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frutty [35]
2 years ago
8

Use mental math to solve 3x1,607

Mathematics
2 answers:
oksian1 [2.3K]2 years ago
6 0

Answer:

The product is 4,821

Step-by-step explanation:

We are given the following information in the question:

We have to multiply an expression using mental maths.

We can expand the numbers and use the distributive property to do so.

  • The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.
  • It help us to perform complex multiplication problem easily.
  • a\times(b+c) = (a\times b) + (a\times c)

The solving is shown below:

3\times (1607)\\=3\times (1000 + 600 + 7)\\=(3\times 1000) + (3\times 600) + (3\times 7)\\=3000 + 1800 + 21\\=4821

The product is 4,821

Alja [10]2 years ago
5 0

Answer:

4821

Step-by-step explanation:

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Solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!​
Misha Larkins [42]

Answer:

[0.25, 2]

Step-by-step explanation:

We have

4t² ≤ 9t-2

subtract 9t-2 from both sides to make this a quadratic

4t²-9t+2 ≤ 0

To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.

4t²-9t+2=0

We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as

4t²-8t-t+2=0

4t(t-2)-1(t-2)=0

(4t-1)(t-2)=0

Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of

4t²-9t+2 ≤ 0

For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct

For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct

For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.

Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]

8 0
3 years ago
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