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natta225 [31]
2 years ago
6

Drag the tiles to the correct boxes to complete the pairs.

Mathematics
1 answer:
andreev551 [17]2 years ago
4 0

Answer:

x² - 16 ⇒ (x + 4)(x - 4)

(2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1

(2x + 3y)² ⇒ 4x² + 12xy + 9y²

x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)

Step-by-step explanation:

* Lets explain how to solve the problem

# x² - 16

∵ x² - 16 is a difference of two squares

- Its factorization is two brackets with same terms and different

 middle signs

- To factorize it find the square root of each term

∵ √x² = x and √16 = 4

∴ The terms of each brackets are x and 4 and the bracket have

   different middle signs

∴ x² - 16 = (x + 4)(x - 4)

* x² - 16 ⇒ (x + 4)(x - 4)

# (2x + 1)³

- To solve the bracket we will separate (2x + 1)³ to (2x + 1)(2x + 1)²

∵ (2x + 1)² = (2x)(2x) + 2(2x)(1) + (1)(1) = 4x² + 4x + 1

∴ (2x + 1)³ = (2x + 1)(4x² + 4x + 1)

∵ (2x + 1)(4x² + 4x + 1) = (2x)(4x²) + (2x)(4x) + (2x)(1) + (1)(4x²) + (1)(4x) + (1)(1)

∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 8x² + 2x + 4x² + 4x + 1 ⇒ add like terms

∴ (2x + 1)(4x² + 4x + 1) = 8x³ + (8x² + 4x²) + (2x + 4x) + 1

∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 12x² + 6x + 1

∴ (2x + 1)³ = 8x³ + 12x² + 6x + 1

* (2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1

# (2x + 3y)²

∵ (2x + 3y)² = (2x)(2x) + 2(2x)(3y) + (3y)(3y)

∴ (2x + 3y)² = 4x² + 12xy + 9y²

* (2x + 3y)² ⇒ 4x² + 12xy + 9y²

# x³ + 8y³

∵ x³ + 8y³ is the sum of two cubes

- Its factorization is binomial and trinomial

- The binomial is cub root the two terms

∵ ∛x³ = x and ∛8y³ = 2y

∴ The binomial is (x + 2y)

- We will make the trinomial from the binomial

- The first term is (x)² = x²

- The second term is (x)(2y) = 2xy with opposite sign of the middle

  sign in the binomial

- The third term is (2y)² = 4y²

∴ x³ + 8y³ = (x + 2y)(x² - 2xy + 4y²)

* x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)

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If one plane is flying at 40mph. While another is flying at 100mph. They are 200 miles apart, how long will it take them to coll
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Answer:

1 and 3/7 hour

Step-by-step explanation:

Every hour they get 140 miles closer (100 + 40). So you divide 200 by 140 which gets you 1.42... or 1 and 3/7 of an hour.

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3 years ago
2 (7-4)÷6 find the value of the expression pls and thanks
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The answer is 1.
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3 years ago
Read 2 more answers
We're testing the hypothesis that the average boy walks at 18 months of age (H0: p = 18). We assume that the ages at which boys
marusya05 [52]

Answer:

II. This finding is significant for a two-tailed test at .01.

III. This finding is significant for a one-tailed test at .01.

d. II and III only

Step-by-step explanation:

1) Data given and notation    

\bar X=19.2 represent the battery life sample mean    

\sigma=2.5 represent the population standard deviation    

n=25 sample size    

\mu_o =18 represent the value that we want to test    

\alpha represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)    

p_v represent the p value for the test (variable of interest)    

2) State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to check if the mean battery life is equal to 18 or not for parta I and II:    

Null hypothesis:\mu = 18    

Alternative hypothesis:\mu \neq 18    

And for part III we have a one tailed test with the following hypothesis:

Null hypothesis:\mu \leq 18    

Alternative hypothesis:\mu > 18  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:    

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)    

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

3) Calculate the statistic    

We can replace in formula (1) the info given like this:    

z=\frac{19.2-18}{\frac{2.5}{\sqrt{25}}}=2.4    

4) P-value    

First we need to calculate the degrees of freedom given by:  

df=n-1=25-1=24  

Since is a two tailed test for parts I and II, the p value would be:    

p_v =2*P(t_{(24)}>2.4)=0.0245

And for part III since we have a one right tailed test the p value is:

p_v =P(t_{(24)}>2.4)=0.0122

5) Conclusion    

I. This finding is significant for a two-tailed test at .05.

Since the p_v. We reject the null hypothesis so we don't have a significant result. FALSE

II. This finding is significant for a two-tailed test at .01.

Since the p_v >\alpha. We FAIL to reject the null hypothesis so we have a significant result. TRUE.

III. This finding is significant for a one-tailed test at .01.

Since the p_v >\alpha. We FAIL to reject the null hypothesis so we have a significant result. TRUE.

So then the correct options is:

d. II and III only

6 0
3 years ago
I don't know how to do these i need help ASAP plz
Eva8 [605]
Plug the x value into the x value for your questions.

8.) -57
9.) -2
5 0
3 years ago
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