Shortern this expression pls​

Shortern This Expression Pls

Answers

Answer 1

Answer:

[tex]c =\frac{8}{3}[/tex]

Step-by-step explanation:

Given

[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]

Required

Shorten

We have:

[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]

Rationalize

[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}[/tex]

Expand

[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} + \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}[/tex]

[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} + \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}[/tex]

[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} + \sqrt{\frac{(4 - \sqrt 7)^2}{9}[/tex]

Take positive square roots

[tex]c =\frac{4 + \sqrt 7}{3} + \frac{4 - \sqrt 7}{3}[/tex]

Take LCM

[tex]c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}[/tex]

Collect like terms

[tex]c =\frac{4 + 4+ \sqrt 7 - \sqrt 7}{3}[/tex]

[tex]c =\frac{8}{3}[/tex]


Related Questions

Can someone check my answers if they are correct or incorrect? If it is incorrect, please let me know why it is incorrect please.

Answers

This answer is incorrect, try again

answer this now please :)

Answers

9514 1404 393

Answer:

  E.  384 cu ft

Step-by-step explanation:

The sum of length and width is half the perimeter, so the width is ...

  (40/2) -12 = 8 . . . feet

The depth is half that, so is 8/2 = 4 feet.

The volume is ...

  V = LWH = (12 ft)(8 ft)(4 ft) = 384 ft³

Help me please with this question

Answers

9514 1404 393

Answer:

  21

Step-by-step explanation:

Let c represent the number of child tickets sold. Then 2c is the number of adult tickets sold. The total revenue is ...

  5.80c +9.50(2c) = 520.80

  24.80c = 520.80 . . . . . . . . . simplify

  c = 21 . . . . . . . . . . . . . . divide by 24.80

21 child tickets were sold that day.

Slide 1.
1) The polygons below ore similor. Find the value of y.
8.
10

Answers

Answer:

y =6

Step-by-step explanation:

We can write a ratio to solve

3           y

----- = ----------

4            8

Using cross products

3*8 = 4y

24 = 4y

Divide by 4

24/4 = 4y/4

6 = y

Ellicott City Manufacturers, Inc., has sales of $6,344,210, and a gross profit margin of 67.3 percent. What is the firm's cost of goods sold? Round your final answer to the nearest dollar.

Answers

Answer:

$3792116

Step-by-step explanation:

that's the answer above

A couple decide to have 5 children what if the probability that they will have at least one girl

Answers

The chance that they will have one girl is 1:5 because they are having 5 children and one is going to be a girl

Answer:

31/32

Step-by-step explanation:

There are 2^5, or 32 combinations.

There is only 1 combination which is all 5 children are boys.

So the probability that will have at least 1 girl is: 1 - 1/32 = 31/32

lvnununuunkmviodjoifmvujibg ibzf

r

Answers

Answer:

speaking giberish

Step-by-step explanation:

cos it is just a word that is rare

Write the equation of a line in slope intercept form that passes through the two points. (-1,3) and (2,9)

Answers

Answer:

[tex]y = 2x +5[/tex]

Step-by-step explanation:

Finding the Slope:

m = rise/run

[tex]m=\frac{9-3}{2-(-1)}=\frac{6}{3}=\boxed{2}[/tex]

The slope is 2.

Finding the y-intercept:

[tex]y = 2x + b\\\\9 = 2(2) + b\\\\9 = 4 + b\\\\9 - 4 = 4 - 4 + b\\\\\boxed{ 5 = b}[/tex]

The y-intercept is (0,5).

The equation should be: [tex]y = 2x +5[/tex].

Hope this helps.

Answer:

y = 2x+5

Step-by-step explanation:

To find the equation in slope intercept form, we first have to find the slope of the two points.

The formula for finding the slope is:

[tex]\frac{y2-y1}{x2-x1}[/tex]

We are given the points:

(-1, 3) and (2, 9)

x1, y1 and x2, y2.

[tex]\frac{9-3}{2-(-1)}[/tex]

[tex]\frac{6}{3}[/tex] or 2 (the slope).

The slope intercept form is written as:

y= mx + b

y=2x+b

To find b, we can plug in either of the points given. Personally, I like to work with positive numbers. I'll be using the point (2, 9), however, either point will get you to the same answer.

y=2x+b

9=2(2)+b

9=4+b

Now subtract 4 from both sides.

5=b

Which then leaves us with the equation:

y = 2x+5

Please help with this qns

Answers

9514 1404 393

Answer:

  $70

Step-by-step explanation:

Four relationships are given among four unknowns. Define the following variables: p, c -- the cost of a pie and a cake, respectively. q, d -- the number of pies and cakes, respectively.

  q/d = 5/2 . . . . . the ratio of pies to cakes sold

  pq +cd = 3780 . . . . revenue from the sales

  p = c -35 . . . . . a pie is $35 less than a cake

  cd = pq -420 . . . . revenue from cakes is $420 less than for pies

__

The equations are non-linear, so we're making up this process as we go along. We observe that 'pq' and 'cd' are involved in relations that give us their sum and difference, so these products are easily found. Their ratio can let us take advantage of our knowledge of q/d.

Substituting for cd in the second equation, we get ...

  pq +(pq -420) = 3780

  2pq = 4200

  pq = 2100

  cd = 2100 -420 = 1680

Now, we can write ...

  pq/cd = 2100/1680 = 5/4

  (p/c)(q/d) = 5/4 = (p/c)(5/2) . . . . substitute for q/d

  p/c = 1/2 = (c -35)/c . . . . . . . . . . substitute for p

  c = 2(c -35) . . . . multiply by 2c

  c = 70 . . . . . . . . add 70-c

The cost of a cake is $70.

_____

Additional comment

24 cakes were sold at $70 each. 60 pies were sold at $35 each.

A certain freezing process requires that room temperature be lowered from 35oC at the rate of 6oC every hour. What will be the room temperature 8 hours after the process begins?​

Answers

Answer:

-13 degrees celcius.

Step-by-step explanation:

6 degrees are lowered every hour. 6*8 = 48 degrees, 48 degrees are lowered.

35-48 is -13. The room temperature will be -13 eight hours after the process begins.

Can someone please help with 25 , please put the way you got it. Please no links it’s serious

Answers

Answer:

X * 0.8 = $64

x = $80

Step-by-step explanation:

What type of line is PQ?
A. median
B. altitude
C. angle bisector
D. side bisector
I need help with this question to pass a test

Answers

Answer:

Option C, angle bisector

Answered by GAUTHMATH

Which description does NOT guarantee that a quadrilateral is a square?
A. A quadrilateral has all sides congruent and all angles congruent.
B. A quadrilateral is a parallelogram with perpendicular diagonals.
C. A quadrilateral is both a rectangle and a rhombus.
D. A quadrilateral has all right angles and has all sides congruent.

Answers

Answer:

C A quadrilateral is both a rectangle and a rhombus

HELP PLEASE ASAPPPP!!

Answers

Answer:

12

Step-by-step explanation:

(10/y + 13) -3

Let y=5

(10/5 + 13) -3

PEMDAS says parentheses first

(2 +13) -3

15 -3

12

PQRS is a parallelogram of area 18 cm. if PQ = 5 cm & QR = 4 cm. calculate the lengths of corresponding heights ?​

Answers

Answer:

2cm

Step-by-step explanation:

area of parallelogram=b*h=18cm

5*4=20

length of corresponding heights=20-18

=2cm

the length of corresponding height of the parallelogram is : 2cm

Meaning of a parallelogram

A parallelogram can be defined as a simple quadrilateral that is it possesses four sides and two pairs of parallel sides.

A opposite sides of a parallelogram are equal and the opposite angles of a parallelogram are equal.

In conclusion, the length of corresponding height of the parallelogram is : 2cm

Learn more about  parallelogram : https://brainly.com/question/970600

#SPJ2

On his recent free-throw attempts, Lamar made 4 shots and missed 6 shots. Considering this
data, how many of his next 20 free-throw attempts would you expect Lamar to miss?

Answers

Answer:

12 free throw attempts

Step-by-step explanation:

First, find what percent of free throw attempts he misses:

6/10

= 0.6

So, he misses 60% of the time. Multiply 20 by 0.6 to find how many you would expect Lamar to miss out of 20 attempts:

20(0.6)

= 12

So, you would expect Lamar to miss 12 free throw attempts

The smallest positive solution of tan bx = 2 is x = 0.3. Determine the general solution of tan bx = 2.

Answers

The general solution of [tex]\tan bx = 2[/tex] and [tex]x = 0.3[/tex] is [tex]x = 0.095\pi \mp 0.271\pi\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

From Trigonometry we remember that Tangent is a Transcendental Function that is positive both in 1st and 3rd Quadrants and have a periodicity of [tex]\pi[/tex] radians.  The procedure consists in using concepts of Direct and Inverse Trigonometric Functions as well as characteristics related to the behavior of the tangent function in order to derive a General Formula for every value of [tex]x[/tex], measured in radians.

First, we solve the following system of equations for [tex]b[/tex]:

[tex]\tan bx = 2[/tex] (1)

[tex]x = 0.3[/tex] (2)

Please notice that angles are measured in radians.

(2) in (1):

[tex]\tan 0.3b = 2[/tex]

[tex]0.3\cdot b = \tan^{-1} 2[/tex]

[tex]b = \frac{10}{3}\cdot \tan^{-1}2[/tex]

[tex]b\approx 3.690[/tex]

Under the assumption of periodicity, we know that:

[tex]y = \tan bx[/tex]

[tex]b\cdot x \pm \pi\cdot i = \tan^{-1} y[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

[tex]b\cdot x = \tan^{-1}y \mp \pi\cdot i[/tex]

[tex]x = \frac{\tan^{-1}y \mp \pi\cdot i}{b}[/tex]

If we know that [tex]y = 2[/tex] and [tex]b \approx 3.690[/tex], then the general solution of this trigonometric function is:

[tex]x = \frac{0.352\pi \mp \pi\cdot i}{3.690}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

[tex]x = 0.095\pi \mp 0.271\pi\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

The general solution of [tex]\tan bx = 2[/tex] and [tex]x = 0.3[/tex] is [tex]x = 0.095\pi \mp 0.271\pi\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

For further information, you can see the following outcomes from another users:

https://brainly.com/question/3056589

https://brainly.com/question/11526967

What is the sum of the coefficients in the expression of 4x^4 - x^3 - 2x^2 + 3 - 4

Answers

9514 1404 393

Answer:

  0

Step-by-step explanation:

The coefficients are the numerical values that are not exponents. Their sum is ...

  4 -1 -2 +3 -4 = 0

morgan got 17/20 of the questions on a science test correct. what percent of the questions did she get correct?

Answers

Answer:

85%

Step-by-step explanation:

100% = 20

1% = 100%/100 = 20/100 = 0.2

now, how often does 1% fit into the actual result of 17 ? and that tells us how many %.

17/0.2 = 17/ 1/5 = 17/1 / 1/5 = 5×17 / 1 = 5×17 = 85%

Answer:

17/20×100=

85%

=85%

hope this helps

Three different classes contain 20, 18, and 25 students, respectively, and no student is a member of more than one class. If a team is to be composed of one student from each of these three classes, in how many different ways can the members of the team be chosen?

Answers

Answer:

9000

Step-by-step explanation:

20 x 18 x 25

20 options for one member

18 options for another member

25 members for the last member

find the answer for 10 points

Answers

Answer:

52.8

Step-by-step explanation:

(3×2.6×2/2)+(3×5×3)

= 7.8+45

= 52.8

Answered by GAUTHMATH

Probability of picking a blue marble and a yellow marble when 2 marbles are picked (without replacement) from a bag containing 4 blue and 4 yellow marbles

Answers

Answer:

9/49

Step-by-step explanation:

that is the procedure above

Leonard made some muffins. He gave 5/8 of them to his grandmother and 10 muffins to his aunt. He then had 11 muffins left. How many muffins did he have at first? ​

Answers

Answer:

56

Step-by-step explanation:

x = number of muffins in total at the beginning.

x - 5/8 x - 10 = 11

x - 5/8 x = 21

8/8 x - 5/8 x = 21

3/8 x = 21

3x = 168

x = 56


Question 3
A bottle of apple juice has 25 ounces. Find the number of quarts of apple juice in a case of 24 bottles. Give the answer as a decimal.

Answers

Answer:

The number of quarts of apple juice in a case of 24 bottles is 18.75.

Step-by-step explanation:

This question is solved by proportions, using rules of three.

Amount of ounces:

1 bottle - 25 ounces

24 bottles - x ounces

Applying cross multiplication:

[tex]x = 25*24 = 600[/tex]

600 ounces to quarts:

Each ounce has 0.03125 quarts.

1 ounce - 0.03125 quarts

600 ounces - x quarts:

[tex]x = 600*0.03125 = 18.75[/tex]

The number of quarts of apple juice in a case of 24 bottles is 18.75.

Please help me!
14
33
46
60
200

Answers

Answer:

46

Step-by-step explanation:

200/2 = 100, and the x coordinate that line up with the y-coordinate of 100 is 46.

The scatterplot shows the selling prices of homes and the square feet of living space.

A graph titled home value has square feet (thousands) on the x-axis, and price (hundred thousand dollars) on the y-axis. Points are at (1.2, 1), (1.5, 1.1), (2, 1.5), (2.5, 2). An orange point is at (3.8, 3.9).

Complete the statements based on the information provided.

The scatterplot including only the blue data points shows
✔ a strong positive
correlation. Including the orange data point at (3.8, 3.9) in the correlation would
✔ strengthen
and
✔ increase
the value of

Answers

Answer:

✔ a strong positive  

✔ strengthen  

✔ increase

ED2021

Answer:

- a strong positive

- strengthen

- increase

Consider this polynomial, where a is an unknown real number.

correctly/incorrectly
and why

Answers

9514 1404 393

Answer:

incorrectly; used 1 in the division instead of -1incorrectly; evaluated higher powers of -1 incorrectly

Step-by-step explanation:

The result each should have obtained is ...

  a +10 = 17

  a = 7

Braulio's mistake was in using 1 as his divisor instead of -1. His bottom row should have been 1, 4, a-4, 1-a, a +10.

Zahra's mistake was improperly evaluating higher powers of -1. Her evaluation should have been 1 -5 +a +3 +11 = a +10.

Last question guys! Help help help

Answers

9514 1404 393

Answer:

slope 125, annual dues payment

Step-by-step explanation:

The two given points can be used to find the slope:

  m = (y2 -y1)/(x2 -x1)

  m = (650 -400)/(4 -2) = 250/2 = 125

The vertical axis is cost, and the horizontal axis is years, so the slope is the ratio of these: cost per year.

The slope of $125 per year is the yearly membership dues cost.

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18

Answers

At the moment it’s in standard form. We can easily turn this into slope int form (y= mx + b) tho

3y= -18x -18
y= -6x - 6

Rotate the given triangle 90°
counter-clockwise about the
origin [ 0 -3 5]
[0 1 2 ]

Answers

9514 1404 393

Answer:

  [tex]\left[\begin{array}{ccc}0&-1&-2\\0&-3&5\end{array}\right][/tex]

Step-by-step explanation:

The rotation matrix for 90° CCW is ...

  [tex]\left[\begin{array}{cc}0&-1\\1&0\end{array}\right][/tex]

Then the rotated coordinates are ...

  [tex]\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\cdot\left[\begin{array}{ccc}0&-3&5\\0&1&2\end{array}\right]=\left[\begin{array}{ccc}0&-1&-2\\0&-3&5\end{array}\right][/tex]

_____

The transformation of each ordered pair is ...

  (x, y) ⇒ (-y, x)

Answer:

Step-by-step explanation:

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