Answer:
<h2>5, 7, 11</h2>
Step-by-step explanation:
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
A prime number has only two divisors: 1 and itself.
Therefore, the prime numbers are:
5, 7 and 11.
12 is not a prime because 12 = 2 × 6 = 3 × 4.
12 has six divisors: 1, 2, 3, 4, 6 and 12.
The vertex of the given quadratic polynomial function is (6, 8)
A quadratic polynomial function is the one which can be represented in the form ax² + bx + c = y where a, b and c are coefficients and x, and y are independent and dependent variables respectively. A parabola is formed when the quadratic polynomial is plotted on graph. The x coordinate of the vertex can be found using formula (-b/2a) and y coordinate can be found by putting the value of x in the equation.
Given polynomial function x² - 12x + 44
Now, x = (-b/2a)
x = (12/2)
=> x = 6
Now, y = 6² - 12×6 + 44
y = 36 - 72 + 44
=> y = 8
Therefore, Vertex = (6, 8)
Learn more about Vertex of quadratic polynomial at:
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I'm not sure if it only wants you to find Equation 1 or go further and solve:
x = the number of 5c coins
y = the number of 10c coins
Equation 1: the total number of coins is 65
x + y = 65
total value of $3.80
0.05x + 0.1y = 3.8
<u>Simultaneous Equations</u>
Make one coefficient the same
10 * (0.05x + 0.1y = 3.80 = 0.5x + y = 38
x + y = 65
0.5x + y = 38
Subtract the equations
(x + y) - (0.5x + y)= 65 - 38
(x - 0.5x) + (y - y) = 65 - 38
0.5x = 27
x = 54
Substitute it into the original equation to find y.
x + y = 65
54 + y = 56
y = 65 - 54 = 11
Substitute it into the other equation to check it's right.
0.05x + 0.1y = 3.8
0.05(54) + 0.1(65) = 3.8
x = 54 5c coins
y = 11 10c coins
Step-by-step explanation:
The ratio cosine tell us that
- In a right angled triangle, the cosine of an angle is the side adjacent to the angle divided by the hypotenuse of the triangle.
In other words,
The side adjacent to angle a is 9. The hypotenuse is 41.
So
