Peter and Derrick are playing hockey, Peter bounces the puck against the wall to Derrick.

Prove algebraically that the straight line with equation x =2y+5 is a tangent to the circle with equation x ² +y ²

mrs_skeptik [129]

The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).

<h3>What is a circle?</h3>

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x² + y² = 5.

x = 2y + 5 ...1

x² + y² = 5 ...2

If the intersection of the point of the circle and line is one. Then the line is tangent to the circle.

Then from equations 1 and 2, we have

(2y + 5)² + y² = 5

4y² + 25 + 20y + y² - 5 = 0

5y² + 20y + 20 = 0

5y² + 10y + 10y + 20 = 0

5y (y + 2) + 10(y + 2) = 0

(5y + 10)(y + 2) = 0

y = -2, -2

Then the value of y is unique then the value of x will be unique.

The value of x will be

x = 2(-2) + 5

x = -4 + 5

x = 1

The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).

More about the circle link is given below.

brainly.com/question/11833983

#SPJ1

4 0

2 years ago

Shelby made 16 quarts of juice for a picnic. How many cups of juice did Shelby make?

jonny [76]

Answer:

64 hope i helped

5 0

3 years ago

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A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole and makes an angle of 58° w

Finger [1]

It is a right triangle
cos 58 = 20/length of rope
length of rope = 20/cos 58 degrees
= 37.74 feet

6 0

3 years ago

Pls I need help and a explanation

tresset_1 [31]

Answer:

20) 7/16 = 0.4375

21) 1/6 = 1.6 repeating

22) 2 4/5 = 2.8

23) 98 2/3 = 98.6 repeating

24) 0.8 = 4/5

25) 26 1/5

26) 72.1 repeating = 72 1/9

27) 0.505 = 101/200

Explanation:

To convert fraction into decimal, divide the numerator by the denominator and that's your answer. For example:

7 ÷ 16 = 0.4375.

To convert a decimal into a fraction, place the number after the decimal point over the number place it's in. For example: If you look at 0.8 , 8 is in the tenths place, so you place it over 10 like this 8/10, and then you simplify. Half of 8 is 4 , and half of 10 is 5, so you'd have 4/5.

For #27, since 505 in 0.505 , is in the thousandths place, you'd put it over 1,000 like this 505/1000 and then you simplify. Look at image above to learn how to simplify 505/1000.⤴⤴⤴

7 0

3 years ago

An isosceles right triangle is always 45 45 90 triangle. True False

Rom4ik [11]

Answer:

Yes, an isosceles triangle is always 45 45 90 so its TRUE!!

3 0

4 years ago

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