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4 years ago

Multiply (x-2)(3x+4) using the distributive property.

Mathematics

1 answer:

vlabodo [156]4 years ago

5 0

The correct answer would be

B.(x-2)(3x)+(x-2)(4)

When distributing you just break up the second parentheses and put the first parentheses infront of both of them, as it is shown in this answer.

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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

Please help will give brainliest!! thank u

Goshia [24]

9514 1404 393

Answer:

Step-by-step explanation:

The centroid divides a median into parts with the ratio 1:2, so RL:LD = 1:2. Then RL:RD = 1:(1+2), and RD = 3RL.

RD = 3·54 cm

RD = 162 cm

5 0

3 years ago

A train travels at a constant rate of 45 miles per hour.

givi [52]

A. d=45t
b. 112.5 miles. 112.5=45•2.5

6 0

4 years ago

Read 2 more answers

160 is 120% of what number?

LuckyWell [14K]

120 % = 160

---------------------------------------------------------------------------
Find 1 % :
---------------------------------------------------------------------------
120% = 160
1% = 160 ÷ 120
1% = 4/3

---------------------------------------------------------------------------
Find 100% :
---------------------------------------------------------------------------
1% = 4/3
100% = 4/3 x 100
100% = 133 1/3

---------------------------------------------------------------------------
Answer: 160 is 120% of 133 1/3
---------------------------------------------------------------------------

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3 years ago

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Please this will determine if I pass

PSYCHO15rus [73]

The answer is B through ASA (Angle-Side-Angle) similarity criterion.

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3 years ago