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4 years ago

Which are perfect squares

Mathematics

1 answer:

Sonbull [250]4 years ago

7 0

Answer:

Numbers that when square rooted give whole numbers

Step-by-step explanation:

E.g. 1,4,9,16,25, and so on.

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Х- а<br>x-b<br>If f(x) = b.x-a÷b-a + a.x-b÷a - b<br>Prove that: f (a) + f(b) = f (a + b)

GenaCL600 [577]

Given:

Consider the given function:

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot(x-b)}{a-b}$

To prove:

$f(a)+f(b)=f(a+b)$

Solution:

We have,

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot (x-b)}{a-b}$

Substituting $x=a$ , we get

$f(a)=\dfrac{b\cdot(a-a)}{b-a}+\dfrac{a\cdot (a-b)}{a-b}$

$f(a)=\dfrac{b\cdot 0}{b-a}+\dfrac{a}{1}$

$f(a)=0+a$

$f(a)=a$

Substituting $x=b$ , we get

$f(b)=\dfrac{b\cdot(b-a)}{b-a}+\dfrac{a\cdot (b-b)}{a-b}$

$f(b)=\dfrac{b}{1}+\dfrac{a\cdot 0}{a-b}$

$f(b)=b+0$

$f(b)=b$

Substituting $x=a+b$ , we get

$f(a+b)=\dfrac{b\cdot(a+b-a)}{b-a}+\dfrac{a\cdot (a+b-b)}{a-b}$

$f(a+b)=\dfrac{b\cdot (b)}{b-a}+\dfrac{a\cdot (a)}{-(b-a)}$

$f(a+b)=\dfrac{b^2}{b-a}-\dfrac{a^2}{b-a}$

$f(a+b)=\dfrac{b^2-a^2}{b-a}$

Using the algebraic formula, we get

$f(a+b)=\dfrac{(b-a)(b+a)}{b-a}$ $[\because b^2-a^2=(b-a)(b+a)]$

$f(a+b)=b+a$

$f(a+b)=a+b$ [Commutative property of addition]

Now,

$LHS=f(a)+f(b)$

$LHS=a+b$

$LHS=f(a+b)$

$LHS=RHS$

Hence proved.

5 0

3 years ago

There are 40 vehicles in the parking lot. Twenty percent of the vehicles are pick-up trucks. How many pick-up trucks are in the

mart [117]

Answer:

Step-by-step explanation:

20% of 40 is 8.

^.^

- Amanda

8 0

3 years ago

Today only , a table is being sold at 34% discount. The sale price is $495. What was the price yesterday?

tekilochka [14]

In the given problem, it is given that the table is sold at a discount of only one day and that is today. so the table would be have been sold at its original price yesterday. The discount given today is 34% and the sale price for today is $495.
Let us assume the price of the table yesterday = x
Then we can write the equation as
x = 295 * (100/34)
= 29500/34
= 867.64
So the selling price of the table yesterday was $867.64.

5 0

4 years ago

Use the graph of f to describe the transformation that results in the graph of g. f(x) = log x; g(x) =

LuckyWell [14K]

Answer:

The function was expanded vertically by 5, and then translated vertically upwards 6 units.

Which is the third option in the list of possible answers.

Step-by-step explanation:

Recall that the types of transformations associated with:

A) a function multiplied by a positive factor larger than one consists on the function expanded vertically by that factor.;

B) a positive number added to the function consists on the vertical translation of the function upwards as many units as the number added.

Therefore, the function $f(x) = log(x)$ being transformed into $g(x)=5\,log(x)+6$

consists of the initial function expanded vertically by 5, and then translated vertically upwards 6 units.

4 0

3 years ago

A culture started with 1,000 bacteria. After 6

Naddik [55]

Answer:

1350

Step-by-step explanation:

1000 to 1100 is an increase of 100 bacteria per 6 hours

100/6 = 16.67 bacteria per hour

16.67 * 15 hours = 250

Total bacteria should be 1100+250= 1350

hope this helps :D

3 0

3 years ago

Read 2 more answers