where c is the hypotenuse (diagonal), the width and height of the TV can be found: height(h)= ratio_height * √(c²/(ratio_width² + ratio_height²)) = 9 * √(42²/(16² + 9²)) ≈ 20.55 inches.

2. Similarly for width(w): w= ratio_width * √(c²/(ratio_width² + ratio_height²)) ≈ 36.61 inches.

3. The movie's aspect ratio is 1.85:1. The height of the black bars can be calculated using ratio of the heights of the movie and the TV: black bar height= (h - w/1.85) / 2 ≈ 1.29 inches. This height is subtracted from the TV's height because the movie with ratio 1.85:1 is wider than 16:9 TV.

4. The percentage coverage is given by (w * (h - 2* black bar height)) / (w * h) ≈ 0.874 or 87.4%

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Final answer:

To find the average distance Nick walks in a year, divide 18,000 steps by 3,500 steps per mile to get 5.14 miles per day, and then multiply by 365 days to estimate around 1,876.1 miles annually.

Explanation:

To estimate the average distance in miles that Nick walks in one year, we need to start with the information that Nick walks 18,000 steps every day and that he walks 1 mile every 3,500 steps. First, we need to calculate the number of miles Nick walks each day by dividing the total daily steps by the number of steps per mile:

Daily miles = 18,000 steps/day ÷ 3,500 steps/mile = 5.14 miles/day (rounded to two decimal places)
Next, we will calculate Nick's annual walking distance by multiplying the miles per day by the number of days in a year (365):

Annual distance = 5.14 miles/day × 365 days/year = 1,876.1 miles/year (rounded to one decimal place)

Therefore, we can estimate that Nick walks approximately 1,876.1 miles in one year.

The algebraic expression that the amount of milk has will be 128 - 16x.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given,

Total milk = 128 ounces

Rate of drinking milk = 16 ounces/day

x equal the number of days

Then,

Amount remaining = 128 - 16x

Hence, The algebraic expression that the amount of milk has will be 128 - 16x.

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Answer:

Real part = -6 and imaginary part = -i

Step-by-step explanation:

A complex number can be written as a + bi,

where both a and b are real numbers,

While, i is an imaginary number ( equals to √-1, because √-1 does not defined as a real number ),

The product of a real number and imaginary number is imaginary number,

∴ bi is called imaginary part of a + bi

Also, a is real number ⇒ a is real part of a + bi

Here, the given complex number,

-6-i

By comparing,

Imaginary part = -i, real part = -6.

We want to see the real and imaginary parts of a given complex number.

The real part is: -6

The imaginary part is: -1

A general complex number is written as:

z = a + b*i

Where a is the real part and b is the imaginary part.

In this case, we have the number:

z = -6 - i

We can rewrite this as:

z = -6 + (-1)*i

Then the real part is the number that is alone, in this case, -6.

The imaginary part is the coefficient that multiplies the "i", which is -1.

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Answer: 0.92v

Step-by-step explanation:

Answer:

The sum of the first 30 terms of the sequence [tex]\( A_n = 3n + 2 \)[/tex] is 1455.

Explanation:

To find the sum of the first 30 terms of the sequence [tex]\( A_n = 3n + 2 \),[/tex] we need to substitute the values of [tex]\( n \)[/tex] from 1 to 30 into the formula and then add them together.

The formula for the [tex]\( n \)[/tex]th term of the sequence is [tex]\( A_n = 3n + 2 \).[/tex]

Let's find the first 30 terms of the sequence:

[tex]\[ A_1 = 3(1) + 2 = 5 \][/tex]

[tex]\[ A_2 = 3(2) + 2 = 8 \][/tex]

[tex]\[ A_3 = 3(3) + 2 = 11 \][/tex]

[tex]\[ \vdots \][/tex]

[tex]\[ A_{30} = 3(30) + 2 = 92 \][/tex]

Now, we need to find the sum of these terms:

[tex]\[ \text{Sum} = A_1 + A_2 + A_3 + \ldots + A_{30} \][/tex]

To find the sum, we can use the formula for the sum of an arithmetic series:

[tex]\[ \text{Sum} = \frac{n}{2}(A_1 + A_{30}) \][/tex]

Where:

- [tex]\( n \)[/tex] is the number of terms (30 in this case)

- [tex]\( A_1 \)[/tex] is the first term (5)

- [tex]\( A_{30} \)[/tex] is the 30th term (92)

Now, let's calculate the sum:

[tex]\[ \text{Sum} = \frac{30}{2}(5 + 92) \][/tex]

[tex]\[ \text{Sum} = \frac{30}{2}(97) \][/tex]

[tex]\[ \text{Sum} = 15 \times 97 \][/tex]

[tex]\[ \text{Sum} = 1455 \][/tex]

Answer:

15i² + 49i + 33.

Step-by-step explanation:

Given : (8 + 3i)(3 + 5i).

To find : Multiply .

Solution : We have given (8 + 3i)(3 + 5i).

Distribute 8 over (3 + 5i) and 3i over (3 + 5i).

8 (3 + 5i) + 3i(3 + 5i).

8 *3 + 8 * 5i + 3 *3i + 3i *5i.

24 + 40 i + 9i + 15 i².

Combine like terms

24 + 9i +40i + 15i².

24 + 49i + 15i².

Therefore,15i² + 49i + 33.

The golf ball is at the point (2.5,2) and the hole is at the point (9.5,2) the golfer wants to bank off the side wall of the green at the point (x,y)

U+xy

Where u=18,x=10,y=8

Sub in all these values

18+10(8)

18+80

98

Hope this helps!