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Effectus [21]
3 years ago
12

Katherine is shopping for cupcakes and donuts. She can purchase at most 30 items in total. She also wants the number of cupcakes

purchased to be greater than or equal to the square of 2 more than the number of donuts.
Create a system of inequalities to model the above situation and use it to determine how many of the solutions are viable.

Mathematics
2 answers:
Nuetrik [128]3 years ago
6 0

Answer:

Part of the solution region includes a negative number of donuts purchased; therefore, not all solutions are viable for the given situation.

Step-by-step explanation:

Elodia [21]3 years ago
5 0

Let the number of cupcakes be represented by = y

Let the number of donuts be represented by = x

She can purchase at most 30 items in total so equation becomes:

x+y\leq30    .... (1)

She also wants the number of cupcakes purchased to be greater than or equal to the square of 2 more than the number of donuts. Hence, equation becomes:

y\geq(x+2)^{2}   ....(2)

The intersection point where value of 'x' is negative is not valid.

Hence, points 3 and 27 is the answer. (rounding off 3.179 and 26.821)

Please find attached the graph.

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For each of the transactions in items 1 through 5, indicate the effects on the accounting equation elements.
oksian1 [2.3K]

Answer:

Decrease I think.

Sorry if it is wrong.

Hope it helped :)

6 0
2 years ago
find the volume of a right circular cone that has a height of 14.7 ft and a base with a circumference of 13 ft
Doss [256]

Answer:

Volume of the cone =650.06 cubic feet

Step-by-step explanation:

Height of the cone= 14.7 feet

Circumference= 13 feet

Radius = 13/2 = 6.5 feet

Volume of the Cone:

         =\pi r^2\frac{h}{3}

As, \pi =\frac{22}{7}=3.14

Putting the values in the formula:

Volume of the cone is :

          =3.14*(6.5*6.5)*\frac{14.7}{3} \\\\=3.14*(6.5*6.5)*4.9\\\\=3.14*42.25*4.9\\\\=3.14*207.03\\\\=650.06feet^3

Volume of the cone is 650.06 cubic feet

8 0
3 years ago
A bag of 8 rolls for $1.89 or a bag of 18<br> rolls for $3.79
Delvig [45]

Answer:

8 rolls for $1.89

Step-by-step explanation:

when you divide to see how much each one costs the 8 rolls is better

4 0
3 years ago
Read 2 more answers
Which expression is equivalent to "10-18"?<br> 10 + 18<br> 18 - 10<br> 10 + -18<br> 18 + -10
JulsSmile [24]

Answer:18 - 10

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Consider the graph of the quadratic function y = 3x2 – 3x – 6. What are the solutions of the quadratic equation 0 = 3x2 − 3x − 6
son4ous [18]
Y = 3x^2 - 3x - 6 {the x^2 (x squared) makes it a quadratic formula, and I'm assuming this is what you meant...}

This is derived from:
y = ax^2 + bx + c

So, by using the 'sum and product' rule:

a × c = 3 × (-6) = -18

b = -3

Now, we find the 'sum' and the 'product' of these two numbers, where b is the 'sum' and a × c is the 'product':

The two numbers are: -6 and 3

Proof:

-6 × 3 = -18 {product}

-6 + 3 = -3 {sum}

Now, since a > 1, we divide a from the results

-6/a = -6/3 = -2

3/a = 3/3 = 1

We then implement these numbers into our equation:

(x - 2) × (x + 1) = 0 {derived from 3x^2 - 3x - 6 = 0}

To find x, we make x the subject of 0:

x - 2 = 0

OR

x + 1 = 0

Therefore:

x = 2

OR

x = -1

So the x-intercepts of the quadratic formula (or solutions to equation 3x^2 - 3x -6 = 0, to put it into your words) are 2 and -1.


We can check this by substituting the values for x:

Let's start with x = 2:

y = 3(2)^2 - 3(2) - 6
= 3(4) - 6 - 6
= 12 - 6 - 6
= 0 {so when x = 2, y = 0, which is correct}

For when x = -1:

y = 3(-1)^2 - 3(-1) - 6
= 3(1) + 3 - 6
= 3 + 3 - 6
= 0 {so when x = -1, y = 0, which is correct}
7 0
3 years ago
Read 2 more answers
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