Show Your Knowledge
2 answers:
<h2><u>Question</u></h2>
Molly has 18 coins, all dimes and nickels. The total value of the coins
is $1.05. How many of each type of coin does Molly have?
<u></u>
15 nickels
3 dimes
Let d represent the number of dimes
Molly has. Then she has 18-d nickels, and
the total value (in cents) of her coins is ..
5(18-d) +10d = 105
5d +90 105.... simplify
5d 15...
. . subtract 90
d 3.. ... divide by 5; number of
dimes
18-d 15... . . number of nickels
<u>Molly has 3 dimes and 15 nickels.</u>
You might be interested in
<h3>Answer:</h3>
y = 8x² -4x +4
<h3>Explanation:</h3>I find it quick and easy to let a graphing calculator do quadratic regression on the given points. It gives the coefficients of the equation directly. (See attached.)
_____
If you want to do this "by hand," you can substitute each of the x and y value pairs into the equation to get three linear equations in a, b, and c. These are generally easy to solve, as the "c" variable can be eliminated right away.
<em>For x = 2</em>
... 28 = a·2² +b·2 +c = 4a +2b +c
<em>For x = 4</em>
... 116 = a·4² +4b +c = 16a +4b +c
<em>For x = -3</em>
... 88 = a·(-3)² +b·(-3) +c = 9a -3b +c
Subtracting the first and third equations from the second, we have ...
... (16a +4b +c) -(4a +2b +c) = (116) -(28) ⇒ 12a +2b = 88
... (16a +4b +c) -(9a -3b +c) = (116) -(88) ⇒ 7a +7b = 28
Dividing the first of these reduced equations by 2, and the second by 7, we have ...
- 6a +b = 44
- a +b = 4
Subtracting the second of these from the first gives ...
... (6a +b) -(a +b) = (44) -(4) ⇒ 5a = 40
From which we find
... a = 8
... b = 4 -a = 4 -8 = -4
We choose the first of the original equations to find c:
... c = 28 -4a -2b = 28 -4·8 -2(-4)
... = 28 -32 +8 = 4
With (a, b, c) = (8, -4, 4), the equation of the parabola is ...
... y = 8x² -4x +4
Answer:
<em>The correct option is: C. </em>
Step-by-step explanation:
The two angles of the triangle are given as 60° and 60°
As the sum of all three angle in any triangle is always 180°, so the measure of the third angle will be: 180°-(60°+60°) = 180° - 120° = 60°
Now each angle of the triangle is 60°, it means the triangle is equilateral.
The base of the triangle is given as 12. So, the length of each side will be 12.
That means, the value of
Now in the left right triangle.....
So, the value of