Find the percent the fog machine is of the total budget

The first term of geometric sequence is 7 and the common ratio is -2. Find the 9th term.

kobusy [5.1K]

$a_{1}$ = 7.

Ratio means multiply/divide.
To get the next number, multiply number by common ratio.
To get a previous number, divide by common ratio.

Since we want the next number...
2nd term: 7 x -2 = -14
3rd term: -14 x -2 = 28
4th term: 28 x -2 = -56
5th term: -56 x -2 = 112

Keep going until 9th term!

5 0

2 years ago

I need some help with this question..

Anuta_ua [19.1K]

It is (B) I think:) hope this helps

6 0

2 years ago

Find the roots of the equation<br> x ^ 2 + 3x-8 ^ -14 = 0 with three precision digits

scoray [572]

Answer:

Step-by-step explanation:

Given quadratic equation:

$x^{2} + 3x - 8^{- 14} = 0$

The solution of the given quadratic eqn is given by using Sri Dharacharya formula:

$x_{1, 1'} = \frac{- b \pm \sqrt{b^{2} - 4ac}}{2a}$

The above solution is for the quadratic equation of the form:

$ax^{2} + bx + c = 0$

$x_{1, 1'} = \frac{- b \pm \sqrt{b^{2} - 4ac}}{2a}$

From the given eqn

a = 1

b = 3

c = $- 8^{- 14}$

Now, using the above values in the formula mentioned above:

$x_{1, 1'} = \frac{- 3 \pm \sqrt{3^{2} - 4(1)(- 8^{- 14})}}{2(1)}$

$x_{1, 1'} = \frac{1}{2} (\pm \sqrt{9 - 4(1)(- 8^{- 14})})$

$x_{1, 1'} = \frac{1}{2} (\pm \sqrt{9 - 4(1)(- 8^{- 14})} - 3)$

Now, Rationalizing the above eqn:

$x_{1, 1'} = \frac{1}{2} (\pm \sqrt{9 - 4(- 8^{- 14})} - 3)\times (\frac{\sqrt{9 - 4(- 8^{- 14})} + 3}{\sqrt{9 - 4(- 8^{- 14})} + 3}$

$x_{1, 1'} = \frac{1}{2}.\frac{(\pm {9 - 4(- 8^{- 14})^{2}} - 3^{2})}{\sqrt{9 - 4(- 8^{- 14})} + 3}$

Solving the above eqn:

$x_{1, 1'} = \frac{2\times 8^{- 14}}{\sqrt{9 + 4\times 8^{-14}} + 3}$

Solving with the help of caculator:

$x_{1, 1'} = \frac{2\times 2.27\times 10^{- 14}}{\sqrt{9 + 42.27\times 10^{- 14}} + 3}$

The precise value upto three decimal places comes out to be:

$x_{1, 1'} = 0.758\times 10^{- 14}$

5 0

3 years ago

Here is a picture that shows one side of a child's wooden block with a semicircle cut out at the bottom.

soldi70 [24.7K]

30.7 cm² (nearest tenth)
Step-by-step explanation:
Area of the wooden block = area of rectangle - area of semi-circle
Area of Rectangle = length × width
Length = 9 cm
Width = 4.5 cm
Area of rectangle = 40.5 cm²
Area of semi-circle = ½(πr²)
Radius (r) = ½ of diameter = ½*5 = 2.5 cm
π = 3.14
Area of semi-circle = ½(3.14*2.5²)
Area of semi-circle = 9.8125 cm²

4 0

2 years ago

The measure of each interoir angle of a regualr polygon is 144 . how many sides does this polygon have

egoroff_w [7]

Each Interior Angle = 180 - (360 / number of sides)
# of sides = -360 / (Each Interior Angle -180)
# of sides = -360 / (144 -180)
# of sides = -360 / -36
# of sides = 10

6 0

2 years ago