prove algebraically that the straight line with the equation x=2y+5 is a tangent of the circle with the equation x^2+y^2=5
Answers
Answer:
Step-by-step explanation:
To prove the straight line is tangent to the circle:
- substitute the straight line into the circle equation
- discriminant of the new equation has to be equals to 0
(1)
substitute x = 2y + 5 into x² + y² = 5
x² + y² = 5
(2y + 5)² + y² = 5
4y² + 20y + 25 + y² = 5
5y² + 20y + 20 = 0
y² + 4y + 4 = 0
(2)
discriminant of y² + 4y + 4 = 0 has to be equals to 0
D = 4² - 4(1)(4)
D = 0
∴ Proven
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Answers
Hard work can boost your personal and professional growth. If we work hard, we deserve respect because you set an example for others.
Working hard will give you a sense of accomplishment, fulfillment, and self-satisfaction. Working hard can help you stay positive and confident.
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Answers
Answer:
4.3 hours
Step-by-step explanation:
Let the number of hours Sally does a job = x
Let the number did hours Joan does a job be equal to y
Sally and Joan were able to dust the house in 3 hours together.
1/x + 1/y = 1/3
It takes Joan 10 hours to finish the same job alone.
Hence,
1/x + 1/10 = 1/3
1/x = 1/3 - 1/10
Least common dey = 30
1/x = 10 - 3/30
1/x = 7/30
Cross Multiply
x × 7 = 30
7x = 30
x = 30/7
x = 4.2857142857 hours
Approximately = 4.3 hours
Without help, it would take Sally 4.3 hours to finish the same job.
x = 39
x = 29
y = 61
y = 29
z = 61
z = 29
Answers
answer:
x = 29
y = 29
z = 61
step-by-step explanation:
all angles in a triangle must equal 180 degrees.
we were already given the angle degree of 61 degrees so we must include that in our formula to determine the degree of y.
the line in the middle already gives us two more angles because they both are 90 degrees for being a perfect quarter turn.
so to figure out y,
we must add 61+90 and then subtract the sum of that from 180.
so, 61+90 = 150 and 180-151 = 29
therefore,
we can conclude that y = 29
now, to determine the degrees of x and z we do the same thing.
we already know one angle equals 90 degrees.
180-90 = 90
that concludes that x and z must have a sum of 90.
if we use our choices,
39+61 = 100 (no)
39+29 = 68 (no)
29+61 = 90 (CORRECT)
29+29 = 28 (no)
therefore, x = 29 and z = 61
so, in total :
x = 29
y = 29
z = 61
hope this helps :)
-audrey <3
Answers
= 8n^2+14x+16n+28
=8n^2+30n+28
that's it :) !!
Step 1: 8n+14n+12n+28
Step 2 Combine like terms: 8n+26+28
Final Answer: 34n+28
Answers
The product of two consecutive integers is 420 is 20 and 21.
Consider x one the two number
Then the successor of x = x + 1
Then x and x+1 are the consecutive numbers
Now according to the question,
The product of two consecutive integers is 420,
Then, multiply x and x+1 and equate it to 420
Therefore,
⇒ x(x+1) = 420
⇒ x² + x = 420
⇒ x² + x - 420 = 0
This is a quadratic equation
Now solve it to find the value of x
We can write it as,
⇒ x² + 21x - 20x - 420 = 0
⇒ x(x + 21) - 20(x + 21) = 0
⇒ (x+21)(x-20) = 0
⇒ x = 20 or x = -21
Since number should be an integer so - 21 is absurd.
Hence, consecutive numbers are,
20 and 21
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Answers
Answer:
Answer C I think
Step-by-step explanation: