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antoniya [11.8K]
3 years ago
10

Greg enjoys jogging 4 times a week. On the first day he jogs 3 1/2 miles. on the second day he jogs 3 2/3 miles. on the third da

y he jogged 2 1/4 miles. on the fourth day he jogged 4 miles. What is the total distance Greg jogs?
Mathematics
1 answer:
Gemiola [76]3 years ago
7 0

Answer:

The exact form is 161/12 but the mixed number is 13 5/12

Step-by-step explanation:

You need to find a common donominator for all of the fractions 2,3,4 all go into 12 so I multiplied 1/2x6 (multiply both 1 and 2 by 6 same with all the others) then 2/3x4 and 1/4x3. That should get you 6/12 8/12 and 3/12. Add all of those and then add all of the whole numbers.

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Which of the following rational functions is graphed below?​
vodomira [7]

Answer:

c

Step-by-step explanation:

3 0
3 years ago
Please give me the answer please
In-s [12.5K]
If there are 4 trucks then the first truck weighs x
then x+2tons
then x+4tons
then x+6tons = 32tons
so 4x+12=32
         -12   -12
     /4         /4
x=5 
so plug it back in 
truck 1= 5tons or 10,000lbs
truck 2= 7tons or 14,000lbs
truck 3= 9tons or 18,000lbs
truck 4= 11tons or 22,000lbs

5 0
3 years ago
Use numerals instead of words. If necessary, use / for the fraction bar(s). A parabola is given by the equation y = x2 + 4x + 4.
Anarel [89]
<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>
6 0
3 years ago
Cedric opened a new gallon jug of milk and poured ¾ cup of milk for his mom, ½ cup milk for his little sister and 2 cups of milk
julia-pushkina [17]

Answer:

12 _3/4

Step-by-step explanation:

3/4 + 1/2 + 2 = 3_1/4

16 cups in a gallon

16-3_1/4

=12_3/4

7 0
3 years ago
Tutorial Exercise A boat leaves a dock at 2:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due
ANTONII [103]

Answer:

Both the boats will closet together at 2:21:36 pm.

Step-by-step explanation:

Given that - At 2 pm boat 1 leaves dock and heads south and boat 2 heads east towards the dock. Assume the dock is at origin (0,0).

Speed of boat 1 is 20 km/h so the position of boat 1 at any time (0,-20t),

        Formula :   d=v*t

at 2 pm boat 2 was 15 km due west of the dock because it took the boat 1 hour to reach there at 15 km/h, so the position of boat 2 at that time was (-15,0)

the position of boat 2 is changing towards east, so the position of boat 2 at any time (-15+15t,0)

      Formula : D=\sqrt{(x2-x1)^2+(y2-y1)^2}

⇒                     D = \sqrt{20^2t^2+15(t-1)^2}

Now let           F(t) = D^2(t)

                ∵    F'(t) = 800t + 450(t-1) =  1250t -450\\F'(t) =0

⇒                     t= 450/1250

⇒                     t= .36 hours

⇒                       = 21 min 36 sec

Since F"(t)=0,

∴ This time gives us a minimum.

Thus, The two boats will closet together at 2:21:36 pm.

3 0
3 years ago
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