Which point is an intercept of the quadratic function

Perform each of the following computations using the measured quantities below.

mylen [45]

<h2>Question </h2>

Perform each of the following computations using the measured quantities below.

Write your final answer with the correct number of significant figures in proper scientific notation (one non-zero number to the left of the decimal point).

a. 917.2 + 45.63 = ___________

b. 3.423 x 10^-4 - 6.42 x 10^-3 =_________

<h2>Answer:</h2>

(a) 9.6 x 10²

(b) -6.1 x 10⁻³

<h2>Step-by-step explanation:</h2>

(a) 917.2 + 45.63

First add the two numbers as follows (ensure that the decimal numbers are well aligned);

9 1 7 . 2

+ 4 5 . 6 3

9 6 2 . 8 3

To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),

i. Express the number is standard form

962.83 = 9.6283 x 10²

Note that;

From the result in (i)

9.6283 = mantissa

10 = base

² = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

9.6 x 10²

Therefore, the result in the proper scientific notation is 9.6 x 10².

(b) 3.423 x 10⁻⁴ - 6.42 x 10⁻³

Find the difference between the two numbers as follows;

i. Re-write the numbers so that they both have the same exponents:

0.3423 x 10⁻³ - 6.42 x 10⁻³

ii. Factor out 10⁻³

10⁻³(0.3423 - 6.42)

iii. Solve the bracket

10⁻³(-6.0777)

iv. Rewrite the result in (iii)

-6.0777 x 10⁻³

To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),

i. Express the number is standard form

-6.0777 x 10⁻³ [already in standard form]

Note that;

From the result in (i)

-6.0777 = mantissa

10 = base

⁻³ = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

-6.1 x 10⁻³

Therefore, the result in the proper scientific notation is -6.1 x 10⁻³.

6 0

2 years ago

My I pless have a little help play just with one little thing (3^2 * 3^3)2

Ymorist [56]

$(3^2 \cdot 3^3)^2 \\\\= (3^{2+3})^2\\\\= (3^5)^2\\\\ =3^{5\cdot 2} \\\\=3^{10}$

8 0

2 years ago

Read 2 more answers

18 points - Qu. If 16 whole numbers factor into 120. You will see how 32 whole numbers factor into 1200 what does the same princ

alexandr402 [8]

Explanation:

Your premise and conclusion are both incorrect.

120 has the prime factorization ...

120 = 2³ × 3 × 5

The exponents of the prime factors are {3, 1, 1}. The number of divisors of 120 is the product of the increments of these numbers: (3+1)(1+1)(1+1) = 4·2·2 = 16.

120 has 16 natural-number divisors

__

1200 has the same prime factor and two more: 2·5, so the factorization is ...

1200 = 2⁴ × 3 × 5²

These exponents are {4, 1, 2} and the product of their increments is 5·2·3 = 30.

1200 has 30 natural-number divisors.

__

When a number is multiplied by 2, its number of natural-number divisors will be (n+1)/n times the previous number of divisors, where n is the increment of the exponent of 2 that is a factor of the original number.

For 120, 2^3 is the power of 2 that is a factor. So, multiplying the number by 2 multiplies the number of divisors by (4+1)/4 = 5/4.

240 will have 20 divisors versus the 16 that 120 has.

Likewise, multiplying this number (240) by 5 will multiply its number of divisors by (2+1)/(1+1) = 3/2, where 1 is the power of 5 that is a factor of 240.

1200 will have 20(3/2) = 30 divisors, versus the 20 that 240 has, or the 16 that 120 has.

__

Summary

The number of divisors of an integer is the product of the increments of the exponents of its prime factors.

_____

For reference

Here are the divisors of 120:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Here are the divisors of 240:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

Here are the divisors of 1200:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200