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2 years ago

May someone please help? thank you!

Mathematics

1 answer:

tester [92]2 years ago

7 0

Answer:

$6\sqrt2\\OR\\8.48528137$

Step-by-step explanation:

The area of a sector of a circle is found by:

$A = \frac{\theta*r^2}{2}$

The question asks for the radius so the equation above can be repurposed

$r = \sqrt\frac{2A}{\theta}$

A = 3pi

angle = pi/12

$\frac{6\pi}{\pi/12} = \frac{72\pi}{\pi} = 72$

$\sqrt{72} = 6\sqrt2 = 8.48528137$

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Write an equation of a line in point-slope, slope-intercept, and standard form that has

Inga [223]

Answer:

(a) $y + 4x - 14 = 0$

(b) $y = -4x + 14$

Step-by-step explanation:

The formula for calculating the equation of line in point - slope form is given as :

$y-y_{1} = m(x-x_{1} )$

where m is the slope

Given from the question :

m = - 4

$x_{1}$ = 2

$y_{1}$ = 6

Substituting into the formula , we have :

$y - 6 = - 4(x - 2)$

$y - 6 = -4x + 8$

$y + 4x - 6 - 8 = 0$

$y + 4x - 14 = 0$

Therefore :

(a) the equation of the line in point - slope form is $y + 4x - 14 = 0$

(b) to write it in slope - intercept form , we will make y the subject of the formula , which will give : $y = -4x + 14$

5 0

2 years ago

How many solutions does the system have?

sertanlavr [38]

If a solution(s) exists y=y so we can say:

x^2-3x=-2x+2 add 2x to both sides

x^2-x=2 subtract 2 from both sides

x^2-x-2=0 factor

(x-2)(x+1)=0

So x=-1 and 2, using y=-2x+2 we find:

y(-1)=4 and y(2)=-2

So the two solutions occur at the points:

(-1,4) and (2,-2)

4 0

3 years ago

Read 2 more answers

(x+3)^2=4

GalinKa [24]

Answer:

x = -1, -5

Step-by-step explanation:

${(x + 3)}^{2} = 4 \\ = > {x}^{2} + 2 \times x \times 3 + {3}^{2} = 4 \\ = > {x}^{2} + 6x + 9 = 4 \\ = > {x}^{2} + 6x = 4 - 9 \\ = > {x}^{2} + 6x = - 5 \\ = > {x}^{2} + 6x + 5 = 0 \\ = > {x}^{2} + 5x + x + 5 = 0 \\ = > x(x + 5) + 1(x + 5) = 0 \\ = > (x + 1)(x + 5) \\ = > x = - 1 \: \: or \: \: - 5$