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serious [3.7K]
2 years ago
15

Can i plz get some help with this!its about finding the conjecture​

Mathematics
1 answer:
Studentka2010 [4]2 years ago
6 0

Answer:

3-they are cubes of consecutive natural numbers

1 cube is 1

2 cube is 8

3 cube is 27

and so on...

let me know if you're asking fourth one or third one

You might be interested in
Please help!!<br> Write a matrix representing the system of equations
frozen [14]

Answer:

(4, -1, 3)

Step-by-step explanation:

We have the system of equations:

\left\{        \begin{array}{ll}            x+2y+z =5 \\    2x-y+2z=15\\3x+y-z=8        \end{array}    \right.

We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:

\begin{bmatrix}x_1& y_1& z_1&c_1\\x_2 & y_2 & z_2&c_2\\x_3&y_2&z_3&c_3 \end{bmatrix}

Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.

In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:

\begin{bmatrix}1 & 0& 0&x\\0 & 1 & 0&y\\0&0&1&z \end{bmatrix}

Where the (x, y, z) is our solution set.

Reducing:

With our system, we will have the following matrix:

\begin{bmatrix}1 & 2& 1&5\\2 & -1 & 2&15\\3&1&-1&8 \end{bmatrix}

What we should begin by doing is too see how we can change each row to the reduced-form.

Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:

\begin{bmatrix}1 & 2& 1&5\\2+(-2) & -1+(-4) & 2+(-2)&15+(-10) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\0 & -5 & 0&5 \\3&1&-1&8 \end{bmatrix}

Now, we can multiply R₂ by -1/5. This yields:

\begin{bmatrix}1 & 2& 1&5\\ -\frac{1}{5}(0) & -\frac{1}{5}(-5) & -\frac{1}{5}(0)& -\frac{1}{5}(5) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3&1&-1&8 \end{bmatrix}

From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:

\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3+(-3)&1+(-6)&-1+(-3)&8+(-15) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&-5&-4&-7 \end{bmatrix}

We can eliminate the -5 in R₃ by adding 5(R₂). This yields:

\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0+(0)&-5+(5)&-4+(0)&-7+(-5) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&-4&-12 \end{bmatrix}

We can now reduce R₃ by multiply it by -1/4:

\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\ -\frac{1}{4}(0)&-\frac{1}{4}(0)&-\frac{1}{4}(-4)&-\frac{1}{4}(-12) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}

Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:

\begin{bmatrix}1+(0) & 2+(-2)& 1+(0)&5+(-(-2))\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 1&7\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}

And finally, we can eliminate the second 1 by adding -(R₃):

\begin{bmatrix}1 +(0)& 0+(0)& 1+(-1)&7+(-3)\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 0&4\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}

Therefore, our solution set is (4, -1, 3)

And we're done!

3 0
2 years ago
Write down down an equation of a line that is parallel to the line with the equation y=7-x
Bingel [31]

Answer:

y=8-x or y=9-x or y=243-x (The spot where the 8 is can be any number as long as the number infront of the 0 is still -1)

Step-by-step explanation:

5 0
2 years ago
Please help!!!!!!<br> ahjjhhhhh
Katarina [22]

Answer:

i need pointsss

Step-by-step explanation:

6 0
2 years ago
You need 3 sticks of butter for every 24 giant cookies you bake.
marta [7]

Answer:

Sticks of butter : 2

Number of cookies : 40

Step-by-step explanation:

<em>Given that :You need 3 sticks of butter for every 24 giant cookies you bake.</em>

<em>----------------------------------------------------------------------------------------------------------</em>

<em>Sticks of butter                    Number of cookies</em>

<em>  3                                           24</em>

<em>  x                                             16</em>

<em>5                                                 y</em>

<em>----------------------------------------------------------------------------------------------------------</em>

<em>Let the unknown be x and y..</em>

<em>Since you need 3 sticks of butter for every 24 giant cookies you back</em>

<em>Then 24/3 = 8</em>

<em>Since the number of cookies is 16 then 16/8 = 2</em>

<em>Thus x = 2</em>

<em>Next for y.</em>

<em>Since you need 3 sticks of butter for every 24 giant cookies you back</em>

<em>Then 5 * 8 = 40</em>

<em>Thus, y = 40</em>

<em>----------------------------------------------------------------------------------------------------------</em>

<em>Completed table below:</em>

<em>Sticks of butter                    Number of cookies</em>

<em>  3                                           24</em>

 2    <em>                                         16</em>

<em>5                                                 </em><em>40</em>

<em>----------------------------------------------------------------------------------------------------------</em>

<u><em>~lenvy~</em></u>

<em />

6 0
2 years ago
Read 2 more answers
Select the correct answer. Which graph represents the solution to the inequality?​
melisa1 [442]

Answer:

A

Step-by-step explanation:

First you simplify both sides to get -2.4x+14.4 > 52.8

then you need to subtract the 14.4 from both sides giving -2.4x> 38.4

then divide both sides by -2.4 giving an answer of

x is less than or equal to -16 meaning you point to the left with a closed circle

8 0
3 years ago
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