MATHEMATICS HIGH SCHOOL

A+√b) (a-√b .)is equal to

Answers

Answer 1

Answer:

Value of given multiply a² - b

Given that;

(a+√b)(a-√b)

Find:

Value of given multiply

Computation:

(a+√b)(a-√b)

Formula used;

⇒ (a + b)(a - b) = a² - b²

So,

⇒ (a+√b)(a-√b)

⇒ (a)² - (√b)²

⇒ a² - b

Learn more:

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Answer 2

Answer:

Answer:

Step-by-step explanation:

$a^(2) - a√(b) + a√(b) - b^(2) \n= a^(2) - b^(2) or (a+b) . (a-b)$

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Write 0.0003532 in scientific notation.a. 3.532 × 105
b. 3.532 × 10 4
c. 3.532 × 104
d. 3.532 × 10 5

Answers

Answer:

b. 3.532×10^-4

Step-by-step explanation:

If you have: 0,0003532

you have to put the comma 4 positions to the right in order to get the number "3,532"

Then you can to express the number in scientific notation like 3.532×10^-4

which means that to return to the original number you must run the comma 4 positions to the left.

The answer should be
B. 3.532 x 10 -4

HELP ASAPFind P (Junior|Boy) Hint: P(A and B)
P(B)
Classroom of Students
Boys Girls
Freshman 4 4 8
[?]
Sophomore 5 7 12
Junior 2 3 5
Senior 1
4 5
12 18

Answers

The Probability of junior boys will be $(1)/(6)$ .

What is Probability ?

Probability is the ratio of the number of possible outcomes to the total number of outcomes.

We have,

Total number of boys = 12

Total Junior boys = 2

So,

Probability $=(number\ of\ possible\ outcomes )/(total\ number\ of\ outcomes)$

So,

P (Junior Boy) $=(number\ of\ junior\ boys)/(total\ number\ of\ boys)$

So,

P (Junior Boy) $=(2)/(12)$

i.e.

P (Junior Boy) $=(1)/(6)$

So,

The Probability of junior boys is $(1)/(6)$ .

Hence, we can say that the Probability of junior boys will be $(1)/(6)$ .

To know more about Probability click here

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Answer:

Step-by-step explanation: 1/6

One day, a person went to a horse racing area. Instead of counting the number of humans an horses, he conuted 74 heads and 196 legs. How many humans and horses were there?A.
37 humans and 98 horses
B.
24 horses and 50 humans
C.
31 horses and 74 humans
D.
24 humans and 50 horses

99 POINTS

Answers

A human has 1 head and 2 legs.
A horse has 1 head and 4 legs.

Let's make two equations from what we know.

There were a total of 74 heads.
There were a total of 196 legs.

Let's call humans 'x' and horses 'y'

The total number of heads were 74.
Humans have 1 head, and so do horses.

Our first equation is:
x + y = 74

There were a total of 196 legs.
Humans have 2 legs, and horses have 4 legs.

Our second equation is:
2x + 4y = 196

Our two equations are:

x + y = 74
2x + 4y = 196

We need to solve this system of equations to find out how many humans and horses were at this racing event.

Multiply the first equation by 2.

2(x + y) = 2(74)
2x + 2y = 148

Our two equations are:

2x + 2y = 148
2x + 4y = 196

Subtract the first equation from the second equation.

2x - 2x + 2y - 4y = 148 - 196
2y - 4y = 148 - 196
-2y = - 48

Divide both sides by -2

y = 24

That means that there were 24 horses.

We can plug back in y = 24 into our first equation to find out how many humans there were.

x + y = 74
x + 24 = 74
x + 24 - 24 = 74 - 24
x = 50

There were 50 humans.

At the horse racing event, there were 24 horses and 50 humans.

Your final answer is B. 24 horses and 50 humans.

50 +24 =74 heads 50 x 2 = 100 human legs 4 x 24 = 96 horse legs 100 + 96 =196 legs total. So b will be your final answer.

Solve.
1.5 - 0.25(a + 4)= 3 + 3(0.05 - 0.5a)

Answers

the answer should be 2.12

Ok HI again but the answer should be -0.68 the steps are below! Simplifying 5 + -0.25(a + 4) = 3 + 3(0.05 + -0.5a) Reorder the terms: 5 + -0.25(4 + a) = 3 + 3(0.05 + -0.5a) 5 + (4 * -0.25 + a * -0.25) = 3 + 3(0.05 + -0.5a) 5 + (-1 + -0.25a) = 3 + 3(0.05 + -0.5a) Combine like terms: 5 + -1 = 4 4 + -0.25a = 3 + 3(0.05 + -0.5a) 4 + -0.25a = 3 + (0.05 * 3 + -0.5a * 3) 4 + -0.25a = 3 + (0.15 + -1.5a) Combine like terms: 3 + 0.15 = 3.15 4 + -0.25a = 3.15 + -1.5a Solving 4 + -0.25a = 3.15 + -1.5a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5a' to each side of the equation. 4 + -0.25a + 1.5a = 3.15 + -1.5a + 1.5a Combine like terms: -0.25a + 1.5a = 1.25a 4 + 1.25a = 3.15 + -1.5a + 1.5a Combine like terms: -1.5a + 1.5a = 0.0 4 + 1.25a = 3.15 + 0.0 4 + 1.25a = 3.15 Add '-4' to each side of the equation. 4 + -4 + 1.25a = 3.15 + -4 Combine like terms: 4 + -4 = 0 0 + 1.25a = 3.15 + -4 1.25a = 3.15 + -4 Combine like terms: 3.15 + -4 = -0.85 1.25a = -0.85 Divide each side by '1.25'. a = -0.68 Simplifying a = -0.68

The following table shows the expressions that represent the sales of 4 companies:Company A B C D

Sales 340(1.03)x 275(0.89)x 180(1.23)x 260(1.90)x

Rank the company sales by smallest to largest percent of increase and select the correct answer below.

A, B, C, D

A, D, B, C

B, A, C, D

C, B, D, A

Answers

Answer:

The correct option is C.

Step-by-step explanation:

A general exponential function is defined as

$y=a(1+r)^x$

Where, a is initial value and r is growth rate.

The sales of company A is

$y=340(1.03)^x$

It can be written as

$y=340(1+0.03)^x$

Therefore the initial sales of company A is 340 and percent of increase is 3%.

The sales of company B is

$y=275(0.89)^x$

It can be written as

$y=275(1-0.11)^x$

Therefore the initial sales of company B is 275 and percent of increase is -0.11%. It means sales decrease by 11%.

The sales of company C is

$y=180(1.23)^x$

It can be written as

$y=180(1+0.23)^x$

Therefore the initial sales of company C is 180 and percent of increase is 23%.

The sales of company D is

$y=260(1.90)^x$

It can be written as

$y=260(1+0.90)^x$

Therefore the initial sales of company D is 260 and percent of increase is 90%.

We have to rank the company sales by smallest to largest percent of increase.

$-11\%<3\%<23\%<90\%$

$B<A<C<D$

Therefore the correct option is C.

I think it might be (B), not for sure but it has to be (B)

I have some white and black marbles in a box. There are 30 white marbles. There are 14 more white marbles than black marbles. How many black marbles do I have?