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Snezhnost [94]
3 years ago
15

Hattie had $3,000 to invest and wants to earn 10.6% interest per year. She will put some of the money into an account that earns

12% per year and the rest into an account that earns 10% per year. How much money should she put into each account?

Mathematics
1 answer:
nevsk [136]3 years ago
8 0

Answer:

900 at 12%

2100 at 10%

Step-by-step explanation:

Let x= amount invested at 12%

let y= amount invested at 10%

with that being said we can write the two equation

Equation 1: x+y=3000

Equation 2: 3000*.106=.12x+.1y

isolte x from equation 1

x= 3000-y

plug this into equation 2

318=.12(3000-y)+.1y

318=360-.12y+.1y

-42= -.02y

y= 2100

Plug this into equation 1

x+2100=3000

x=900

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Let f(x) = x2 – 4, x < 0. What is f-1?
Galina-37 [17]

Answer:

-3

Step-by-step explanation:

f(x) = x2 – 4

replace x with -1

f(-1) = (-1)^2 – 4

= -3

5 0
2 years ago
A rectangle has a perimeter of 30 ft. Find a function that models its area A in terms of the length x of one of its sides. What
Vedmedyk [2.9K]

Answer:

Step-by-step explanation:

Let the other side of the rectangle be y. The perimeter of the rectangle is expressed as P = 2(x+y)

Given P = 30ft, on substituting P = 30 into the expression;

30 = 2(x+y)

x+y = 15

y = 15-x

Also since the area of the rectangle is xy;

A = xy

Substitute y = 15-x into the area;

A = x(15-x)

A = 15x-x²

The function that models its area A in terms of the length x of one of its sides is A = 15x-x²

The side of length x yields the greatest area when dA/dx = 0

dA/dx = 15-2x

15-2x = 0

-2x = -15

x = -15/-2

x = 7.5 ft

Hence the side length, x that yields the greatest area is 7.5ft.

Since y = 15-x

y = 15-7.5

y = 7.5

Area of the rectangle = 7.5*7.5

Area of the rectangle = 56.25ft²

6 0
3 years ago
Lisa and her daughter weigh 185 pounds all together. The ratio of lisa’s weight to her daughter weight is 4:1 . How much does li
zzz [600]

Since the ratio of mother to daughter is 4:1, the weight of the mother and daughter together is five times the weight of the daughter.

In fact, if the daughter weights d pound, the mother weights 4d pounds, and the total weight is d+4d = 5d.

We know that this total is 185 pounds, so we have

5d = 185 \iff d = \dfrac{185}{5} = 37

So, the daughter weights 37 pounds.

6 0
3 years ago
Amy bought 3 2/3 of material to make pillows. The fabric cost $5.00 per yard. How much did Amy pay for fabric
mrs_skeptik [129]

She paid $18.33 for her fabric.

3*5=15

2/3*5=3.333

15+3.333+18.333. or $18.33

5 0
3 years ago
Which is the solution to the system 3x+y=8 and 7x−4y=25
tatyana61 [14]

Answer:

(3, - 1 )

Step-by-step explanation:

Given the 2 equations

3x + y = 8 → (1)

7x - 4y = 25 → (2)

Multiplying (1) by 4 and adding to (2) will eliminate the y- term

12x + 4y = 32 → (3)

Add (2) and (3)  term by term to eliminate y

19x + 0 = 57

19x = 57 ( divide both sides by 19 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (1)

3(3) + y = 8

9 + y = 8 ( subtract 9 from both sides )

y = - 1

solution is (3, - 1 )

7 0
3 years ago
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