To find the value of k such that (k, k) is equidistant from (-2, 0) and (0, 5), we can use the distance formula.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
Let's calculate the distances from (k, k) to (-2, 0) and (0, 5) and set them equal to each other:
√((k - (-2))² + (k - 0)²) = √((k - 0)² + (k - 5)²)
Simplifying this equation:
√((k + 2)² + k²) = √(k² + (k - 5)²)
Squaring both sides of the equation to eliminate the square roots:
(k + 2)² + k² = k² + (k - 5)²
Expanding and simplifying:
k² + 4k + 4 + k² = k² + k² - 10k + 25
2k² + 4k + 4 = 2k² - 10k + 25
Rearranging terms:
4k + 4 = -10k + 25
Combining like terms:
14k = 21
Dividing both sides by 14:
k = 21 / 14
Simplifying the fraction:
k = 3 / 2
Therefore, the value of k that makes (k, k) equidistant from (-2, 0) and (0, 5) is k = 3/2.
The total number of spearmint gums will be 27
Given is that a container has peppermint gum and spearmint gum. There are 18 pieces of peppermint gum in the container and the ratio of peppermint gum to spearmint gum is 2 : 3.
Let the number of spearmint gum be {x}. So, we can write -
2/3 = 18/x
{x} = (18 x 3)/2
{x} = 27
Therefore, the total number of spearmint gums will be 27.
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Answer:
27 is your answer
Step-by-step explanation:
if 2;3 is your ratio and u have 18 peppermint gum then divide 18 by 2 and u get 9 then u multiply 9 by 3 and u get 27
Round your answer, if necessary, to the nearest tenth. Express 0(theta) between -180 and 180 degrees.
Answer:
76.0 degrees
Step-by-step explanation:
Just got it right on the Khan Academy quiz.
The angle θ that z makes in the complex plane is approximately 75.96°.
The complex plane is a mathematical concept used in complex numbers. It's a two-dimensional Cartesian coordinate system where the horizontal axis represents the real part of a complex number, and the vertical axis represents the imaginary part. Complex numbers are plotted as points in this plane, facilitating operations like addition, subtraction, multiplication, and division of complex numbers.
To find the angle θ that z makes in the complex plane, we can use the formula: θ = arctan(y/x), where x and y are the real and imaginary parts of z respectively. In this case, x = 1 and y = 4 as given. Plugging these values into the formula, we get: θ = arctan(4/1). Using a calculator, we find that θ ≈ 75.96°.
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The total cost of Dara's purchases was $38.07. Upon subtracting this amount from her initial $50, she is left with $11.93 change.
To solve the problem, you need to add up how much Dara spends and subtract that from $50. First, add the cost of the sandals, shorts, and hat together:
When you add these three amounts together, you get $38.07. So, Dara has spent $38.07 in total. Now, subtract that amount from $50:
$50.00 - $38.07 = $11.93
This means Dara should get back $11.93 in change.
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