Answer:
- (x + 10)² + (y + 4)² = 232
Step-by-step explanation:
<h3>Given </h3>
- Center = (-10, -4)
- Point on circle = (4, 2)
<h3>To find </h3>
<h3>Solution</h3>
<u>Remember the standard equation of circle:</u>
- (x - h)² + (y - k)² = r², where (h, k) is the center and r is radius
<u>We have</u>
Use distance formula (Pythagorean theorem) to work out the length of the radius. We know that radius is the distance from the center to any point on the circle.
<u>Here we are finding the distance between points (-10, -4) and (4, 2)</u>
- r² = (-10 - 4)² + (-4 - 2)²
- r² = 14² + 6²
- r² = 232
<u>So the equation is:</u>
- (x + 10)² + (y + 4)² = 232
Answer:
a. 
and 41.6
b. 52.1
Step-by-step explanation:
a.
Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.
<u>Note:</u> the exact value of tan 60 is 
Thus, we can write 
Approximate value (rounded to nearest tenth): 
b.
Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.
Thus we can write and solve:
Answer:
C. Both (1, 11) and (-1, -5)
Step-by-step explanation:
The missing options are:
<em>
A. Only (1, 11)
</em>
<em>B. Only (-1, -5) </em>
<em>C. Both (1, 11) and (-1, -5)
</em>
<em>D. Neither </em>
To check if an ordered pair is a solution of an equation, replace one variable into the equation an calculate the other one.
Replacing x = 1, we get:
y = 8(1) + 3
y = 11
then (1, 11) is a solution
Replacing x = -1, we get:
y = 8(-1) + 3
y = -5
then (-1, -5) is a solution
The third option as you can must flip the second devision part of the equation and make the devision in the middel a multiplication.
Answer:
#7 = 430
#9 = 16
#11 = 930
Step-by-step explanation:
7 to the power of 2 is 49 / 49+3 is 52 / 52-9 is 43 / 43x10 is 430
66 divided by 11 is 5 / 5 +3 is 8 / 8 X2 is 16
18 -3 is 15 / 15 + 3 is 18 / 18 to the power of 2 is 324 / 324 - 14 is 310
310x3 is 930
