Ann got 6.25 gallons of gas at $3.12 per gallon. how much did she pay

Mathematics

1 answer:

matrenka [14]3 years ago

7 0

19 dollars and 5 cents

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What is the area of this figure?

Mazyrski [523]

I believe the area is 66

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Given the circle with the equation (x + 1)2 + y2 = 36, determine the location of each point with respect to the graph of the cir

kati45 [8]

$\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad 
radius=\stackrel{}{ r}\\\\
-------------------------------\\\\
(x+1)^2+y^2=36\implies [x-(\stackrel{h}{-1})]^2+[y-\stackrel{k}{0}]^2=\stackrel{r}{6^2}~~~~
\begin{cases}
\stackrel{center}{(-1,0)}\\
\stackrel{radius}{6}
\end{cases}$

so, that's the equation of the circle, and that's its center, any point "ON" the circle, namely on its circumference, will have a distance to the center of 6 units, since that's the radius.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(1-0)^2}\implies d=\sqrt{(-1+1)^2+1^2}
\\\\\\
d=\sqrt{0+1}\implies d=1$

well, the distance from the center to A is 1, namely is "inside the circle".

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\\\\\\
\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(6-0)^2}\implies d=\sqrt{(-1+1)^2+6^2}
\\\\\\
d=\sqrt{0+36}\implies d=6$

notice, the distance to B is exactly 6, and you know what that means.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})
\\\\\\
\stackrel{distance}{d}=\sqrt{[4-(-1)]^2+[-8-0]^2}\implies d=\sqrt{(4+1)^2+(-8)^2}
\\\\\\
d=\sqrt{25+64}\implies d=\sqrt{89}\implies d\approx 9.43398$

notice, C is farther than the radius 6, meaning is outside the circle, hiking about on the plane.

3 0

3 years ago

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- is dilated to be ' ' ' '. The original is the center of dilation.

Oliga [24]

The scale factor is 5

In the first image, you can see that the pre image square it 1 unit long and the image is 5. How do you get 1 to 5, you multiply by 5. So the scale factor is 5.

7 0

3 years ago

THIS IS THE FOURTH TIME I'VE ASKED PLEASE ANSWER<br> √(10 + 4 √(6))<br> not decimal form

nalin [4]

Answer:

$\huge\boxed{\sqrt{10+4\sqrt6}=\sqrt6+2}$

Step-by-step explanation:

$\sqrt{10+4\sqrt6}=\sqrt{6+4+(2)(2)(\sqrt6)}=\sqrt{\underbrace{(\sqrt6)^2}_{=6}+(2)(2)(\sqrt6)+\underbrace{2^2}_{=4}}\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=\sqrt{(\sqrt6+2)^2}\\\\\text{use}\ \sqrt{a^2}=|a|\\\\=|\sqrt6+2|=\sqrt6+2$

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3 years ago

Please help I'm timed!!

s2008m [1.1K]

Answer:

I believe i t is 61. Could be wrong though.

Step-by-step explanation:

Angle r plus angle u equals 180. Set the sum of the two equations and solve for x. Then, substitute that number for a and solve.

5 0

2 years ago