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3 years ago

16(a+b)^2-49(a-b)^2 factorize the expression

Mathematics

1 answer:

noname [10]3 years ago

4 0

The given expression is a difference of squares, so we have

16 (a + b)² - 49 (a - b)² = 4² (a + b)² - 7² (a - b)²

… = (4 (a + b))² - (7 (a - b))²

… = (4 (a + b) - 7 (a - b)) (4 (a + b) + 7 (a - b))

… = (4a + 4b - 7a + 7b) (4a + 4b + 7a - 7b)

… = (-3a + 11b) (11a - 3b)

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4 years ago

Express 20minutes as ratio of 2hours

Flauer [41]

Answer:

1hr : 10min

Step-by-step explanation:

2 hrs = 120 min

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3 0

3 years ago

Re-write the equation without the h component.

levacccp [35]

Answer:

$f(x) = 2[\frac{3^x}{9}] + 2$

$f(x) = 8(4)^x$

Step-by-step explanation:

Given

$f(x) = 2(3)^{x-2} + 2$

$f(x) = \frac{1}{2}(4)^{x+2}$

Required

Remove the h component

In a function, the h component is highlighted as:

$f(x) = a^{x+h}$

So, we have:

$f(x) = 2(3)^{x-2} + 2$

Split the exponents using the following law of indices:

$a^m/a^n = a^{m-n}$

$f(x) = 2*\frac{3^x}{3^2} + 2$

$f(x) = 2*\frac{3^x}{9} + 2$

$f(x) = 2[\frac{3^x}{9}] + 2$

The h component has been removed

$f(x) = \frac{1}{2}(4)^{x+2}$

Split the exponent using the following law of indices

$a^{m+n} =a^m * a^n$

So, we have:

$f(x) = \frac{1}{2}(4)^x * 4^2$

Express 4^2 as 16

$f(x) = \frac{1}{2}(4)^x * 16$

Divide 16 by 2

$f(x) = 8(4)^x$

3 0

3 years ago

The Ford family decides they want to go see a movie at the local movie theater. The family consists of two adults, and five chil

Brrunno [24]

Ford Family consists of:

a) 2 adults

The price of ticket for each adult is $18.55. This can be approximated to $19 if we round it to nearest dollar. So the price of ticket for 2 adults will be 2 x 19 = $38

b) 3 children between ages 2 and 10.

Ticket for each child between ages 2 - 10 is $12.59 which can be approximated to $13. So ticket price for 3 children will be 3 x 13 = $39

c) 2 children below the age of 2.

Ticket price for each child is $6.54 which can approximated as $7. So ticket price for 2 children will be 2 x 7 = $14

The estimated total amount due on the family equals = 38 + 39 + 14 = $91

In each of the 3 cases we rounded up the values. So this means the actual amount must be slightly lesser than $91. The actual bill was $87.95 which is close to $91 and lesser than it. Hence we can conclude that $87.95 is the correct amount due for Ford Family.

3 0

3 years ago

If x Is a real number such that x3 = 64, the x2 + x equals what?

Annette [7]

Answer:

Step-by-step explanation:

Assuming that the equation is x³ = 64, that can be solved by putting cube root on both sides like so: ∛(x³) = ∛64, which simplifies to x = 4.

Plugging that into our expression gives us 4² + 4, which is 20.

7 0

3 years ago

16(a+b)^2-49(a-b)^2 factorize the expression​

16(a+b)^2-49(a-b)^2 factorize the expression