X + y = 90

Let's make 'x' the bigger angle and 'y' the smaller.
X is 24 more than twice y.
x = 24 + 2y

Now plug that into the x of the first equation.
(24 + 2y) + y = 90

Combine like terms.
24 + 3y = 90

Subtract 24 from both sides.
3y = 66

Divide both sides by 3.
y = 22

The measure of the smaller angle is 22°

3 0

3 years ago

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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It’s really confusing, I could really use some guidance.

Dafna1 [17]

Answer:

See below.

Step-by-step explanation:

Let x equal each of the values on the table, and find the value of the function for that value of x.

f(x) = 5x - 5

x = -4

f(-4) = 5(-4) - 5

f(-4) = -20 - 5

f(-4) = -25

x = 0

f(0) = 5(0) - 5

f(0) = 0 - 5

f(0) = -5

x = 1

f(1) = 5(1) - 5

f(1) = 5 - 5

f(1) = 0

x = 3

f(3) = 5(3) - 5

f(3) = 15 - 5

f(3) = 10

x = 5

f(5) = 5(5) - 5

f(5) = 25 - 5

f(5) = 20

x f(x)

-4 -25

0 5

1 0

3 10

5 20

5 0

3 years ago

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Helpppppppppppppppppppp

PIT_PIT [208]

Answer:

$( {4}^{3} \div {5}^{ - 2} {)}^{5}$

Step-by-step explanation:

${4}^{15} . {5}^{10}$

hope this will help you more

have a great day..

5 0

3 years ago

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