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ASHA 777 [7]
3 years ago
14

Solve the simultaneous equations x2 + y2 = 10 and x – 3y + 10 = 0.

Mathematics
1 answer:
ch4aika [34]3 years ago
3 0

Answer:

x = - 1, y = 3  or     (-1 , 3)

Step-by-step explanation:

x – 3y + 10 = 0              x = 3y - 10    ... plug in

x² + y² = 10

(3y-10)² + y² = 10

10y² - 60y +90 = 0

y² - 6y + 9 = 0

(y - 3)² = 0

y = 3

x = - 1

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If a certain cannon is fired from a height of 8.8 meters above the​ ground, at a certain​ angle, the height of the cannonball ab
Dennis_Churaev [7]

Answer:

It would take approximately 6.50 second for the cannonball to strike the ground.

Step-by-step explanation:

Consider the provided function.

h(t)=-4.9t^2+30.5t+8.8

We need to find the time takes for the cannonball to strike the ground.

Substitute h(t) = 0 in above function.

-4.9t^2+30.5t+8.8=0

Multiply both sides by 10.

-49t^2+305t+88=0

For a quadratic equation of the form ax^2+bx+c=0 the solutions are: x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Substitute a = -49, b = 305 and c=88

t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}

Ignore the negative value of t as time can't be a negative number.

Thus,

t=\frac{305+\sqrt{110273}}{98}\approx6.50

Hence, it would take approximately 6.50 second for the cannonball to strike the ground.

6 0
3 years ago
A city water tank holds 20 gallons of water. A technician empties 25% of the tank. How many more gallons of water must be remove
Alja [10]

Answer: 15 gallons

Step-by-step explanation:

There is 100% in any full thing. When the water tank was full, it had 20 gallons. After 25% of the water was removed, there is 75% left (100% - 25% = 75%). 75% can also equal 0.75. 20 × 0.75 = 15 gallons.

6 0
3 years ago
what is the upward acceleration of a helicopter with a mass of 5,000kg if a force of 10,000 N acts on it in an upward direction
morpeh [17]
I think that would be: 2 m/s^2
7 0
4 years ago
Quadrilateral A has side lengths 2, 3, 5, and 6. Quadrilateral B has side lengths 4, 5, 8,
Dahasolnce [82]

Answer:

No.

Step-by-step explanation:

2, 3, 5, 6

4, 5, 8, 10

If all of the sides are scaled, that must mean it is possible to maintain a ratio of each side.

2/4 = 0.5

3/5 = 0.6

5/8 = ?

6/10 = 0.6

No.

6 0
4 years ago
Kyle uses a school gym to run a weekly yoga class. He must pay the school a fee for the use of the gym. Each person who comes pa
77julia77 [94]

Answer:

I believe it is D

Step-by-step explanation:

The entire equation y=nx-d means that d is the fee Kyle pays the school. SO that means that nx is the amount of money he earns from the people attending a yoga class.

6 0
3 years ago
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