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katovenus [111]
2 years ago
9

Consider the equation

Mathematics
1 answer:
muminat2 years ago
5 0

Answer:

A. a=10\\ \\b\neq -8

B. a=10\\ \\b= -8

Step-by-step explanation:

Consider the equation

2(5x-4) = ax + b

A. This equation has no solutions when the coefficients at x are the same and the free coefficients are not the same.

First, use distributive property:

2(5x-4)=2\cdot 5x-2\cdot 4=10x-8

So, the equation is

10x-8=ax+b

This equation has no solutions when

a=10\\ \\b\neq -8

B. The equation has infinitely many solutions when the coefficients at x are the same and the free coefficients are the same too.

So, the equation

10x-8=ax+b

has infinitely many solutions when

a=10\\ \\b= -8

In other cases, the equation has a unique solution

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Did I get it correct?
VikaD [51]

Answer:

No they are proprotional.

Step-by-step explanation:

the tables eqaution is

y=3x+1

7 0
2 years ago
Read 2 more answers
Will the following side lengths make a triangle? 7, 5, 4
Greeley [361]

Okay too answer this you have to take the two smallest numbers and add them, in this case the answer would be 5 + 4 = 9. The answer has to be greater than the last number, In this case, 7. So the answer is yes.

8 0
2 years ago
Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. Whe
Rama09 [41]

You can see how this works by thinking through what's going on.

 

In the first year the population declines by 3%.  So the population at the end of the first year is the starting population (1200) minus the decline: 1200 minus 3% of 1200.  3% of 1200 is the same as .03 * 1200.  So the population at the end of the first year is 1200 - .03 * 1200.  That can be written as 1200 * (1 - .03), or 1200 * 0.97

 

What about the second year?  The population starts at 1200 * 0.97.  It declines by 3% again.  But 3% of what???  The decline is based on the population at the beginning of the year, NOT based no the original population.  So the decline in the second year is 0.03 * (1200 * 0.97).  And just as in the first year, the population at the end of the second year is the population at the beginning of the second year minus the decline in the second year.  So that's 1200 * 0.97 - 0.03 * (1200 * 0.97), which is equal to 1200 * 0.97 (1 - 0.03) = 1200 * 0.97 * 0.97 = 1200 * 0.972.

 

So there's a pattern.  If you worked out the third year, you'd see that the population ends up as 1200 * 0.973, and it would keep going like that.

 

So the population after x years is 1200 * 0.97x

5 0
3 years ago
If y varies inversely as x and y=16 when x=4, find y when x=3
iren [92.7K]

Answer:

21.33 to nearest hundredth

Step-by-step explanation:

Inverse Variation is y = k / x where k is a constant.

Plug in the given values to find k:-

16 = k/4

k = 4*16 = 64 so the equation  of variation is y = 64/x.

So when x = 3,   y = 64/3 = = 21.33 to nearest hundredth.

6 0
3 years ago
An accessories store sells $8 custom socks and $11 custom hats. If 11 items were sold on Monday, and the
Vanyuwa [196]

Answer:

7 socks were sold

Step-by-step explanation:

7*8=56

11-7=4

4×11=44

56+44=100

This proves the answer of 7 to be correct

7 0
2 years ago
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