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3 years ago

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Solve (x + 9)2 = 25. Apply the square root property of equality: Isolate the variable. StartRoot (x + 9) squared EndRoot = Plus

or minus StartRoot 25 EndRoot If x + 9 = 5, then x = . If x + 9 = –5, then x = .
answer is x= 4
x= -14

2 answers:

Diano4ka-milaya [45]3 years ago

5 0

Answer: X1=-4 X2=-14

Licemer1 [7]3 years ago

4 0

Answer:1

Step-by-step explanation: I dont know

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If there is 12 inches in 1 foot, then do 12 times 12.

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Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

2 years ago

Find the slope of the line that passes through (23, -30) and (-7, 18).

babymother [125]

Answer:

slope = - $\frac{8}{5}$

Step-by-step explanation:

Calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (23, - 30) and (x₂, y₂ ) = (- 7, 18)

m = $\frac{18-(-30)}{-7-23}$ = $\frac{18+30}{-30}$ = $\frac{48}{-30}$ = - $\frac{8}{5}$

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3 years ago

Expand and simplify (x+5)(x-2)

salantis [7]

Answer:

${x}^{2} - x - 12 = (x + 3)(x - 4)$

${x}^{2} + 3x + 2 = (x + 2)(x + 1)$

${x}^{2} + 3x - 10 = (x + 5)(x - 2)$

Step-by-step explanation:

F [First terms] - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT

O [Outside terms] - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT

I [Inside terms] - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT

L [Last terms] - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT

${x}^{2} - x - 12 = {x}^{2} - 4x + 3x - 12$

${x}^{2} + 3x + 2 = {x}^{2} + x + 2x + 2$

${x}^{2} + 3x - 10 = {x}^{2} - 2x + 5x - 10$

I am joyous to assist you anytime.

8 0

2 years ago