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olchik [2.2K]
3 years ago
13

Let f(x)=x2-3x + 9. Find f(-1).

Mathematics
1 answer:
netineya [11]3 years ago
3 0
X^2 - 3x + 9
(-1)^2 - 3(-1) + 9
1 - 3(-1) + 9
1 + 3 + 9
13
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In order to prove that traingle ADC is congruent to triangle ABC by SAS, we would need to show that
IRISSAK [1]

Answer:

D) Angle DAC is congruent to Angle BAC

Step-by-step explanation:

Given:

The triangles ABC and ADC are congruent by SAS postulate.

SAS postulate means two corresponding sides are congruent to each other and the included pair of angles are also congruent to each other.

From the figure, consider the triangles ABC and ADC.

AB = AD  (Given)

AC = AC ( Reflexive property. Side AC is a common side to both triangles)

Now, the pair of angles included between these two pair of sides are angle BAC and angle DAC.

So, in order to prove the two triangles congruent by SAS postulate, we need to prove angle DAC congruent to angle BAC. Therefore, the correct option is option D.

8 0
3 years ago
Among a sample of 55 male soldiers the average shower time was found to be 2.95 minutes and the population standard deviation is
Oksanka [162]

Answer: -3.0593

Step-by-step explanation:

The test statistic for the difference between two population mean (when population standard deviations \sigma_1\ \&\ \sigma_2  are known ) is given by :-

z=\dfrac{\overline{x}_1-\overline{x}_2}{\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}}

where ,

n_1\ \&\ n_2 = Sample sizes taken from two  populations 1 and 2.

\overline{x}_1-\overline{x}_2 = Difference between two Sample mean.

\sigma_1\ \&\ \sigma_2 = Standard deviations of populations 1 and 2.

As per given , we have

n_1=55\ \&\ n_2=58

\overline{x}_1=2.95\ \&\ \overline{x}_2=3.3

\sigma_1=0.65\ \&\ \sigma_2=0.56

We assume that the data follows a normal distribution.

Then, the test statistic will be :-

z=\dfrac{2.95-3.3}{\sqrt{\dfrac{(0.65)^2}{55}+\dfrac{(0.56)^2}{58}}}\\\\=\dfrac{-0.35}{\sqrt{0.0130887}}\\\\=\dfrac{-0.35}{0.1144059}=3.05928278174\approx-3.0593  

Hence, the test statistic= -3.0593

5 0
3 years ago
In Ms. Henrick's class, there are 10 boys and 12 girls. What is the ratio of boys to girls? Express your answer as a fraction in
andreev551 [17]

Answer:

The ratios is 10:12 and if you were to write it in a fraction you get 10/12 which is simplified as 5/6

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Yesterday, 64% of the 6th grade students chose to drink chocolate milk with their lunch. What fraction of 6th grade students Did
Talja [164]

Answer:

\frac{9}{25}

Step-by-step explanation:

First subtract 100 and 64. To find how many didn't choose to drink chocolate milk.

100-64=36

Percentages put into fractions will be Percentage over 100.

So, the fraction will be \frac{36}{100}. Now simplify.

\frac{36}{100}=\frac{18}{50} =\frac{9}{25}

4 0
3 years ago
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A circle has a radius of 4 meters and a central angle AOB that measures 120°. What is the length of the intercepted arc AB? Use
Valentin [98]
<span>120 degs --> 1/3 of the circumference :) hope i helped!</span>
6 0
3 years ago
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