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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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In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz
BabaBlast [244]

Answer:

C (2, -1)

Step-by-step explanation:

C has the same x coordinate as A = 2

that eliminates A and B.

and the y value of C has to be closer to the y value of B than to the y value of A (due to the 5:3 ratio).

so, without spending unnecessary effort on actual calculation, we can directly derive the correct answer to be C.

but to show in numbers, the "coordinate triangle" of the difference between D and B is a similar triangle to ACD. and so, the ratio of one side pair applies then to all other sides too. including the individual coordinate differences.

so, also the y difference of A to D relates to the y difference between D and B in the same ratio of 5:3 of the overall y difference of A to B.

the y difference A to B is 2 - -6 = 8

the 5/3 split of 8 units is actually 5 and 3.

so, the y coordinate of D is -6 + 5 = -1

and C must have the same y coordinate.

therefore, it is proven that answer C (2, -1) is the right answer.

4 0
3 years ago
What’s the surface area 6ft, 4.5ft, 8ft, 6ft
umka21 [38]

Answer:

i need more information like what is the length width etc.

Step-by-step explanation:

6 0
3 years ago
Hat is the value of the expression –5x4 when x = –2?
sleet_krkn [62]

\bold{Hey\ there!}

\bold{Assuming,\ you\ meant: -5(-2)^4}

  • \bold{If\ so\ follow\ these\ steps\downarrow}
  • \bold{(-2)^4=16}
  • \bold{(-5)\times 16=-80}
  • \boxed{\boxed{\bold {Thus,\ your\ answer\ is: -80}}}\checkmark

\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!}

~\frak{LoveYourselfFirst:)}

7 0
3 years ago
If (x^2−1)/(x+1) = 3x + 5, then x + 3 =<br> (A) -3<br> (B) -2<br> (C) 0<br> (D) 2<br> (E) 4
sineoko [7]
The answer is C) 0
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Neko [114]
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from 0 to pi/2 (sub pi/2 minus sub 0 for x) and then solve
= -cos(2*pi/2)-(-cos0)
= -cos pi + cos 0
= 1 + 1
= 2 
8 0
3 years ago
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