Multiply 6−√5 by its conjugate and simplify

Answers

Answer 1

[tex]6 - \sqrt{5} \times \frac{6 + \sqrt{5} }{6 + \sqrt{5} } [/tex]

[tex] \frac{(6 - \sqrt[]{5})(6 + \sqrt{5} ) }{6 + \sqrt{5} } = \frac{36 - 5}{6 + \sqrt{5} } = \frac{31}{6 + \sqrt{5} } [/tex]


Related Questions

what is the derivative and the slop of the tangent line of f(x)=3x+5 at (1,8)

Answers

Step-by-step explanation:

To find the derivative of

3x+5, apply sum rule

[tex] \frac{d}{dx}(3x + 5) = \frac{d}{dx} 3x + \frac{d}{dx} 5[/tex]

The derivative of

[tex] \frac{d}{dx} kx = k[/tex]

And

[tex] \frac{d}{dx} c = 0[/tex]

So we have

[tex] \frac{d}{dx} 3x + 5 = 3[/tex]

So the derivative of the function is 3,

Since linear equations have a constant slope, the slope at any point will be 3.

So the slope of the tangent line is 3.

44. What three-dimensional figure can be made by folding the net?
ASSESSMENT 1
A rectangular pyramid
B. triangular pyramid
C. triangular prism
D. square pyramid

Answers

You forgot to add a picture of the net!

Answer:

Its B square pyramid

Step-by-step explanation:

Because

Find the values of x for which the denominator is equal to zero for 5x+6/x^2+6x+9 . none
x = −3
x = 3
x = −3, x = 3

Answers

The denominator would be x = -3.

Option (A) is correct.

What is the denominator?

A denominator is a bottom number in a fraction. It represents the divisor or the number by which the numerator is being divided.


In this case, the denominator is x^2+6x+9. To find the values of x for which the denominator is equal to zero, we need to set the denominator equal to 0 and solve for x. The equation would be x^2+6x+9=0. By factorizing the denominator we get (x+3)^2=0.

x + 3 = 0

x = -3

Hence, the denominator would be x = -3.

Option (A) is correct.

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Help help help math math help

Answers

Answer:

x = - 4

Step-by-step explanation:

i hope its helped. thank you !

Pls help im struggling :p

Answers

When creating a histogram it is best to create a range for the different variables that are available.

So for the sake of covering all the possible ranges from 1 - 22, let's divide it into 5 categories.

0 - 5        6 - 10   11 - 15   16 - 20   21 - 25

Now that we have set ranges for the different variables, we then find the frequencies.

0 - 5  : 3 

6 - 10 : 2

11 - 15 : 3

16 - 20 : 1

21 - 25 : 3

Now that we have all the values we can then create our histogram.

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Naomi was measuring and cutting yarn in inches for an art project.she cut 9 pieces of the yarn.

Answers

Answer:

i don't know this question but you can just measure it

Which of the following is true for the function y = log3(x)?
It is the inverse of the function y = x3.
It is the inverse of the function y = 3x.
It is the reciprocal of the function y = x3.
It is the reciprocal of the function y = 3x.

Answers

Answer:

B

Step-by-step explanation:

ED

Solve -5(3n + 4) = 40.

Answers

N=-4
Distribute the -5
-15n-20=40
-15n=60
n=-4

A store receives a shipment of boxes of tea. The total mass shipment is 6kg.

-each box has a mass of 0.040 kg.
-boxes of green tea make up 18% of the shipment.

How many boxes of green tea were in the shipment?
A. 7
B. 27
C. 58
D. 108

Answers

Answer: I think that the answer would be b or 27Step-by-step explanation: I did the math problem in my head.

Find the value of the expression 1/2x + 3 if x = 12

Answers

1/2(12) + 3 = 9

Change 1/2 into a decimal, multiply by 12, and then add 3

Step-by-step explanation:

please mark me as brainlest

Explain how using a line plot will help you to collect data

Answers

Answer:

i hope this helps you

Step-by-step explanation:

A line graph is commonly used to display change over time as a series of data points connected by straight line segments on two axes. The line graph therefore helps to determine the relationship between two sets of values, with one data set always being dependent on the other set

and please dont forgets to markas BRAINLIEST answer please

X2 -2x -24=0 is equivalent to

Answer(S):

Answers

Answer:

x= 6, -4

Step-by-step explanation:

x^2 - 2x - 24 = 0

(x-6) (x+4) = 0

x = 6, x= -4

Aidan earned a total of $117 in one week. His babysitting job pays him $15 per hour. His after-school job at a barber shop pays him $9 per hour. He worked a total of 9 hours that week. The system of linear equations represents this situation, where x represents the number of hours Aidan spent babysitting and y represents the number hours he worked at the barber shop.

x + y = 9

15x + 9y = 117

How many hours did Aidan work at each job?

Answers

The hours worked at the babysitting job is 6 hours.

The hours worked at the barber shop is 3 hours.

What are the hours worked at the babysitting job?

Given the two linear equations:

x + y = 9 equation 1

15x + 9y = 117 equation 2

Multiply equation 1 by 9

9x + 9y = 81 equation 3

Subtract equation 3 from 1

36 = 6x

x = 6

What are the hours worked at the barber shop?

Substitute for x in equation 1

6 + y = 9

y = 9 - 6

y = 3 hours

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hello, id like to order3 halves of a cupcake for my family plus some extra for my 2 friends.

Answers

Answer:

They'll each want a quarter of a cupcake.

Step-by-step explanation:

The number of people in the family is 14.

The number of cupcakes ordered is 4.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Number of cakes for the family = 3 (1/2)

Number of friends = 2

Now,

Each person's amount of cake = 1/4

The number of people in the family.

= 3(1/2) ÷ 1/4

= 7/2 x 4

= 14

The total number of cupcakes ordered.

= 2 x 1/4 +3(1/2)

= 1/2 + 3(1/2)

= 1/2 + 7/2

= 8/2

= 4

Thus,

There are 14 people in the family.

The total number of cupcakes ordered is 4.

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The complete question is:

Hello, id like to order3 halves of a cupcake for my family plus some extra for my 2 friends.

They'll each want a quarter of a cupcake.

Let f(x)=3/4x2-1 The function g(x) is a vertical stretch of f(x) by a factor of 8.What is the equation of g(x)?

Answers

Answer:

g(x) = 6x^2-1

Step-by-step explanation:

f(x)=3/4x^2 −1.

A vertical stretch by a factor of 8 you multiply the number with x by the factor:

3/4 x 8 = 6

g(x) = 6x^2-1

CAN SOMEONE PLS ANSWER THIS QUESTION FAST
WILL MARK BRAINLIEST

Answers

Answer:

C. 9 miles/gallon

Step-by-step explanation:

Answer:

Maybe 10? I'm sure though

Step-by-step explanation:

If f(x) = 2x² - 5, f(5) =

Answers

Answer:

45

Step-by-step explanation:

Put in '5' where 'x' is

2 (5)^2 - 5 = 45

What is the equation: [tex]2x^2-5[/tex]

What do we want to find: f(5)

To find f(5), we must plug the value '5'

     ⇒ into the 'x' position

        ⇒ f(x)

So: [tex]f(5) = 2(5^2)-5 = 2 * 25 - 5 = 50 -5 = 45[/tex]

Thus f(5) = 45

Hope that helps!

These numbers are multiples of ________.
6, 18, 24, 36
A) 4
B) 5
C) 6
D) 8

Answers

Answer:

C. 6

Step-by-step explanation:

Multiples refer to the way their numbers are counted from 1 to 100.

These numbers are multiples of 6.

Multiples of 6 are:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, and 72.

Therefore, the correct answer is C. 6.

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

The answer is C.

Step-by-step explanation:

6÷6=1

18÷6=3

24÷6=4

36÷6=6

13, 19, 25, ...
Find the 48th term.

Answers

Answer:

so you should add 6 to 13 in case to find 19, then add 6 to 19 to get to 25.

so the first is 13 and we keep adding 6 to get to the answer. we do it 47 times. so we have 13+ (6) (47) = 295 which is the 48th term.

The 12th term of the arithmetic sequence13, 19, 25,... is 79.

What are arithmetic and geometric sequence?

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, an arithmetic sequence 13, 19, 25,...

The first term a₁ = 13 and the common difference is = (25 - 19) = (19 - 13) = 6.

We know nth term of an arithmetic sequence is aₙ = a₁ + (n - 1).d.

∴ The 12th term of this arithmetic sequence is a₁₂ = a₁ + (12 - 1).d

a₁₂ = 13 + (12 - 1).6.

a₁₂ = 13 + 11.6

a₁₂ = 13 + 66.

a₁₂ = 79.

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The measures of the angles of a triangle are shown in the figure below. Solve for x.

Answers

46 + 72 + (2x + 20) = 180
2x = 180 - 138
2x = 42
x = 21

Step-by-step explanation:

by using formula a+b+c=180

Sally planted 3/8 rows of beans and 1/8 rows of Tyrion’s in a garden. In total how many rows of vegetables did sally plant?

Answers

Answer:

4/8 or 1/2 rows

Step-by-step explanation:

Hope this helps! ^^

As a cold front passed, the temperature dropped steadily
2 degrees each hour. It dropped a total of 10 degrees. How
many hours did it take for the temperature to drop this far?

Answers

Answer:

5

Step-by-step explanation:

because 10 divided by 2 is 5

Solve for b. -36 + 2.5 = 4

Answers

Answer:

False

Step-by-step explanation:

The sides are not equal

I'LL MARK AS THE BRAINLIEST!!!!! a− (10 − a) = 30

Answers

Answer:

a=20

Step-by-step explanation:

a-10+a=30

a+a-10=30

2a-10=30

2a=30+10

2a=40

a=20

What is the area of a pillow that is 12 1/2 inches long and 15 1/2 inches wide?

Answers

Answer:

193.75in or 193 3/4 in.

Step-by-step explanation:

To find the area, multiply the length x width.

12.5 x 15.5 = 193.75in

:)

Answer:

193.75 inch

Step-by-step explanation:

Area= Length ×Width

12.5*15.5

Evaluate the limit

[tex]\lim \limits_{x\to 0} \dfrac{\ln \left(1-\dfrac x4 \right) - (1-x)^{\tfrac 14} +1}{x^2}[/tex]

Answers

Answer:

1/16

Step-by-step explanation:

Place x=0 and you can see [tex]\frac{0}{0}[/tex] indefinitness. So you can apply the l'hosptial rule. Its basic you should

[tex]\lim_{x \to \ 0} \frac{g(x)}{f(x)} = \\[/tex]  [tex]lim_{x \to \ 0} \frac{g'(x)}{f'(x)}[/tex] so apply the derivative

[tex]\frac{\frac{1}{x-4} +\frac{1}{\sqrt[4]{(1-x})^3 } }{2x}[/tex] and replace the x=0 and you'll see same answer [tex]\frac{0}{0}[/tex] re-apply the l'hospital rule and answer

[tex]\frac{\frac{-1}{(x-4)^2} + \frac{3}{16\sqrt[4]{(1-x)^7} } }{2}[/tex] and replace the 0 you can see the answer [tex]\frac{1}{16}[/tex]

A square with diagonals is shown. The distance from one point to the middle point is 3. The length from the center point to another point is 3.
What is the approximate side length of the square?

3.0 units
3.5 units
4.2 units
4.9 units

Answers

Step-by-step explanation:

in a square 2 sides with a diagonal creates a right-angled triangle, with the diagonal being the Hypotenuse (the side opposite of the 90° angle).

the diagonal is 3+3 = 6 units long.

let's call the square side length "s".

then we have via Pythagoras

6² = s² + s² = 2s²

36 = 2s²

18 = s²

s = 4.242640687 ≈ 4.2 units

What are the x-intercepts of this conic section?



no x-intercepts

(0, −3) and (0, 3)

(−5, 0) and (5, 0)

(−3, 0) and (3, 0)

Answers

Answer:

D. (-3, 0) (3, 0)

Step-by-step explanation:

An x-intercept is means when the line/shape crosses the x axis, or when y=0

So in this case, we can see that the shape crosses the x axis when

x = -3 and 3

So to put it in coordinate form (x, y)

It is: (-3, 0) and (3, 0)

(Whenever it crosses the x-axis, the y coordinate will always be 0)

(150 Points If Ur right.) Quadrilateral LMNO is similar to quadrilateral PQRS. Find the measure of side RS. (ROUND PLEASE.)

Answers

Answer: 39.7

Step-by-step explanation:18/55 = 13/x you can get x by solving for it.

what is the intial value of the function f(x)=3{5/4}^x

Answers

Answer:

  3

Step-by-step explanation:

The "initial value" of a function is the value when the independent variable is zero.

  f(0) = 3(5/4)^0 = 3×1 = 3

The initial value of the function is 3.

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