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3 years ago

Use the Quadratic Formula to solve x2 + 20x + 98 = 0

1 answer:

3 0

$ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta \ \textless \ 0\ then\ no\ solution\\\\if\ \Delta =0\ then\ one\ solution\ x_0=\dfrac{-b}{2a}\\\\if\ \Delta \ \textgreater \ 0\ then\ two\ solutions\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\-----------------------------$

$x^2+20x+98=0\\a=1;\ b=20;\ c=98\\\\\Delta=20^2-4\cdot1\cdot98=400-392=8 \ \textgreater \ 0\\\sqrt\Delta=\sqrt8=\sqrt{4\cdot2}=\sqrt4\cdot\sqrt2=2\sqrt2\\\\x_1=\dfrac{-20-2\sqrt2}{2\cdot1}=\dfrac{-20-2\sqrt2}{2}=-10-\sqrt2\\\\x_2=\dfrac{-20+2\sqrt2}{2\cdot1}=\dfrac{-20+2\sqrt2}{2}=-10+\sqrt2$

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Alan needs to manufacture a circular metal plate with a perimeter of `10pi` centimeters. If the allowed error tolerance in the p

AnnZ [28]

The ideal radius Alan must control is $\frac{1}{2\pi }$ cm.

<h3>Define perimeter of circle.</h3>

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The area of a circle determines the space it takes up. A circle's diameter is equal to the length of a straight line traced through its center. Usually, it is stated in terms of units like cm or m.

Given data -

Perimeter of circular plate = 10 $\pi$ cm

We know that perimeter of a circle is 2 $\pi$ r

Therefore 10 $\pi$ = 2 $\pi$ r

r = 5 cm

The given error Alan can make is +-1 cm.

Minimum radius is given by

2 $\pi$ r = 10 $\pi$ - 1

r = $\frac{10\pi - 1 }{2\pi }$

r = 5 - $\frac{1}{2\pi }$

Maximum radius is given by

2 $\pi$ r = 10 $\pi$ + 1

r = $\frac{10\pi + 1 }{2\pi }$

r = 5 + $\frac{1}{2\pi }$

The ideal radius Alan must control is $\frac{1}{2\pi }$ cm.

To know more about perimeter of circle, visit:

brainly.com/question/2718232

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5 0

1 year ago

8 reduced by the product of four and g

lana66690 [7]

Answer:

I'm confused what????

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3 years ago

Which expression is equivalent to 5y^3 over (5y)-^2

Flura [38]

Answer:

$125y^5$

Step-by-step explanation:

$\mathrm{Factor}\:\left(5y\right)^{-2}:\quad 5^{-2}y^{-2}$

$\mathrm{Cancel\:}\frac{5y^3}{5^{-2}y^{-2}}:\quad 5^3y^5$ $=5^3y^5$

$5^3=125$

<em>Hope this helps!!!</em>

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3 years ago

if you roll a pair of six-sided number cubes what is the probability of rolling two numbers whose sum is 6

Afina-wow [57]

6/6 so 10% pls don’t get mad if I’m wrong lol

3 0

2 years ago

You received your first credit card with a spending limit of $2,000 at 18.9% interest. You decide you need to upgrade your sound

kari74 [83]

Answer:

It will take approximately 25 months

Step-by-step explanation:

The amount owed on the credit card statement, P = $2,000

The interest rate of the credit on the credit card, r = 18.9%

The minimum monthly payment made, M = $100

The equal monthly installment formula is given as follows;

$M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}$

Therefore, we get;

$100 = \dfrac{2,000 \cdot \left(\dfrac{0.189}{12} \right) \cdot \left(1+\dfrac{0.189}{12} \right)^n }{\left(1+\dfrac{0.189}{12} \right)^n - 1} = \dfrac{2,000 \times\left(0.01575 \right) \cdot \left(1.01575 \right)^n }{\left(1.01575\right)^n - 1}$

100×1.01575ⁿ - 100 = 31.50×1.01575ⁿ

100×1.01575ⁿ - 31.50×1.01575ⁿ = 100

68.5×1.01575ⁿ = 100

1.01575ⁿ = 100/68.5

n = ln(100/68.5)/ln(1.01575) ≈ 24.21 (which is approximately 25 months, by rounding up to the nearest whole number)

Therefore, it will take approximately 25 months to pay off the credit card debt

8 0

3 years ago