Please PLEASE HELP THIS IS ALGEBRA 2

Answer:

a = 49

b = - 20√2

Step-by-step explanation:

5 - 2√6 / 5 + 2√6

We can rationalise the denominator as follow:

5 - 2√6 / 5 + 2√6

Multiply the numerator and the denominator by the conjugate of

5 + 2√6. The conjugate of 5 + 2√6 is

5 - 2√6

(5 - 2√6 / 5 + 2√6) x (5 - 2√6 / 5 - 2√6)

(5 - 2√6) (5 - 2√6) /(5 + 2√6) (5 - 2√6)

Expand

(25 - 10√6 - 10√6 + 4×6) / (25 - 10√6 + 10√6 + 4×6)

25 - 20√6 + 24 / 25 - 24

25 + 24 - 20√6 / 1

49 - 20√6

Equating 49 - 20√6 with a + b√3, we can obtain the value of a and b as follow:

49 - 20√6 = a + b√3

From the above

a = 49

b√3 = - 20√6

Divide both side by √3

b = - 20√6/√3

Rationalise

b = - 20√6/√3 x √3/√3

b = - 20√(6×3)/ √3×√3

b = - 20√18 / 3

b = - 20√(9×2) / 3

b = - 20 × 3√2 / 3

b = - 20√2

Given info:- Rationalise the denominator and find out the value of "a" and "b"

Given expression: {(5-2√6)/(5+2√6)} = a+b√3

Explanation:-

{(5-2√6)/(5+2√6)} = a+b√3

We know that Rationalising factor of a+b√c is a-b√c.

Therefore, the rationalising factor of 5+2√6 is 5-2√6.

⇛{(5-2√6)/(5+2√6)} × {(5-2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)(5-2√6)}/{(5+2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)²}/{5+2√6)(5-2√6)} = a+b√3 [∵(a-b)(a-b)=(a-b)²]

⇛{(5-2√6)²}/{(5)²-(2√6)²} = a+b√3 [∵(a+b)(a-b)=a²-b²]

⇛{(5-2√6)²}/({5*5)-(2*2√6*6)} = a+b√3

⇛{(5-2√6)²}/(25 - 4√6) = a+b√3

⇛{(5-2√6)²}/(25-24) = a+b√3

⇛{(5-2√6)²}/1 = a+b√3

⇛(5-2√6)² = a+b√3

⇛(5)²-(2√6)²+2(5)(2√6) = a+b√3

⇛(5*5) - (2*2√6*6) - 10 - 2√6 = a+b√3

⇛25 - 10 - 4√6 - 2√6 = a+b√3

⇛15 - 4√6 - 2√6 = a+b√3

⇛15 + 6√6 = a+b√3

∴ 15 + 6√6 = a+b√3

On, comparing with both RHS we notice that:

The value of a = 15 and b = 6.

Hope this helps!!

If you have any doubt, then you can ask me in the comments.

Answer:

Step-by-step explanation:

[tex] \sf{9 - 4x = 17}[/tex]

Move 9 to right hand side and change it's sign

⇒[tex] \sf{ - 4x = 17 - 9}[/tex]

Subtract 9 from 17

⇒[tex] \sf{ - 4x = 8}[/tex]

Divide both sides of the equation by -4

⇒[tex] \sf{ \frac{ - 4x}{ - 4} = \frac{8}{ - 4}} [/tex]

Calculate

⇒[tex] \sf{x = - 2}[/tex]

Hope I helped!

Best regards!!

Answer:

This will be -8x^3y^9.

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question the equation of the line is

y = - 4x + 9

Comparing the equation with the general equation of a line above

Slope / m = - 4

Hope this helps you

Answer:

Jake can use 19.70 ccf to not exceed $ 64.00 in water bill.

Step-by-step explanation:

The cost function of water bill is:

[tex]C = C_{f}+C_{v}[/tex]

Where:

[tex]C_{f}[/tex] - Fix costs, measured in USD.

[tex]C_{v}[/tex] - Variable costs, measured in USD.

The fix and variable costs are, respectively:

[tex]C_{f} = 24.60[/tex]

[tex]C_{v} =2\cdot \left(\frac{Q}{100} \right)[/tex]

Where [tex]Q[/tex] is the water capacity consumed within a month, measured in cubic feet. Therefore, first formula is expanded:

[tex]C = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]

If [tex]C = 64\,USD[/tex], the maximum water capacity is:

[tex]64 = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]

[tex]39.40 = 2\cdot \left(\frac{Q}{100} \right)[/tex]

[tex]Q = 1970\,ft^{3}[/tex]

Which is equivalent to 19.70 ccf.

Answer:

25°

Step-by-step explanation:

180-130=50

50÷2=25°

Answer:

D. divide by -8

Step-by-step explanation:

Answer:

90 degrees

Step-by-step explanation:

I don't really have an explanation but I'm 100% sure that it is

Answer:

90 degrees

Step-by-step explanation:

Answer:

10x² + -18

Step-by-step explanation:

g(f(x)) means you substitute 2x²-5 for every occurrance of x in g(x).

g(f(x)) = 5(2x²-5) + 7 = 10x² - 25 + 7 = 10x² - 18 =  10x² + -18

Answer:

Two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]

Step-by-step explanation:

Given

[tex]2^8 = 256[/tex]

Required

Write two exponential expression that equals 256

[tex]2^8 = 256[/tex]

Expand 8 as 4 * 2

[tex]2^{4*2} = 256[/tex]

Using laws of indices, we have

[tex](2^4)^2 = 256[/tex]

2⁴ = 16; So, we have

[tex]16^2 = 256[/tex] --- This is one

Recall that

[tex]2^{4*2} = 256[/tex]

This can also be rewritten as

[tex]2^{2*4} = 256[/tex]

Using laws of indices, we have

[tex](2^2)^4 = 256[/tex]

2² = 4; So, we have

[tex]4^4 = 256[/tex] --- This is another one

Hence, two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]

Answer:

1.3888888888889 mps

Step-by-step explanation:

1 kph = 0.27777777777778 mps, so just multiply that by 5.

Answer:

x = 2

Step-by-step explanation:

Hello!

Since y varies directly with x what happens to y also happens to x

From y = -12 to y = -4 you divide by 3 so we do that to x

6 / 3 = 2

The answer is 2

Hope this helps!

Answer:

b so  it doesnt tell you how many people come to the hospital a day

Step-by-step explanation:

a--->b--->=c

Answer:

A) A nonresponse occurred

Step-by-step explanation:

We understand that in the span of 10 years, 1000 patients were monitored, and among those were some individuals who had moved. These certain individuals are not responsive anymore, and can not be a source of data, and the poll would be incorrect if the hospital decided to switch out the patients in the midst of the decade. Therefore we are to assume a nonresponse occurred. (To define nonresponse, it is simply a failure to respond, which is indeed what is defined for those who had moved.)

It is not B for the two variables have no correlation, it is not C for all patients were at first patrons and the problem did not explicitly state there was missing info, and D is incorrect for it said the sample group was selected at random. Therefore, with process of elimination, A would still be correct.

Answer:

1.54 and 1.7 I believe

Step-by-step explanation:

Answer:

The full steel tire is 1.76 pounds and the lighter wheel is 1.54 pounds

Step-by-step explanation:

To find how many pounds each tire is, divide the weight in grams by 453.592

Full steel tire:

800/453.592 = 1.76 pounds

Lighter wheel:

700/453.592 = 1.54 pounds

So, the full steel tire is 1.76 pounds and the lighter wheel is 1.54 pounds

Answer:

2.18

Step-by-step explanation:

Answer:

70 km/h

9 hr 22.5 min

Step-by-step explanation:

Given

Difference in time as equation:

Average speed was 70 km/h

Total time = 350/70 + 350/(70+10) = 5 + 4.375 = 9.375 hr = 9 hr 22.5 min

Answer:

12 hours

Step-by-step explanation:

Let x hours be the time it will take you to mow the greens at the golf course.

Since Kim can mow twice as fast, it will take Kim x / 2 hours to mow the greens.

In 1 hour, you will mow 1 / x of the greens

in 1 hour, Kim will mow 1 / (x / 2) of the greens= 2 / x of the greens

In 4 hours, you will mow 4 * 1 / x of the course = 4 / x of the greens

In 4 hours, Kim will mow 4 * 1 / (x / 2) of the course = 4 / (x / 2) = 8 / x of the greens.

Since we are dealing in fraction, the sum of the amount of greens that they would individually mow in 4 hours should be 1. i.e

(4 / x) + (8 / x) = 1

12 / x = 1

Solve for x;

x = 12

Therefore, it will take you 12 hours to mow the greens alone.

=================================================

Work Shown:

b = unknown number

2b = 2 times a number

2b+3 = the sum of 2 times a number and 3

2b+3 = 7, since the expression above is set equal to 7

The equation represents the given algebric phrase is 2b + 3 = 7 and that number will be 2.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

As per the given phrase,

The sum of 2 times a number and 3 equals 7.

2 times b = 2b

The Sum of 2b with 3 equal to 7 will be 2b + 3 = 7

2b = 7 - 3

2b = 4

b = 4/2 = 2

Hence"The equation represents the given algebric phrase is 2b + 3 = 7 and that number will be 2".

For more about the equation,

https://brainly.com/question/10413253

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Answer:8640 square inches

Step-by-step explanation:

Answer:

A model that shows a pitcher holding 8 times the amount of a glass

Step-by-step explanation:

I would need a picture of the models, but I think I can still help.

Any model that shows a pitcher holding 8 times as much as a glass is the correct model. Be sure to read carefully so you pick the right model.

The equation y = 8x shows the relationship between the holding capacity of the pitcher and glass, and x = 64/8 shows the total amount held by the glass.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the pitcher can hold x ounces

And the glass can hold y ounces

From the given problem:

y = 8x

The above equation modeled the relationship between the holding capacity of the pitcher and glass.

If y = 64

Then x = 64/8 = 8 ounces

Thus, the equation y = 8x shows the relationship between the holding capacity of the pitcher and glass, and x = 64/8 shows the total amount held by the glass.

Learn more about the linear equation here:

brainly.com/question/11897796

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Answer:

x≤9

Step-by-step explanation:

x−6≤3

Add 6 to both sides.

x≤3+6

Add 3 and 6 to get 9

x≤9

Answer: x ≤ 9

Step-by-step explanation: When solving an inequality, your goal is the same as it would be if you were solving an equation – to get the variable by itself or isolated on one side of the equals sign.

Since 6 is being subtracted from x, add 6 to both sides of the inequality.

On the left, the -6 +6 cancel out and on the right, 3 + 6 is 9.

So we have x ≤ 9.

=================================================

Work Shown:

We have two sequences, which we'll call A and B

Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.

The terms in bold are what the two sequences have in common.

-----------

It turns out that the bold terms follow an arithmetic sequence of their own.

The sequence {17, 38, 59, ...} is arithmetic.

Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is

C(n) = a+d(n-1)

C(n) = 17+21(n-1)

C(n) = 17+21n-21

C(n) = 21n-4

Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.

-----------

The question is now "what is the largest term in sequence C such that it is less than 500?".

In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.

Use a bit of algebra to get

C(n) < 500

21n - 4 < 500

21n < 500+4

21n < 504

n < 504/21

n < 24

So n must be smaller than 24 to get what we want.

Because n is a natural number (positive whole number), we drop to n = 23 to find that

C(n) = 21n-4

C(23) = 21(23)-4

C(23) = 479

The largest value, less than 500, the two original sequences have in common is 479.

If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.

Answer:

467

Step-by-step explanation:

We have two sequences, which we'll call A and B

A = {2,5,8,11,14, 17 ,20,23,26,29,32,35, 38, 41,44,47,50,53,56, 59 ,62...}

B = {3,10, 17 ,24,31, 38 ,45,52, 59 , 66...}

Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.

The terms in bold are what the two sequences have in common.

-----------

It turns out that the bold terms follow an arithmetic sequence of their own.

The sequence {17, 38, 59, ...} is arithmetic.

Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is

C(n) = a+d(n-1)

C(n) = 17+21(n-1)

C(n) = 17+21n-21

C(n) = 21n-4

Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.

-----------

The question is now "what is the largest term in sequence C such that it is less than 500?".

In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.

Use a bit of algebra to get

C(n) < 500

21n - 4 < 500

21n < 500+4

21n < 504

n < 504/21

n < 24

So n must be smaller than 24 to get what we want.

Because n is a natural number (positive whole number), we drop to n = 23 to find that

C(n) = 21n-4

C(23) = 21(23)-4

C(23) = 479

The largest value, less than 500, the two original sequences have in common is 479.

If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.We have two sequences, which we'll call A and B

A = {2,5,8,11,14, 17 ,20,23,26,29,32,35, 38, 41,44,47,50,53,56, 59 ,62...}

B = {3,10, 17 ,24,31, 38 ,45,52, 59 , 66...}

Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.

The terms in bold are what the two sequences have in common.

-----------

It turns out that the bold terms follow an arithmetic sequence of their own.

The sequence {17, 38, 59, ...} is arithmetic.

Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is

C(n) = a+d(n-1)

C(n) = 17+21(n-1)

C(n) = 17+21n-21

C(n) = 21n-4

Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.

-----------

The question is now "what is the largest term in sequence C such that it is less than 500?".

In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.

Use a bit of algebra to get

C(n) < 500

21n - 4 < 500

21n < 500+4

21n < 504

n < 504/21

n < 24

So n must be smaller than 24 to get what we want.

Because n is a natural number (positive whole number), we drop to n = 23 to find that

C(n) = 21n-4

C(23) = 21(23)-4

C(23) = 479

The largest value, less than 500, the two original sequences have in common is 479.

If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.

Answer:

y = -5, 1

Step-by-step explanation:

2y² - 10y + 44 = (y - 7)²

expand (y - 7)²

(y - 7)² = y² - 14y + 49

move it to the left

(2y² - 10y + 44) - (y² - 14y + 49) = 0

distribute the (-)

2y² - 10 y + 44 - y² + 14y - 49 = 0

combine like terms

y² - 4y -5

factor with factoring X

y² + 5y - y - 5 = 0

factor by grouping ↓

factor out a y from first half of equation

y(y + 5) - y - 5 = 0

factor out a (-) from second half of equation

y(y +5) - (y + 5) = 0

(y +5)(y - 1) = 0

y = -5, 1

Answer:

r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8

Simplified - r = 820

Step-by-step explanation:

I don't know how to explain it exactly, but I know you have to find out how much the carnations, tulips, and irises all cost,subtract that from how much money he has, and divide what left by the cost of the roses (by multiplying the 0.8 cents, because it's a decimal).

r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8

r = (5000 - [1500 + 2400 + 75])0.8

r = (5000 - 3975)0.8

r = 1025(0.8)

r = 820

Answer:

i)-240*a^4*b^3*c^2

ii)-15*x^2*y^2+3*x^3*y^2

iii)x^4*y^3*z^2-x^2*y^3*z^3+x^3*y^2*z^3

iv)p*q+6*q-7*p-42

v)2*x^3-3*x^2-23*x+42

vii)2*x^2-2*y^2+7*x-12*y-15

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{-x^2+2x}[/tex]

Step-by-step explanation:

2 times x subtracted by x².

[tex]\Rightarrow 2 \cdot x-x^2[/tex]

[tex]\Rightarrow 2x-x^2[/tex]

Rearranging the expression.

[tex]\Rightarrow -x^2+2x[/tex]

Answer:

2x -x^2

Step-by-step explanation:

[tex]2(x) - x^2\\= 2x-x^2[/tex]

Answer:

0.00432 km = 4320 mm

Step-by-step explanation:

There are 1000000 millimeters in a kilometer. To convert kilometers to millimeters, multiply the kilometer value by 1000000.

Quick check 0.00432 * 1000000 = 4320 mm

Answer:

4320

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

False, if you get a negitive it would be - square root symbol 9

This is just an example

Step-by-step explanation:

Answer:

[tex]\Large \boxed{k=2x + \frac{-7}{3}} \\ \\ \\ \Large \boxed{x=\frac{1}{2} k+\frac{7}{6}}[/tex]

Step-by-step explanation:

Solving for k:

[tex]\sf 3k+16=9+6x[/tex]

Subtracting 16 from both sides.

[tex]\sf 3k=6x-7[/tex]

Dividing both sides by 3.

[tex]\displaystyle \sf k=2x + \frac{-7}{3}[/tex]

Solving for x:

Flipping the original equation.

[tex]\sf 6x+9=3k+16[/tex]

Subtracting 9 from both sides.

[tex]\sf 6x=3k+7[/tex]

Dividing both sides by 6.

[tex]\sf \displaystyle x=\frac{1}{2} k+\frac{7}{6}[/tex]

Answer:

x = 5.98

Step-by-step explanation:

Step 1: Use tangent to solve for x

tan50.1 = [tex]\frac{x}{5}[/tex]

x = 5tan50.1

x = 5.98

Therefore x is equal to 5.98