All categories

2 years ago

What is the form of the Difference of Squares identity?

Mathematics

1 answer:

Feliz [49]2 years ago

3 0

The difference identity of two squares can be stated as:

a² - b² = (a + b)(a -b)

i.e. the product of sum of two numbers with the difference of two numbers. This can be easily proved.

For example, Let a = 4 and b = 3

so, a² - b² = 16 - 9 = 7

a + b = 4 + 3 = 7
a - b =4 - 3 = 1

(a + b )(a - b) = 7 x 1 = 7

Thus,

a² - b² = (a+b)(a-b)

So, option C gives the correct answer

You might be interested in

The position function for a free-falling object is s(t) = -16t^2 + vt +5. A ball is thrown upward from the top of a 400-foot bui

mixer [17]

Answer:

6.21 seconds

Step-by-step explanation:

The position function of a free-falling object is,

$s(t) = -16t^2+v_0t+s_0$

Where,

$s_0$ = initial height of the object,

$v_0$ = initial velocity of the object,

Here,

$s_0=400\text{ feet}$

$v_0=35\text{ feet per sec}$

Hence, the height of the ball after t seconds,

$s(t)=-16t^2+35t+400$

When s(t) = 0,

$\implies -16t^2+35t+400=0$

$t=\frac{-35\pm \sqrt{35^2-4\times -16\times 400}}{2\times -16}$

$t=\frac{-35\pm \sqrt{1225+25600}}{-32}$

$\implies t\approx -4.02\text{ or }t\approx 6.21$

∵ Time cannot be negative,

Hence, after 6.21 seconds the ball will reach the ground.

4 0

2 years ago

4 students from a class of 15 are going to be chosen to be on the dance committee. Find the number of different 4-person committ

Andrej [43]

We know that
The formula for combinations is
C=n!/[(n-r)!*r!]
where
n is the total number of objects you choose from
r is the number that you choose to arrange

in this problem
n=15 students
r=4 students
C=15!/[(15-4)!*4!]-----> C=15!/[11!*4!]---> (15*14*13*12*11!)/(11!*4*3*2*1)
C=(15*14*13*12)/(24)----->C=1365

the answer is
1365

7 0

2 years ago

Read 2 more answers

There are 240 students going on a field trip each school bus can hold 48 students complete the equation to show which operation

NeTakaya

If you calculate 240/48, you will get 5 without any remainder, which means if you get 5 buses it can exactly take all students?

8 0

2 years ago

Which of the following is a perfect square trinomial?

shutvik [7]

Answer:

Step-by-step explanation:

Take a look at what happens when squaring either of these...

$(ax-by)^2=(ax-by)(ax-by)=a^2x^2-2abxy+b^2y^2\\\\(ax+by)^2=(ax+by)(ax+by)=a^2x^2+2abxy+b^2y^2\\$

Notice a couple of patterns.

1. The last term has a positive coefficient. That rules out answer choices C and D.

2. The coefficient of the middle term is either $+2ab \text{ or } -2ab$ . So what are a and b? a is the square root of the x^2 term and b is the square root of the y^2 term.

$25x^2 \Rightarrow a=5\\\\9y^2 \Rightarrow b=3\\\\ab=15\\\\2ab=30$

The middle coefficient needs to be either +30 or -30. The answer is choice A.

5 0

2 years ago

Why will percent of change always be represented by a positive number?

Murljashka [212]

Percent of change will always be positive because the change is an absolute value. As we know, absolute value is always a positive value because you don't pay attention to the direction, only the distance is important.

3 0

2 years ago