All categories

2 years ago

Factorise 125x^3 -27y^3

Mathematics

1 answer:

telo118 [61]2 years ago

6 0

Answer:

(5x - 3y)(25x² +15xy + 9y²)

Step-by-step explanation:

125x³ - 27y³ is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

Given

125x³ - 27y³

= (5x)³ - (3y)³

= (5x - 3y)((5x)² + (5x)(3y) + (3y)²)

= (5x - 3y)(25x² + 15xy + 9y²)

You might be interested in

Jeremy analyses one of his parachute jumps.

NikAS [45]

Answer:

A.) Acceleration = 4.6 m/s^2

B.) Average speed = 47 m/s

Step-by-step explanation:

A.) From the graph, at t = 10s,

Velocity V = 46 m/s

Acceleration a = (change in V)/ time t

a = (46 - 0)/10

a = 46/10 = 4.6 m/s^2

B.) If we estimate the speed at 5 seconds intervals, then we have

Average speed = (36 + 46 + 49 + 50 + 50 +50 + 50) ÷ 7

Average speed = 331/7 = 47.29 m/s

Average speed = 47 m/s

5 0

3 years ago

Which expression is equivalent to the following complex fraction?

marta [7]

Answer:

$\dfrac{-4x+7}{2(x-2)}$

Step-by-step explanation:

The first step is to combine the parts of the numerator and denominator into one rational expression each. Those will have the same denominator, so their ratio is the ratio of their numerators.

$\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}=\dfrac{\left(\dfrac{3-4(x-1)}{x-1}\right)}{\left(\dfrac{2(x-1)-2}{x-1}\right)}=\dfrac{3-4(x-1)}{2(x-1)-2}\\\\=\dfrac{3-4x+4}{2x-2-2}=\boxed{\dfrac{-4x+7}{2(x-2)}}$

5 0

2 years ago

Read 2 more answers

1. You are saving to buy a new house in 7 years. If you invest $4,500 now at 5.5% interest compounded

motikmotik

Answer:

Part 1) $\$6,595.94$

Part 2) $\$3,449.23$

Part 3) $\$17,040.06$

Part 4) $\$20,773.90$

Part 5) The Option A is the best way to invest the money by $4,223.94 than Option B

Step-by-step explanation:

Part 1)

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=7\ years\\ P=\$4,500\\ r=5.5\%=5.5/100=0.055\\n=4$

substitute in the formula above

$A=4,500(1+\frac{0.055}{4})^{4*7}$

$A=4,500(1.01375)^{28}$

$A=\$6,595.94$

Part 2)

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=2\ years\\ P=\$3,200\\ r=3.75\%=3.75/100=0.0375$

substitute in the formula above

$A=3,200(e)^{0.0375*2}$

$A=\$3,449.23$

Part 3)

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=18\ years\\ A=\$40,000\\ r=4.75\%=4.75/100=0.0475\\n=12$

substitute in the formula above

$40,000=P(1+\frac{0.0475}{12})^{12*18}$

$40,000=P(\frac{12.0475}{12})^{216}$

$P=40,000/[(\frac{12.0475}{12})^{216}]$

$P=\$17,040.06$

Part 4)

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=7\ years\\ A=\$30,000\\ r=5.25\%=5.25/100=0.0525$

substitute in the formula above

$30,000=P(e)^{0.0525*7}$

$30,000=P(e)^{0.3675}$

$P=30,000/(e)^{0.3675}$

$P=\$20,773.90$

Part 5)

Option A

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=8\ years\\ P=\$11,500\\ r=5.6\%=5.6/100=0.056\\n=2$

substitute in the formula above

$A=11,500(1+\frac{0.056}{2})^{2*8}$

$A=11,500(1.028)^{16}$

$A=\$17,889.07$

Option B

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=5\ years\\ P=\$11,500\\ r=3.45\%=3.45/100=0.0345$

substitute in the formula above

$A=11,500(e)^{0.0345*5}$

$A=11,500(e)^{0.1725}$

$A=\$13,665.13$

Compare the options

Option A ------> $\$17,889.07$

Option B -----> $\$13,665.13$

Option A > Option B

Find out the difference

$\$17,889.07-$13,665.13=$4,223.94$

therefore

The Option A is the best way to invest the money by $4,223.94 than Option B

3 0

2 years ago

You work for a landscaper that has a customer needing to seed an area of land 80 feet by 40 feet in size. The garden center has

Andreas93 [3]

You need to convert your 3200 sq ft into yards which is 355.556 sq yards then you divide 355.556 by 25 to get 14.22224 bags of seed needed

3 0

2 years ago

Read 2 more answers

In the equation below, a and b are constants. If a = b, what is the value of x in terms of y ? 2xa=8yb Select one:

Bas_tet [7]

Answer: $x=4y$

Step-by-step explanation:

The equation is $2xa=8yb$ .

To find the value of the variable "x" in terms of "y", you need to apply the Division property of equality and divide both sides of the equation by "2a". Then:

$\frac{2ax}{2a}=\frac{8yb}{2a}$

$x=\frac{8yb}{2a}$

You know that the costants "a" and "b" are equal ( $a=b$ ), then:

$\frac{b}{a}=1$

Knowingt this, you can simplify.

Therefore, you get that the value of "x" in terms of "y" is:

$x=4y$

7 0

2 years ago