The factored form of the expression (49y² - 64) is ( 7y + 8 )( 7y - 8 )
<h3>What is the factored form of the given expression?</h3>
Given the expression in the question;
49y² - 64
To determine the form, let's break down 49y².
49 can be written as 7 × 7, y² can be written as y × y and 64 can be written as 8 × 8
Hence
49y² = 7y × 7y = (7y)²
64 = 8 × 8 = 8²
So we have,
(7y)² - 8²
Since both terms are perfect square, we can factor using the difference of square.
a² - b² = ( a + b )( a - b )
a is 7y and b is 8
(7y)² - 8² = ( 7y + 8 )( 7y - 8 )
Therefore, the factored form of the expression (49y² - 64) is ( 7y + 8 )( 7y - 8 )
Learn more about difference of square here: brainly.com/question/11801811
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Answer:
33
Step-by-step explanation:
angles on a straight line sum up to 180°
104+x+x+10=180
114+2x=180
2x=180-114
2x=66
x=33
Answer:
The p-value of the test is 0.0013.
Step-by-step explanation:
The test statistic is:
![z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
In which X is the sample mean,
is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
12 is tested at the null hypothesis:
This means that ![\mu = 12](https://tex.z-dn.net/?f=%5Cmu%20%3D%2012)
Standard deviation of 0.5 kilograms.
This means that ![\sigma = 0.5](https://tex.z-dn.net/?f=%5Csigma%20%3D%200.5)
Sample of n = 4 specimens. Observed statistic is Xbar (average) = 11.25.
This means that ![n = 4, X = 11.25](https://tex.z-dn.net/?f=n%20%3D%204%2C%20X%20%3D%2011.25)
Value of the test statistic:
![z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![z = \frac{11.25 - 12}{\frac{0.5}{\sqrt{4}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B11.25%20-%2012%7D%7B%5Cfrac%7B0.5%7D%7B%5Csqrt%7B4%7D%7D%7D)
![z = -3](https://tex.z-dn.net/?f=z%20%3D%20-3)
P-value:
Probability of finding a sample mean belo 11.25, which is the p-value of z = -3.
Looking at the z-table, z = -3 has a p-value of 0.0013, thus the this is the p-value of the test.
<h3>
<u>Explanation</u></h3>
- Given the system of equations.
![\begin{cases} 6x - 2y = 10 \\ x - 2y = - 5 \end{cases}](https://tex.z-dn.net/?f=%20%5Cbegin%7Bcases%7D%206x%20-%202y%20%3D%2010%20%5C%5C%20x%20-%202y%20%3D%20%20-%205%20%5Cend%7Bcases%7D)
- Solve the system of equations by eliminating either x-term or y-term. We will eliminate the y-term as it is faster to solve the equation.
To eliminate the y-term, we have to multiply the negative in either the first or second equation so we can get rid of the y-term. I will multiply negative in the second equation.
![\begin{cases} 6x - 2y = 10 \\ - x + 2y = 5 \end{cases}](https://tex.z-dn.net/?f=%20%5Cbegin%7Bcases%7D%206x%20-%202y%20%3D%2010%20%5C%5C%20%20-%20x%20%20%2B%20%202y%20%3D%20%205%20%5Cend%7Bcases%7D)
There as we can get rid of the y-term by adding both equations.
![(6x - x) + ( - 2y + 2y) = 10 + 5 \\ 5x + 0 = 15 \\ 5x = 15 \\ x = \frac{15}{5} \longrightarrow \frac{ \cancel{15}}{ \cancel{5}} = \frac{3}{1} \\ x = 3](https://tex.z-dn.net/?f=%286x%20-%20x%29%20%2B%20%28%20-%202y%20%2B%202y%29%20%3D%2010%20%2B%205%20%5C%5C%205x%20%2B%200%20%3D%2015%20%5C%5C%205x%20%3D%2015%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B15%7D%7B5%7D%20%20%5Clongrightarrow%20%20%5Cfrac%7B%20%5Ccancel%7B15%7D%7D%7B%20%5Ccancel%7B5%7D%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B1%7D%20%20%5C%5C%20x%20%3D%203)
Hence, the value of x is 3. But we are not finished yet because we need to find the value of y as well. Therefore, we substitute the value of x in any given equations. I will substitute the value of x in the second equation.
![x - 2y = - 5 \\ 3 - 2y = - 5 \\ 3 + 5 = 2y \\ 8 = 2y \\ \frac{8}{2} = y \\ y = \frac{8}{2} \longrightarrow \frac{ \cancel{8}}{ \cancel{2}} = \frac{4}{1} \\ y = 4](https://tex.z-dn.net/?f=x%20-%202y%20%3D%20%20-%205%20%5C%5C%203%20-%202y%20%3D%20%20-%205%20%5C%5C%203%20%2B%205%20%3D%202y%20%5C%5C%208%20%3D%202y%20%5C%5C%20%20%5Cfrac%7B8%7D%7B2%7D%20%20%3D%20y%20%5C%5C%20y%20%3D%20%20%5Cfrac%7B8%7D%7B2%7D%20%5Clongrightarrow%20%20%5Cfrac%7B%20%5Ccancel%7B8%7D%7D%7B%20%5Ccancel%7B2%7D%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7B1%7D%20%20%5C%5C%20y%20%3D%204)
Hence, the value of y is 4. Therefore, we can say that when x = 3, y = 4.
- Answer Check by substituting both x and y values in both equations.
<u>First</u><u> </u><u>Equation</u>
![6x - 2y = 10 \\ 6(3) - 2(4) = 10 \\ 18 - 8 = 10 \\ 10 = 10 \longrightarrow \sf{true} \: \green{ \checkmark}](https://tex.z-dn.net/?f=6x%20-%202y%20%3D%2010%20%5C%5C%206%283%29%20-%202%284%29%20%3D%2010%20%5C%5C%2018%20-%208%20%3D%2010%20%5C%5C%2010%20%20%3D%2010%20%5Clongrightarrow%20%5Csf%7Btrue%7D%20%5C%3A%20%20%5Cgreen%7B%20%5Ccheckmark%7D)
<u>Second</u><u> </u><u>Equation</u>
![x - 2y = - 5 \\ 3 - 2(4) = - 5 \\ 3 - 8 = - 5 \\ - 5 = - 5 \longrightarrow \sf{true} \: \green{ \checkmark}](https://tex.z-dn.net/?f=x%20-%202y%20%3D%20%20-%205%20%5C%5C%203%20-%202%284%29%20%3D%20%20-%205%20%5C%5C%203%20-%208%20%3D%20%20-%205%20%5C%5C%20%20-%205%20%3D%20%20-%205%20%5Clongrightarrow%20%20%5Csf%7Btrue%7D%20%5C%3A%20%20%5Cgreen%7B%20%5Ccheckmark%7D)
Hence, both equations are true for x = 3 and y = 4. Therefore, the solution is (3,4)
<h3>
<u>Answer</u></h3>
![\begin{cases} x = 3 \\ y = 4 \end{cases} \\ \sf \underline{Coordinate \: \: Form} \\ (3,4)](https://tex.z-dn.net/?f=%20%5Cbegin%7Bcases%7D%20x%20%3D%203%20%5C%5C%20y%20%3D%204%20%5Cend%7Bcases%7D%20%5C%5C%20%20%5Csf%20%5Cunderline%7BCoordinate%20%5C%3A%20%20%5C%3A%20Form%7D%20%5C%5C%20%283%2C4%29)
Answer:
The answer is x=294 (B)
Step-by-step explanation:
Remember, all interior angles of a hexagon add to 720.
So add all the given numbers first.
92+100+94+140+x= 720
426+x=720
-426 from both sides
x= 294
I know this is a week later since you posted the question, sorry.