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Sveta_85 [38]
2 years ago
14

X squared+ y squared = 2 y = 2x squared – 3 Which of the following describes the system?

Mathematics
1 answer:
cluponka [151]2 years ago
4 0

Answer:

x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}} and y=-1,\frac{1}{2}

The ordered pair solutions are (-\sqrt{\frac{7}{4}},0.5), (\sqrt{\frac{7}{4}},0.5), (-1,-1), and (1,-1).

Step-by-step explanation:

I'm assuming the system is \left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.:

x^2+y^2=2

x^2+(2x^2-3)^2=2

x^2+(4x^4-12x^2+9)=2

x^2+4x^4-12x^2+9=2

4x^4-11x^2+9=2

4x^4-11x^2+7=0

x^4-11x^2+28=0

(x^2-7)(x^2-4)=0

(4x^2-7)(x^2-1)=0

4x^2-7=0

4x^2=7

x^2=\frac{7}{4}

x=\pm\sqrt{\frac{7}{4}}

x^2-1=0

x^2=1

x=\pm1

y=2x^2-3

y=2(\pm\sqrt{\frac{7}{4}})^2-3

y=2({\frac{7}{4}})-3

y=\frac{7}{2}-3

y=\frac{1}{2}

y=2x^2-3

y=2(\pm1)^2-3

y=2(1)-3

y=2-3

y=-1

Therefore, x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}} and y=-1,\frac{1}{2}

The ordered pair solutions are (-\sqrt{\frac{7}{4}},0.5), (\sqrt{\frac{7}{4}},0.5), (-1,-1), and (1,-1).

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London has 1/3 of a rectangular block of sculpting clay. She wants to split it equally among 3 people. Which model shows how muc
trasher [3.6K]

Answer:

1/9

Step-by-step explanation:

Given that:

Original block of clay = 1/3

Number of divisions = 3

The amount of original block of clay gotten by each :

Original block of clay ÷ number of divisions

1/3 ÷ 3

1/3 * 1/3

= 1/9

Hence, each person will get 1/9 of the original block of clay.

7 0
2 years ago
1/3(z+4)-6=2/3(5-z) solve for z and check solution
Marat540 [252]

Answer:

z = 8

Step-by-step explanation:

Solve for z:

(z + 4)/3 - 6 = (2 (5 - z))/3

Put each term in (z + 4)/3 - 6 over the common denominator 3: (z + 4)/3 - 6 = (z + 4)/3 - 18/3:

(z + 4)/3 - 18/3 = (2 (5 - z))/3

(z + 4)/3 - 18/3 = ((z + 4) - 18)/3:

(z - 18 + 4)/3 = (2 (5 - z))/3

Add like terms. 4 - 18 = -14:

(z - 14)/3 = (2 (5 - z))/3

Multiply both sides by 3:

(3 (z - 14))/3 = (3×2 (5 - z))/3

(3 (z - 14))/3 = 3/3×(z - 14) = z - 14:

z - 14 = (3×2 (5 - z))/3

(3×2 (5 - z))/3 = 3/3×2 (5 - z) = 2 (5 - z):

z - 14 = 2 (5 - z)

Expand out terms of the right hand side:

z - 14 = 10 - 2 z

Add 2 z to both sides:

2 z + z - 14 = (2 z - 2 z) + 10

2 z - 2 z = 0:

2 z + z - 14 = 10

z + 2 z = 3 z:

3 z - 14 = 10

Add 14 to both sides:

3 z + (14 - 14) = 14 + 10

14 - 14 = 0:

3 z = 10 + 14

10 + 14 = 24:

3 z = 24

Divide both sides of 3 z = 24 by 3:

(3 z)/3 = 24/3

3/3 = 1:

z = 24/3

The gcd of 24 and 3 is 3, so 24/3 = (3×8)/(3×1) = 3/3×8 = 8:

Answer:  z = 8

7 0
3 years ago
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Given the conversion factors 12 in/1 ft and 3.28 ft/1 m, which line segment is longer?
chubhunter [2.5K]

Answer:

Line segment A

Step-by-step explanation:

The apostrophe symbol represents feet.

1 meter can be converted into 3.28'

Since 5.5' > 3.28', Line segment A is larger

8 0
1 year ago
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What is an itrational number between 5 and 7
wariber [46]
Answer is √35 (square root of 35)

Reason: square root of 35 (which is = 5.9160797831.....) which is a non-terminating decimal, which means it is irrational.

An irrational number is any real number that cannot be expressed as a simple fraction or terminating decimals. There are many answers to this question.
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25 points
Andrei [34K]

Answer:

34 + x = 70 ; 36

Step-by-step explanation:

Given that:

Current amount = 34

Final amount = 70

Number of roses planted by the workers today ;

Current amount + number planted today = final amount

Let number planted today = x

34 + x = 70

x = 70 - 34

x = 36

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2 years ago
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