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

Reaner Recycling collected 7/4 tons of aluminum last Saturday. If 7 ton of
aluminum can be shredded each day, how many days will it take to process what
was collected on Saturday?

Answers

Answer:

1/4

Step-by-step explanation:

since 7 tonnes can be shredded per day you need o divide the amount you have by 7

so 7/4 /7 = 1/4

so it will  take 1/4 days

Answer:

[tex] \frac{1}{4} [/tex]

Step-by-step explanation:

Make a ratio

7 : 1

7/4:x

Cross multiple

7x = 7/4

Then make x a subject formula

x =1/4

Your student is struggling with basic addition skills. you can help them by

Answers

You can help by making addition fun with colours and other things to engage the student, you can also spend one on one time with them to help them understand

Answer:

1) focus in the positive

2)keep thing in perspective

3) ask students where there fear is coming

4)help students create a study schedule

5) priotize classroom preparation efforts.

7 days 8 hours 20 minutes
- 4 days 10 hours 30 minutes
2 days 21 hours
50 minutes
3 days 2 hours
10 minutes
7 days 8 hours
20 minutes
J 11 days 8 hours
50 minutes
K none of these

Answers

Answer:

A

Step-by-step explanation:

         1                                          2                                       3  

days hours minutes       days   hours   minutes     days    hours  minutes  

  7        8         20             6       24+8       20              6        31        60+20

  4       10         30

 -

_______________

         4

days     hours    minutes

  6           31           80

  4            10          30

-

____________________

  2             21          50

___________________

A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students were recorded and analyzed. The results are shown in the computer output.




Which of the following represents the standard deviation of the residuals?


1.223

34.55

78.712

124.13

I think it's (B), 34.55

Answers

Answer:

34.55

Step-by-step explanation:

S = 34.55 represents the standard deviation of the residuals which is the correct answer that would be option (B).

What is the standard deviation?

A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.

Students' proficiency in math and English is assessed by a particular standardized test. Ten students were chosen at random, and their math and English test results were recorded and examined.

The computer output displays the outcomes.

Predictor    Coef     SE Coef     t-ratio        p

Constant   -124.13     78.712      0.046

Math           1.223      0.1966      6.220  0.000

S = 34.55     R-Sq = 82.8%      R-Sq (Adj) = 83.5%

In the above ANOVA table, S = 34.55 represents the residual standard deviation.

Therefore, the correct answer is Option B = 34.55.

Option A = 1.223 represents the coefficient of the math score.

Option C = 78.712 represents the Standard Error (S.E).

Option D = 124.13 is the coefficient value.

Hence, the correct answer would be an option (B).

Learn more about the standard deviation here:

https://brainly.com/question/16555520

#SPJ2

Convert 413 in base 5 to base 10

Answers

Answer:

108

Step-by-step explanation:

4×5² + 1×5¹ + 3×5⁰

4×25 + 5+ 3×1

100+5+3

Q4.A/Find the linearization L(x, y) of the function f(x, y) = (x + y + 2)² at p. = (1,2)

Answers

Answer:

Find the linearization L(x,y) of the function at each point. f(x,y) = x2 + y2 + 1 a. (4,0) b. (2,0) a. L(x,y) = Find the linearization L(x,y,z) of the function f(x,y,z) = 1x2 + y2 +z2 at the points (7,0,0), (3,4,0), and (4,4,7). The linearization of f(x,y,z) at (7,0,0) is L(x,y,z)= (Type an exact answer, using radicals as needed.)

Graph y=|x|+5, how does it compare to parent graph y=|x|

Answers

9514 1404 393

Answer:

  it is shifted 5 units upward

Step-by-step explanation:

The y-coordinate is a measure of the distance above the x-axis. When 5 is added to a y-coordinate, the point is shifted 5 units upward.

The function y = |x| +5 adds 5 units to the y-value of every point of the graph of y = |x|. The graph of y=|x|+5 is shifted 5 units upward from the parent graph.

what is the maximum number of students among whom 100 orange ,150 cirtrus, and 250 guavas can be equally distirbuted ? what is the share of each fruits for a student?​

Answers

Answer:

Hello,

Step-by-step explanation:

HCF(100,150,250)=50*HCF(2,3,5)=50*1=50

Part of each fruits for a student:

2 oranges, 3 cirtrus and 5 guavas.

How many 4-digit passcodes can be created if each digit can be any number, 0-9?
6,561
10,000
40
5,040

Answers

Answer:

6,561

that's a good number

0 thru 9 is 10 numbers.

Each digit can be 1 of 10 numbers:

Total combinations = 10 x 10 x 10 x 10 = 10,000

Answer: 10,000

Select all sets in which the number - 15 is an element.
A. natural numbers
B. real numbers
C. irrational numbers
D. rational numbers
E. whole numbers
F. integers

Answers

the answer is A. natural numbers

-15 is an element of-

B. real numbers

D. rational numbers

F. integers

What is a number?

A number is a mathematical object used to count, measure, and label. The original examples are natural number 1,2,3,4 and so forth.

Given number is 15.

A. natural numbers

The natural numbers are the set of all the whole numbers excluding zero. They are positive whole number.

Here, -15 is a negative number,

Hence, -15 is an not element of natural number.

B. real numbers

Real numbers are those numbers that has no imaginary part. It also include both rational and irrational number.

Since -15 has no imaginary part

Hence, -15 is an element of real number.

C. irrational numbers

An irrational number is real number that cannot be expressed as a ratio of two integers.

Here -15 can be expressed as ratio of two integers,

Hence,-15 is not an element of irrational number.

D. rational numbers
A rational number is real number that can be expressed as a ratio of two integers.

Here -15 can be expressed as ratio of two integers,

Hence, -15 is an element of rational number.

E. whole numbers

Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."

Since,Negative numbers are not considered whole numbers

Hence, -15 is not an element of whole number.

F. integers

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043

Hence, -15 is an element of integers.

Hence, we conclude that,

-15 is an element of-

B. real numbers

D. rational numbers

F. integers

More about classification of number :

https://brainly.com/question/14213693

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write your answer in simplest radical form​

Answers

Answer:

n = 8√2

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 60°

Opposite = 4√6

Hypothenus = n =?

The value of n can be obtained by using the sine ratio as illustrated below:

Sine θ = Opposite / Hypothenus

Sine 60 = 4√6 / n

√3/2 = 4√6 / n

Cross multiply

n × √3 = 2 × 4√6

n × √3 = 8√6

Divide both side by √3

n = 8√6 / √3

Rationalise

n = 8√6 / √3 × (√3/√3)

n = 8√(6×3) / 3

n = 8√18 / 3

Recall

√18 = √(9×2) = √9 × √2 = 3√2

Thus,

n = 8√18 / 3

n = 8 × 3√2 / 3

n = 8√2

If the mean of a given dataset is
42 and the standard deviation is
4, where will a majority of the
data lie?

Answers

Answer:

A majority of the data will lie between 38 and 46.

Step-by-step explanation:

It can be said that a majority of the data of a distribution lies within 1 standard deviation of the mean.

In this question:

Mean of 42, standard deviation of 4.

42 - 4 = 38

42 + 4 = 46

A majority of the data will lie between 38 and 46.

If X²+1=2x then what the value of x²?

Answers

Answer:

x² = 2x - 1

Step-by-step explanation:

x² + 1 = 2x

→ Minus 1 from both sides

x² = 2x - 1

x^2 + 1 = 2x

x^2 = 2x - 1

Also value of x = Root(2x -1)

Answered by Gauthmath must click thanks and mark brainliest

Charlotte has to read a book for school. There are 513 pages in the book. She read 113 pages on
Saturday, she read 78 pages on Sunday, and 101 pages on Monday. How many pages does Charlotte
have left to read?




A.221 pages
B.513 pages
C.292 pages
D.400 pages

Answers

the answer is A. 221 pages.

11 divided by 9876



Thank youuuu

Answers

Answer:

770,7272727272727

Step-by-step explanation:

Answer:

8478 divided by 11= 770.7272727

the figure below is made up of a square, a quadrant and a semicircle. the length of the square is 12cm. find the area of the shaded parts.

Answers

Answer:

P=2pi×r

P=2×12pi=24pi

24pi÷4=6pi

6pi÷2=3pi

p=2×6×pi

p=12pi

12pi÷2=6pi

permiter=3pi+6pi+12=40.27

that is for part a

Please help me to find this problem

Answers

9514 1404 393

Answer:

  3. 42.21 in

  4. 4.38 cm

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between an angle in a right triangle and the basic trig functions. The triples of letters stand for ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

where the terms "opposite" and "adjacent" refer to sides of the triangle that are opposite the angle of interest or adjacent to it, respectively.

In these problems, the measure of the hypotenuse is shown, and the problem requests the measure of the side opposite the given angle. The sine function is relevant.

__

3. sin(79°) = GE/GB = GE/(43 in)

   GE = (43 in)sin(79°) ≈ (43 in)(0.981627) ≈ 42.21 in

__

4. sin(26°) = BC/BA = BC/(10 cm)

  BC = (10 cm)sin(26°) ≈ (10 cm)(0.438371) ≈ 4.38 cm

please give me correct answer​

Answers

Answer:

36 = 17+19 ---> They are twin primes and their sum is 36

84 = 41+43 ---> They are twin Primes and sum is 84

120 = 59+61 ---> They also are twin primes and their sum is 120

144 = 71+73 ---> They are also twin primes and the sum is 144

Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 17, reflected across the x-axis, and shifted by 19 units left.
A. g(x) = −17ln (x + 19)
B. g(x) = 17ln (x − 19)
C. g(x) = 17ln (x + 19)
D. g(x) = −17ln (x − 19)

Answers

Answer:

b

Step-by-step explanation:

ANSWER. EXPLANATION. The given logarithmic function is. The transformation,. stretches the graph of y=f(x) vertically by a factor of c units ...

4 votes

ANSWER[tex]y = - 3 ln(x - 7) [/tex]EXPLANATIONThe given logarithmic function is [tex]f(x) = ln(x) [/tex]The transformation, [tex]y = - cf(x - k)[/tex]stretches

Need help please ^-^

Answers

Factored form: (x + 1/5)(x + 1/4)

Foil: x^2 + 1/4x + 1/5x + 1/20

Simplify: x^2 + 9/20x + 1/20

Hope this helps!

Which ratio is equal to 27 : 81?

Answers

3:9 and if you reduce it again, 1:3

Answer:

1:3

Step-by-step explanation:

27 : 81

Divide each side by 27

27/27 : 81/27

1:3

please solve the question ​

Answers

Answer:

[tex]g(-1) = -1[/tex]

[tex]g(0.75) = 0[/tex]

[tex]g(1)= 1[/tex]

Step-by-step explanation:

Given

See attachment

Solving (a): g(-1)

We make use of:

[tex]g(x) = -1[/tex]

Because: [tex]-1 \le x < 0[/tex] is true for x =-1

Hence:

[tex]g(-1) = -1[/tex]

Solving (b): g(0.75)

We make use of:

[tex]g(x) = 0[/tex]

Because: [tex]0 \le x < 1[/tex] is true for x =0.75

Hence:

[tex]g(0.75) = 0[/tex]

Solving (b): g(1)

We make use of:

[tex]g(x) = 1[/tex]

Because: [tex]1 \le x < 2[/tex] is true for x =1

Hence:

[tex]g(1)= 1[/tex]

Solve for x: 10/3 = x/(−5/2)

Answers

9514 1404 393

Answer:

  x = -25/3

Step-by-step explanation:

Multiply by the inverse of the coefficient of x. Reduce the fraction.

  (-5/2)(10/3) = (-5/2)(x/(-5/2))

  -50/6 = x = -25/3

Answer:

-25/3

Step-by-step explanation:

the other person is also correct. khan said so

Which shapes are quadrilaterals?
1. Scalene right triangle
2. Obtuse scalene triangle
3. Isosceles right triangle
4. Hexagon
5. Pentagon
6. Right trapezoid
7. Venn diagram

Answers

Hey there! I'm happy to help!

A quadrilateral is any polygon (enclosed shape) with four sides. Let's see what each of these shapes are.

Scalene right triangle - the prefix tri- means three  (tricycle, tripod, triple, etc.), and all triangles have three sides, so this is not a quadrilateral.Obtuse scalene triangle - once again a triangle, so not a quadrilateral.Isosceles right triangle - would you look at that, another triangle! Not a quadrilateral.Hexagon - a hexagon is a six-sided polygon (hex=six), so this is not a quadrilateral.Pentagon - a pentagon is a five-sided polygon (pent=five, like Pentatonix!). Not a quadrilateralRight trapezoid - a trapezoid is a quadrilateral with at least one pair of parallel sides!Venn diagram - a Venn diagram is a compare and contrast chart made of two overlapping circles (ZERO sides), so this is not a quadrilateral.

So, the only shape on your list that is a quadrilateral is 6. right trapezoid.

Have a wonderful day! :D

The product of the roots of the equation x2 + x=2 is:
0-2
01

Answers

Answer:

-2

Step-by-step explanation:

x^2 + x=2

Subtract 2 from each side

x^2 + x-2=2-2

x^2 + x-2=0

Factor

What 2 numbers multiply to -2 and add to 1

2*-1 = -2

2+-1 =1

(x-1)(x+2)=0

Using the zero product property

x-1 = 0  x+2 = 0

x=1        x = -2

Product of the roots

1*-2 = -2

Write the standard form of the equation of the circle with center (8,−1) that passes through the point (6,7)

Answers

Answer:

(x - 8)^2 + (y + 1)^2 = 68

Step-by-step explanation:

The standard form of the equation of the circle with center (8,−1) is :

(x - 8)^2 + (y + 1)^2 = R^2

If the circle passes through the point (6,7) that means that the point (6,7) is a solution of the equation and we can replace (x,y) with (6,7) to find R.

Which of the following is an example of a producer?
1. tree
2. hawk
3.rabbit
4. mushroom

Answers

Answer:

1. tree

Step-by-step explanation:

Tree as an autotroph can prepare its own food and which animals and humans feed upon, so the tree is a producer

The length of a rectangle is twice its width. If the area of the rectangle is 72in², find its perimeter

Answers

Let breadth be x

Length=2x

[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]

[tex]\\ \sf\longmapsto 72=2x(x)[/tex]

[tex]\\ \sf\longmapsto 2x^2=72[/tex]

[tex]\\ \sf\longmapsto x^2=\dfrac{72}{2}[/tex]

[tex]\\ \sf\longmapsto x^2=36[/tex]

[tex]\\ \sf\longmapsto x=\sqrt{36}[/tex]

[tex]\\ \sf\longmapsto x=6[/tex]

Length=6×2=12inBreadth=6in

[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]

[tex]\\ \sf\longmapsto Perimeter=2(12+6)[/tex]

[tex]\\ \sf\longmapsto Perimeter=2(18)[/tex]

[tex]\\ \sf\longmapsto Perimeter=36in[/tex]

Answer anyone ? Tyia :)

Answers

The correct answer is m<2=80°

I got a negative number as an answer for this sine rule question and I don't know what did I do wrong​

Answers

Answer:

x=14.42192

Step-by-step explanation:

Angle A = 180 - 86 =94

The sum of the angles of a triangle is 180

sin A        sin 46

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

20            x

sin 94 * x = 20 sin 46

x = 20 sin 46 / sin 94

x=14.42192

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