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2 years ago

Trapezoid FGHI is rotated using the origin as the center of rotation. The preimage and image are graphed below.

Mathematics

2 answers:

skelet666 [1.2K]2 years ago

8 0

The rotated image if below the original image, so this shows it was rotated clockwise.

In the original image line FG is a horizontal line, if it is rotated 90 degrees, it would become a vertical line. In the rotated image line FG is at an angle, so this means it was rotated 45 degrees.

The answer is a 45 degree clockwise rotation.

Alisiya [41]2 years ago

8 0

Answer: A 45° clockwise rotation transformed FGHI to F’G’H’I’.

Step-by-step explanation:

Hi, to answer this question we have to analyze the image.

The correct option is A 45° clockwise rotation.

If we put our focus in one line of the trapezoid, for example, the line FG we can see that if we compare the line FG with F'G', F'G' is positioned in a 45° angle (positive).

Feel free to ask for more if it´s necessary or if you did not understand something.

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What are the possible numbers of positive, negative, and complex zeros of f(x) = x6 − x5 − x4 + 4x3 − 12x2 + 12?

FrozenT [24]

Using Descartes' rule of signs.
There are 4 changes of signs of coefficients:
+ to - (+x^6-x^5)
- to + (-x^4+4x^3)
+ to - (+4x^3-12x^2)
- to + (-12x^2+12)
Therefore, there are 4,2 or 0 positive roots at most. So it must be the third answer.

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3 years ago

Read 2 more answers

Use the Factor Theorem to find ALL zeros of f(x) = x^3 - x^2 - 11x + 15, given that 3 is a zero. Show all work and express zeros

ELEN [110]

Answer:

Step-by-step explanation:

by synthetic division

3) 1 -1 -11 15

| 3 6 -15 (add)

____________

1 2 -5 |0

x²+2x-5=0

$x=\frac{-2 \pm\sqrt{2^{2} -4*1*-5} }{2*1} \\or~x=\frac{-2 \pm\sqrt{4+20} }{2} \\or~x=\frac{-2 \pm2\sqrt{6} }{2} \\or ~x=-1 \pm \sqrt{6}$

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3 years ago

A sandwich shop offers 3 rypes of bread and 4 types of meat. How many different sandwiches consisting of 1 type of bread and 1 t

lisabon 2012 [21]

So if theres 3 rypes of bread and 4 type of meat u just have to multiply 3×4 gives u 12
Answer : u can make 12

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3 years ago

The figure shows a line graph and two shaded triangles that are similar:

dlinn [17]

True:

3rd One

4th One

False: All of the others.

It's a straight line, so it is going to have straight qualities and straight inequalities throughout the graph.

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3 years ago

A college infirmary conducted an experiment to determine the degree of relief provided by three cough remedies. Each cough remed

KiRa [710]

Answer:

$p_v = P(\chi^2_{4,0.05} >3.81)=0.43233$

Since the p values is higher than the significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences between the 3 remedies analyzed. So we can say that the 3 remedies ar approximately equally effective.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

NyQuil Robitussin Triaminic Total

No relief 11 13 9 33

Some relief 32 28 27 87

Total relief 7 9 14 30

Total 50 50 50 150

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is no difference in the three remedies

H1: There is a difference in the three remedies

The level os significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{50*33}{150}=11$

$E_{2} =\frac{50*33}{150}=11$

$E_{3} =\frac{50*33}{150}=11$

$E_{4} =\frac{50*87}{150}=29$

$E_{5} =\frac{50*87}{150}=29$

$E_{6} =\frac{50*87}{150}=29$

$E_{7} =\frac{50*30}{150}=10$

$E_{8} =\frac{50*30}{150}=10$

$E_{9} =\frac{50*30}{150}=10$

And the expected values are given by:

NyQuil Robitussin Triaminic Total

No relief 11 11 11 33

Some relief 29 29 29 87

Total relief 10 10 10 30

Total 50 50 50 150

And now we can calculate the statistic:

$\chi^2 = \frac{(11-11)^2}{11}+\frac{(13-11)^2}{11}+\frac{(9-11)^2}{11}+\frac{(32-29)^2}{29}+\frac{(28-29)^2}{29}+\frac{(27-29)^2}{29}+\frac{(7-10)^2}{10}+\frac{(9-10)^2}{10}+\frac{(14-10)^2}{10} =3.81$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(3-1)=4$

And we can calculate the p value given by:

$p_v = P(\chi^2_{4,0.05} >3.81)=0.43233$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(3.81,4,TRUE)"

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3 years ago