Lease solve I will give brainliest

Write an expression in factored form that is equivalent to the expression 1/8x+16

vredina [299]

Step-by-step explanation: In order to factor an integer (the 8 in the fraction 1/8) we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5)

The number that each prime divides the original integer becomes it's exponent in the final result.

In the example: $\frac{1}{8} x+16$

Prime number 2 to the power of 3 equals 8.

$\frac{1}{2^3} x+16$

Now, we need to perform a multiplication. The following rule is applied: $\frac{A}{B} C=\frac{AC}{B}$

In the example: $\frac{1}{2^3} x+16$

The new factors in the numerator are: 1x.

Notice that all non-fractions are placed in the numerator.

The factors in the new denominator are: $2^3$

$\frac{x}{2^3} +16$

Now, we need to add the fractions. We use this rule: $\frac{A}{B} +\frac{C}{D} =\frac{\frac{LCD}{B}A+\frac{LCD}{D}C }{LCD}$

The example involved 2 terms. $\frac{x}{2^3} +16$

Note that 1 non-fractional term are treated as fractions with a denominator equal to 1.

The LCD is: $2^3$

$\frac{x}{2^3} +16$ changes to $\frac{x+(2^3)16}{2^3}$

We need to evaluate a power by multiplying the base by itself as many times as the exponent indicates.

In the example: $\frac{x+(2^3)16}{2^3}$ (the one in parenthesis)

Base 2 will be multiplied by itself 3 times.

2 x 2 x 2 = 8 ( $2^3$ = 8)

$\frac{x+8\times16}{2^3}$ (Notice that $2^3$ is now 8 in the fraction.)

Lastly, we multiply the 8 by 16 in the fraction, $\frac{x+8\times16}{2^3}$

8 x 16 = 128

$\frac{x+128}{2^3}$ (Notice that 8 x 16 is now 128 in the fraction)

Therefore, your answer is: $\frac{x+128}{2^3}$

5 0

3 years ago

Would you rather use color tiles or your ruler to measure the length of an object?explain your choice

horrorfan [7]

A ruler, because it has accurate markings.

5 0

4 years ago

Read 2 more answers

Graph y = 2x + 3 A? B? C? OR D

alexandr402 [8]

Answer:

the answer is B

Step-by-step explanation:

im not sure what else to say but my answer had to be longer

7 0

3 years ago

Each marble bag sold by Deon's Marble Company contains 7 green marbles for every 5 yellow marbles. If a bag has 40 yellow marble

weeeeeb [17]

Answer:

if a bag has 40 yellow marbles there will be 56 green marbles.

this may help you

8 0

3 years ago

The equation of function h is h... PLEASE HELP MATH

Flura [38]

Answer:

Part A: the value of h(4) - m(16) is -4

Part B: The y-intercepts are 4 units apart

Part C: m(x) can not exceed h(x) for any value of x

Step-by-step explanation:

Let us use the table to find the function m(x)

There is a constant difference between each two consecutive values of x and also in y, then the table represents a linear function

The form of the linear function is m(x) = a x + b, where

a is the slope of the function
b is the y-intercept

The slope = Δm(x)/Δx

∵ At x = 8, m(x) = 2

∵ At x = 10, m(x) = 3

∴ The slope = $\frac{3-2}{10-8}=\frac{1}{2}$

∴ a = $\frac{1}{2}$

- Substitute it in the form of the function

∴ m(x) = $\frac{1}{2}$ x + b

- To find b substitute x and m(x) in the function by (8 , 2)

∵ 2 = $\frac{1}{2}$ (8) + b

∴ 2 = 4 + b

- Subtract 4 from both sides

∴ -2 = b

∴ m(x) = $\frac{1}{2}$ x - 2

Now let us answer the questions

Part A:

∵ h(x) = $\frac{1}{2}$ (x - 2)²

∴ h(4) = $\frac{1}{2}$ (4 - 2)²

∴ h(4) = $\frac{1}{2}$ (2)²

∴ h(4) = $\frac{1}{2}$ (4)

∴ h(4) = 2

∵ m(x) = $\frac{1}{2}$ x - 2

∴ m(16) = $\frac{1}{2}$ (16) - 2

∴ m(16) = 8 - 2

∴ m(16) = 6

- Find now h(4) - m(16)

∵ h(4) - m(16) = 2 - 6

∴ h(4) - m(16) = -4

Part B:

The y-intercept is the value of h(x) at x = 0

∵ h(x) = $\frac{1}{2}$ (x - 2)²

∵ x = 0

∴ h(0) = $\frac{1}{2}$ (0 - 2)²

∴ h(0) = $\frac{1}{2}$ (-2)² =

∴ h(0) = 2

∴ The y-intercept of h(x) is 2

∵ m(x) = $\frac{1}{2}$ x - 2

∵ x = 0

∴ m(0) = $\frac{1}{2}$ (0) - 2 = 0 - 2

∴ m(0) = -2

∴ The y-intercept of m(x) is -2

- Find the distance between y = 2 and y = -2

∴ The difference between the y-intercepts of the graphs = 2 - (-2)

∴ The difference between the y-intercepts of the graphs = 4

∴ The y-intercepts are 4 units apart

Part C:

The minimum/maximum point of a quadratic function f(x) = a(x - h) + k is point (h , k)

Compare this form with the form of h(x)

∵ h = 2 and k = 0

∴ The minimum point of the graph of h(x) is (2 , 0)

∵ k is the minimum value of f(x)

∴ 0 is the minimum value of h(x)

∴ The domain of h(x) is all real numbers

∴ The range of h(x) is h(x) ≥ 2

∵ m(8) = 2

∵ m(14) = 5

∵ h(8) = $\frac{1}{2}$ (8 - 2)² = 18

∵ h(14) = $\frac{1}{2}$ (14 - 2)² = 72

∴ h(x) is always > m(x)

∴ m(x) can not exceed h(x) for any value of x

<em>Look to the attached graph for more understand</em>

The blue graph represents h(x)

The green graph represents m(x)

The blue graph is above the green graph for all values of x, then there is no value of x make m(x) exceeds h(x)

7 0

3 years ago