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Nataly [62]
3 years ago
9

Can yall help me with this. -4(2x-7)<10-2x Write the solution in the form x ? A, where ? Represents the correct inequality sy

mbol and a represents the value of the solution.
Mathematics
1 answer:
alex41 [277]3 years ago
5 0

Answer: x > 3

Step-by-step explanation:

We have the inequality:

-4*(2*x - 7) < 10 - 2*x

We want to find the possible values for x.

first, we expand the left side.

-8x + 28 < 10 - 2x

now we want to have all the terms with x in one side and the terms without x in the other side.

-8x + 2x < 10 - 28

-6x < -18

now we divide both sides by -6, as we divide by a negative number, the direction of the inequality changes:

x > 18/6 = 3

x > 3

This means that x must be larger than 3.

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Pair 2 is true if Jeff's monthly income is $1200/10% = $12,000.

Both pairs can be true if Jeff's monthly income increased by a factor of 4 in the 20 years from 1990 to 2010.

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Find the recursive rule, explicit rule, and f(20)
DiKsa [7]

Answer:

Recursive:

f(1)=35, f(n)=f(n-1)+10

Explicit:

f(n)=35+10(n-1)

And the 20th term is 225.

Step-by-step explanation:

We have the sequence:

35, 45, 55, 65.

Notice that each subsequent term is 10 more than the previous term.

Therefore, our common difference is (+)10.

Recursive Rule:

The standard format for the recursive rule is:

f(n)=a, f(n)=f(n-1)+d

Where a is the initial term and d is the common difference.

From our sequence, we know that a the initial term is 35.

And as determined, our common difference d is 10.

Substitute. Hence, our recursive rule is:

f(1)=35, f(n)=f(n-1)+10

Explicit Rule:

The standard format for the explicit rule is:

f(n)=a+d(n-1)

Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:

f(n)=35+10(n-1)

Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:

f(20)=35+10(20-1)

Evaluate:

\begin{aligned} f(20)&=35+10(19) \\ f(20)&=35+190 \\ f(20)&=225 \end{aligned}

Hence, the 20th term is 225.

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