Find the balance in the account after the given period. $4000 principal earning 4% compounded annually, 5 years

Triangle RST has vertices located at R (2, 3), S (4, 4), and T (5, 0). Part A: Find the length of each side of the triangle. Sho

deff fn [24]

Answer:

(a) Side lengths

$RS = \sqrt{5}$ $ST = \sqrt{17}$ $RT = \sqrt{18}$

(b) Slope

$RS = \frac{1}{2}$ $RT = 1$ $ST = -4$

(c) Scalene triangle

Step-by-step explanation:

Given

$R = (2,3)$

$S = (4,4)$

$T = (5,0)\\$

Solving (a): Length of each side

This is calculated using distance formula

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

So, we have:

$RS = \sqrt{(4 - 2)^2 + (4 - 3)^2}$

$RS = \sqrt{5}$

$ST = \sqrt{(5 - 4)^2 + (0- 4)^2}$

$ST = \sqrt{17}$

$RT = \sqrt{(5 - 2)^2 + (0 - 3)^2}$

$RT = \sqrt{18}$

Solving (b): The slope of each side

This is calculated using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$RS = \frac{4- 3}{4- 2}$

$RS = \frac{1}{2}$

$RT = \frac{0 - 3}{5- 2}$

$RT = \frac{ - 3}{- 3}$

$RT = 1$

$ST = \frac{0 - 4}{5- 4}$

$ST = \frac{- 4}{1}$

$ST = -4$

Solving (c): Classify the triangle

In (a), we have:

$RS = \sqrt{5}$

$ST = \sqrt{17}$

$RT = \sqrt{18}$

None of the sides are equal;

The triangle is scalene

5 0

3 years ago

A sample of students is taken from the school’s A honor roll. The school estimates that there are actually 360 students on the A

zlopas [31]

Answer:

Number of 8th Graders = 360 - X

As you can see this question is not complete and lacks the essential data. But we will try to create a mathematical expression to calculate the number of students on the A honor roll which are from 8th grade.

As we know:

Total number of students on the A honor roll = 360

We are asked to calculate, number of students from 8th grade on the A honor roll.

So, let's assume that "X" represents all the students who are on the A honor roll except 8th grade.

Mathematical Expression:

Number of 8th Graders = Total number of students on the A honor roll - X

Number of 8th Graders = 360 - X

So, if you know the value of X, you can easily calculate the number of students which are from 8th grade on the A honor roll.

I am not sure if it is wrong I am sorrry.

6 0

3 years ago

To find the distance across the river, the given diagram is laid out. what is the distance rounded to the nearest meter?

kati45 [8]

Given:

Angle A = 18.6°

Angle B = 93°

Length of side AB = 646 meters

To find:

the distance across the river, distance between BC

Steps:

Since we know the measure of 2 angles of a triangle we can find the measure of the third angle.

18.6° + 93° + ∠C = 180°

111.6° + ∠C = 180°

∠C = 180° - 111.6°

∠C = 68.4°

Therefore the measure of angle C is 68.4°.

now we can use the law of Sines,

$\frac{BC}{sinA}=\frac{AB}{SinC}$

$\frac{BC}{sin(18.6)}= \frac{646}{sin(68.4)}$

$BC[sin(68.4)] = 646 [sin(18.6)]$

$BC = \frac{646*sin(18.6)}{sin(68.4)}$

$BC = \frac{646 * 0.3190}{0.9298}$

$BC = 221.63$

$BC = 222$ meters

Therefore, the distance across the river is 222 meters.

Happy to help :)

If anyone need more help, feel free to ask

7 0

3 years ago

Element X is a radioactive isotope such that its mass decreases by 59% every day. If an experiment starts out with 390 grams of

miss Akunina [59]

Answer:

The function that represents the mass of the sample after t days is $A(t) = 390(0.41)^t$ .

The percentage rate of change per hour is of -2.46%.

Step-by-step explanation:

Exponential amount of decay:

The exponential amount of decay for an amount of a substance after t days is given by:

$A(t) = A(0)(1-r)^t$

In which A(0) is the initial amount, and r is the decay rate, as a decimal.

Element X is a radioactive isotope such that its mass decreases by 59% every day. The experiments starts out with 390 grams of Element X.

This means, respectively, that $r = 0.59, A(0) = 390$

So

$A(t) = A(0)(1-r)^t$

$A(t) = 390(1-0.59)^t$

$A(t) = 390(0.41)^t$

The function that represents the mass of the sample after t days is $A(t) = 390(0.41)^t$ .

Hourly rate of change:

Decreases by 59% every day, which means that for 24 hours, the rate of change is of -59%. So

-59%/24 = -2.46%

The percentage rate of change per hour is of -2.46%.

5 0

3 years ago

In a standard deck of 52 playing cards, what is the complement (not below 8)?

Damm [24]

Answer 2/13

Step-by-step explanation:

There are 52 cards in a standard deck: 13 ordinal cards (Ace -10, jack, Queen, King)and 4 of them

- one to each sute (hearts, diamonds, clubs, spades ) and so we have 4x13=52

There are 8 card that fit the question (4 each of access and kings).

so if you in a random draw the odds of drawing one of those 8 card out of the total number of 52 is 8/52

which we simplify

8/2=2/13

8 0

3 years ago

Find the balance in the account after the given period. ​$4000 principal earning 4​% compounded​ annually, 5 years

Find the balance in the account after the given period. $4000 principal earning 4% compounded annually, 5 years