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2 years ago

Please solve the system of equations below thank you explain if u can

Mathematics

1 answer:

ivanzaharov [21]2 years ago

7 0

First let’s try to cancel out the x
5x + -5x = 0
Add the y and the numbers together
-3y + -2y = -5y
26 + -16 = 10
-5y = 10
y = -2
Use y=-2 in one of the equations
-3(-2) + 5x = 26
6 + 5x = 26
5x = 20
X = 4

So
Y= -2
X= 4

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Factor the polynomial and use the zeros to identify its graph. x4 − 5x3 − 20x2 + 60x + 144

Monica [59]

The zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)

<h3>How to factor the polynomial?</h3>

The polynomial is given as:

P(x) = x^4 - 5x^3 - 20x^2 + 60x + 144

Expand the polynomial function

P(x) = x^4 - 10x^3 + 5x^3 + 24x^2 - 50x^2 + 6x^2 + 120x - 60x + 144

Rewrite the function as:

P(x) = x^4 - 10x^3 + 24x^2 + 5x^3 - 50x^2 + 120x + 6x^2 - 60x + 144

Factorize the function

P(x) = x^2(x^2 - 10x + 24) + 5x(x^2 - 10x + 24) + 6(x^2 - 10x + 24)

Factor out x^2 - 10x + 24

P(x) = (x^2 + 5x + 6)(x^2 - 10x + 24)

Expand each bracket

P(x) = (x^2 + 3x + 2x + 6)(x^2 - 4x - 6x + 24)

Factorize each bracket

P(x) = [x(x + 3) + 2(x + 3)][x(x - 6) - 4(x - 6)]

Factor out x + 3 and x - 6

P(x) = (x + 3)(x + 2)(x - 4)(x - 6)

Set to 0

(x + 3)(x + 2)(x - 4)(x - 6) = 0

Solve for x

x =-3, -2, 4 and 6

Hence, the zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)

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2 years ago

Situation:

omeli [17]

The half life of the substance is 6.92 days.

Half life can be defined as the time required to reduce the concentration to half of its initial value.

Here the equation given is

$\rm N = N_o e^{-kt}$

The concentration will reduce to half therefore

$\rm N= \dfrac{N_o}{2}$

so,

$\rm 39/2 = 39 e^{- 0.1001 * t_{1/2}}$

ln 0.5 = - 0.1001 * t(1/2)

-0.693 = -.1001 * t(1/2)

t(1/2) = 6.92 days.

Therefore the half life of the substance is 6.92 days.

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2 years ago

Need help in 5 and 6 PLEASEE!!

klasskru [66]

5) Step-by-step solution:
Step 1 of 2
Write the numbers (other than dates) in this statement in scientific notation.
The mass of Pluto, the smallest planet, is 0.0021 times that of Earth; The mass of Jupiter, the largest planet, is 317.83 times that of earth.
The first number is 0.0021.
Now move the decimal point to the right of the first nonzero digit and count the number of places it was moved.

The original number (0.0021) was small so the exponent will be .
Therefore, the scientific notation is .
Step 2 of 2
The second number is 317.83.
Now move the decimal point to the right of the first nonzero digit and count the number of places it was moved.

The original number (317.83) was large so the exponent will be .
Therefore, the scientific notation is .

6) Simply move the decimal point 16 places to the right of where it currently is.

9.803 moved three times = 9803.
Then just add 13 zeroes (because 16 minus those first three = 13) to 9803, giving you a final result of 98030000000000000. Then if you wanted to make it pretty on your eyes with commas, it would be 98,030,000,000,000,000.

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How many solutions are there to the equation n^2-13n=-40

Marizza181 [45]

It has 2 real solutions which are 5 and 8

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3 years ago

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Arte-miy333 [17]

Answer:

Step-by-step explanation:

4, 7, 12, 21, 38, ...

2+2=2¹+2
4+3= 2²+3
8+4= 2³+4
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32+6= 2⁵+6

next term:

2⁶+7= 64+7=71

nth term:

2ⁿ+(n+1)

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3 years ago