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erica [24]
3 years ago
7

Which shows a difference of squares?

Mathematics
2 answers:
borishaifa [10]3 years ago
7 0

Answer:

The expression which shows the difference  of squares is (16y)^{2}  - (x)^{2} .

Step-by-step explanation:

Here, the given expressions are :

1. (10y)^{2}  - (4x)^{2}\\2.(16y)^{2}  - (x)^{2}\\3. (8x)^{2}  - (4x + 25)\\4. (64x)^{2}  - (48x + 9)

Now, DIFFERENCE of SQUARES is an expression where one perfect square term is subtracted from another perfect square term.

And each difference of square can be expanded using algebraic identity

a^{2} - b^{2}  = (a-b)(a+b)

Now, here only the terms in expression 2 are perfect squares, as

(16y)^{2}  = (4y)^{2} =(-4y)^{2}  , (x)^{2}  = (x)^{2} =(-x)^{2}

Hence, the expression which shows the difference  of squares is (16y)^{2}  - (x)^{2} .

Also, here(16y)^{2} - (x)^{2}  = (4y-x)(4y+x)

kirill [66]3 years ago
3 0

Answer:

Option A and B.

Step-by-step explanation:

We need to find the expression which shows a difference of squares.

Difference of squares:

a^2-b^2=(a-b)(a+b)

The given expression can be written as

10y^2-4x^2=(\sqrt{10}y)^2-(2x)^2

The expression 10y^2-4x^2 represents shows a difference of squares.

Second expression is

16y^2-x^2=(4y)^2-x^2

The expression 16y^2-x^2 represents shows a difference of squares.

Third expression is

8x^2-40x+25

It can not be written as difference of squares.

Fourth expression is

64x^2-48 x + 9

(8x)^2-2(8)(3) x + 3^2

(8x-3)^2

It can not be written as difference of squares.

Therefore, the correct options are A and B.

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Answer:

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Step-by-step explanation:

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3 years ago
The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean
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Answer:

t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549    

Step-by-step explanation:

Data given and notation  

\bar X=3.8 represent the sample mean

s=0.5 represent the sample standard deviation for the sample  

n=15 sample size  

\mu_o =4 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)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean weight is less than 4 ounces, the system of hypothesis would be:  

Null hypothesis:\mu \geq 68  

Alternative hypothesis:\mu < 4  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-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".  

Calculate the statistic

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

t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549    

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Step-by-step explanation:

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