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Mariana [72]
3 years ago
5

Write the equation of the line perpendicular to 3x+2y=-8 that passes through (3,1). Write in slope intercept form and show all y

our work.
Mathematics
1 answer:
weqwewe [10]3 years ago
6 0

First, put the equation of the line given into slope-intercept form by solving for y. You get y = 2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6

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Find the area of the figure
VLD [36.1K]

Answer:

132 cm²

Step-by-step explanation:

Consider the shape as a trapezoid with a rectangle added on top.

The area of the trapezoid is (7+19)/2 × 8 =104

The area of the rectangle is 7×4 = 28

Add the two areas: 104+28= 132

OR consider the shape as a tall rectangle with the two triangles added to the sides.

The area of the rectangle is 7(4+8) = 84

The area of the triangles is 8(19-7)/2= 48

[Each triangle is 24 cm²]

Add those areas

84+48=132

Same result: 132 cm²

4 0
2 years ago
If y= 3x + 6, what is the minimum value of (x^3)(y)?
Rainbow [258]

Answer:

Given the statement: if y =3x+6.

Find the minimum value of (x^3)(y)

Let f(x) = (x^3)(y)

Substitute the value of y ;

f(x)=(x^3)(3x+6)

Distribute the terms;

f(x)= 3x^4 + 6x^3

The derivative value of f(x) with respect to x.

\frac{df}{dx} =\frac{d}{dx}(3x^4+6x^3)

Using \frac{d}{dx}(x^n) = nx^{n-1}

we have;

\frac{df}{dx} =(12x^3+18x^2)

Set \frac{df}{dx} = 0

then;

(12x^3+18x^2) =0

6x^2(2x + 3) = 0

By zero product property;

6x^2=0   and 2x + 3 = 0

⇒ x=0 and x = -\frac{3}{2} = -1.5

then;

at x = 0

f(0) = 0

and  

x = -1.5

f(-1.5) = 3(-1.5)^4 + 6(-1.5)^3 = 15.1875-20.25 = -5.0625


Hence the minimum value of (x^3)(y) is, -5.0625






3 0
3 years ago
What is log of 1/100
sesenic [268]
Log of 1 / 100 is - 2 because 10^( - 2 ) = 1 / 10^2 = 1 / 100 ;
5 0
3 years ago
Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression −0.75 to fin
Salsk061 [2.6K]

Answer:

Step-by-step explanation:

Adam plans to choose a video game from a section of the store where everything is 75% off.

The expression written by him for this situation is d - 0.75d.

Here, the part d represents the sale price before discount and the part 0.75d is the discount amount.

The expression written by Rena is 0.25d.

Here, the part 0.25d is the price after discount. Since 75% is the discount, the rate after disount is 25% and 25% of d is 0.25d.

6 0
3 years ago
1.11 x 10^-5 standard form
zavuch27 [327]

Answer:

.0000111

Step-by-step explanation:

move the decimal five places to the left because the 5 is negative

8 0
3 years ago
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