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nikitadnepr [17]
3 years ago
14

How do you know whether a function is going to be horizontally stretched or compressed or vertically stretched or compressed wit

hout parentheses? Ex: f(x) = 2x^2 or f(x)= (2x)^2 or f(x)= 2f(x)^2
Mathematics
1 answer:
Valentin [98]3 years ago
4 0

Answer:

  it depends

Step-by-step explanation:

When the transformation is written in functional form:

  g(x) = a·f(x) . . . . vertical expansion by a factor of "a"

  g(x) = f(a·x) . . . . horizontal compression by a factor of "a"

the transformation can be determined by the locations of the various scale factors (and offsets).

__

When the function is written out, as in two of your examples, the transformation is subject to some "interpretation."

  y = 2x² . . . . . can be considered a vertical stretch of x²

  y = (2x)² . . . . can be considered a horizontal compression of x²

  y = 4x² . . . . . can be considered a vertical stretch of x²

Please note that these last two examples have identical graphs. It depends on what you consider to be the parent function, and how you consider the transformation to be applied. The use of parentheses can guide your interpretation of the transformation.

Different transformations can have the same result, so which way you interpret the equation depends on what you consider to be the parent function and how you consider the transformation to be applied. Often, the context of the question is involved, too.

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Write an algebraic equation to solve for the triangle’s height. Area of the triangle =36.8 inches . Height is x and base is 4.6
Minchanka [31]
The formula to find the Height of a triangle when you have the Area and the base is H = 2 * A/b
if the Area is 36.8 then divide it by 4.6.  You get 8.  put 36.8 in calculator first, then 4.6 = 8
2 x 8 = 16...so the answer should be 16 inches.
2 is in the formula to multiply to the number you get after dividing the base into the Area.
16 Answer
3 0
3 years ago
PLEASE HELP MEEEE HURRRY!!! :)
sammy [17]

Answer:

Option D

Step-by-step explanation:

We are given the following equations -

\begin{bmatrix}-5x-12y-43z=-136\\ -4x-14y-52z=-146\\ 21x+72y+267z=756\end{bmatrix}

It would be best to solve this equation in matrix form. Write down the coefficients of each terms, and reduce to " row echelon form " -

\begin{bmatrix}-5&-12&-43&-136\\ -4&-14&-52&-146\\ 21&72&267&756\end{bmatrix}  First, I swapped the first and third rows.

\begin{bmatrix}21&72&267&756\\ -4&-14&-52&-146\\ -5&-12&-43&-136\end{bmatrix}  Leading coefficient of row 2 canceled.  

\begin{bmatrix}21&72&267&756\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\\ -5&-12&-43&-136\end{bmatrix}  The start value of row 3 was canceled.

\begin{bmatrix}21&72&267&756\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\\ 0&\frac{36}{7}&\frac{144}{7}&44\end{bmatrix}       Matrix rows 2 and 3 were swapped.

\begin{bmatrix}21&72&267&756\\ 0&\frac{36}{7}&\frac{144}{7}&44\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\end{bmatrix}      Leading coefficient in row 3 was canceled.

\begin{bmatrix}21&72&267&756\\ 0&\frac{36}{7}&\frac{144}{7}&44\\ 0&0&0&\frac{4}{9}\end{bmatrix}

And at this point, I came to the conclusion that this system of equations had no solutions, considering it reduced to this -

\begin{bmatrix}1&0&-1&0\\ 0&1&4&0\\ 0&0&0&1\end{bmatrix}

The positioning of the zeros indicated that there was no solution!

<u><em>Hope that helps!</em></u>

6 0
3 years ago
The graph shows the relationship between the total cost and the number of erasers bought at the student store. Which statement i
hjlf

The graph shows the relationship between the total cost. The true statement is

Seven erasers cost $3.50. Option D

This is further explained below.

<h3>The graph shows the relationship between the total cost and the number of erasers bought at the student store. Which statement is true?</h3>

Generally, A cost is the worth of the money that has been spent in the process of producing something or delivering a service, and as a result, it is no longer accessible for use.

This concept is utilized in manufacturing, research, retail, and accounting. In the world of business, a cost may refer to a purchase, in which case the sum of money spent on the item in question is considered to be the cost of the item.

In conclusion, each eraser will cost u 50 cents

so 7 erasers will cost (7 * 0.50) = 3.50

Read more about costs

brainly.com/question/15135554

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6 0
1 year ago
What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw? T
Xelga [282]
Break it down into two parts. First, what is the probability of drawing a blue marble on the first draw?Since there are 5 blue marbles and 10 total, the probability is 5⁄10, or 1/2. Now since we no longer have that blue marble, there are 4 blue marbles and 9 total. The chances of drawing a blue marble are 4/9. Therefore, the chance that both marbles drawn are blue is the chance that the first one is blue times the chance that the second one is blue. 1/2 * 4/9 = 4/18 = 2/9 Remember, math is always trying to trick you. It wants you to try and do the whole big problem at once, which can be difficult. Break it down into smaller problems, then use your answers to small parts to find the answer to the big question.

Ishrat
6 0
3 years ago
Read 2 more answers
Consider the diagram below. which of the following represents the values x,y and z?
Gemiola [76]

Answer:

x=4\sqrt{6}\ units

y=4\sqrt{2}\ units

z=4\sqrt{3}\ units

Step-by-step explanation:

The picture of the question in the attached figure

step 1

In the right triangle ABD

Applying the Pythagorean Theorem

x^2=y^2+(12-4)^2

x^2=y^2+64

y^2=x^2-64 ----> equation A

step 2

In the right triangle BDC

Applying the Pythagorean Theorem

z^2=y^2+4^2

z^2=y^2+16

y^2=z^2-16 ----> equation B

step 3

In the right triangle ABC

Applying the Pythagorean Theorem

12^2=x^2+z^2

144=x^2+z^2 ----> equation C

step 4

Equate equation A and equation B

x^2-64=z^2-16

x^2=z^2+48 -----> equation D

step 5

substitute equation D in equation C

144=z^2+48+z^2

solve for z

2z^2=144-48

2z^2=96

z^2=48

z=\sqrt{48}\ units

simplify

z=4\sqrt{3}\ units

Find the value of x

x^2=z^2+48

x^2=48+48=96

x=\sqrt{96}\ units

x=4\sqrt{6}\ units

Find the value of y

y^2=z^2-16

y^2=48-16

y^2=32

y=\sqrt{32}\ units

y=4\sqrt{2}\ units

3 0
3 years ago
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