I’ll mark brainliest!!

The trick is to exploit the difference of squares formula,

[tex]a^2-b^2=(a-b)(a+b)[/tex]

Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:

[tex](\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2[/tex]

Whatever you do to the denominator, you have to do to the numerator too. So

[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2[/tex]

Expand the numerator:

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)[/tex]

[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}[/tex]

So we have

[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2[/tex]

But √12 = √(3•4) = 2√3, so

[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}[/tex]

Answer:

P(B) = 0.85

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

[tex]P(A) = 0.24, P(B|A) = 0.85[/tex]

These events are independent.

This means that [tex]P(A \cap B) = P(A)*P(B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(B|A) = \frac{P(A)*P(B)}{P(A)}[/tex]

[tex]P(B|A) = P(B)[/tex]

So

[tex]P(B) = 0.85[/tex]

Answer:

7,1 × 10-⁶

Step-by-step explanation:

Once you move the comma 1 time by right (,) you have -1, so by moving it six times, you have 7,1 × 10-⁶

Answer: 22 AUD x 1.2USD / 1AUD

Step-by-step explanation: The expression would be like this:   22 Australian dollars/1.2 (value of Australian dollars to US dollars) = X US dollars/1 We would get the value of x by multiplying 1 to 22 then divide it by 1.2 and we would get the US conversion from it. We could also put the expression 22=1.2x directly and we would get the US conversion from it.

Answer:

We can find the radius from circumference and then area

Circumference(C) = 2πr

r = C/2π

r = 20/2π

r = 10/π

Area = πr²

Area = π × 10/π × 10/π

Area = 100/π

Area = 100/3.14

Area = 10000/314 = 31.84 cm² (approx)

Area = 32 cm² (Rounding to nearest whole number)

Answer:

32 m²

Step-by-step explanation:

We need to work out the area of the flower garden when we are given the circumference. First we need to know the formula's for area of circle and circumference of circle which are

→ Area of a circle = π × r² where 'r' is the radius

→ Circumference of a circle = 2 × π × r where 'r' is the radius

So we need to form an equation with the circumference of a circle formula and work out the radius in order to find the area so,

In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we divided by 2  only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.

2 × π × r = 20

→ Substitute 3.14 for π

2 × 3.14 × r = 20

→ Simplify

6.28 × r = 20

→ Divide both sides by 6.28 to isolate 'r'

r = 3.18471338

So now we now the radius of the circle we can substitute the radius into the area of circle formula

Area = π × r²

→ Substitute 3.14 for π and r for 3.18471338

Area = 3.14 × 3.18471338²

Area = 31.847133842

To the nearest whole number your answer is 32 m²

Answer:

C

Step-by-step explanation:

(x-4)(x+10)=x^2+6x-40

Answer:

C. X-4

Step-by-step explanation:

A P E X

Answer:

$55

Step-by-step explanation:

5 tickets = $25

1 ticket = $5 (divide by 5 on both sides)

multiply by 11

11 tickets = 5 ×11

11 tickets = $55

Answer:

Step-by-step explanation:

For example, if your money earns an 8 percent interest rate, it will triple in 14 years and 5 months (115 divided by 8 equals 14.4). If your money earns a 5 percent interest rate, it will triple in 23 years (115 divided by 5 equals 23).

Answer:

For online calculators you can type sqrt() or just sqrt and it will do it for you

Answer:

Step-by-step explanation:

To simplify radicals that are not perfect squares, we need a new method.

Example: [tex]\sqrt{27}[/tex]

27 is not a perfect square square the square root cannot be used.

[tex]\sqrt{27} = 5.19615242271[/tex]

To solve this, we need to break down the radical into simpler parts.

[tex]\sqrt{27} = \sqrt{3} * \sqrt{9}[/tex]

[tex]\sqrt{9} = 3[/tex]

[tex]\sqrt{3}[/tex] cannot be simplified

[tex]\sqrt{27}[/tex] = 3[tex]\sqrt{3}[/tex]

Good luck on your test!

I'm always happy to help :)

Answer:

3540

Step-by-step explanation:

There are 3520 yards in two miles and 1760 in one mile you multiply 1760 by 2 then add 20

Answer:

work is shown and pictured

The answer is B part

As the requirement for the student is either a senior or one who studies maths or both.

So, just add the values within the two venn circles divide it by total no of values.

=> 240+40+110/240+40+110+840

=> 360/1200

Answer:

B

Step-by-step explanation:

840 people aren't senior or don't takes math.

210 + 40 = 250 are seniors

110 + 40 = 150 people take math

In this class has 840 + 210 + 40 + 110 = 1200 people => All

210 + 40 + 110 = 360 people are seniors or take math. => P( S U M)

Probabilty that a randomly selected student is a senior or takes math =>[tex]\frac{P(S U M)}{All}[/tex]

[tex]\frac{P(S U M)}{All} = \frac{360}{1200}[/tex]

Hope this helps ^-^

Answer:

x varies inversly inversly with z,

so it Maries linearly.

x to y and then to a can be expressed as

x = m/y

y = n/z

so we can say

x = m/(n/z) = m/n * z

m & n could be any constant numbers, like 5 or 3.7

Here is an example where both are just one:

x = 1/y

y = 1/z

so we can say

x = 1/(1/z) = 1/1 * z

(would really, really appreciate the brainliest)

Answer:C

Step-by-step explanation:There is definitely enough info.

And there are no angles so it has to be SSS~ (It's dilated by 1.5 by the way)

Only one of those is actually a prime factorization.  Demand better from your teacher.  Anyway, I think they're just asking us to take out the calculator and enter the multiplication into it.

5) 22 isn't prime, neither is 52.  Answer:  3432

6) 32 isn't prime.  Answer: 448

7) 33 isn't prime.  Answer: 165

8)  Finally a real prime factorization.  Answer: 106

Answer:

∠ MON = 15°

Step-by-step explanation:

∠ LOM + ∠ MON = ∠ LON, substitute values

9x + 44 + 6x + 3 = 77, that is

15x + 47 = 77 ( subtract 47 from both sides )

15x = 30 ( divide both sides by 15 )

x = 2

Thus

∠ MON = 6x + 3 = 6(2) + 3 = 12 + 3 = 15°

Answer:

a) $926.40

b) $606.32

Step-by-step explanation:

a)

If she worked a total of 45.5 hours, she will receive $19.20 per hour in the first 40 hours and 1.5 * $19.20 for the exceeding 5.5 hours, so her earnings is:

19.2 * 40 + 1.5 * 5.5 * 19.2 = $926.40

b)

The deduction is $34.75, so the remaining will be:

926.40 - 34.75 = $891.65

Then, after this deduction, the taxes is 32% of the remaining, so:

891.65 - 0.32 * 891.65 = $606.32

She received $606.32

Answer:

The probability is 1/36.

Step-by-step explanation:

2/3 are dog owners

1/6 are cat owners

1/6 are bird owners

If you choose two owners, there is a 1/6 chance that you will choose a cat owner and a 1/6 chance you will choose a bird owner. Each of these are independent, so you simply multiply 1/6 by 1/6.

1/6 * 1/6= 1/36

Answer:

45 degrees

Step-by-step explanation:

angle QRS is same as (2x + 3) because it is an isosceles triangle

so, 90 + (2x+3) + (2x+3) =180 degrees

             2x+3 +2x+3=180-90

2x+2x +3+3=90

4x+6=90

4x=90-6

4x=84

x=84/4

x=21

substitute x=21 in (2x+3)

2*21+3=45

Answer:

(x + 9)(x - 7)

Step-by-step explanation:

We want to factorize [tex]x^2 + 2x - 63[/tex]

We need to find two numbers such that their product is -63 and they add up to +2. The two numbers are +9 and -7:

[tex]x^2 + 9x - 7x - 63\\\\= x(x + 9) -7(x +9)\\\\ = (x +9)(x -7)[/tex]

The complete factorization is (x + 9)(x - 7)

The factored form of the expression x² + 2x - 63 is (x + 9)(x - 7).

Given the expression in the question:

x² + 2x - 63

To determine the complete factorization of the quadratic expression x² + 2x - 63, we aim to break it down into its simplest factors.

This is achieved through factoring, a process of identifying the expressions that, when multiplied, result in the original quadratic expression.

x² + 2x - 63

Now, find a pair of integers whose sum equals 2,

and whose product equals -63.

We use integers 9 and -7.

Next, rewrite the quadratic expression using these factors:

(x + 9)(x - 7)

Therefore, the complete factorization of x² + 2x - 63 is (x + 9)(x - 7).

Option C) (x + 9)(x - 7) is the correct answer.

Learn more about factorization here: brainly.com/question/20293447

#SPJ6

Answer: a ≤ 4 or (-∞, 4]

Step-by-step explanation:

Here we have the inequality:

4a ≤ 16

this means that the left sides is less or equal than the right side.

First, find the equal part:

4*a = 16

a = 16/4 = 4

So the maximum possible value of a is 4.

Now, all the values of a smaller than 4 also make the inequality true (even the negative values) so the possible values of a are:

a ≤ 4 or (-∞, 4]

Answer:

Any number that is less or equal to 4 makes this inequality true.

Step-by-step explanation:

In order to calculate the numbers that make this inequality valid, we need to solve it for "a". This can be done in the same manner as we would solve an equation, although we must pay attention to the inequality. This is done below:

[tex]4*a \leq 16\\a \leq 16/4\\a \leq 4[/tex]

Any number that is less or equal to 4 makes this inequality true.

Answer:

0

Step-by-step explanation:

if x stade for any number like 5 then it will be 5-5=0

hope this helps you out need more help ask me

Answer:

b=10, a=13

Step-by-step explanation:

let s number of yellow = a

number of blue = b

we have

a+b =23

2b - a = 7

->a+b +2b -a = 23+7

-> 3b = 30

->b = 10

->a = 13

Answer:

6 + 6x

Step-by-step explanation:

9 - (3-6x) = 9 - 3 - (-6x)

= (9-3) +6x

= 6 + 6x

1) expand the bracket

2) group like terms together

3) simplify to form expression

Answer:a

Step-by-step explanation:

Answer:

It is A, y = 9,958(0.972)x

Step-by-step explanation:

Answer:

b=9

Step-by-step explanation:

move the 4b over to the other side by adding it to both sides

[tex]-3b(+4b)=9-4b(+4b)[/tex]

[tex]1b=9[/tex]

option b is the correct answer

Answer:

log2(0.25) = -2

512 = 8^3

Step-by-step explanation:

Rewrite the following equation in logarithmic form.   0.25 = 2^-2

Rewrite the following equation in exponential form.  log8 (512) = 3

Answer:

Step-by-step explanation:

Given

Solving for z: