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4 years ago

Factor this problem ? 125 +27y^3

Mathematics

1 answer:

koban [17]4 years ago

6 0

Answer:

(5 + 3y)(25 - 15y + 9y²)

Step-by-step explanation:

This is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²), thus

125 + 27y³

= 5³ + (3y)³ with a = 5 and b = 3y

= (5 + 3y)(5² - 5(3y) + (3y)² )

= (5 + 3y)(25 - 15y + 9y²)

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If p(x) = x2 – 1 and q (x) = 5 (x minus 1), which expression is equivalent to (p – q)(x)?

svetlana [45]

Answer:

Step-by-step explanation:

P(x) = x² - 1 and Q(x) = 5(x - 1)

(P - Q)(x) = x² - 1 - 5(x - 1)

= x² - 1 - 5x + 5

= x² - 5x + 4

5 0

3 years ago

Read 2 more answers

Determine the domain on which of the following function is increasing

AlekseyPX

Given:

The graph of a function.

To find:

The domain on which of the following function is increasing.

Solution:

Domain is the set of x-values or input values.

From the given graph it is clear that the vertex of the given function is at (4,75).

Before the point (4,75) the graph is increasing and after the point (4,75) the graph is decreasing.

The function is defined for $0\leq x\leq 9$ .

Since the graph is increasing when $0\leq x\leq 4$ , therefore the function is increasing over the interval [0,4].

Therefore, the domain on which of the following function is increasing is [0,4].

4 0

3 years ago

What is the answer+explanation to:

Virty [35]

Since the formula for the area of a four sided figure is:

A=base*height

Rearrange the equation to solve for height:

h=A/b

63cm squared/7cm=9cm

height=9cm

x=9cm

4 0

3 years ago

Your dog eats 7/8 lb of food in 4 meals , how many meals will it take your dog to eat 1 lb of food

choli [55]

Answer:

x = 32/7, or 4 4/7 meals

Step-by-step explanation:

Write and solve an equation of ratios, as follows:

7/8 lb 4 meals

------------ -------------

1 lb x

x will be the number of meals necessary for the dog to eat 1 lb of food.

Cross-multiplying, (7/8)x = 4.

Multiplying both sides by 8/7 is an easy way to isolate x:

(8/7)(7/8)x = (8/7)(4)

x = 32/7, or 4 4/7 meals

3 0

3 years ago

12. Solve x^2 + 6x - 16 = 0 by completing the square. Please help and show work

alekssr [168]

Answer:

x is 2 and -8

Step-by-step explanation:

${x}^{2} + 6x - 16 = 0$

general equation

${ax}^{2} + (sum)x + product = 0$

sum is 6, product is -16

for completing squares,

first divide the sum by 2:

$= \frac{6}{2} = 3$

add the square of the result on (x² + 6x) and subtract it from the product:

$( {x}^{2} + 6x + {3}^{2} ) - 16 - {3}^{2} = 0 \\ {(x + 3)}^{2} - 25 = 0 \\ {(x + 3)}^{2} = 25$

take square root:

$\sqrt{ {(x + 3)}^{2} } = \sqrt{25 } \\ x + 3 = ±5 \\ x = ±5 - 3$

x is either: 5-3 or -5-3

$x = 2 \: \: and \: - 8$

4 0

3 years ago