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3 years ago

12

When asked his age,Micheal said,"if you square my age,then subtract 12 times my age, the result is 85. "How old is she?

1 answer:

Mrac [35]3 years ago

4 0

Answer:

Micheal is 17 years old.

Step-by-step explanation:

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Yasmin swims at a constant rate of 2 km/h for 2.5 h. How far does Yasmin swim? 4.5 km 5 km 6 km 6.5 km

Neporo4naja [7]

She swims for 2.5 hours at a rate of 2 km/hr
Multiply 2.5 * 2 = 5 km

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3 years ago

Mr. Patel’s house is 1,850 ft 2 . He tiles 30% of the house on the first day. He tiles 185 ft 2 each day after that. How many mo

Black_prince [1.1K]

Step-by-step explanation:

Tile A $9.75

Tile BTiles are $11 per tile if fewer than 50 tiles are purchased. For 50 or more tiles, tiles are $9.50 per tile.

Tiles are purchased by the box

Tile C There are 24 tiles per box. Each box is $185.

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3 years ago

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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

3 years ago

A stack of playing cards contains 4 jacks, 5 queens, 3 kings, and 3 aces. two cards will be randomly selected from the stack. wh

Kipish [7]

Answer:

1/9.

Step-by-step explanation:

There is a total of 15 cards in the stack.

Prob( Queen is chosen) = 5/15 = 1/3.

The probability of a second queen being chosen is also 1/3

Required probability = 1/3 * 1/3 = 1/9.

7 0

3 years ago

I NEED HELP PLEASE, THANK YOU!

bixtya [17]

Answer:

$\sqrt{37}$

Step-by-step explanation:

To find the distance between a point (m, n ) and the line

Ax + By + C = 0

d = $\frac{|Am +Bn+C|}{\sqrt{A^2+B^2} }$

Here (m, n) = (6, 2) and rearranging the line

6x - y + 3 = 0 ← in general form

with A = 6, B = - 1 and C = 3 , then

d = $\frac{|6(6)-1(2)+3|}{\sqrt{6^2+(-1)^2} }$

= $\frac{|36-2+3|}{\sqrt{36+1} }$

= $\frac{37}{\sqrt{37} }$

Rationalise the denominator by multiplying numerator/ denominator by $\sqrt{37}$

= $\frac{37}{\sqrt{37} }$ × $\frac{\sqrt{37} }{\sqrt{37} }$

= $\frac{37\sqrt{37} }{37}$ ← cancel 37 on numerator/ denominator

= $\sqrt{37}$

5 0

3 years ago

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