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3 years ago

Find the y-coordinates of the points that are 10 units away from the point (-7, 6) that have an x-coordinate of 1.

1 answer:

7 0

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-7}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{y})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ 10=\sqrt{[1-(-7)]^2+[y-6]^2}\implies 10^2=[1-(-7)]^2+[y-6]^2 \\\\\\ 100=(1+7)^2+(y-6)(y-6)\implies 100=8^2+\stackrel{F~O~I~L}{(y^2-12y+36)} \\\\\\ 100=64+36+y^2-12y\implies 100=100+y^2-12y \\\\\\ 0=y^2-12y\implies 0=y(y-12)\implies y= \begin{cases} 0\\ 12 \end{cases}$

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Which expression is equivalent to ( 4mn / m^-2n^6)^-2

inn [45]

Here are a few rules with exponents that apply here:

Raising a power to a power: $(x^m)^n=x^{m*n}$
Dividing exponents of the same base: $\frac{x^m}{x^n}=x^{m-n}$
Converting negative exponents to positive ones: $x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m$

Firstly, solve the outer exponent:

$(\frac{4mn}{m^{-2}n^{6}})^{-2}=\frac{4^{-2}m^{-2}n^{-2}}{m^{-2*-2}n^{6*-2}}=\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}$

Next, divide:

$\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}=4^{-2}m^{-2-4}n^{-2-(-12)}=4^{-2}m^{-6}n^{10}$

Next, convert the negative exponents:

$4^{-2}m^{-6}n^{10}=\frac{n^{10}}{4^2m^6}=\frac{n^{10}}{16m^6}$

<u>Your final answer is n^10/16m^6 , or B.</u>

8 0

3 years ago

Steve invested money in the stock market. In the first year, his stock increased 50%. He paid his stockbroker $350 and then lost

telo118 [61]

Answer:

Original amount invested = $3400 .

Step-by-step explanation:

Let the original investment of Steve = $x

Stock increased in the first year = 50% of amount invested

Therefore total amount after one year = x + 0.5x = 1.5x

Commission paid to the stock broker = $350

Amount lost by him = $400

Amount withdrawn by him = $300

Total amount decreased from the amount after 1 year

= 1.5x - (350 + 400 + 300)

= 1.5x - 1050

This remaining amount is doubled, so the final amount

= 2(1.5x - 1050)

= 3x - 2100

This final amount is equal to $8100

3x - 2100 = 8100

3x = 8100 + 2100

3x = 10200

x = $3400

Therefore original amount invested in the stock market was $3400 .

8 0

3 years ago

Please help meeee I have 20 minutes to turn this in

lana66690 [7]

Answer:

RSU = 75.2°

Step-by-step explanation:

this is because:

⇒ RSU = RST + TSU

⇒ RSU = 48 + 27.2

⇒ RSU = 75.2°

Hence proved

6 0

3 years ago

Read 2 more answers

The temperature of a freezer started at 18 degrees Celsius.After cooling for a few hours, the freezer had a temperature of -12 d

bixtya [17]

Answer:

Step-by-step explanation:

Difference = New temperature - original temperature

= -12 - (18)

= - 30

New temperature is 30° less than the original temperature

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3 years ago

What does A(2,5) become after rotated 360 degrees?

Salsk061 [2.6K]

Answer:

Step-by-step explanation:

Its D because when you rotate 360 degrees you end up back where you were

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3 years ago

Find the​ y-coordinates of the points that are 10 units away from the point (-7, 6) that have an​ x-coordinate of 1.

Find the y-coordinates of the points that are 10 units away from the point (-7, 6) that have an x-coordinate of 1.