So are the bottom numbers the answers? Becasue if the top are the questions then gallon would be largest, 2pt, then 0.95 liter If this doesn't help let me know because the problem doesn't look complete. Let me know!
Answer:
There are 144 Php 5-coins, 72 Php 10-coins and 130 Php-1 coins
Step-by-step explanation:
The amount of the coins in the coin bank = Php 1,570
The number of Php 5-coins = 2 × The number of Php 10-coins
The number of Php 5 coins = The number of Php 1-coins + 14
Let 'x' represent the number of Php-5 coins, let 'y' represent the number of Php 10-coins, and let 'z' represent the number of Php 1-coins, we get;
x = 2 × y...(1)
x = z + 14...(2)
5·x + 10·y + z = 1,570...(3)
From equation (1) equation (2), and equation three, we have;
y = x/2
z = x - 14
5·x + 10·x/2 + x - 14 = 1,570
11·x - 14 = 1,570
x = (1,570 + 14)/11 = 144
The number of Php 5-coins, x = 144
y = x/2
∴ y = 144/2 = 72
The number of Php 10-coins, y = 72
z = x - 14
∴ z = 144 - 14 = 130
The number of Php 1-coins, z = 130
<span><span>Graph <span>x2<span> = 4</span>y</span><span> and state the vertex, focus, axis of symmetry, and directrix.</span></span><span>This is the same graphing that I've done in the past: </span><span>y = (1/4)x2</span><span>. So I'll do the graph as usual:</span></span><span> </span><span>The vertex is obviously at the origin, but I need to "show" this "algebraically" by rearranging the given equation into the conics form:<span>x2 = 4y</span> Copyright © Elizabeth Stapel 2010-2011 All Rights Reserved<span>
(x – 0)2 = 4(y – 0)</span><span>This rearrangement "shows" that the vertex is at </span><span>(h, k) = (0, 0)</span><span>. The axis of symmetry is the vertical line right through the vertex: </span><span>x = 0</span>. (I can always check my graph, if I'm not sure about this.) The focus is "p" units from the vertex. Since the focus is "inside" the parabola and since this is a "right side up" graph, the focus has to be above the vertex.<span>From the conics form of the equation, shown above, I look at what's multiplied on the unsquaredpart and see that </span><span>4p = 4</span><span>, so </span><span>p = 1</span><span>. Then the focus is one unit above the vertex, at </span>(0, 1)<span>, and the directrix is the horizontal line </span><span>y = –1</span>, one unit below the vertex.<span>vertex: </span>(0, 0)<span>; focus: </span>(0, 1)<span>; axis of symmetry: </span><span>x<span> = 0</span></span><span>; directrix: </span><span>y<span> = –1</span></span></span><span><span><span>Graph </span><span>y2<span> + 10</span>y<span> + </span>x<span> + 25 = 0</span></span>, and state the vertex, focus, axis of symmetry, and directrix.</span><span>Since the </span>y<span> is squared in this equation, rather than the </span>x<span>, then this is a "sideways" parabola. To graph, I'll do my T-chart backwards, picking </span>y<span>-values first and then finding the corresponding </span>x<span>-values for </span><span>x = –y2 – 10y – 25</span>:<span>To convert the equation into conics form and find the exact vertex, etc, I'll need to convert the equation to perfect-square form. In this case, the squared side is already a perfect square, so:</span><span>y2 + 10y + 25 = –x</span> <span>
(y + 5)2 = –1(x – 0)</span><span>This tells me that </span><span>4p = –1</span><span>, so </span><span>p = –1/4</span><span>. Since the parabola opens to the left, then the focus is </span>1/4<span> units to the left of the vertex. I can see from the equation above that the vertex is at </span><span>(h, k) = (0, –5)</span><span>, so then the focus must be at </span>(–1/4, –5)<span>. The parabola is sideways, so the axis of symmetry is, too. The directrix, being perpendicular to the axis of symmetry, is then vertical, and is </span>1/4<span> units to the right of the vertex. Putting this all together, I get:</span><span>vertex: </span>(0, –5)<span>; focus: </span>(–1/4, –5)<span>; axis of symmetry: </span><span>y<span> = –5</span></span><span>; directrix: </span><span>x<span> = 1/4</span></span></span><span><span>Find the vertex and focus of </span><span>y2<span> + 6</span>y<span> + 12</span>x<span> – 15 = 0</span></span></span><span><span>The </span>y<span> part is squared, so this is a sideways parabola. I'll get the </span>y stuff by itself on one side of the equation, and then complete the square to convert this to conics form.<span>y2 + 6y – 15 = –12x</span> <span><span>
y</span>2 + 6y + 9 – 15 = –12x + 9</span> <span>
(y + 3)2 – 15 = –12x + 9</span> <span>
(y + 3)2 = –12x + 9 + 15 = –12x + 24</span> <span>
(y + 3)2 = –12(x – 2)</span> <span>
(y – (–3))2 = 4(–3)(x – 2)</span></span><span><span>Then the vertex is at </span><span>(h, k) = (2, –3)</span><span> and the value of </span>p<span> is </span>–3<span>. Since </span>y<span> is squared and </span>p<span> is negative, then this is a sideways parabola that opens to the left. This puts the focus </span>3 units to the left of the vertex.<span>vertex: </span>(2, –3)<span>; focus: </span><span>(–1, –3)</span></span>
Change the underlined words if it is not correct and write true if it is correct.
<h3>Integers</h3>
<u>1.</u><u> </u><u>P</u><u>ositive</u> integers are not whole numbers.
Negative integers are not whole numbers.
2. All whole numbers are <u>integers</u>.
True
3. <u>Zero</u> is the smallest whole number.
True
4. Any whole number greater than <u>zero</u> is a positive integers.
True
5. Fractions and Decimals are not integer.
6. 1 is a counting number and a positive integers.
True
7. Rational number include all integers , fraction, or terminating decimals.
True
8. Any whole number that is <u>greater</u> than 0 is a negative integers.
- Any whole number that is <u>less</u> than 0 is a negative integers.
Learn more about integers:
brainly.com/question/10853762
