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77julia77 [94]
2 years ago
11

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 <span>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 </span><span><span>at most</span>. So it must be the third answer.
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3 0
3 years ago
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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}

5 0
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
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7 0
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.

8 0
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)"

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.

4 0
3 years ago
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