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3 years ago

URGENT ALGEBRA 2 Anyone know these answers? Will award brainliest.

Mathematics

1 answer:

stiv31 [10]3 years ago

6 0

Correct Answer:
Second option

Solution:
The given sequence is:

2.2, 6.6, 11, ...

If we observe the sequence it is an Arithmetic Sequence as the difference between two consecutive terms is the same.

6.6 - 2.2 = 4.4
11 - 6.6 = 4.4

First we find the general term for this sequence.

$a(n)= a_{1}+(n-1)d$

$a_{1}=$ first term = 2.2
d = 4.4

So,

$a(n) = 2.2 +(n-1)*4.4 \\ \\ 
a(n) = 2.2 + 4.4n - 4.4 \\ \\ 
a(n) = 4.4n - 2.2$

This general term will be placed inside the summation sign with limits from 1 to 5 to give the sum of first 5 terms of the given sequence. So the correct answer is Second Option

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Twice the sum of two numbers is 36 If one of the numbers is 10 find the other number

Dahasolnce [82]

Answer:

Step-by-step explanation:

10 + 8 = 18

18 x 2 = 36

3 0

3 years ago

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A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto

Gre4nikov [31]

$\begin{cases}y=2x-2\\y=2x+2\end{cases}\implies\begin{cases}-2x+y=-2\\-2x+y=2\end{cases}$

For these lines, let $u=-2x+y$ .

$\begin{cases}y=2-x\\y=4-x\end{cases}\implies\begin{cases}x+y=2\\x+y=4\end{cases}$

And for these, let $v=x+y$ .

Now,

$\begin{cases}u=-2x+y\\v=x+y\end{cases}\implies \begin{bmatrix}u\\v\end{bmatrix}=\underbrace{\begin{bmatrix}-2&1\\1&1\end{bmatrix}}_{\mathbf T}\begin{bmatrix}x\\y\end{bmatrix}$

The vertices of $S$ in the x-y plane are (0, 2), (2/3, 10/3), (2, 2), and (4/3, 2/3). Applying $\mathbf T$ to each of these yields, respectively, (2, 2), (2, 4), (-2, 4), and (-2, 2), which are the vertices of a rectangle whose sides are parallel to the u-v plane.

6 0

3 years ago

(answer questions about the picture above)

jeka57 [31]

Answer:

Part a) The dilation is a contraction

Part b) The scale factor is 0.75

Part c) $AR=1.1\ cm$

Part d) $TN=4.8\ cm$

Step-by-step explanation:

Part a) Assume ∆TRI was dilated to become the image ∆TAN. Is the dilation an expansion or a contraction?

We have that

The pre-image is the triangle TRI (original figure)

The image is the triangle TAN (dilated figure)

we know that

If the image is smaller than the pre-image then the dilation is a contraction or reduction

If the image is greater than the pre-image then the dilation is a expansion or enlargement

The triangle TAN is smaller than triangle TRI

the image is smaller than the pre-image

therefore

The dilation is a contraction

Part b) What is the scale factor?

we know that

A dilation is a non-rigid transformation that produces similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

triangle TAN ~ triangle TRI

Let

z ----> the scale factor

$z=\frac{AN}{RI}$

AN and RI are corresponding sides

substitute the given values

$z=\frac{6}{8}=0.75$

Part c) Calculate AR. Show your work

Remember that the ratio of its corresponding sides is proportional and is equal to the scale factor

$\frac{TA}{TR}=z$

substitute the given values

$\frac{3.3}{TR}=0.75$

Solve for TR

$TR=3.3/0.75\\TR=4.4\ cm$

Find the length of AR

we know that

$TR=TA+AR$ ----> by segment addition postulate

substitute the given values

$4.4=3.3+AR\\AR=4.4-3.3=1.1\ cm$

Part d) Use the Side-Splitting Theorem to find TN.

we know that

The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally

Applying the Side-Splitting Theorem

$\frac{TN}{NI}=\frac{TA}{AR}$