Answer:
(x - 10)² + y² = 29
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (10, 0), thus
(x - 10)² + (y - 0)² = r²
The radius is the distance from the centre to a point on the circle
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (10, 0) and (x₂, y₂ ) = (5, 2)
r =
=
= =
Thus
(x - 10)² + (y - 0)² = ( )², that is
(x - 10)² + y² = 29 ← equation of circle
Answer:
Option D is correct.
Value of z =5
Step-by-step explanation:
Given the equation:
Using distributive property:
Apply distributive property in the given equation we have;
⇒
Subtract 4 from both sides we get;
6z + 4 -4 = 34-4
Simplify:
6z = 30
Divide by 6 to both sides of an equation, we get;
z = 5
Therefore, the value of z is, 5
Answer:
1 gallon every 16 minutes
Step-by-step explanation:
If after 32 minutes the container has 6 gallons left that means it has lost 2 gallons of water. So we now divide the 32 minutes by the 2 gallons of water to get that 1 gallon of water leaks every 16 minutes.
Answer: x = 4
Step-by-step explanation:
Given : A coordinate grid with 2 lines.
One line, labeled f(x) passing through (- 3, 3), (0, 3), and the point (4, 3). (i)
The other line is labeled g(x) and passes through (- 4, -3), (0, 0), and the point (4, 3). (ii)
We generally denote x values as input values and y values as output values.
From (i) and (ii), the common point on both lines = (4,3)
Here, input value = 4
Output value = 3
Hence, the input value produces the same output value for the two functions on the graph : x=4
Answer:
5.006
41.056
31.289
51.977
7.884
Step-by-step explanation:
1) sin x = opposite side / hypotenuse
sin 24.3° = 2.06 / hyp
hyp = 2.06 / sin 24.3 = 5.<u>0059</u>006616019108320511866543651
rounding to 3 significant figures
= 5.006
2)cos x = adjacent side / hypotenuse
cos 47 = 28 / x
x = 28 / cos 47 = 41.<u>0558</u>17197909497891901840157945
= 41.056
3) cos x = adjacent side / hypotenuse
cos 56.1 = x / 56.1
x = 56.1 * cos 56.1 = 31.<u>2895</u>00613760617368691451544764
= 31.289
4) tan x = opposite side / adjacent side
tan 68 = x / 21
x = 21 * tan 68 = 51.<u>9768</u>239217422123300402781676
= 51.977
5) sin x = opposite side / hypotenuse
sin 21 = x / 22
x = 22 * sin 21 = 7.<u>8840</u>948899966060166510313670963
= 7.884