MATHEMATICS HIGH SCHOOL

Sara puts $4000 into an investment yielding 5% annual simple interest; she left the money in for five years. How much interest does Sara get at the end on those 5 years?

Answers

Answer 1

Answer:

Answer:

1000

Step-by-step explanation:

4000.

5% annual, so 5x5=25

4000 of 25%

1000

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the total distance of a car moves varies directly with the time in hours.the car moves a total distance of 812 miles in 14 hours.what is the time in hours the car moves when the total distance is 1276 miles?

Answers

Answer:

J (22hrs)

Step-by-step explanation:

812 divided by 14= 58

1,276 divided by 58= 22 hrs

Does anyone know the pattern to this? Does anyone also know the slope to it and where the line intersects at the y-axis and the equation of the line?

Answers

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $(y_(2)-y_(1) )/(x_(2)-x_(1) )$

with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (3, 7) ← 2 ordered pairs from the table

m = $(7-3)/(3-1)$ = $(4)/(2)$ = 2

The line crosses the y- axis at (0, 1 ) ← from table

Then c = 1

y = 2x + 1 ← equation of line

Water fills a tank at a rate of 150 litres during the first hour, 350 litres during the second, 550 litres during the third and so on. Find the number of hours necessary to fill a rectangular tank 16m x 7m x 7m.

Answers

Putting this as an arithmetic sequence gives:

$u_n = 150+200(n-1)$

The sum of the series = 16 x 7 x 7 = 784 m^3 = 784 000 L

The sum of an arithmetic series can be written as:

$S_n=n/2 [2a+(n-1)d] = 784 000\nn/2[2(150)+(n-1)200] = 784 000\nn[300+200(n-1)=1 568 000\n300n+200n^2-200n = 1 568 000\n200n^2+100n- 1 568 000 = 0\n2n^2 +n- 15680 = 0\nn= 88.2...,-88.7$

n has to be positive, so we get

n = 88.2 hours (3 s.f.)

Volume of tank = (16m)(7m)(7m) = 784 m³

Conversion of m³ to L:
(784 m³) × (1000L / 1m³) = 784,000 L

Rate in the 1st hour:
150 liters/hr

Rate in the 2nd hour:
350 liters/hr

Rate in the 3rd hour:
550 liters/hr

It is apparent that the Fill Rate is increasing by 200 liters/hr every subsequent hour . . . so that can be represented by the following equation

where:
t = number of hours

Fill rate (i.e. volume of water filled into tank within the specified hour) = 150 + 200(t - 1)

For t = 1 . . . Fill rate = 150 L/hr
For t = 2 . . . Fill rate = 350 L/hr
For t = 3 . . . Fill rate = 550 L/hr

Because after every hour there has been more water added to the tank, this problem can be represented as a geometric sequence in order to account for the compounding of the volume after each time step, but it can also be tabulated (which seems to me to be the more direct/simple approach), so I will build a table that accounts for the increasing Fill Rate and the compounding of water volume after each time step . . .

(see attached)

The answer (after all of this) is . . . t = 88 hrs 17 1/2 mins (approx)

PLEASE HELPWhat is the perimeter of DEFG, shown?

A. 26.12
B. 18.06
C. 36.12
D. 13.06

Answers

The answer is the option A: A. 26.12

The explanation is shown below:

1. As you need the perimeter, you can divide the figure into three triangles (as you can see in the figure attached) to calculate the length of the diagonal lines, which would be the hypotenuses of the triangles.

2. You must apply the Pythagorean Theorem to calculate the hypotenuse of each triangle:

- Red triangle (The legs are 3 and 4):

$h=\sqrt{3^(2)+4^(2)} =5$

- Blue triangle (The legs are 1 and 2):

$h=\sqrt{1^(2)+2^(2)} =2.23$

-Green triangle (The legs are 3 and 5):

$h=\sqrt{3^(2)+5^(2)} =5.83$

3. The figure has is symmetric with respect to the y-axis. So, you can multiply the sum of the hypotenuses obtained by two to calculate the perimeter:

$Perimeter=2(5+2.23+5.83)=26.12$

Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36 Given ⇒ 3(x − 4) + 5x = 9x − 36 Step 1 ⇒ 3x − 12 + 5x = 9x − 36 Step 2 ⇒ 3x + 5x − 12 = 9x − 36 Step 3 ⇒ 8x − 12 = 9x − 36 Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36 Step 5 ⇒ 0 − 12 = x − 36 Step 6 ⇒ −12 = x − 36 Step 7 ⇒ −12 + 36 = x − 36 + 36 Step 8 ⇒ 24 = x + 0 Step 9 ⇒ 24 = x Which property yields Step 1?

Answers

Answer:

Step-by-step explanation:

Distributive property

a(b - c) = ab - ac

3(x-4) = 3*x - 3*4

= 3x - 12

The variables x and y are directly proportional, and y=2 when x=3. What is the value of y when x=9

Answers

$If\ x\ and\ y\ are\ directly\ proportional\ then\ (y)/(x)\ is\ constans\n---------------------------\n\n(2)/(3)=(y)/(9)\n\ncross\ multiply\n\n3y=2*9\n\n3y=18\ \ \ \ |divide\ both\ sides\ by\ 3\n\ny=6$

you cross multiply and you should get i think 6?

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