MATHEMATICS HIGH SCHOOL

The balance in Alex's bank account is $675. The accountearns 6% simple interest calculated twice per year. If Alex
makes no deposits or withdrawals for 2 full years, the
balance in his account (rounded to the nearest dollar) will
be -
Select one:
O
$852
$715
$837
$756

Answers

Answer 1

Answer:

Answer:

$852

Step-by-step explanation:

From the given question, the following are given:

Present value, PV = $675

Rate, r = 6% = 0.06

Number of years, n = 2 years

Number of times per year, m = 2

The balance in his account is the future value (FV), so that;

Future value = PV $(1+r)^(nm)$

= 675 $(1+0.06)^((2*2))$

= 675 x 1.26248

= 852.174

Future value = $852

Thus, the balance in Alex's account would be $852.

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You are going to have a swimming pool put your back yard this summer. The dimensions of the pool are going to be 15 ft by 30 ft. There is going to be a concrete walkway around the outside of the pool, but they are not sure how wide it will be. The design of the pool, including the walkway, is shown below.

Answers

The perimeter of a shape is the sum of the all visible side lengths of the shape. The perimeter of the pool including the walkway is 90 + 8x

Given that:

$Length = 15$

$Width = 30$

Let the width of the walkway be x.

The dimension of the pool including the walkway is calculated by adding the dimension of the pool to the width of the walkway (on both sides):

So, we have:

$Length = 15 + x + x$

$Length = 15 + 2x$

$Width = 30 + x + x$

$Width = 30 + 2x$

The perimeter (P) of the walkway is then calculated using:

$P = 2 * (Length + Width)$

This gives:

$P = 2 * (15 + 2x + 30 + 2x)$

Collect like terms

$P = 2 * (15 + 30+ 2x + 2x)$

$P = 2 * (45+ 4x)$

Open brackets

$P = 2 * 45+ 2 * 4x$

$P = 90+ 8x$

Hence, the perimeter of the pool including the walkway is 90 + 8x (see attachment)

Answers

y coordinates control up and down

increase by 8 means go up by 8

8 units up

So,

A translation is a transformation in which the figure is simply moved across space; the preimage is congruent to the image.

We are told that the y-coordinate of the preimage increase by 8. We know that the y-coordinates have to do with vertical movement on a coordinate plane. Since the y-coordinates increased by 8, the preimage was moved up 8 units.

The correct option is A.

Andy drove 840 miles in 12 hours how far could he drive in 3.5 hours

Answers

12/12 840/12 = 1 hr 7miles
7 per hr
3.5x7 = 24.5 miles

Factor the perfect square trinomials

24. 9x^2 + 42x + 49

Answers

Answer:

(3x+7)^2

Step-by-step explanation:

Nina wants to download games for her video game console. Older games cost 100 points and new releases cost 200 points to use. The equation 100a+200b=4000, where a is the number of der games and b is the number of new releases, models the situation. How many older games can she download if she downloads 4 new games? 5 new games?

Answers

Replace b with 4: 100a+200(4)=4000. 100a+800=4000. Combine like terms: 100a=3,200. Get the unknown by itself: A=32. She can download 32 old games if she downloads 4 new ones. Same steps: 100a+200(5)=4000. 100a+1000=4000. 100a=3000. A=30. She can download 30 old games if she downloads 5 new ones. :)

Final answer:

If Nina downloads 4 new games, she can additionally download 16 older games. If she downloads 5 new games, she can download 15 older games.

Explanation:

The problem can be solved by substituting the number of new games into the equation and solving for 'a' which represents the number of older games.

For 4 new games, the equation becomes 100a+200*4=4000. Solving this, we get 'a' as 16. Hence, Nina can download 16 older games.

For 5 new games, the equation becomes 100a+200*5=4000. Solving this, we get 'a' as 15. Hence, Nina can download 15 older games when she downloads 5 new games.