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otez555 [7]
3 years ago
10

Mark invests $4200 in two different accounts. The first account paid 3 %, the second account paid 7 % in interest. At the end of

the first year he had earned $186 in interest. How much was in each account?
Mathematics
1 answer:
nexus9112 [7]3 years ago
8 0

Answer:

3% interest account = $2,700

7% interest account = $1,500

Step-by-step explanation:

We have to use equation to find the answer. Again, we are using simple interest to find how much is in each account.

We know, Interest = Capital x Interest rate x year

Let,

3% interest account = X

7% interest account = Y

According to the question,

X*0.03*1 + Y*0.07*1 = 186 ................. (i)

Again, X + Y = 4200 .................. (ii)

From equation (Ii), we get,

or X = 4,200 - Y ...................... (iii)

Putting the value of X in equation (i), we can get,

(4,200 - Y)*0.03*1 + Y*0.07*1 = 186

or, 126 - 0.03Y + 0.07Y = 186

or, 0.04Y = 186-126

or, 0.04Y = 60

or, Y = 1,500

Putting Y = 1,500 in equation (iii), we get

X = 4,200 - 1,500

X = 2,700

Therefore, 3% account had $2,700 balance

7% account had $1,500 balance.

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Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29
hram777 [196]

Answer:

\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }

Step-by-step explanation:

Hello,

I assume that we are working in \mathbb{C}, otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

   p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }

Now, we need to find the zeroes of the second factor, meaning finding x so that:

x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4}  \\ \\  x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\  x = 2+5i \ \text{ or } \ x = 2-5i

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0
3 years ago
Will mark brainliest
SVETLANKA909090 [29]

Answer:

I think the answer should be Mat A cause it has more space.

3 0
2 years ago
Will give brainliest!!
marin [14]

the answer its 12.5% i swer its ok and hope helps you

3 0
3 years ago
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