If i=Square root of -1, what is the value of i^3?
A.-1
B.i
C.1
D.-i

we know that

the equation of the line in the form point-slope is equal to

[tex]y-y1=m*(x-x1)[/tex]

in this problem we have

[tex]point(4,-1)\\\\m=\frac{3}{2}[/tex]

Substitute the values

[tex]y+1=\frac{3}{2}*(x-4)[/tex]

[tex]y=\frac{3}{2}x-6-1\\\\y=\frac{3}{2}x-7[/tex]

therefore

the answer is

[tex]y=\frac{3}{2}x-7[/tex]

Using trigonometry, Claire is approximately 19.42 feet away from Marisa, given their angles of elevation and the hoop's height.

Using trigonometry, we can find the distance between Claire and Marisa:

[tex]\[ \text{Let } h \text{ be the height of the basketball hoop.} \][/tex]

[tex]\[ \text{Distance}_{\text{Claire}} = \frac{h}{\tan(35°)} \][/tex]

[tex]\[ \text{Distance}_{\text{Marisa}} = \frac{h}{\tan(25°)} \][/tex]

[tex]\[ \text{Distance}_{\text{Claire-Marisa}} = \text{Distance}_{\text{Claire}} - \text{Distance}_{\text{Marisa}} \][/tex]

[tex]\[ \text{Distance}_{\text{Claire-Marisa}} = \frac{h}{\tan(35°)} - \frac{h}{\tan(25°)} \][/tex]

[tex]\[ \text{Distance}_{\text{Claire-Marisa}} = h \times \left( \frac{1}{\tan(35°)} - \frac{1}{\tan(25°)} \right) \][/tex]

Given [tex]\( h = 10 \)[/tex] feet:

[tex]\[ \text{Distance}_{\text{Claire-Marisa}} = 10 \times \left( \frac{1}{\tan(35°)} - \frac{1}{\tan(25°)} \right) \][/tex]

[tex]\[ \text{Distance}_{\text{Claire-Marisa}} \approx 19.42 \text{ feet} \][/tex]

So, Claire and Marisa are standing approximately 19.42 feet apart.

A square can be divided into two right-angled triangles with one line, but it can't be divided into two obtuse triangles because none of the angles in a square is more than 90 degrees.

No, it is not possible for Kateri to divide the square into two obtuse triangles by drawing just one line. An obtuse triangle is a triangle that has an angle greater than 90 degrees. However, a square is made up of four 90-degree angles. Therefore, when a square is divided into two triangles with one line, the maximum degrees any angle in resulting triangles would get is 90, hence they would be right-angled triangles and not obtuse triangles.

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Since RSTW is a rhombus, the area of ∆WXT is equal to 18√3 square units.

In Mathematics and Geometry, the length of the hypotenuse (longest side) of a 30°-60°-90° triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30°-60°-90° triangle is √3 times the length of the shorter leg (adjacent side):

Hypotenuse = 12 units.

Adjacent side = 12/2 = 6 units.

For the value of x, we have;

Opposite side = √3 × adjacent side

x = √3 × 6

x = 6√3 units.

Now, we can determine the area of triangle WXT;

Area of triangle = 1/2 × base × height

Area of ∆WXT = 1/2 × XT × WX

Area of ∆WXT = 1/2 × 6 × 6√3

Area of ∆WXT = 18√3 square units.

Complete Question:

If RSTW is a rhombus, what is the area of ∆WXT?

Answer:

Option 4

Step-by-step explanation:

Given : d to the 7th power times g to the 13th power all over d to the 2nd power times g to the 7th power.

To find : The correct  simplification

Solution :

d to the 7th power = [tex]d^7[/tex]

g to the 13th power = [tex]g^{13}[/tex]

d to the 7th power times g to the 13th power =  [tex]d^7\times g^{13}[/tex]

d to the 2nd power = [tex]d^2[/tex]

g to the 7th power = [tex]g^7[/tex]

d to the 2nd power times g to the 7th power =  [tex]d^2\times g^{7}[/tex]

According to question,

d to the 7th power times g to the 13th power all over d to the 2nd power times g to the 7th power.

[tex]=\frac{d^7\times g^{13}}{d^2\times g^7}[/tex]

[tex]=d^{7-2}\times g^{13-7}[/tex]

[tex]=d^{5}\times g^{6}[/tex]

Therefore, Option 4 is correct.

The easiest option will definitely be:

x = 5 and y = y

Hope it helped,

Happy homework/ study/ exam!

Final answer:

By setting up an equation based on the given ratio 2:5 and the additional information that Julie receives £45 more than Pat, we find that Pat received £30.

Explanation:

The question deals with understanding ratios and how they can be used to solve problems involving sharing amounts in specified proportions. Pat and Julie share some money in the ratio 2:5, and it's given that Julie gets £45 more than Pat. To approach this problem, let's designate the amount Pat receives as 2x and the amount Julie receives as 5x, where x is a common multiplier.

It is stated that Julie gets £45 more than Pat, which can be represented as 5x = 2x + 45.

Solving the equation for x gives us 3x = 45, hence x = 15.

To find out how much Pat received, we substitute x = 15 into 2x, giving us 2(15) = 30.

Therefore, Pat got £30.

Final answer:

To decide the better purchase between two sizes of shampoo, the cost per ounce is calculated, showing that the 18oz option at $0.22 per ounce is more economical than the 24oz option at $0.25 per ounce.

Explanation:

To determine which shampoo option is the better buy, we calculate the cost per ounce for each option. Cost per ounce is calculated by dividing the total cost of the product by the total number of ounces.

For the 18oz shampoo at $3.99, cost per ounce = $3.99 / 18oz = $0.22 per ounce.

For the 24oz shampoo at $5.99, cost per ounce = $5.99 / 24oz = $0.25 per ounce.

The 18oz shampoo at $0.22 per ounce is the better buy compared to the 24oz shampoo at $0.25 per ounce because you are paying less per ounce.

Answer:2/10 is equal to

any even number has to have a half like 2 4 6 8

2 is half of 4      1 is half of 2      4 is half of 8     and so on

the fractiom is shaded into 2/10

5/10

your wecs                              :0              ;)

Final answer:

The expression 27x^2z/-3x^2z^6 simplifies to -9/z^5, so the simplified exponent on the variable z is -5.

Explanation:

When simplifying the expression 27x^2z/-3x^2z^6, we divide the coefficients and apply the laws of exponents. This means we divide 27 by -3 and subtract the exponents of like terms with variables of the same base.

27/-3 equals -9, and for the variables we subtract the exponents, for x^2 we have x^2/x^2 which simplifies to x^0 and for z we have z^1/z^6, simplifying to z^(1-6) which is z^-5. However, because negative exponents denote division by that variable to the positive exponent, z^-5 represents 1/z^5.

The final simplified expression is -9/z^5. Thus, the exponent on the variable z when the expression 27x^2z/-3x^2z^6 is completely simplified is -5.

Answer:

its false, i did the test

Step-by-step explanation:

There were [tex]\(38\)[/tex] votes for blue and [tex]\(13\)[/tex] votes for green.

Let's break it down step by step:

1. Votes for Blue:

  Initially, [tex]\(5/8\)[/tex] of the votes were for blue. Let's denote the total number of votes as [tex]\(T\).[/tex]

  So, the number of votes for blue initially is [tex]\(5/8\) of \(T\)[/tex], which is [tex]\((5/8) \times T\)[/tex].

2. Remaining votes after blue:

  After blue votes are accounted for, the remaining votes are [tex]\(T - (5/8) \times T = (3/8) \times T\).[/tex]

3. Votes for Green:

  [tex]\(5/9\)[/tex] of the remaining votes are for green. So, the number of votes for green is [tex]\((5/9) \times (3/8) \times T\)[/tex].

4. Votes for Red:

  The remaining votes after blue and green are accounted for are 48 votes.

To find the solution, we need to set up equations based on the information given:

Equation 1: Votes for blue + Votes for green + Votes for red = Total votes

Equation 2: Votes for green = \(5/9\) of remaining votes

Equation 3: Votes for red = 48

Let's solve these equations:

Equation 1:

[tex]\[\frac{5}{8}T + \frac{5}{9} \times \frac{3}{8}T + 48 = T\][/tex]

Equation 2:

[tex]\[\frac{5}{9} \times \frac{3}{8}T = \frac{15}{72}T = \frac{5}{24}T\][/tex]

Now, let's substitute the value of [tex]\(T\)[/tex] from Equation 3 into Equation 1:

[tex]\[\frac{5}{8} \times \frac{48}{5} + \frac{5}{9} \times \frac{3}{8} \times \frac{48}{5} + 48 = \frac{48}{8} + \frac{15}{24} \times \frac{48}{5} + 48 = 6 + 3 \times 2 + 48 = 60\][/tex]

So, we have [tex]\(T = 60\).[/tex]

Now, let's find the number of votes for blue and green:

Votes for blue:

[tex]\[\frac{5}{8} \times 60 = 37.5\][/tex]

Votes for green:

[tex]\[\frac{5}{24} \times 60 = 12.5\][/tex]

Since we can't have half votes, we round 37.5 to 38 and 12.5 to 13.

So, there were [tex]\(38\)[/tex] votes for blue and [tex]\(13\)[/tex] votes for green.

The correct question is:

5/8 of the votes were for blue. 5/9 of the remaining votes were for green and the remaining 48 votes were for red. How many votes were for blue? How many votes were for green?

Answer:

im sorry i dont get it

Step-by-step explanation:

since y+y=y^2 also they following

To memorize your timetables, you can use mnemonic techniques, break down the tables into smaller chunks, and practice regularly.

Multiplication tables, also known as timetables, can be challenging to memorize. However, there are several strategies that you can use to make the process easier. One effective method is to create mnemonics, which are memory aids that help you associate numbers with images or phrases. For example, you can associate the number 9 with the shape of a cat's tail, and whenever you see the number 9 in a multiplication problem, you can visualize a cat's tail to help you remember the answer.

Another useful strategy is to break down the tables into smaller, more manageable chunks. Start by memorizing the tables for numbers 0-5, and once you feel comfortable with them, move on to the tables for numbers 6-10. By tackling smaller chunks, you can avoid overwhelming yourself and improve your retention.

Finally, practice regularly and consistently. The more you review the timetables, the more familiar they will become. Consider using online resources, flashcards, or interactive games to make the practice sessions more engaging and enjoyable. Over time, with practice and perseverance, you will gradually memorize your timetables.

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Answer: 120 people like brand A better

Step-by-step explanation: