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Alinara [238K]
2 years ago
7

Solve the system of equations. Show your work. y = x^2 -3x +4 x + y = 4

Mathematics
1 answer:
sesenic [268]2 years ago
3 0

Answer:

x + y = 2 ,  y = x 2 − 4 x + 4

Replace all occurrences of  

y

with  x 2 − 4 x + 4

in each equation.

x 2 − 3 x + 4 = 2 y = x 2 − 4 x + 4

Solve for  

x

in the first equation.

x = 2 , 1 y = x 2 − 4 x+ 4

Replace all occurrences of  

x  with  2

in each equation.

y=0 x = 2

Replace all occurrences of  x

with  1

in each equation.

y = 1 x = 1

The solution to the system is the complete set of ordered pairs that are valid solutions.

( 2 , 0 ) ( 1 , 1 )

The result can be shown in multiple forms.

Point Form:

( 2 , 0 ) , ( 1 , 1 )

Equation Form:

x=2 , y = 0 x = 1 , y = 1

Step-by-step explanation:

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AlexFokin [52]

Answer:

15

Step-by-step explanation:

Diagram would be helpful.... I am assuming this is a right triangle with legs ratio 3:4

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2 years ago
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Tasya [4]

Step-by-step explanation:

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7 0
2 years ago
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Sue Brown is a salesperson at a car dealership. She earned a gross pay of $8000 for the month of June. Her state tax rate is 3.5
Neporo4naja [7]

Sue Brown owes $280.00 in state taxes for the month.

Step-by-step explanation:

Given,

Gross pay of Sue in June = $8000

Tax rate = 3.5%

As full amount is taxable; therefore

Amount of tax to be paid = 3.5% of pay of June

Amount of tax to be paid = \frac{3.5}{100}*8000

Amount of tax to be paid = 0.035*8000

Amount of tax to be paid = $280.00

Sue Brown owes $280.00 in state taxes for the month.

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Learn more about percentage at:

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4 0
3 years ago
Which expressions are equivalent to the one below? Check all that apply. 2^5 • 2^x
umka21 [38]
When you multiply exponential expressions that have the same base, you simply add the exponents. This is true for both numbers and variables. When you include other numbers in the multiplication, you simply factor and break the expression into several multiplications.
2^5 * 2^x= 2^(5 + X)
3 0
3 years ago
Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours. Then pumps Y and Z started working an
madam [21]

Answer:

The correct option is B) 12.

Step-by-step explanation:

Consider the provided information.

Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours.

As we know: rate =\dfrac{ work}{time},

The rate of pump X is \frac{\frac{1}{4}}{2} = \frac{1}{8}

\frac{1}{4} of the water is pumped out of the tank, that means only \frac{3}{4} is left to be pumped out.  

All 3 pumps pumped out the remaining \frac{3}{4} of the water out in 3 hours.

The combined rate of all three pumps is: \frac{\frac{3}{4}}{3} = \frac{1}{4}

Pump Y, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water.

The rate of pump Y = \frac{\frac{3}{4}}{18} = \frac{1}{24}

Let z is the time taken by pump Z, then the rate of pump Z is \frac{1}{z}.

Therefore,

\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{z}=\dfrac{1}{4}

Multiplying both sides by 24 z.

3z + z + 24 = 6z\\24 = 2z\\12 = z

Hence, the correct option is B) 12.

5 0
3 years ago
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