the figure below is a square . Find the length of side x in simplest radical form with a rational denominator.

The Figure Below Is A Square . Find The Length Of Side X In Simplest Radical Form With A Rational Denominator.

Answers

Answer 1

Answer:

[tex]\sqrt{14}[/tex]

Step-by-step explanation:

In any square with side length [tex]s[/tex], the diagonal of the square is equal to [tex]s\sqrt{2}[/tex]. Since the side length of this square is [tex]\sqrt{7}[/tex], the diagonal is equal to [tex]\sqrt{7}\cdot \sqrt{2}=\boxed{\sqrt{14}}[/tex].

Alternatively, you can form two 45-45-90 triangles with the diagonal of the square. The diagonal acts as the hypotenuse for the both these triangles, and the legs of both triangles are equal to the side length of the square. To find the length of the diagonal, use the Pythagorean Theorem, which states [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle, and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.

In this question, both legs are equal to [tex]\sqrt{7}[/tex], and we're solving for the diagonal, which is the hypotenuse in this case:

[tex]\sqrt{7}^2+\sqrt{7}^2=c^2,\\c^2=14,\\c=\boxed{\sqrt{14}}[/tex]


Related Questions

y(0.5 + 4)
PLEASE HELP!!

Answers

Answer: 8

Step-by-step explanation:

Answer:

4.5y

Step-by-step explanation:

0.5y + 4y

4.5y

if you can bake 14 cupcakes in one hour how long will it take to bake 126 cupcakes?

Answers

Answer:

9 hours

Step-by-step explanation:

126 dived by 14 is 9, so it will take 9 hours to bake 126 cupcakes.

Answer: It will take maybe 9 hours

hope this helps :)

Step-by-step explanation:

PLEASE HELP ME I NEED AN ANSWER ASAP!! <3

(photo included)

Answers

Answer: B.

tan 45=perpendicular/base

1=8/AB

So, AB=8

Since it's a right-angled triangle, BC is a hypotenuse.

BC=√(AC^2+AB^2)

     =r√(8^2+*^2)

     =8 √2

Earth is the third planet from the Sun, with an average distance of
93,000,000 miles. It takes light about 8 minutes to travel from the Sun
to Earth.
Pluto, a dwarf planet, has an average distance of 3.7 X10° miles
from the Sun. How many times farther from the Sun is Pluto than
Earth? How long does it take light to reach Pluto?

Answers

Answer:

The ratio of the distance of Pluto and the earth to the Sun is 40.

Time taken by light to travel from Sun to Pluto is 5.3 hours.

Step-by-step explanation:

Distance between Earth an Sun = 93,000,000 miles

Time from Sun to Earth = 8 minutes

Distance beteen Pluto and Sun = 3.7 x 10^9 miles

The ratio of the distance between Pluto and Sun to the Earth and Sun is

[tex]\frac{3.7\times 10^9}{93000000}\\\\=39.8 =40[/tex]

Now let the time taken by the light to move from Sun to Pluto is t.

[tex]\frac{93000000}{8}=\frac{3.7\times 10^9}{t}\\\\t =318.28 minutes = 5.3 hours[/tex]

It twice the difference of a number and gig add to 4 the result is 22 more than four time the number. Find the number.

PLEASE HELP!!!!!!!!!!!!!!!!!

will mark brainlist​

Answers

Answer:

I have given the answer in the picture!

Step-by-step explanation:

Hey mate my answer is the correct one!

Math question too tough for me, for every math question, i have to ask

Answers

Answer:

I'm pretty sure that the answer is 55.

Sorry if I'm wrong.

The answer should be $55. Explanation if you take $440 you divide it into 8 you get $55. Please tell me if my answer is wrong if correct please mark brainleist

a que taxa mensal devo empregar um capital de r$ 20.000 para que no fim de 10 meses renda 18.000 de juros

Answers

Answer:

Following are the solution to the given question:

Step-by-step explanation:

[tex]\to 18000=2000 \times i \times 10 \\\\\to 18000=200000 \times i\\\\\to i=\frac{18000}{200000}\\\\\to i= \frac{18}{200}\\\\ \to i= \frac{9}{100}\\\\ \to 0.09\\\\[/tex]

Calculating the percentage:

[tex]\to 0.09\times 100=9\%[/tex]

A rectangle I'd formed by placing two identical squares side by side. The area of the rectangle is two centimeters squared. What is the perimeter of one square.

Answers

Answer:

4cm

Step-by-step explanation:

first find the length of one side of the square

let x represent that

making 2x length of the rectangle

area of a rectangle=length x width

2cm²=2x×x

2cm²=2x²

2cm²/2=2x²/2

1cm²=x²

1√cm²=√x²

1cm=x

perimeter of a square=4xside

4x1cm

4cm

What is 10000 - 82583 + 81627 X 2

Answers

Answer:

90,671

Step-by-step explanation:

10,000- 82,583+ (81,627 x 2)

Answer:

-235,837

Step-by-step explanation:

Given :

10000-82583+81627×2

Now,

10000-82583+163254

10000-245837

-235,837

Answer will be -235,837

I need to know the answer pleaseeee

Answers

Answer:

4:49

Step-by-step explanation:

Explain how to use a graph of the function f(c) to find f(3).​

Answers

In the graph locate the point (3,0) and draw a line parrallel to Y-axis passing through (3,0) . Then your line will cut the graph of f(x) at some point, that point's y-coordinate will be your value of f(3).

Find the area of the circle.

452.16 ft2

37.68 ft2

1808.64 ft2

113.04 ft2

Answers

Answer:

113.04^2

Step-by-step explanation:

radius = diameter / 2

=12/2

=6 ft

area of circle = πr^2

=3.14 * 6^2

=3.14 *36

=113.04 ft^2

Answer:

[tex]{ \boxed{ \tt{ formular : { \tt{area}} = \pi {r}^{2}}}} \\ { \green{radius = \frac{diameter}{2} = \frac{12}{2}}} \\ area = \frac{22}{7} \times { (\frac{12}{2} )}^{2} \\ { \boxed{area = 113.04 \: {ft}^{2} }} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]

If a + b = 2 and a - b = -4 what is the value of ab A. 5 B. -5 c.3 D. -3​

Answers

Answer:

D

Step-by-step explanation:

Given the 2 equations

a + b = 2 → (1)

a - b = - 4 → (2)

Add the equations term by term to eliminate b

2a + 0 = - 2

2a = - 2 ( divide both sides by 2 )

a = - 1

Substitute a = - 1 into (1) and solve for b

- 1 + b = 2 ( add 1 to both sides )

b = 3

Then

ab = - 1 × 3 = - 3 → D

Answer:

option d

Step-by-step explanation:

a+b=2. ,. a-b = -4

a= 2-b

substituting values, we get

(2-b) - b = -4

2 -b -b =-4

2 -2b =-4

-2b = -4-2

2b= 6

b =3

a = 2-3

a= -1

ab = 3×-1

ab = -3

Simplify (5np3)3
Question shown as picture

Answers

Answer:

[tex]125 {n}^{3} {p}^{9} [/tex]

Answers the question in the picture

Answers

Answer:

see explanation

Step-by-step explanation:

- 6 would represent a $6 debt

- 6 would represent 6 feet below sea level

Solve the system of equations.
3x + 4y + z = 3
4x + 3y + 32 - 4
5x+67+72-5

Answers

Answer:

First, we write the augmented matrix.

1

1

1

2

3

1

3

2

9

|

8

2

9

[1−1123−13−2−9 | 8−29]

Next, we perform row operations to obtain row-echelon form.

2

R

1

+

R

2

=

R

2

1

1

1

0

5

3

3

2

9

|

8

18

9

3

R

1

+

R

3

=

R

3

1

1

1

0

5

3

0

1

12

|

8

18

15

−2R1+R2=R2→[1−1105−33−2−9|8−189]−3R1+R3=R3→[1−1105−301−12|8−18−15]

The easiest way to obtain a 1 in row 2 of column 1 is to interchange

\displaystyle {R}_{2}

R 2

and

\displaystyle {R}_{3}

R 3

.

Interchange

R

2

and

R

3

1

1

1

8

0

1

12

15

0

5

3

18

InterchangeR2andR3→[1−11801−12−1505−3−18]

Then

5

R

2

+

R

3

=

R

3

1

1

1

0

1

12

0

0

57

|

8

15

57

1

57

R

3

=

R

3

1

1

1

0

1

12

0

0

1

|

8

15

1

−5R2+R3=R3→[1−1101−120057|8−1557]−157R3=R3→[1−1101−12001|8−151]

The last matrix represents the equivalent system.

x

y

+

z

=

8

y

12

z

=

15

z

=

1

x−y+z=8 y−12z=−15 z=1

Using back-substitution, we obtain the solution as

\displaystyle \left(4,-3,1\right)

(4,−3,1)

What's the perimeter of this shape?​

Answers

Answer:

32m

Step-by-step explanation:

7+5+5+4+4+1+3+3=32


Simplify (12^0)(12^6). Write your answer using an exponent. Explain how you found your answer.​

Answers

Step-by-step explanation:

(12^0)(12^6)

1 ×12⁶. (a⁰=1, a is a number)

=12⁶

Nathan dove −4 feet into a pool. Jenny dove deeper into the same pool. Which could represent the depth that Jenny dove?
A −5 feet
B −3 feet
C 2 feet
D 6 feet

Answers

A. -5 feet
This is because when you are diving into a pool the lower the number the deeper into the pool you are going
Since Jenny dove deeper, the only number lower than -4 is -5

Write twelve thousand twelve hundred and twelve in numbers ​

Answers

13,212

Step-by-step explanation:

12000+1200+12

This is such a mind bending question

Goodluck

simplify the following

(2p+1)(2p-1)​

Answers

(2p+1)(2p-1) Simplified is 4p2−1

find the value of x and y, (3x - 2y, 7) = (11, x + y)

Answers

Answer:

Step-by-step explanation:

Given,(3x-2y,7)=(11,x+y)

So,3x-2y=11...............(i)

      7=x+y

   or,x+y=7................(ii)

Now,Multiplying eqn.(ii) by 2,we get,

       2x+2y=14...........(iii)

Adding eqn(i) and eqn(iii),

        3x-2y+2x+2y=11+14

     or,5x=25

     or,x=5

Substituting value of x in eqn(i),

         5+y=7

      or,y=2

Hence,the values of x and y are 5 and 2 respectively.    

Help I’m to lazy to do it

Answers

Bro use school cheats

"4 + 3" is an example of a(n) ___

Answers

Answer:

Additive property of association?

You did not specify what kind of answer you are looking for.

You could just be looking for something like "addition problem" or "polynomials" or anything.

I will edit or comment an answer if this gets editted with a bit more specification. :D

Step-by-step explanation:

I need help please!!

Answers

10 since it is the y axis

Answer:

10  or in coordinate form(0,10)

Step-by-step explanation:

The y intercept is where the line crosses the y axis

The graph crosses the y axis at 10

(0,10)

A graph of f(x)=acos(bx) is shown, where b is a positive constant. Determine the values of a and b.

Answers

Answer:

Option (1)

Step-by-step explanation:

Equation of the given wave function,

f(x) = acos(bx)

Here, a = amplitude of the wave

Period of the wave = [tex]\frac{2\pi }{B}[/tex]

From the graph attached,

Amplitude = [tex]\frac{4-(-4)}{2}[/tex]

                 = [tex]\frac{4+4}{2}[/tex]

                 = 4

Period of the wave = π - 0

                                = π

From the formula of the period,

Period = [tex]\frac{2\pi }{b}[/tex]

[tex]\pi =\frac{2\pi }{b}[/tex]

b = 2

Therefore, a = 4 and b = 2.

Option (1) will be the answer.

A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were rejected at the final inspection and could not be sold. A new process is introduced that is intended to reduce the proportion of rejected screens. After the process has been in place for several months a random sample of 100 screens is selected and inspected. Of the 100 screens 6 are rejected. What are the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected?
A. H0:p=0.12Ha:p<0.12 A
B. H0:p=0.12Ha:p>0.12 B
C. H0:p=0.06Ha:p<0.06 C
D. H0:pˆ=0.06Ha:pˆ>0.06 D
E. H0:pˆ=0.12Ha:pˆ<0.12 E

Answers

Answer: A.

[tex]H_0:p=0.12\\\\H_a:p<0.12[/tex]

Step-by-step explanation:

Null hypothesis[tex](H_0)[/tex] : A statement describing population parameters as per the objective of the study. It usually takes "≤,≥,=" signs.  

Alternative hypothesis [tex](H_a)[/tex]: A statement describing population parameters as per the objective of the study. It usually takes ">, <, ≠" signs.

Let p be the proportion of screens that will be rejected.

12 percent of the screens manufactured using a previous process were rejected at the final inspection.

(i.e. p= 0.12)

Objective of the study = whether the new process reduces the population proportion of screens that will be rejected

i.e. p< 0.12

So, the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected:

[tex]H_0:p=0.12\\\\H_a:p<0.12[/tex]

Which fraction equals the ratio of rise to run between the points (0, 0) and (6, 7)? A. B. C. D.

Answers

Answer:

7 / 6

Step-by-step explanation:

Given the points:

points (0, 0) and (6, 7)

Point 1 : x1 = 0 ; y1 = 0

Point 2 : x2 = 6 ; y2 = 7

The rise = y2 - y1 = 7 - 0 = 7

The run = x2 - x1 = 6 - 0 = 6

Ratio of Rise to Run = Rise / Run = 7 / 6

Please help. I really need to pass this.​

Answers

Answer:

3.75

Step-by-step explanation:

r²+9²=(6+r) ²

r²+81 = 36+12r + r²

81=36+12r

=> 12r = 45

r = 45/12 = 3.75

3.75 is the correct answer because pemdas

Which of the following functions is graphed below?

Answers

Answer:

Answer B - y=[x]+7

Step-by-step explanation:

A normal [x] function has a slope of one, a y intercept of 0, and all the other basic values.

7 changes this.

Looking at the graph, we see that the y intercept is now 7.

How can this be? x was added to by 7.

If it was subtracted, it would be -7, not postive 7.

So the answer is y=[x]+7

Hope this helps!

Answer:

A

Step-by-step explanation:

when we accept X to 0, y should be 7 and when we accept X to 2 or 4 or 6, y should be in order to 9, 11 and 13.

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