Answer:
Step-by-step explanation:
The sum of the two costs is $52, so we can write ...
x + y = 52
The shoes cost $4 more than the jacket, so we can write ...
x - y = 4
These are your system of equations.
__
Subtract the second equation from the first:
(x +y) -(x -y) = (52) -(4)
2y = 48 . . . . . simplify
y = 24 . . . . . . .divide by 2
The cost of the jacket is $24.
Answer:
1330.808 euros
Step-by-step explanation:
Let's first calculate the total amount of kilograms,
for the first 60, we have to:
50 kg
4 hg = 0.5 kg
60 dag = 0.6
5 g = 0.005 kg
adding: 50 + 0.5 +0.6 + 0.005 = 51.105 kg per tree, but they are 60
51.105 * 60 = 3066.3
now for the other 20:
53 kg
2 hg = 0.2 kg
16 dag = 0.16
5 g = 0.005
adding: 53 + 0.2 +0.16 + 0.005 = 53.365 kg per tree, but they are 20
53,365 * 20 = 1067.3
in total it would be: 3066.3 + 1067.3 = 4133.6
they tell us that 1/5 is the quantity in liters:
4133.6 * 1/5 = 826.72 liters
so to calculate the earnings it would be:
2.65 * 826.72 - 860 = 1330.808
which means that in net earnings are 1330.808 euross
Answer:
(4.25, - 1.75)
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ), thus
(- 4.25, - 1.75 ) → (4.25, - 1.75 ) ← original point
4x-30=2x+50
+30 +30
4x=2x+80
-2x -2x
2x=80
/2 /2
X=40
4(40)-30=130°
2(40)+50=130°
180-130=50°
Angle 7=50°
Check the picture below.
since the vertical distance, namely the y-coordinate, is twice as much as the horizontal, then if the horizontal is "x", the vertical one must be 2x.
let's find the hypotenuse first.
![\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{2x}\\ \end{cases} \\\\\\ c=\sqrt{x^2+(2x)^2}\implies c=\sqrt{x^2+4x^2}\implies c=\sqrt{5x^2}\implies c=x\sqrt{5} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%20%5C%5C%5C%5C%20c%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20c%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%20%5Cqquad%20%5Cbegin%7Bcases%7D%20c%3Dhypotenuse%5C%5C%20a%3D%5Cstackrel%7Badjacent%7D%7Bx%7D%5C%5C%20b%3D%5Cstackrel%7Bopposite%7D%7B2x%7D%5C%5C%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20c%3D%5Csqrt%7Bx%5E2%2B%282x%29%5E2%7D%5Cimplies%20c%3D%5Csqrt%7Bx%5E2%2B4x%5E2%7D%5Cimplies%20c%3D%5Csqrt%7B5x%5E2%7D%5Cimplies%20c%3Dx%5Csqrt%7B5%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf sin(\theta )=\cfrac{\stackrel{opposite}{2~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}{\stackrel{hypotenuse}{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \sqrt{5}}}\implies \stackrel{\textit{and rationalizing the denominator}~\hfill }{\cfrac{2}{\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{2\sqrt{5}}{(\sqrt{5})^2}\implies \cfrac{2\sqrt{5}}{5}}](https://tex.z-dn.net/?f=%5Cbf%20sin%28%5Ctheta%20%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B2~~%5Cbegin%7Bmatrix%7D%20x%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%20%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B~~%5Cbegin%7Bmatrix%7D%20x%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%20%5Csqrt%7B5%7D%7D%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Band%20rationalizing%20the%20denominator%7D~%5Chfill%20%7D%7B%5Ccfrac%7B2%7D%7B%5Csqrt%7B5%7D%7D%5Ccdot%20%5Ccfrac%7B%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B5%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%7B5%7D%7D%7B%28%5Csqrt%7B5%7D%29%5E2%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%7B5%7D%7D%7B5%7D%7D)
