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Temka [501]
3 years ago
8

Plz help (This is the whole problem it says "one part remaining")

Mathematics
2 answers:
stiks02 [169]3 years ago
8 0
Hey there!

To start, let x represent the cost of the mutual fund that earned 9%.

This cost will be represented by the term 0.09x.

Now, let (1200-x) represent the cost of the mutual fund that earned 3% profit, since the two amounts must add up to be 1200, the amount the investor originally invested. 

This cost will be represented by 0.03(1200-x)

Next, because the overall profit of the two mutual funds earned was 78 dollars, you can set up this equation:
0.09x+0.03(1200-x)=78

Now, solve for the value of x:
0.09x+0.03(1200-x)=78
0.09x+36-0.03x=78
0.06x+36=78
0.06x=42
x=700

Therefore, the amount invested in the 9% mutual fund would be $700 dollars.

Hope this helps and have a wonderful day! :)
Shalnov [3]3 years ago
3 0
He invested two unknown amount that add to $1200.
Let the amount invested at 9% be x.
Let the amount invested at 3% be y.

The amounts add to $1200.
x + y = 1200           First Equation

The profit from the 9% part is 0.09x.
The profit from the 3% part is 0.03y.
The two profits add to $78.
0.09x + 0.03y = 78        Second Equation

We have two equations in two unknowns, so we can solve this problem as a system of equations.

x + y = 1200
0.09x + 0.03y = 78

Multiply the first equation by -0.09 and add to the second equation.

-0.09x - 0.09y = -108
 0.09x + 0.03y =   78
----------------------------
             -0.06y = -30

Divide both sides by -0.06

y = 500

Now we substitute 500 into y in the first equation.

x + y = 1200

x + 500 = 1200

x = 700

Answer: The amount invested at 9% is $700
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Step-by-step explanation:

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3 years ago
An ice cream shop offers the toppings below. How many 4-topping ice cream sundaes can you make?
marishachu [46]
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3 years ago
What are the real and complex solutions of the polynomial equation? x^4-41x^2=-400. *work needed*
pickupchik [31]
<h3>Answer: x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>

Step-by-step explanation:

Given the polynomial equation x^4-41x^2=-400.

Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get

x^4-41x^2+400=-400+400.

x^4-41x^2+400=0.

Factoring by product sum rule.

We need product of 400 and sum upto -41.

We can see that 400 = -25 × -16 = 400 and -25-16 = -41.

Therefore,

x^4-25x^2-16x^2+400=0

Making it into two groups, we get

(x^4-25x^2)+(-16x^2+400)=0

Factoring out GCF of each group, we get

x^2(x^2-25)-16(x^2-25)=0

(x^2-25)(x^2-16) =0

Factoring out  (x^2-25) and (x^2-16) separately by difference of the squares identity a^2-b^2=(a-b)(a+b), we get

(x^2-25) = x^2-5^2= (x-5)(x+5) and

x^2-16 = x^2-4^2 =(x-4)(x+4).

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(x-5)(x+5)(x-4)(x+4) =0

Applying zero product rule,

x-5=0

x+5=0

x-4=0 and

x+4=0.

Therefore,

<h3>x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>
6 0
3 years ago
In a two digit number, the tens digit is 2 less than the units digit multiplied by three. The reversed number is half the origin
Papessa [141]

Answer:

73

Step-by-step explanation:

Original number: XY

x = 3y - 2

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substitution: 10y + 3y - 2 = 13y - 2 = (10 * (3y - 2) + y) / 2 + 1/2

* 2 both sides and simplify: 26y - 4 = 31y - 19

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5y = 15

y = 3

x = 7

Original number: 73

8 0
2 years ago
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PIT_PIT [208]
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Then the linear relation may be in the following form y=2x+b
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The relation is then y=2x+19.
We check that the other point are on the above line:
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We have then a linear relation.
3 0
3 years ago
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