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3 years ago

What is the slope of the line perpendicular to the line with equation 4x-5y+13=0

Mathematics

1 answer:

motikmotik3 years ago

4 0

Answer:

m = - 5/4

Step-by-step explanation:

If two lines are perpendicular, their slopes are negative reciprocals, which means that their product is -1

We can write the equation

4*x - 5*y + 13 = 0

as: 5*y = 4*x + 13 or

y = (4/5)*x + 13 (1)

Equation (1) is the equation of a straight line in its slope point form, 4/5 is the slope, according to this the slope of a perpendicular line is

-5/4

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How many years will it take for the account to reach $18,600? Round your answer to the nearest hundredth

Margarita [4]

<span>it depends how the interest is calculated, but there's not much of a difference

assuming its continuously compouned, you use this formula: A(t)=Pe^(rt), where A is the final amount, P is the initial investment, r is the interest, and t is the time in years

you want to find t such that A(t)=18,600 so 18,600=1000e^(.0675t)

you need to use logarithm to figure it out, take the natural log of both sides

the following properties will come into use:

ln(a*b)=ln(a)+ln(b)
ln(a^b)=bln(a)
ln(e)=1

taking the natural log

ln(18,600)=ln(1000e^(.0675t))

ln(18,600)=ln(1000)+ln(e^.0675t)

ln(18600)=ln(1000) + .0675t

now solve for t: t= (ln(18600)-ln(1000))/.0675

t=43.31</span>

4 0

3 years ago

Annie is opening a savings account which earns 5.2% interest, compounded continuously.

diamong [38]

Answer:

1686.22

Step-by-step explanation:

2300=P(1+(0.052x7))

2300=P1.364

P=2300/1.364

=1686.217...

=1686.22...

=1686 FOR THE NEAREST DOLLAR

7 0

2 years ago

The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo

PolarNik [594]

Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

length XY = $\sqrt{x^2+y^2}$

Therefore, the length between points AB is

length AB = $\sqrt{(-4 - (-2))^2+(-1-3)^2}$

= $\sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2} = \sqrt{20}$ = 4.472 units

Similarly, length BC is given by

Length BC = $\sqrt{(-4)^2+1^2} = \sqrt{17}$ = 4.123 units

Length CD = $\sqrt{(-2)^2+5^2} = \sqrt{29}$ = 5.385 units

Length DA = $\sqrt{(8)^2+(-2)^2} = \sqrt{68}$ = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A = $\sqrt{(7)^2+(0)^2} = \sqrt{49}$ =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

$S_{\bigtriangleup}$ = $(\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|$

= $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

$S_{{\bigtriangleup}ABC}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|$

= $=(\frac{1}{2})|-4-6 -8|= 9 units^2$

Triangle ACD'

A(-4,-1)

C(2,2)

D'(3, -1)

$S_{{\bigtriangleup}ACD'}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(2+1)+(2)(-1+1) +3((-1)-2)| = \frac{21}{2}$ = 10.5 units²

Area of polygon = $S_{{\bigtriangleup}ABCD'}$ = $S_{{\bigtriangleup}ABC}$ + $S_{{\bigtriangleup}ACD'}$ = (9 + 10.5) units²

Area of polygon ABCD' = 19.5 units².

8 0

3 years ago

Why is investing in the stock market riskier than saving cash or bond investments? Describe one way to mitigate, or lessen, that

Vesnalui [34]

If the company performs badly, or there's a perception it does so, then the stock's value will go down and you'll lose money. The only way to earn money from stocks is if the company is able to be innovative and survive the competition. The worst case scenario is that you lose all your money if the company goes bankrupt.

To reduce the risk, you should diversify your investments so that you invest in multiple companies along multiple sectors of the economy. This spreads out the risk so that if one company fails, then its unlikely they all fail (assuming there isn't some catastrophic event in the market). Alternatively, you can invest with mutual funds or index funds to let other people/entities invest your money with a range of diverse companies.

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butalik [34]

Answer

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Step-by-step explanation:

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3 years ago

Read 2 more answers