Simplify fully
(x²+3)² - (x²-1)²

Answer:  [tex]2\sqrt{2}+\sqrt{3}\\\\[/tex]

a = 2 and b = 1

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Explanation:

Set the expression equal to the given form we want. Then square both sides so we get rid of the outer-most square root

[tex]\sqrt{11+4\sqrt{6}} = a\sqrt{2}+b\sqrt{3}\\\\\left(\sqrt{11+4\sqrt{6}}\right)^2 = \left(a\sqrt{2}+b\sqrt{3}\right)^2\\\\11+4\sqrt{6} = \left(a\sqrt{2}\right)^2+2*a\sqrt{2}*b\sqrt{3}+\left(b\sqrt{3}\right)^2\\\\11+4\sqrt{6} = 2a^2+2ab\sqrt{2*3}+3b^2\\\\11+4\sqrt{6} = 2a^2+3b^2+2ab\sqrt{6}\\\\[/tex]

In the third line, I used the rule that (x+y)^2 = x^2+2xy+y^2

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At this point, we equate the non-radical and radical terms to get this system of equations

[tex]\begin{cases}11 = 2a^2+3b^2\\ 4\sqrt{6} = 2ab\sqrt{6}\end{cases}[/tex]

The second equation turns into 4 = 2ab when we divide both sides by sqrt(6)

Then 4 = 2ab turns into ab = 2 after dividing both sides by 2.

We're told that a,b are rational numbers. Let's assume that they are integers (which is a subset of the rational numbers).

If so, then we have these four possibilities

If a,b are negative, then you'll find that [tex]a\sqrt{2}+b\sqrt{3}[/tex] overall is negative. But this contradicts that [tex]\sqrt{11+4\sqrt{6}}[/tex] is positive. So a,b must be positive.

Let's assume that a = 1 and b = 2. If so, then,

2a^2+3b^2 = 2(1)^2+3(2)^2 = 14

but we want that result to be 11 instead.

Let's try a = 2 and b = 1

2a^2+3b^2 = 2(2)^2+3(1)^2 = 11

which works out perfectly.

Therefore,

[tex]\sqrt{11+4\sqrt{6}} = 2\sqrt{2}+\sqrt{3}\\\\[/tex]

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Checking the answer:

Use a calculator to find that

[tex]\sqrt{11+4\sqrt{6}} \approx 4.5604779\\\\2\sqrt{2}+\sqrt{3} \approx 4.5604779\\\\[/tex]

both have the same decimal approximation, so this is a fairly informal way to confirm the answer.

Another thing you can do is to take advantage of the idea that if x = y, then x-y = 0

So if you want to see if two things are equal, you subtract them. You should get exactly 0 or something very small (pretty much equal to 0).

Answer:

5000

Step-by-step explanation:

[tex] \frac{52}{100} = \frac{2600}{x} \\ x = 5000[/tex]

Answer:

3. first make Y the subject, then x^2 will become negative which will make the the parabola open up

Step-by-step explanation:

2x/3 -4 = x

multiply both side by 3

2x - 12 = 3x

-x = 12

x = -12

Answer:

B

Step-by-step explanation:

Based on the given information, option 4 seems to be the most likely candidate to be positive for the entire interval [-3, -2]. Correct option is 4.

To determine which function is positive for the entire interval [-3, -2], we need to look for the part of the curve that lies above the x-axis within this interval.

The curve has a minimum value of (0, -3) and crosses the x-axis at (-3, 0) and (3, 0), which means it goes below the x-axis in the interval [-3, -2]. So, this option is not positive for the entire interval.

The curve has a minimum value of (2, -3) and crosses the x-axis at (-1, 0) and (5, 0). Since it crosses the x-axis at -1 which is outside the interval [-3, -2], this option is not positive for the entire interval.

The curve has a minimum value of (2, 4) and a maximum value of (0.5, 6). Since the minimum value is above the x-axis, this option is not positive for the entire interval.

The curve has a minimum value of (-1.75, -3.9) and a maximum value of (0, 2). It also crosses the x-axis at (-2.2, 0), (-0.75, 0), and (0.75, 0). Since the minimum value is above the x-axis, and all the points where it crosses the x-axis are outside the interval [-3, -2], this option could potentially be positive for the entire interval.

To know more about interval:

https://brainly.com/question/34520204

#SPJ3

Answer:

C. Yes, 3.5.

Step-by-step explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality ([tex]k[/tex]) is described by the following expression:

[tex]k = \frac{y}{x}[/tex] (1)

Where:

[tex]x[/tex] - Input.

[tex]y[/tex] - Output.

If we know that [tex](x_{1}, y_{1}) = (13, 45.5)[/tex], [tex](x_{2}, y_{2}) = (14, 49)[/tex] and [tex](x_{3}, y_{3}) = (15, 52.5)[/tex], then the constants of proportionalities of each ordered pair are, respectively:

[tex]k_{1} = \frac{y_{1}}{x_{1}}[/tex]

[tex]k_{1} = \frac{45.5}{13}[/tex]

[tex]k_{1} = \frac{7}{2}[/tex]

[tex]k_{2} = \frac{y_2}{x_2}[/tex]

[tex]k_{2} = \frac{49}{14}[/tex]

[tex]k_{2} = \frac{7}{2}[/tex]

[tex]k_{3} = \frac{y_{3}}{x_{3}}[/tex]

[tex]k_{3} = \frac{52.5}{15}[/tex]

[tex]k_{3} = \frac{7}{2}[/tex]

Since [tex]k_{1} = k_{2} = k_{3}[/tex], the constant of proportionality is 3.5.

Answer:

a) 41.666...%

b) 10/120 or 1/12

Step-by-step explanation:

50 students like volleyball and tennis out of 120 students surveyed. 50/120 as a percent is 41.6666666...%

10 students like volleyball but not tennis out of 120 students surveyed. 10/120 can also simplify to 1/12

:) ur welcome

Answer: 18,27,36

Step-by-step explanation: We have to add all the ratios to get 9 and then divide 81 by 9 and get 9. The multiple 2, 3 and 4 by 9 getting 18, 27 and 36 respectively.

Answer:

y = 6x - 19

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 4 ← is in slope- intercept form

with slope m = 6

Parallel lines have equal slopes , then

y = 6x + c ← is the partial equation

To find c substitute (3, - 1) into the partial equation

- 1 = 18 + c ⇒ c = - 1 - 18 = - 19

y = 6x - 19 ← equation of parallel line

i didn't get it what is the question

Answer:

my previous account deleted...how r u sadie??

Answer:

C. Only statements #1 & #3 are true.

Step-by-step explanation:

A plane is made up of various number of points or line that extend till infinity on a flat surface. It can be named by with 3 non-collinear points that lie on the plane or by a letter in the plane (e.g plane A).

All plane shape are derived by their required dimensions in a plane. So that they can all be expressed on a flat surface i.e in 2 dimensions only.

Thus from the given question, the appropriate option that are statements that defines a plane accurately is C. i.e only statements #1 & #3 are true.

Answer:

-4/5

Step-by-step explanation:

If you use the number line, after adding 3/5 you can see that it still doesn't make it positive but brings it up to -4/5 (Hope this helps)

Answer:

You subtract them:

3/5-7/5 (the plus disappears when faced with a minus)

-4/5

Given:

Bananas are $2.40 per pound.

To find:

The graph and unit rate on the graph.

Solution:

Let y be the total cost of x pounds of bananas.

Cost of 1 pound of banana = $2.40

Cost of x pound of bananas = $2.40x

So, the required equation for the given situation is:

[tex]y=2.4x[/tex]

The graph of [tex]y=2.4x[/tex] describes the proportional relationship between the two quantities.

The graph of [tex]y=2.4x[/tex] is a line passing through (0, 0) with a slope of 2.4; the slope 2.4 is the unit rate of each pound of bananas.

Therefore, the correct option is (b).

Answer:

a

Step-by-step explanation:

Answer:

width?

8-W-52

2(w-8) +2w=52

(W-8)+W=52

2(8-W) +2w=52

Answer:

graph "B"

at 0 graph = -1200 that is the production cost

Step-by-step explanation:

Answer:

0.125

Step-by-step explanation:

Becuase math

Answer:

C

Step-by-step explanation:

Answer:

hi its c because its not a traight line

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Given

24x² - 22x + 5

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 24 × 5 = 120 and sum = - 22

The factors are - 12 and - 10

Use these factors to split the x- term

24x² - 12x - 10x + 5 ( factor the first/second and third/fourth terms )

= 12x(2x - 1) + 5(2x - 1)  ← factor out (2x - 1) from each term

= (12x - 5)(2x - 1) ← in factored form → C

Answer:

x = 82

Step-by-step explanation:

1/3(12/7 + 9/7) + 3⁴ =

1/3(21/7) + 3⁴ =

1/3(3) + 3⁴ =

1 + 81 = 82

Answer:

[tex]7,500[/tex]

Step-by-step explanation:

Let's solve this problem step-by-step. The library had 1,500 books in 2011. The ratio of books in 2011 and in 2012 is 1:2. Therefore, let the number of books in 2012 be [tex]x[/tex].

We have the following proportion:

[tex]\frac{1}{1,500}=\frac{2}{x},\\x=2\cdot 1,500=3,000[/tex]

Therefore, there were 3,000 books in 2012. The ratio of books in 2012 and in 2013 is 2:5. Let the number of books in 2013 be [tex]y[/tex].

We have:

[tex]\frac{2}{3,000}=\frac{5}{y},\\2y=5\cdot 3,000,\\2y=15,000\\y=\boxed{7,500}[/tex]

Therefore, there were 7,500 books in 2013.

Answer:

7,500 books

Step-by-step explanation:

Answer:

B yes, because it pases the vertical line test

Answer:

The answer would be B

Answer:

-2

Step-by-step explanation:

We know that the object is at 12 on a horizontal line.

The horizontal line of a graph is the x axis, so lets think of 12 as 12x

On a graph, left is negative, and right is postive.

In this case we need to move 14x to the right, or -14x.

We start at 12x, so its going to be:

12x-14x=-2x

So -2 is the postition of the object on the x axis.

This is answer B.

Hope this helps!

Answer:

[tex]\frac{1+3(n-1)}{3+4(n-1)}[/tex]

Step-by-step explanation:

First find the pattern.

1/3 gets 5/21 added to it but doing that to 4/7 does not get 7/11, so it's nto normal adding.

if you multiply 1/3 gets 12/7, but if you multiply that by 4/7 you don't get 7/11 so it's not normal multiplcation.

I would next try only adding to the numerator and denominator separately.  

so 1/3 gets 3 added to the 1 and 4 added to the 3.  Doing that again gets us (4+3)/(7+4) = 7/11 and doing it again gets us 10/15 = 2/3.  So that is the right answer.

So we know what is happening.  if you start with 1/3 and increasingthe numerator by 3 and denominator by 4 then we know it's going to look like (1+3(n-1))/(3+4(n-1)) because the first term  is when n=1 and we want that to cancel out.  You can also simplify it and get (3n-2)/(4n-1)

Let me know if it doesn't make sense.  

Step-by-step explanation:

(-13) + 7 – (-2) + (-6) + ( ) = 0

Let the unknown be "y"

-13 + 7 + 2 - 6 + y = 0

-10 + y = 0

y=10.

The missing Number is 10.

Verify

-13 +7 + 2 -6 + 10 = 0.

Answer:

10

Step-by-step explanation:

1) 1 hour and 15 minutes

2) 4:07

3) 30 minutes

4) 8:35

9) 1 hour and 53 minutes

10) 4:17

11) 2 hours and 52 minutes

12) 3:35

13) 9:55

14) 8:10

15) 1 hour and 45 minutes

16) 3:05

17) 6:48

18) 9:45

19) 1 hour and 25 minutes

20) 2 hours and 45 minutes

Brainliest would be appreciated :)

Answer:

the answer is 2.8

Step-by-step explanation:

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

Given:

[tex]\frac{3x}{5} -0.5=1.9[/tex]

Add 0.5 to both sides

[tex]\frac{3x}{5} =2.4[/tex]

Multiply 5 from both sides

[tex]3x=12[/tex]

Divide both sides by 3

[tex]x=4[/tex]

Hope this helps

Answer:

Sundeep will arrive in Barcelona at 12pm

Answer:

It is not a solution

Step-by-step explanation:

Plug the point into the equations and check to see if they are true

y=3x - 3

3 = 3(6) -3

3 = 18-3

3 = 15

False

We do not need to check the other equation since this is false