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Radda [10]
3 years ago
8

Adam needs both small and large cones to set up for a soccer practice. He knows there are fewer than 30 cones in the storage roo

m. He needs at least a dozen large cones. Let x represent the number of small cones and y represent the number of large cones. Select all inequalities that model this situation.
    x>0  
   y≥12
 x+y≤30
  y>12
  x≥0
 x+y<30
Mathematics
1 answer:
sdas [7]3 years ago
4 0
X:  <span>the number of small cones
y: </span><span> the number of large cones

a "dozen" means 12.


"</span>Adam needs both small and large cones to set up for a soccer practice<span>" mean that x must not be 0, and y must not be 0.

"</span>there are fewer than 30 cones in the storage room." mean that : x+y<30

"He needs at least a dozen large cones." means that y≥12

so we have:

i) x≠0, y≠0, that is x>0, y>0

ii) x+y<30

iii) y≥12


now let's check all choices we have:

<span>    x>0         True by i
   y≥12         True by iii
 x+y≤30       Not True by ii  (x+y is smaller than 30, the sum cannot be 30)
  y>12          Not true by iii (y may be = 12)
  x≥0             Not true by i, Adam needs small cones to (so we are assuming there are some in the storage room. Though this is open to interpretation)
 x+y<30      True</span>
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Step-by-step explanation:

<u>Method 1: </u>

You could find the whole figure surface area than divided by 1/2

<u>Method 2:</u> (the one I'm going to personally be doing)

Break the figure into two rectangular figures

Formula for surface area of rectangular prism:

A = 2(width x length + height x length + height x width)

Figure 1:

A = 2(width x length + height x length + height x width)

height = 3.8 yd

length = 10.1 yd

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A = 2((4.3) x (10.1) + (3.8) x (10.1) + (3.8) x (4.3))

A = 2(98.15)

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Figure 2:

A = 2(width x length + height x length + height x width)

height = 8.4 yd

length = 10.1 yd

width = 2 yd

A = 2((2) x (10.1) + (8.4) x (10.1) + (8.4) x (2))

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There is overlapping surface area that shouldnt be include so we need to subtract it...

<u>For one face of figure 1</u>

3.8 x 10.1 = 38.38

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Figure 1 + Figure 2 - 2(one face)

196.3 - 38.38 = 157.92

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3 years ago
Plsss help no one answered the other times I put this question
svetlana [45]

Answer:

a) <em>The equation</em> (10s + 8w) <em>represents </em><em>the </em><em>calories </em><em>Bridget </em><em>ate </em><em>on </em><em>Monday </em><em>and </em><em>the </em><em>equation</em> (20s + w) <em>represents </em><em>the </em><em>calories</em><em> </em><em>she </em><em>ate</em><em> </em><em>the </em><em>next </em><em>day.</em>

<em>b)</em><em> </em><em>The </em><em>number </em><em>of </em><em>calories</em><em> </em><em>in </em><em>each </em><em>strawberry</em><em> </em><em>is </em>4 <em>and </em><em>the </em><em>number </em><em>of </em><em>calories </em><em>in </em><em>each </em><em>vanilla</em><em> </em><em>wafer</em><em> cookie</em><em> </em><em>is </em>19. The solution is s= 4 and w = 19.

Step-by-step explanation:

For part A, Bridget ate 10 strawberries and 8 vanilla wafer cookies on Monday. Since the the number of calories in a strawberry is <em>s</em> and the number of calories in a vanilla wafer cookie is <em>w </em>, the number of calories Bridget ate on Monday is <em>10s + 8w</em><em>.</em><em> </em>The next day, Bridget ate 20 strawberries and 1 vanilla wafer cookie. Hence, the number of calories Bridget ate on the next day is 20s<em> + w</em>.

For part B,

we will create two different simultaneous equations.

Equation 1: 10s + 8w = 192

Equation 2: 20s + w = 99

We need to find one of the terms first to solve the other term. For this case, I will solve for w first.

Multiply the first equation by 2.

Equation 3: 20s + 16w = 192*2 = 384.

Now, subtract equation 2 from this new equation.

Equation 4:

(20s + 16w) - (20s + w) = 384 - 99

20s + 16w - 20s - w = 285

15w = 285

This leaves only w left and we can solve w.

w = 285 / 15 = 19

Now, we can solve for s using equation 2.

20s + 19 = 99

20s = 99-19 = 80

Hence,

s = 80/20 = 4

7 0
3 years ago
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