Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).

Usimov [2.4K]

Answer:

Option A

Explanation:

$\rightarrow \sf sin\left(\dfrac{7\pi }{6}\right)$

$\rightarrow \sf \sin \left(\pi +\dfrac{\pi }{6}\right)$

$\rightarrow \sin \left(\pi \right)\cos \left(\dfrac{\pi }{6}\right)+\cos \left(\pi \right)\sin \left(\dfrac{\pi }{6}\right)$

$\rightarrow \sf 0 * \dfrac{\sqrt{3}}{2}+\left(-1\right) * \dfrac{1}{2}$

$\rightarrow \sf -\dfrac{1}{2}$

7 0

2 years ago

Giovanni orders a pastry from the bakery. The price of the pastry before tax is $4.50. Giovanni wants to know the total price in

Gennadij [26K]

Answer:

$4.95

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Write an expression for the 12th partial sum of the series 3/2+7/3+19/6+... using summation notation

lapo4ka [179]

Answer:

$S_{12}=\sum_{i=1}^{12} [\frac{3}{2}+(i-1)\times \frac{5}{6}]$

$S_{12}=73$

Step-by-step explanation:

$First\ term\ of\ the\ series(a_1)=\frac{3}{2}\\\\Second\ term\ of\ the\ series(a_2)=\frac{7}{3}\\\\Third\ term\ of\ the\ series(a_3)=\frac{19}{6}\\\\a_2-a_1=\frac{7}{3}-\frac{3}{2}=\frac{5}{6}\\\\a_3-a_2=\frac{19}{6}-\frac{7}{3}=\frac{5}{6}\\\\Hence\ it\ is\ an\ Arithmetic\ Series\ with\ first\ term=\frac{3}{2}\ and\ constant\ difference=\frac{5}{6}$

$a_1=\frac{3}{2}+0\times \frac{5}{6}\\\\a_2=\frac{3}{2}+1\times \frac{5}{6}\\\\a_3=\frac{3}{2}+2\times \frac{5}{6}\\\\.\\.\\.\\a_n=\frac{3}{2}+(n-1)\times \frac{5}{6}\\\\S_n=a_1+a_2+a_3+......+a_n\\\\S_n=(\frac{3}{2}+0\times \frac{5}{6})+(\frac{3}{2}+1\times \frac{5}{6})+(\frac{3}{2}+2\times \frac{5}{6})+....+(\frac{3}{2}+[n-1]\times \frac{5}{6})\\\\S_n=\sum_{i=1}^n [\frac{3}{2}+(i-1)\times \frac{5}{6}]\\\\S_n=(\frac{3}{2}+\frac{3}{2}+\frac{3}{2}+...n\ times)+\frac{5}{6}(1+2+3+4+...+(n-1))\\\\$

$S_n=\frac{3}{2}\times n+\frac{5}{6}\times \frac{n(n-1)}{2}\\\\$

$S_{12}=\sum_{i=1}^{12} [\frac{3}{2}+(i-1)\times \frac{5}{6}]$

$S_{12}=\frac{3}{2}\times 12+\frac{5}{6}\times \frac{(12)(12-1)}{2}\\\\S_{12}=18+55\\\\S_{12}=73$

5 0

3 years ago

A triangular flower bed is to be created. The following figure represents the layout of the flower bed. How many feet of landsca

VladimirAG [237]

Answer:

8 feet

Step-by-step explanation:

The diagram is attached below.

Note that the values are different but the diagram is similar. In this case,

Hypotenuse =17ft

Adjacent = 15²

Required

Opposite side

To get the feet of landscape edging would be required to outline the edge of the bed, we will use the Pythagoras theorem as shown;

Hyp² = Opp²+Adj²

Opp² = Hyp²-Adj²

l² = 17²-15²

l² = 289-225

l² = 64

l = √64

l = 8feet

Hence the feet of landscape edging would be required to outline the edge of the bed is 8 feet

8 0

3 years ago

A ramp is used to load a snowmobile onto the back of a pickup truck. The truck bed is 1.3m above the ground. For safety, the ang

kiruha [24]

Answer:

2.02 m

or 2 m 2 cm

Step-by-step explanation:

Imagine a triangle containing the 40° angle and that this angle is at the left. Then the height of the truck bed is 1.3 m and the "shortest possible length of the ramp" is the hypotenuse of this triangle. We need to find the length of this ramp, that is, the length of the hypotenuse.

The sine function relates this 40° angle and the 1.3 m height of the truck bed:

sin 40° = opp / hyp = 1.3 m / hyp

which can be solved for 'hyp' as follows:

1.3 m

hyp = ----------------- = (1.3 m) / 0.6428)

sin 40°

1.3 m

Thus, the length of the ramp must be less than -------------- or 2.02 m

0.6428

where this last result is to the nearest cm.

If the ramp is shorter the angle of the ramp will be smaller and the ramp angle considered safer.

3 0

3 years ago