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3 years ago

HELP PLEASE: 40 POINTS

Mathematics

2 answers:

galben [10]3 years ago

5 0

Answer: The required match is

$\left(x^{-2},\dfrac{1}{9}\right);~\left(x^{-1},-\dfrac{1}{3}\right);~(x^0,1);~(x^1,-3),~(x^2,9).$

Step-by-step explanation: We are given to match the following items with the given options by evaluating the expression for x = -3.

$x^{-2},~~x^{-1},~~x^0,~~x^1,~~x^2.$

We will be using the following property of exponents :

$a^{-b}=\dfrac{1}{a^b}.$

we have

$x^{-2}=\dfrac{1}{x^2}=\dfrac{1}{(-3)^2}=\dfrac{1}{9},\\\\\\x^{-1}=\dfrac{1}{x}=\dfrac{1}{(-3)}=-\dfrac{1}{3},\\\\\\x^0=1,\\\\\\x^1=x=-3,\\\\\\x^2=(-3)^2=9.$

Thus, the required match is

$\left(x^{-2},\dfrac{1}{9}\right);~\left(x^{-1},-\dfrac{1}{3}\right);~(x^0,1);~(x^1,-3),~(x^2,9).$

geniusboy [140]3 years ago

4 0

X^ -2: 1/9

x^ -1: -1/3

x^0: 1

x^1: -3

x^2: 9

Really hope this helped have a good day ;)

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Use the quadratic formula to solve the equation x^2-7x-6=0

olganol [36]

Answer:

$\frac{7\pm\sqrt{73}} {2}$

Explanation:

We have been given with the quadratic equation $x^2-7x-6=0$

We have general formula to find the roots of a quadratic equation first we find the discriminant with formula

$D=b^{2}-4ac$

and after that to find the variable suppose x we have the formula

$x=\frac{-b\pm\sqrt{D}} {2a}$

And general quadratic equation is

$ax^2+bx+c=0$

On comparing the given quadratic equation with genral quadratic equation we will have values

a=1, b=-7 and c=-6

After substituting these values in the formula we will get

$D=(-7)^2-4(1)(-6)={73}$

After substituting in the formula to find x we will get

$\frac{-(-7)\pm\sqrt{73}} {2}= \frac{7\pm\sqrt{73}} {2}$

4 0

3 years ago

Read 2 more answers

a ferris wheel rotates 9pi/8 radians prior to making a stop the total height of the ferris wheel is 246 ft how far around did th

Zinaida [17]

Answer:

ferris wheel travel approx = 434.72 ft

Step-by-step explanation:

given data

wheel rotates = 9pi/8 radians

total height of the ferris wheel = 246 ft

solution

we can say here that height of the ferris wheel is same as the diameter of the wheel

and wheel is circular in shape

so we get here first radius of wheel that is

radius = half of diameter ..........................1

put here value and we get

radius = 0.5 × 246

radius = 123 ft

and

wheel travel distance = length of arc by a angle of wheel rotates

so here length of arc will be

arc length = radius × wheel rotates angle .....................2

put here value and we get

arc length = 123 × $\frac{9\pi }{8}$

arc length = 434.7178 ft

so ferris wheel travel approx = 434.72 ft

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3 years ago

After releasing of radioactive material into.The atnosphere from.A nuclear.Powe plant in a country in 1988, the hay in that coun

Radda [10]

Answer:

the question is incomplete, so I looked for a similar one:

<em>After the release of radioactive material into the atmosphere from a nuclear power plant, the hay was contaminated by iodine 131 ( half-life, 8 days). If it is all right to feed the hay to cows when 10% of the iodine 131 remains, how long did the farmers need to wait to use this hay? </em>

iodine's half life (we are given x, we need to find b):

0.5A₀ = A₀eᵇˣ

x = 8 days

we eliminate A₀ from both sides

0.5 = eᵇ⁸

ln 0.5 = ln eᵇ⁸

-0.69315 = b8

b = -0.69315 / 8 = -0.08664

since the farmers need to wait until only 10% of the iodine remains (we already calculated b, now we need to find x):

0.1A₀ = A₀eᵇˣ

0.1 = eᵇˣ

ln 0.1 = bx

where b = -0.08664

x = ln 0.1 / -0.08664 = -2.302585 / -0.08664 = 26.58 days

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2 years ago

This scatter plot shows the number of baskets made and the time in minutes that has passed.

irina1246 [14]

Scatter plots are used to relate variables using scattered dots.

The best prediction for the number of baskets made in 16 minutes is (c) 14 baskets

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Also, from the graph; as the minutes increases, the number of baskets either remain the same or increases.

This means that, for 16 minutes, the number of baskets would either be 12 (same as 14 minutes) or greater.

The closest to 12 baskets in the option is 14.

Hence, the best prediction for the number of baskets made in 16 minutes is (c) 14 baskets