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Andreyy89
3 years ago
11

Factor by completing the square 5x^2-21=10x

Mathematics
1 answer:
velikii [3]3 years ago
4 0
Solve for x over the real numbers:
5 x^2 - 21 = 10 x

Subtract 10 x from both sides:
5 x^2 - 10 x - 21 = 0

Divide both sides by 5:
x^2 - 2 x - 21/5 = 0

Add 21/5 to both sides:
x^2 - 2 x = 21/5

Add 1 to both sides:
x^2 - 2 x + 1 = 26/5

Write the left hand side as a square:
(x - 1)^2 = 26/5

Take the square root of both sides:
x - 1 = sqrt(26/5) or x - 1 = -sqrt(26/5)

Add 1 to both sides:
x = 1 + sqrt(26/5) or x - 1 = -sqrt(26/5)

Add 1 to both sides:
Answer:  x = 1 + sqrt(26/5) or x = 1 - sqrt(26/5)
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Which inequality represents all possible solutions of −6n<−12?
muminat

Answer:

B n>2

Step-by-step explanation:

−6n<−12

Divide each side by -6, remembering to flip the inequality

-6n/-6 > -12/-6

n >2

5 0
3 years ago
A student is making a project that requires a large triangular base. The student has two pieces of wood that are 20in and 17in l
IRISSAK [1]

Answer:

Write a short story about a character who experiences a turning point in life. Use this Writing Plan/Graphic Organizer below to format (construct) your story. It must also be submitted with your short story and I will issue you two separate grades (one for the organizer one for the write-up).

Start with a writing plan (organizer)

1. Title - Your choice

2. Audience - Classmates and teacher

3. Theme - Your choice

4. Purpose - To entertain, share insight

5. Time Frame - Start today and due on 11-7-20 at 11:59 pm

6. Beginning - Introduce characters etc.

7. Middle - Turning point

8. End - Resolution

Use a minimum 150 words

Step-by-step explanation:

Write a short story about a character who experiences a turning point in life. Use this Writing Plan/Graphic Organizer below to format (construct) your story. It must also be submitted with your short story and I will issue you two separate grades (one for the organizer one for the write-up).

Start with a writing plan (organizer)

1. Title - Your choice

2. Audience - Classmates and teacher

3. Theme - Your choice

4. Purpose - To entertain, share insight

5. Time Frame - Start today and due on 11-7-20 at 11:59 pm

6. Beginning - Introduce characters etc.

7. Middle - Turning point

8. End - Resolution

Use a minimum 150 words

7 0
3 years ago
SOMEONE PLEASEEEE HELPPPP
andrew11 [14]

Answer:

The triangles are not similar

Step-by-step explanation:

6 0
2 years ago
I got 47.01816163 metres. When I tried to round it I got it wrong. Can someone please help me?
DerKrebs [107]

Answer:

28 m

Step-by-step explanation:

The top angle in the triangle = 90° - 62° = 28°

Using the cosine ratio in the right triangle

cos28° = \frac{adjacent}{hypotenuse} = \frac{25}{x}

cross- multiply

x × cos28° = 25 ( divide both sides by cos28° )

x = \frac{25}{cos28} = 28.31425... ≈ 28 m

Thus the distance from the top to the crocodile is 28 m

6 0
3 years ago
Read 2 more answers
We are conducting a hypothesis test to determine if fewer than 80% of ST 311 Hybrid students complete all modules before class.
Juli2301 [7.4K]

Answer:

z=\frac{0.881 -0.8}{\sqrt{\frac{0.8(1-0.8)}{110}}}=2.124  

Null hypothesis:p\geq 0.8  

Alternative hypothesis:p < 0.8  

Since is a left tailed test the p value would be:  

p_v =P(Z  

So the p value obtained was a very high value and using the significance level assumed \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis:p\leq 0.8  

Alternative hypothesis:p > 0.8

p_v =P(Z>2.124)=0.013  

So the p value obtained was a very low value and using the significance level assumed \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation  

n=110 represent the random sample taken

X=97 represent the students who completed the modules before class

\hat p=\frac{97}{110}=0.882 estimated proportion of students who completed the modules before class

p_o=0.8 is the value that we want to test

\alpha represent the significance level

z would represent the statistic (variable of interest)

p_v{/tex} represent the p value (variable of interest)  2) Concepts and formulas to use  We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.8 or 80%:  Null hypothesis:[tex]p\geq 0.8  

Alternative hypothesis:p < 0.8  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.881 -0.8}{\sqrt{\frac{0.8(1-0.8)}{110}}}=2.124  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(Z  

So the p value obtained was a very high value and using the significance level assumed \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis:p\leq 0.8  

Alternative hypothesis:p > 0.8

p_v =P(Z>2.124)=0.013  

So the p value obtained was a very low value and using the significance level assumed \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis.

5 0
3 years ago
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