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svp [43]
3 years ago
6

Gustavo and yuki were asked to find an explicit formula for the sequence 19, 0, -19, -38...

Mathematics
1 answer:
KiRa [710]3 years ago
4 0

Answer:

<h2>Neither Gustavo nor Yuki</h2>

Step-by-step explanation:

It's an arithmetic sequence.

0-19=-19\\-19-0=-19\\-38-(-19)=-38+19=-19

The difference is constant.

The explicit formula of an arithmetic sequence:

a_n=a_1+(n-1)d

Substitute:

a_1=19,\ d=-19

a_n=19+(n-1)(-19)             <em>use distributive property</em>

a_n=19-19n+19\\\\a_n=(19+19)-19n\\\\a_n=38-19n

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5 0
3 years ago
Read 2 more answers
You rotate a triangle 90° counterclockwise about the origin. Then you translate its image 1 unit left and 2 units down. The vert
sergiy2304 [10]

Answer:

The coordinates of the original triangle are (2,4). (4,1) and (1,1)

Step-by-step explanation:

About the origin, I have to rotate a triangle 90° counterclockwise. Then I translate its image 1 unit left and 2 units down.

The vertices of the final image are (-5,0), (-2,2), and (-2,-1).

We need to get the vertices of the original triangle.

So, start from a triangle with vertices (-5,0), (-2,2), and (-2,-1) and do the reverse to get the original triangle.

So, we will translate the image triangle by 1 unit right and 2 units up and we will get the triangle with vertices (-5 + 1, 0 + 2), (- 2 + 1, 2 + 2) and (- 2 +1, - 1 + 2)  ≡ (-4,2), (-1, 4) and (-1,1).

Now, we have to rotate this intermediate triangle by 90° clockwise.

Therefore, the coordinates of the original triangle are (2,4). (4,1) and (1,1) (Answer)

{Since, for 90° rotation the coordinates of all the vertices will interchange their location (i.e. x-value to y-value and y-value to x-value) and a negative sign will be added to the y-coordinate of the interchanged coordinates}  

5 0
3 years ago
A 10-pound bag of wildflower seed covers 25 square feet. How many pounds of seed does it take to cover 1 square​ foot?
adell [148]

Answer:

0.4 pounds

Step-by-step explanation:

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10 / 25 = 0.4

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3 years ago
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saul85 [17]
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3 years ago
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Solve the following quadratic equation for all values of x in simplest form.<br> 20+ 2x= 28
n200080 [17]

Answer:

x = 4

Step-by-step explanation:

<em>To solve, we need to isolate </em><em>x</em><em>.</em>

<em>Start by moving the </em><em>20</em><em> to the other side by subtracting it from both sides.</em>

2x = 8

<em>Since </em><em>x</em><em> is being multiplied by </em><em>2</em><em>, we need to </em><u><em>divide</em></u><em> both sides by </em><em>2</em><em> to move it to the other side.</em>

x = 4

6 0
3 years ago
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