Suppose that Tom has x quarters. Since Tom has 16 coins in all, the rest of the coins, 16 - x of them, must be nickels.
The value of x dimes is 0.25x dollars (since each quarter is 25 cents), and the value of 16 - x dimes is 0.10(16 - x) (since each dime is 10 cents). The total value of these coins, in dollars, is:
0.25x + 0.10(16 - x).
Since these coins are worth $2.50, we have the equation:
0.25x + 0.10(16 - x) = 2.50.
Solving this yields x = 6. Therefore, Tom has 6 quarters and 16-6 = 10 dimes.
Answer:
![\large \boxed{\angle A = 51.83 ^{\circ}; \, \angle B = 70.88 ^{\circ}; \, \angle C = 57.29 ^{\circ}}](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Cangle%20A%20%3D%20%2051.83%20%5E%7B%5Ccirc%7D%3B%20%5C%2C%20%5Cangle%20B%20%3D%2070.88%20%5E%7B%5Ccirc%7D%3B%20%5C%2C%20%5Cangle%20C%20%3D%2057.29%20%5E%7B%5Ccirc%7D%7D)
Step-by-step explanation:
You use the Law of Cosines when you know all three sides and want to find the angles of a triangle.
For example, if you want to find ∠A, you use the formula
![\cos A = \dfrac{b^{2} + c^{2} - a^{2}}{2bc}](https://tex.z-dn.net/?f=%5Ccos%20A%20%3D%20%5Cdfrac%7Bb%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-%20a%5E%7B2%7D%7D%7B2bc%7D)
1. ∠ A
![\begin{array}{rcl}\cos A &=& \dfrac{b^{2} + c^{2} - a^{2}}{2bc}\\\\& = & \dfrac{13.7^{2} + 12.2^{2} - 11.4^{2}}{2\times 13.7 \times 12.2}\\\\& = & \dfrac{187.69 + 148.84 - 129.96}{334.28}\\\\&=& \dfrac{206.57}{334.28}\\\\& = & 0.6180\\A& = & \arccos 0.6180\\& = & \mathbf{51.83 ^{\circ}}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D%5Ccos%20A%20%26%3D%26%20%5Cdfrac%7Bb%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-%20a%5E%7B2%7D%7D%7B2bc%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7B13.7%5E%7B2%7D%20%2B%2012.2%5E%7B2%7D%20-%2011.4%5E%7B2%7D%7D%7B2%5Ctimes%2013.7%20%5Ctimes%2012.2%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7B187.69%20%2B%20148.84%20-%20129.96%7D%7B334.28%7D%5C%5C%5C%5C%26%3D%26%20%5Cdfrac%7B206.57%7D%7B334.28%7D%5C%5C%5C%5C%26%20%3D%20%26%200.6180%5C%5CA%26%20%3D%20%26%20%5Carccos%200.6180%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B51.83%20%5E%7B%5Ccirc%7D%7D%5C%5C%5Cend%7Barray%7D)
2. ∠B
![\begin{array}{rcl}\cos B &=& \dfrac{a^{2} + c^{2} - b^{2}}{2ac}\\\\& = & \dfrac{11.4^{2} + 12.2^{2} - 13.7^{2}}{2\times 11.4 \times 12.2}\\\\& = & \dfrac{129.96 + 148.84 - 187.69}{278.16}\\\\&=& \dfrac{91.11}{278.16}\\\\& = & 0.3275\\B& = & \arccos 0.3275\\& = & \mathbf{70.88 ^{\circ}}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D%5Ccos%20B%20%26%3D%26%20%5Cdfrac%7Ba%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-%20b%5E%7B2%7D%7D%7B2ac%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7B11.4%5E%7B2%7D%20%2B%2012.2%5E%7B2%7D%20-%2013.7%5E%7B2%7D%7D%7B2%5Ctimes%2011.4%20%5Ctimes%2012.2%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7B129.96%20%2B%20148.84%20-%20187.69%7D%7B278.16%7D%5C%5C%5C%5C%26%3D%26%20%5Cdfrac%7B91.11%7D%7B278.16%7D%5C%5C%5C%5C%26%20%3D%20%26%200.3275%5C%5CB%26%20%3D%20%26%20%5Carccos%200.3275%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B70.88%20%5E%7B%5Ccirc%7D%7D%5C%5C%5Cend%7Barray%7D)
3. ∠C
![\begin{array}{rcl}\cos C &=& \dfrac{a^{2} + b^{2} - c^{2}}{2bc}\\\\& = & \dfrac{11.4^{2} + 13.7^{2} - 12.2^{2}}{2\times 11.4 \times 13.7}\\\\& = & \dfrac{129.96 + 187.69 - 148.84}{312.36}\\\\&=& \dfrac{168.81}{312.36}\\\\& = & 0.5404\\C& = & \arccos 0.5404\\& = & \mathbf{57.29 ^{\circ}}\\\end{array}\\\text{The three angles are $\large \boxed{\mathbf{\angle A = 51.83 ^{\circ}; \, \angle B = 70.88 ^{\circ}; \, \angle C = 57.29 ^{\circ}}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D%5Ccos%20C%20%26%3D%26%20%5Cdfrac%7Ba%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20-%20c%5E%7B2%7D%7D%7B2bc%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7B11.4%5E%7B2%7D%20%2B%2013.7%5E%7B2%7D%20-%2012.2%5E%7B2%7D%7D%7B2%5Ctimes%2011.4%20%5Ctimes%2013.7%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7B129.96%20%2B%20187.69%20-%20148.84%7D%7B312.36%7D%5C%5C%5C%5C%26%3D%26%20%5Cdfrac%7B168.81%7D%7B312.36%7D%5C%5C%5C%5C%26%20%3D%20%26%200.5404%5C%5CC%26%20%3D%20%26%20%5Carccos%200.5404%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B57.29%20%5E%7B%5Ccirc%7D%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Ctext%7BThe%20three%20angles%20are%20%24%5Clarge%20%5Cboxed%7B%5Cmathbf%7B%5Cangle%20A%20%3D%20%2051.83%20%5E%7B%5Ccirc%7D%3B%20%5C%2C%20%5Cangle%20B%20%3D%2070.88%20%5E%7B%5Ccirc%7D%3B%20%5C%2C%20%5Cangle%20C%20%3D%2057.29%20%5E%7B%5Ccirc%7D%7D%7D%24%7D)
Answer:
10^12
Step-by-step explanation:
Add the exponents when you multiply numbers with exponents
X^2 + y^2 = 9 . . . . . . . . circle
y = x + 3 . . . . . . . (linear graph)
They intersect at (-3, 0) and (0, 3)
Opposite angles of a rhombus have equal measure.
angle LNM= 23 (interior alternate angles here are angle LNM and angle KLN)
since ML =MN (sides of a rhombus are equal)
angle LNM = angle MLN = 23
angle LNK = 23 (interior alternate angles LNK and LNM )
angle x= 23 +23 = 46
angle y = 180 - (23+23)
= 180 - 46 = 134
in short,,
angle x= 46 and angle y = 134
hope it helps you