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oksian1 [2.3K]
3 years ago
14

Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4

)? a 180 rotation about the origin a 90 counterclockwise rotation about the origin and a translation down 4 units a 90 clockwise rotation about the origin and a reflection over the y-axis a reflection over the y-axis and then a 90 clockwise rotation about the origin

Mathematics
2 answers:
antiseptic1488 [7]3 years ago
8 0

Answer:

C. a 90 clockwise rotation about the origin and a reflection over the y-axis

Step-by-step explanation:

jek_recluse [69]3 years ago
5 0
Notice that every pair of point (x, y) in the original picture, has become (-y, -x) in the transformed figure.

Let ABC be first transformed onto A"B"C" by a 90° clockwise rotation.

Notice that B(4, 1) is mapped onto B''(1, -4). So the rule mapping ABC to A"B"C"   is (x, y)→(y, -x)

so we are very close to (-y, -x).

The transformation that maps (y, -x) to (-y, -x) is a reflection with respect to the y-axis. Notice that the 2. coordinate is same, but the first coordinates are opposite.


ANSWER:

"<span>a 90 clockwise rotation about the origin and a reflection over the y-axis</span>"


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The table below represents an exponential function what is the common ratio
Greeley [361]

Solution:

Given:

A table representing an exponential function.

The x-values represent the terms, while the y-values represent the numbers.

The common ratio is gotten from the numbers (y-values).

The formula for common ratio is given by;

\begin{gathered} r=\frac{present\text{ term}}{preceed\text{ ing term}} \\  \\ \text{Hence,} \\ r=\frac{108}{36}=\frac{36}{12}=\frac{12}{4}=\frac{4}{1.33\ldots}=\frac{1.33\ldots.}{0.44\ldots} \\ r=3 \end{gathered}

Therefore, the common ratio is 3.

3 0
1 year ago
List x1, x2, x3, x4 where xi is the left endpoint of the four equal intervals used to estimate the area under the curve of f(x)
n200080 [17]

Answer:

Option A. 4, 4.5, 5, 5.5

Step-by-step explanation:

Left point: a=x=4

Right point: b=x=6

Range: r=b-a→r=6-4→r=2

Width of each of the four equal intervals: w=2/4→w=0.5

The first left endpoint is x1=a→x1=4

The second left endpoint is x2=x1+w→x2=4+0.5→x2=4.5

The third left endpoint is x3=x2+w→x3=4.5+0.5→x3=5

The fourth left endpoint is x4=x3+w→x4=5+0.5→x4=5.5

Then, the list is: x1, x2, x3, x4 = 4, 4.5, 5, 5.5

4 0
3 years ago
How do you find the limit?
coldgirl [10]

Answer:

2/5

Step-by-step explanation:

Hi! Whenever you find a limit, you first directly substitute x = 5 in.

\displaystyle \large{ \lim_{x \to 5} \frac{x^2-6x+5}{x^2-25}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{5^2-6(5)+5}{5^2-25}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{25-30+5}{25-25}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{0}{0}}

Hm, looks like we got 0/0 after directly substitution. 0/0 is one of indeterminate form so we have to use another method to evaluate the limit since direct substitution does not work.

For a polynomial or fractional function, to evaluate a limit with another method if direct substitution does not work, you can do by using factorization method. Simply factor the expression of both denominator and numerator then cancel the same expression.

From x²-6x+5, you can factor as (x-5)(x-1) because -5-1 = -6 which is middle term and (-5)(-1) = 5 which is the last term.

From x²-25, you can factor as (x+5)(x-5) via differences of two squares.

After factoring the expressions, we get a new Limit.

\displaystyle \large{ \lim_{x\to 5}\frac{(x-5)(x-1)}{(x-5)(x+5)}}

We can cancel x-5.

\displaystyle \large{ \lim_{x\to 5}\frac{x-1}{x+5}}

Then directly substitute x = 5 in.

\displaystyle \large{ \lim_{x\to 5}\frac{5-1}{5+5}}\\&#10;&#10;\displaystyle \large{ \lim_{x\to 5}\frac{4}{10}}\\&#10;&#10;\displaystyle \large{ \lim_{x\to 5}\frac{2}{5}=\frac{2}{5}}

Therefore, the limit value is 2/5.

L’Hopital Method

I wouldn’t recommend using this method since it’s <em>too easy</em> but only if you know the differentiation. You can use this method with a limit that’s evaluated to indeterminate form. Most people use this method when the limit method is too long or hard such as Trigonometric limits or Transcendental function limits.

The method is basically to differentiate both denominator and numerator, do not confuse this with quotient rules.

So from the given function:

\displaystyle \large{ \lim_{x \to 5} \frac{x^2-6x+5}{x^2-25}}

Differentiate numerator and denominator, apply power rules.

<u>Differential</u> (Power Rules)

\displaystyle \large{y = ax^n \longrightarrow y\prime= nax^{n-1}

<u>Differentiation</u> (Property of Addition/Subtraction)

\displaystyle \large{y = f(x)+g(x) \longrightarrow y\prime = f\prime (x) + g\prime (x)}

Hence from the expressions,

\displaystyle \large{ \lim_{x \to 5} \frac{\frac{d}{dx}(x^2-6x+5)}{\frac{d}{dx}(x^2-25)}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{\frac{d}{dx}(x^2)-\frac{d}{dx}(6x)+\frac{d}{dx}(5)}{\frac{d}{dx}(x^2)-\frac{d}{dx}(25)}}

<u>Differential</u> (Constant)

\displaystyle \large{y = c \longrightarrow y\prime = 0 \ \ \ \ \sf{(c\ \  is \ \ a \ \ constant.)}}

Therefore,

\displaystyle \large{ \lim_{x \to 5} \frac{2x-6}{2x}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{2(x-3)}{2x}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{x-3}{x}}

Now we can substitute x = 5 in.

\displaystyle \large{ \lim_{x \to 5} \frac{5-3}{5}}\\&#10;&#10;\displaystyle \large{ \lim_{x \to 5} \frac{2}{5}}=\frac{2}{5}

Thus, the limit value is 2/5 same as the first method.

Notes:

  • If you still get an indeterminate form 0/0 as example after using l’hopital rules, you have to differentiate until you don’t get indeterminate form.
8 0
3 years ago
7. Veronica is choosing between two health clubs.
vesna_86 [32]

Answer:

The total cost for  each health club will be the same after 4 months.

Step-by-step explanation:

  • Let A = membership fee for studio A
  • B = membership fee for studio B
  • x= membership month

  • A = 22 + 24.5x
  • B = 47.00 + 18.25x

We want to when the total cost at each health studio is the same.

In other words, when A = B.

Therefore, the expression becomes

A = B

22\:+\:24.5x=47.00\:+\:18.25x

Step 1: Simplify both sides of the equation.

24.5x+22=18.25x+47

Step 2: Subtract 18.25x from both sides.

24.5x+22-18.25x=18.25x+47-18.25x

6.25x+22=47

Step 3: Subtract 22 from both sides.

6.25x+22-22=47-22

6.25x=25

Step 4: Divide both sides by 6.25

\frac{6.25x}{6.25}=\frac{25}{6.25}

x=4

Therefore, the total cost for  each health club will be the same after 4 months.

8 0
3 years ago
I need someone to answer a s a p!!!!​
Bogdan [553]
30 square units is what i got
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