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julsineya [31]
3 years ago
12

last year Jim had $10,000 to invest. he invested some of it in an account that paid 7% simple interest per year and he invested

the rest in an account that paid 6% simple interest per year. after one year he received a total of $690 what's an interest how much did he invest and each account
Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
7 0

He invested $345.00 each account

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Apply The Remainder Theorem, Fundamental Theorem, Rational Root Theorem, Descartes Rule, and Factor Theorem to find the remainde
Over [174]

9514 1404 393

Answer:

  possible rational roots: ±{1/3, 2/3, 1, 4/3, 2, 3, 4, 6, 12}

  actual roots: -1, (2 ±4i√2)/3

  no turning points; no local extrema

  end behavior is same-sign as x-value end-behavior

Step-by-step explanation:

The Fundamental Theorem tells us this 3rd-degree polynomial will have 3 roots.

The Rational Root Theorem tells us any rational roots will be of the form ...

  ±{factor of 12}/{factor of 3} = ±{1, 2, 3, 4, 6, 12}/{1, 3}

  = ±{1/3, 2/3, 1, 4/3, 2, 3, 4, 6, 12} . . . possible rational roots

Descartes' Rule of Signs tells us the two sign changes mean there will be 0 or 2 positive real roots. Changing signs on the odd-degree terms makes the sign-change count go to 1, so we know there is one negative real root.

The y-intercept is 12. The sum of all coefficients is 22, so f(1) > f(0) and there are no positive real roots in the interval [0, 1]. Synthetic division by x-1 shows the remainder is 22 (which we knew) and all the quotient coefficients are all positive. This means x=0 is an upper bound on the real roots.

The sum of odd-degree coefficients is 3+8=11, equal to the sum of even-degree coefficients, -1+12=11. This means that -1 is a real root. Synthetic division by x+1 shows the remainder is zero (which we knew) and the quotient coefficients alternate signs. This means x=-1 is a lower bound on real roots. The quotient of 3x^2 -4x +12 is a quadratic factor of f(x):

  f(x) = (x +1)(3x^2 -4x +12)

The complex roots of the quadratic can be found using the quadratic formula:

  x = (-(-4) ±√((-4)^2 -4(3)(12)))/(2(3)) = (4 ± √-128)/6

  x = (2 ± 4i√2)/3 . . . . complex roots

__

The graph in the third attachment (red) shows there are no turning points, hence no relative extrema. The end behavior, as for any odd-degree polynomial with a positive leading coefficient, is down to the left and up to the right.

4 0
3 years ago
) Tara earns twice as much per hour as Kayte.
Cerrena [4.2K]

Answer:

Austin's hourly wage is $8.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

Tara's hourly wage is x.

Kayte's hourly wage is y.

Austin's hourly wage is z.

Tara earns twice as much per hour as Kayte.

This means that x = 2y

Kayte earns $3 more per hour than Austin.

This means that y = z + 3

As a group, they earn $41 per hour.

This means that x + y + z = 41

What is Austin's hourly wage?​

This is z.

x + y + z = 41

y = z + 3 and x = 2y, so x = 2(z + 3) = 2z + 6

x + y + z = 41

2z + 6 + z + 3 + z = 41

4z + 9 = 41

4z = 32

z = \frac{32}{4}

z = 8

Austin's hourly wage is $8.

5 0
3 years ago
Read 2 more answers
Hey there is a link! It would mean a lot if you would give me the awnsers to these 3 questions! It’s grade 7 math! Thanks, all y
joja [24]

Answer:

a

Step-by-step explanation:

5 0
3 years ago
out of every 100£ that Judy earns at her part-time job, she saves 25£ for college. The amount she saves is directly proportional
poizon [28]

Answer: 970

Step-by-step explanation:

3,880 divided by 100= 38.8*25=970

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3 years ago
PLEASE HELP MEEEEE!! WILL MARK BRAINLIST!!
Lynna [10]
I believe the answer is D, I’m almost 100% positive this is correct
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