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GrogVix [38]
2 years ago
8

How many intersections are there of the graphs of the equations below? One-halfx + 5y = 6 3x + 30y = 36 none one two infinitely

many
Mathematics
2 answers:
Keith_Richards [23]2 years ago
5 0

Answer:

infinitely many

Step-by-step explanation:

  • 1/2x + 5y = 6 ⇒ x+10y=12
  • 3x + 30y = 36 ⇒ x+10y=12

As we see, these are equal lines, they overlap, so there are infinitely many intersections

Sergeu [11.5K]2 years ago
4 0

Answer:

infinitely many

Step-by-step explanation:

You have the system

(1/2)x + 5y = 6

  3x  + 30y = 36

Multiplying the first equation by 6 results in 3x + 30y = 36, which is exactly the same as the second equation.  The two graphs coincide, and so there are infinitely many solutions to this system

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Stella wants to build up her emergency fund to $10,000. She has $2,000 now and plans on saving $320 every month. To model the si
MA_775_DIABLO [31]

Answer:

Anwers are top to bottom:

1.   y − 2,000 = 2,000 + 320x − 2,000

2.  division property of equality

3.    Y - 2000/320 = X

4.  10,000 - 2,000/360 = 25 = x

Step-by-step explanation:

7 0
2 years ago
The solutions to a quadratic equation are x = 2 and x = 7. If k is a nonzero constant, which of the following must be equal to t
Serggg [28]
ANSWER


The correct option is,
k(x - 2)(x - 7) = 0

EXPLANATION

We were given that the solutions of the quadratic equation are
x = 2
and
x = 7.

This tells us that,

x - 2

and
x - 7

are factors of the quadratic equation.



This implies that the quadratic equation is of the form,

(x - 2)(x - 7) = 0

We were also told that

k


is a non zero constant.



This means that we can use k to multiply the whole equation and the solution will not be affected.


Our equation now becomes,

k(x - 2)(x - 7) = 0


Hence the correct answer is A.
5 0
2 years ago
Read 2 more answers
A potato chip company makes chips to fill snack-size bags and family size bag. in one week production cannot exceed 2400 units,
Ainat [17]

Answer:

600 units of for snack-size, 1800 units for family-size

Step-by-step explanation:

7 0
2 years ago
What is 5×20+2raised to the power 2​
Neporo4naja [7]

Answer:

10,404

Step-by-step explanation:

5x20+2=102

102^2=102x102=10,404

7 0
2 years ago
Conservation of Species A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sol
JulijaS [17]

Answer:

The turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

Ten years after the conservation measures are implemented the population will be 3260 turtles.

Step-by-step explanation:

To find the rate of growth of the turtle population at any time <em>t</em> you need to find N'(t)

\frac{d}{dt}N(t)=\frac{d}{dt}(2t^3+3t^2-4t+1000)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\\frac{d}{dt}(2t^3)+\frac{d}{dt}(3t^2)-\frac{d}{dt}(4t)+\frac{d}{dt}(1000)\\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}\\\\N'(t)=6t^2+6t-4

In particular, when t = 2 and t = 6, we have

N'(2)=6(2)^2+6(2)-4=32\\\\N'(6)=6(6)^2+6(6)-4=248

so the turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

The turtle population at the end of the tenth year will be

N(10)=2(10)^3+3(10)^2-4(10)+1000\\N(10)=3260 \:turtles

3 0
2 years ago
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