Answer:
(4, 3)
Step-by-step explanation:
#1. Isolate x:
3x + y = 15
y = 15 - 3x
Substitute and solve for x:
5x - 3y = 11
5x - 3(15 - 3x) = 11
5x - 45 + 9x = 11
5x + 9x = 11 + 45
14x = 56
x = 4
Substitute and solve for y:
y = 15 - 3x
y = 15 - 3(4)
y = 15 - 12
y = 3
circumference = 2*pi*r
50.27 = 2* 3.14 *r
50.27 = 6.28 *r
divide by 6.28 on each side
r is approximately 8.005
Answer:
![-\dfrac{7}{25}](https://tex.z-dn.net/?f=-%5Cdfrac%7B7%7D%7B25%7D)
Step-by-step explanation:
<u>Trigonometric Identities</u>
![\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B](https://tex.z-dn.net/?f=%5Ccos%28A%20%5Cpm%20B%29%3D%5Ccos%20A%20%5Ccos%20B%20%5Cmp%20%5Csin%20A%20%5Csin%20B)
<u>Trigonometric ratios</u>
![\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}](https://tex.z-dn.net/?f=%5Csf%20%5Csin%28%5Ctheta%29%3D%5Cdfrac%7BO%7D%7BH%7D%5Cquad%5Ccos%28%5Ctheta%29%3D%5Cdfrac%7BA%7D%7BH%7D%5Cquad%5Ctan%28%5Ctheta%29%3D%5Cdfrac%7BO%7D%7BA%7D)
where:
is the angle- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
Using the trig ratio formulas for cosine and sine:
Therefore, using the trig identities and ratios:
![\begin{aligned}\implies \cos(2 \cdot \angle ABC) & = \cos(\angle ABC + \angle ABC)\\\\& = \cos (\angle ABC) \cos (\angle ABC) - \sin(\angle ABC) \sin (\angle ABC)\\\\& = \cos^2(\angle ABC)-\sin^2(\angle ABC)\\\\& = \left(\dfrac{3}{5}\right)^2-\left(\dfrac{4}{5}\right)^2\\\\& = \dfrac{3^2}{5^2}-\dfrac{4^2}{5^2}\\\\& = \dfrac{9}{25}-\dfrac{16}{25}\\\\& = \dfrac{9-16}{25}\\\\& = -\dfrac{7}{25} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Ccos%282%20%5Ccdot%20%5Cangle%20ABC%29%20%26%20%3D%20%5Ccos%28%5Cangle%20ABC%20%2B%20%5Cangle%20ABC%29%5C%5C%5C%5C%26%20%3D%20%5Ccos%20%28%5Cangle%20ABC%29%20%5Ccos%20%28%5Cangle%20ABC%29%20-%20%5Csin%28%5Cangle%20ABC%29%20%5Csin%20%28%5Cangle%20ABC%29%5C%5C%5C%5C%26%20%3D%20%5Ccos%5E2%28%5Cangle%20ABC%29-%5Csin%5E2%28%5Cangle%20ABC%29%5C%5C%5C%5C%26%20%3D%20%5Cleft%28%5Cdfrac%7B3%7D%7B5%7D%5Cright%29%5E2-%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5E2%5C%5C%5C%5C%26%20%3D%20%5Cdfrac%7B3%5E2%7D%7B5%5E2%7D-%5Cdfrac%7B4%5E2%7D%7B5%5E2%7D%5C%5C%5C%5C%26%20%3D%20%5Cdfrac%7B9%7D%7B25%7D-%5Cdfrac%7B16%7D%7B25%7D%5C%5C%5C%5C%26%20%3D%20%5Cdfrac%7B9-16%7D%7B25%7D%5C%5C%5C%5C%26%20%3D%20-%5Cdfrac%7B7%7D%7B25%7D%20%5Cend%7Baligned%7D)
Answer:
A. The probability of event A
Step-by-step explanation:
The proportion of times a particular event A occurs is known as the probability of event A because the probability is the measure of uncertainty and by definition probability is calculated as
P(x)=X/n
where
P(x) is the probability of occurring of random variable X
X=number of favorable outcomes
and
n= total number of outcomes.
Thus, the proportion of times a particular event A occurs is known as the probability of event A.
Answer:
![W=(x-6)\ m](https://tex.z-dn.net/?f=W%3D%28x-6%29%5C%20m)
Step-by-step explanation:
we know that
The area of rectangle is equal to
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
we have
![A=(x^{2} -11x+30)\ m^2](https://tex.z-dn.net/?f=A%3D%28x%5E%7B2%7D%20-11x%2B30%29%5C%20m%5E2)
![L=(x-5)\ m](https://tex.z-dn.net/?f=L%3D%28x-5%29%5C%20m)
substitute the given values in the formula of area
![(x^{2} -11x+30)=(x-5)W](https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20-11x%2B30%29%3D%28x-5%29W)
Remember that
----> by completing the square
substitute
![(x-5)(x-6)=(x-5)W](https://tex.z-dn.net/?f=%28x-5%29%28x-6%29%3D%28x-5%29W)
Simplify
![W=(x-6)\ m](https://tex.z-dn.net/?f=W%3D%28x-6%29%5C%20m)