Answer: The value of x is 3.
Step-by-step explanation:
so we know the surface area of the shape as 112.
And to find the missing angle we could use the equation
20 + 20 + (10 *x) + ( 10* x) +(2 * x) + (2 * x) =112 solve for x and that is x
20 + 20 + 10x + 10x + 2x + 2x = 112
40 + 24x = 112
-40 -40
24x = 72
x= 3
Check: 3 * 10 = 30
3 * 10 = 30
2 * 3 = 6
2 * 3 = 6
2 * 10 = 20
2* 10 = 20
30 + 30 + 6 + 6 +20 +20 = 112
112 = 112
Answer:△DEF is congruent to △D′E′F′ because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.
Step-by-step explanation:
A rigid motion of the plane is a motion which maintain distance.
Translation is a kind of rigid motion used in geometry to trace a function that moves an object a particular distance.
A reflection is also a kind of rigid motion . It is mainly a 'toss' of a shape across the line of reflection.
So,△DEF is mapped to △D′E′F′ using the rule (x,y)→(x,y+1) ( which is a translation.) followed by (x,y)→(x,−y)(which is reflection),therefore it is a sequence of rigid motions.
Answer:
![{5 x }^{2} +10x](https://tex.z-dn.net/?f=%20%7B5%20x%20%7D%5E%7B2%7D%20%2B10x)
Step-by-step explanation:
![5x(x+2)](https://tex.z-dn.net/?f=5x%28x%2B2%29)
![5x \times x+5x \times 2](https://tex.z-dn.net/?f=5x%20%5Ctimes%20x%2B5x%20%5Ctimes%202)
![5(x \times x)+5x \times 2](https://tex.z-dn.net/?f=5%28x%20%5Ctimes%20x%29%2B5x%20%20%5Ctimes%202)
![5 {x}^{2} +5x \times 2](https://tex.z-dn.net/?f=5%20%7Bx%7D%5E%7B2%7D%20%2B5x%20%5Ctimes%202)
![5 {x}^{2} + 10x](https://tex.z-dn.net/?f=5%20%7Bx%7D%5E%7B2%7D%20%20%2B%2010x)
<h3>Hope it is helpful....</h3>
Answer:
a) 0.3495
b) (9.65, 10.35)
Step-by-step explanation:
We are given the following in the question:
Sample mean,
= 10 hours
Sample size, n = 64
Alpha, α = 0.02
Population standard deviation, σ = 1.2 hours
a) Margin of error
Formula
![z_{critical}\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=z_%7Bcritical%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
Putting values, we get,
![M.E = (2.33)\dfrac{1.2}{\sqrt{64}} = 0.3495](https://tex.z-dn.net/?f=M.E%20%3D%20%282.33%29%5Cdfrac%7B1.2%7D%7B%5Csqrt%7B64%7D%7D%20%3D%200.3495)
b) the sample mean is 10 hours, then the 98% confidence interval
![\bar{x} \pm M.E](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%20%5Cpm%20M.E)
Putting the values, we get,
![10\pm 0.3495\\=(9.6505, 10.3495)\\\approx (9.65, 10.35)](https://tex.z-dn.net/?f=10%5Cpm%200.3495%5C%5C%3D%289.6505%2C%2010.3495%29%5C%5C%5Capprox%20%289.65%2C%2010.35%29)
Answer:
30
Step-by-step explanation:
120÷4=30 (4 because a square has 4 sides)
and you can check it by doing 4×30=120
hope this helped