❗️❗️❗️Find the length of side x in simplest radical form with a rational denominator.❗️❗️❗️
Plzzz helppp meeee

Find The Length Of Side X In Simplest Radical Form With A Rational Denominator.Plzzz Helppp Meeee

Answers

Answer 1

Answer:

[tex]x=\frac{\sqrt{14} }{2}[/tex]

Step-by-step explanation:

Notice that you are given an isosceles right-angle triangle to solve, since each of its two acute angles measures [tex]45^o[/tex]. Then such means that the sides opposite to these acute angles (the so called "legs" of this right angle triangle) must also be of the same length (x).

We can then use the Pythagorean theorem that relates the square of the hypotenuse to the addition of the squares of the triangles legs:

[tex](\sqrt{7})^2=x^2+x^2\\7=2\,x^2\\x^2=\frac{7}{2} \\x=+/-\sqrt{\frac{7}{2}} \\x=+/-\frac{\sqrt{14} }{2}[/tex]

We use just the positive root, since we are looking for an actual length. then, the requested side is:

[tex]x=\frac{\sqrt{14} }{2}[/tex]


Related Questions

Length of Triangles.

Answers

Answer:

9

Step-by-step explanation:

Since the scale factor is 12/8 = 1.5, to find LA we have to multiply FI by 1.5 which is 6 * 1.5 = 9.

whats the answers to this ?

Answers

Answer:

Hi there!

The correct answers are: A, B, D, E

Step-by-step explanation:

First of all, perpendicular means when two lines intersect to form a 90° angle.

Second ⊥ means perpendicular.

When something is a bisector it means it evenly slices a line in half.

Please help! The table below shows the elevations of the three animals that Fernanda can see from her boat.

Answers

Answer:

Sea Lion, fish, Bird

Step-by-step explanation:

Find the absolute value of the animals, and then compare them from least to greatest

Question 10 of 32
1 Point
The standard form of the equation of a parabola is
y=1x2 - 4x +21. What is the vertex form of the equation?
O A. y =(x+4)2 +13
O B. y=2(x+4)2 +21
C. y = 2(x-4)2 + 21
D. y = -(x-4)? +13

Answers

i thinhk is C DONT NOW

The answer is c ) y=2(x-4) 2+21

25x^4 +120x^2y +144y^2

Answers

Answer:

We can factor this into (5x+12y)^2

Step-by-step explanation:

Use the end behavior of the graph to solve 3x^3+9x^2-12x < 0

Answers

Answer:

1.  x = 4

2. x = -1

3. x = 0

Answer:

Step-by-step explanation:

Suppose the time it takes a barber to complete a haircuts is uniformly distributed between 8 and 22 minutes, inclusive. Let X = the time, in minutes, it takes a barber to complete a haircut. Then X ~ U (8, 22). Find the probability that a randomly selected barber needs at least 14 minutes to complete the haircut, P(x > 14) (round answer to 4 decimal places) Answer:

Answers

Answer:

[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]

And replacing we got:

[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]

The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714

Step-by-step explanation:

We define the random variable of interest as x " time it takes a barber to complete a haircuts" and we know that the distribution for X is given by:

[tex] X \sim Unif (a= 8, b=22)[/tex]

And for this case we want to find the following probability:

[tex] P(X>14)[/tex]

We can find this probability using the complement rule and the cumulative distribution function given by:

[tex] P(X<x) = \frac{x-a}{b-a} ,a \leq x \leq b[/tex]

Using this formula we got:

[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]

And replacing we got:

[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]

The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714

Two random samples were drawn from two employers to obtain information about hourly wages. Use the following information and the PopMeanDiff template to determine if there is a significant difference in wages across the two employers.

Kroger Wal-Mart
Sample size 80 60
Sample mean $6.75 $6.25
Population standard deviation $1.00 $0.95

The p-value is _____.

a. 0.0026
b. 0.0013
c. 0.0084
d. 0.0042

Answers

Answer:

a) 0.0026

P- value is 0.0026

Step-by-step explanation:

Step(i):-

Given data

first sample size n₁= 80

mean of the first sample  x⁻₁= $6.75

Standard deviation of the first sample   (σ₁) = $1.00

second sample size (n₂) = 60

mean of the second sample( x₂⁻) = $6.25

Standard deviation of the second sample (σ₂) = $0.95

step(ii):-

Test statistic

[tex]Z = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{\frac{(S.D)_{1} ^{2} }{n_{1} } +\frac{(S.D)_{2} ^{2} }{n_{2} } } }[/tex]  

  Null Hypothesis :H₀: There is no significant difference in wages across the two employers.

x⁻₁= x₂⁻

Alternative Hypothesis :H₁: There is significant difference in wages across the two employers.

x⁻₁≠ x₂⁻

[tex]Z = \frac{6.75 -6.25 }{\sqrt{\frac{(1^{2} }{80 } +\frac{((0.95)^{2} }{60} } }[/tex]

Z = 3.01

P- value:-

Given data is two tailed test

The test statistic Z = 3.01

First we have to find the Probability of z-statistic

P(Z>3.01) =  1- P( z <3.01)

                 = 1- (0.5 + A(3.01)

                = 0.5 - A(3.01)

             =    0.5 - 0.49865   ( from normal table)

             = 0.0013

P(Z>3.125) = 0.0013

Given two tailed test

   P- value = 2 × P( Z > 3.01)

                 = 2 × 0.0013

                = 0.0026

Final answer:-

The calculated value Z = 3.125 > 1.96 at 0.05 level of significance

null hypothesis is rejected

Conclusion:-

P- value is 0.0026

               

Find the volume of this cone.
Round to the nearest tenth.
10ft
8ft
[? ] ft

Answers

Answer:

V ≈ 670.2 [tex]ft^3[/tex]

Step-by-step explanation:

Use the formula of the volume of a cone, which is [tex]V=\pi r^{2} \frac{h}{3}[/tex]

Plug in your given components and solve for V:

[tex]V=\pi (8)^2\frac{10}{3} \\V=\pi (64)\frac{10}{3} \\V=\pi (64)(3.33)\\V=\pi (213.33)\\V=670.2[/tex]

The remainder when 2x^2-x-5 divided by (x-3) is​

Answers

Answer:

10

Step-by-step explanation:

2x^2-x-5= 2x^2-6x + 5x -15 +10= 2x(x-3) +5(x-3) + 10= (2x+5)(x-3) + 10

(2x^2-x-5)/(x-3)= 2x+5 + 10/(x-3)

So the remainder is 10​

Rata-rata markah matematik untuk Amin, azman dan aziz adalah 73. Tanda Azman lebih 35 berbanding Amin manakala aziz dua kali ganda daripada Amun. Apakah tanda Amin?

Answers

Answer:

The Amin's score in math was 46.

Step-by-step explanation:

The question is:

The average math score for Amin, azman and aziz is 73. Azman marks 35 more than Amin while aziz is twice that of Amun. What is Amin's sign?

Solution:

Let us denote that:

x = Amin's score in math

y = Azman's score in math

z = Aziz's score in math.

The average of x, y and z is, 73.

That is:

[tex]\frac{x+y+z}{3}=73\\\\\Rightarrow x+y+z = 219[/tex]

Now it is provided that:

[tex]y=x+35...(i)\\z=2x...(ii)[/tex]

Use the equations (i) and (ii) to determine the value of x as follows:

[tex]x+y+z=219\\\\x+x+35+2x=219\\\\4x=184\\\\x=46[/tex]

Thus, the Amin's score in math was 46.

A student is given data that follows a normal distribution. According to the data, the mean amount of time that students spent reading outside of school each month was 10 hours, and the standard deviation was 2 hours. The student creates a normal distribution curve to model the situation and labels the curve so that 34% of the students fall in the range between 10 and 12 hours. Select the information that justifies the student's labeling.

a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.
b. Only 95% of the students will fall in the range of 10-2 and 10+2 hours
c. Only 68% of the students will fall in the range of 10-6 and 10+6 hours
d. Only 95%of the students will fall in the range of 10 -8 and 10 + 8 hours.

Answers

Answer:

a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.

Step-by-step explanation:

He appies the empirical 68-95-99.7 rule, where 68% of the data is expected to be within ne standard deviation from the mean, to the right and to the left.

Half of this (68%/2=34%) will be between the mean and one deviation standard to the right. This is between 10 hours and 10+2=12 hours.

The right answer is:

a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.

The selection of a password of a computer account has the followingrestrictions: The password must be 6, 7, or 8 characters long. A charactercan be lower case letter or a decimal digit. The first character must be alowercase letter. Determine the total number of possible passwords with thegiven restrictions

Answers

Answer:

2,095,636,800,000 possible passwords.

Step-by-step explanation:

There are:

26 lower case characters.

10 decimal digits.

Passwords with 6 characters:

The first character must be a lower case letter, so 26 possible outcomes.

Any of the other 6 - 1 = 5, there are 36 possible options. So

[tex]T_{6} = 26*36^{5} = 1572120576[/tex]

Passwords with 7 characters:

Same logic as above, just the last 6 with 36 possible options. So

[tex]T_{7} = 26*36^{6} = 56596340736[/tex]

Passwords with 8 characters:

7 with 36 possible options

[tex]T_{8} = 26*36^{7} = 2037468300000[/tex]

Total:

[tex]T = T_{6} + T_{7} + T_{8} = 1572120576 + 56596340736 + 2037468300000 = 2095636800000[/tex]

2,095,636,800,000 possible passwords.

Assume that 1700 births are randomly selected and 4 of the births are girls. Use subjective judgment to describe the number of girls as significantly​ high, significantly​ low, or neither significantly low nor significantly high.

Answers

Answer: Significantly low.

Step-by-step explanation:

Ok, we know that out of 1700 randomly selected, only 4 of them are girls.

Then the frequency is:

p = 4/1700

Now, using the subjective judgement (meaning that it is based on the opinion only, there is no real math involved)

I can conclude that the number of girls is significantly low, meaning that out of 1700 births we have 4 girls, then the other 1694 must be boys.

Please heeeelllllllpppppp

Answers

Answer:

point A90°CCW

Step-by-step explanation:

a) All of the arcs show point A is the center of rotation.

__

b) The angle marked at point A is 90°.

__

c) The arrows indicate the direction of rotation is counterclockwise.

Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!

Answers

Hey there! :)

Answer:

a. 3

b. -22

c. -2

d. -2

e. 5a + 8

f. a² + 6a + 3

Step-by-step explanation:

Calculate the answers by substituting the values inside of the parenthesis for 'x':

a. f(1) = 5(1) - 2 = 3

b. f(-4) = 5(-4) - 2  = -22

c. g(-3) = (-3)² + 2(-3) - 5 = 9 - 6 - 5 = -2

d. g(1) = 1² + 2(1) - 5 = 1 + 2 -5 = -2

e. f(a+ 2) = 5(a+2) - 2 = 5a + 10 - 2 = 5a + 8

f. g(a + 2) = (a + 2)² + 2(a + 2) - 5 = a² + 4a + 4 + 2a + 4 - 5 =

a² + 6a + 3

There are 7 times as many female students as male students at a university. What fraction of the university are female

Answers

Let’s give total students a number. Let’s say there are 800 total students

Men = x

Women = 7x. ( 7 times more)

Together there are 8x students.( 7x + x)

We have 8 x = 800

Divide both sides by 8

X = 100

100 men

700 women

Now find the fraction which is number of women / total students = 700/800 = 7/8

7/8 of the students are women.

The process used to collect data will __________ of the study.

affect the validity and the bias

affect only the validity

affect only the bias

not affect the validity and the bias

Answers

Affect only the validity so the second one

The process used to collect data will affect the validity and the bias of the study.

What is validity

The way data is gathered is very important for making sure a study is accurate and doesn't have any unfair influences. Validity means how well the information collected correctly shows the things the study is trying to find out. If the way data is collected is not done correctly, it can cause incorrect or untrustworthy results, making the study less reliable

Bias means when we make mistakes or go away from the correct value or truth. If the way we collect data is biased, it can lead to unfair outcomes or favor certain groups.

Learn more about validity  from

https://brainly.com/question/26251731

#SPJ2

Hoping to increase the chances fo reaching a performance goal, the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are 0.90, 0.80, 0.70 for successfully completing the task in the allotted time. Assuming that the teams work independently, what is the probability that the task will NOT be completed in time

Answers

Answer:

P = 0.006

Step-by-step explanation:

If the first team have a probability of 0.9 to complete the task, we can said that the probability to not complete the task in time is 0.1. It is calculated as:

1 - 0.90 = 0.1

At the same way, the probability to not complete the task for the second and third team are 0.2 and 0.3 respectively and they are calculated as:

1 - 0.80 = 0.2

1 - 0.70 = 0.3

Finally, the the probability that the task will NOT be completed in time is the probability that any of the teams completed the task. So, it is equal to:

P = 0.1 * 0.2 * 0.3 = 0.006

What is the explicit formula for this sequence?
-1, -4, -16, -64, ...

Answers

Answer:

a, ar, ar²,ar³,ar⁴...

Find the equation of the line given
the gradient
Parrallel to the line y= - 2x+4
point ( 1-3)

Answers

Answer:

y = -2x - 1

Step-by-step explanation:

Step 1: Find the parallel line

y = -2x + b

Step 2: Solve for b

-3 = -2(1) + b

-3 = -2 + b

b = -1

Step 3: Write parallel equation

y = -2x - 1

If ABCD is a rectangle, and m∠ADB=55°, what is the value of x?

Answers

Answer:

x= 70

Step-by-step explanation:

Rectangles have four right angles (angles of 90 degrees).

The point of intersection of the diagonals divides each one of them into two equal parts.

Knowing this, we can conclude that:

m\angle c=m\angle b=55\°

Therefore, since the sum of the interior angles of a triangle is 180 degrees, we can find the value of "x":

x+m\angle c+m\angle b=180\°\\x=180\°-55\°-55\°\\x=70\°

Please answer this correctly

Answers

Answer:

14.3%

Step-by-step explanation:

There is only one four out of 7 total numbers.

1/7 = 0.142857 = 14.29%

We are given 7 numbers.

4 is only one card in that 7 card set so, 1/7.

1/7 = 0.1428

0.1428 * 100% = 14.28%

Therefore, the answer is roughly 14.3%

Best of Luck!

An anatomy teacher hypothesizes that the final grades in her class are distributed as 10% A's, 23% B's, 45% C's, 14% D's, and 8% F's. At the end of the semester, she has the following grades.
A 6
B 14
C 22
D 8
E 4
Test her claim at 5% significance level.

Answers

Answer:

At a plus or minus 5%

Her claim is wrong

Step-by-step explanation:

Ok..

Let's calculate the total amount of result first.

6 +14+22+8+4= 54.

Let's take the percentage of each.

For A

6/54= 0.11

11.1%

11.1%*5%= 10.5

For B

14/54

=0.25925

= 25.9%

25.9%*5%= 24.605

For C

22/54

0.4074

40.7%

40.7*5%= 42.73%

For D

8/54

= 0.148

14.8%

14.8%*5% = 14.06%

For E

4/54

= 0.074

= 7.4%

7.4%*5%=7.77%

But she suggested

10% A's, 23% B's, 45% C's, 14% D's, and 8% F's

7. Evaluate 4P2

O

22

O

12

O

14

5

Answers

Answer:

12

Step-by-step explanation:

To evaluate 4P2, we will use the permutation formula as shown;

nPr = [tex]\frac{n!}{(n-r)!}[/tex]

4P2 = [tex]\frac{4!}{(4-2!}[/tex]

[tex]= \frac{4!}{2!} \\= \frac{4*3*2!}{2!}\\ = 4*3\\= 12[/tex]

4P2 = 12

. Draw a unit circle. A unit circle is a circle whose radius is 1 and whose center is located at the origin of a rectangular coordinate system. On this unit circle let θ be the angle measured from the positive x‐axis to the point P = (x, y). Label the angles 0, 6  , 4  , 3  , 2  ,  , 2 3 , 2 and the coordinates of the points on the unit circle that correspond to each of these angles. 2. Plot the point         2 3 , 2 1 . How can you check that the point is on the unit circle? (Hint: recall the equation of the unit circle). Plot the points symmetric to it with respect to the y-axis, to the x-axis, and to the origin. Label the coordinates of the points you found. Find positive angles (expressed in radians) which correspond to the points. 3. Explain how symmetry can be used to find the coordinates of points on the unit circle for angles whose terminal sides are in quadrants II, III, and IV. 4. If   x, y is a point on the unit circle in quadrant I and if 2 3 x  , what is y ? 5. Find two negative and three positive angles, expressed in ra

Answers

Answer:

When drawing a rectangle the point of origin is P = xy and the 0 be upon the positive x axis back to P this way we have a rectangle length.

The circle is inscribed in the middle of the rectangle.

Step-by-step explanation:

0,6  as this is 1/6th of circle

9,45 as this is 3/9th of a circle

36, 22.5 as this is 5/10 of a circle

-27, -16.5 as this is   7/10 of a circle

When we join up -27 to 0 with the end line of a rectangle the base, we find it is at point for -16 for y and joined to 6 at y and has formed 10/10 of a circle.

This is not correct but may help as they are in proportion.

PLEASE ANSWER, URGENT!!! In a math exam, Zach, Wendy, and Lee have an average score 91. Wendy, Lee and Chen have an average score 89. Zach and Chen have an average score 95. What is Zach's score?

Answers

Answer:

98

Step-by-step explanation:

Z as Zach; W as Wendy; L as Lee; C as Chen

We know that average score of Z,W, and L is 91, so:

(z + w + l)/3 = 91

z + w + l = 273

Average score W, L, C = 89, so:

(w + l + c)/3 = 89

w + l + c = 267

We take both:

(z + w + l) – (w + l + c) = 273 – 267

z – c = 6

Average score Z and C = 95

(z + c)/2 = 95

z + c = 190

(z + c) – (z – c) = 184

2c = 184

c = 92

z + c = 190

z + 92 = 190

z = 98

So, Zachs score is 98

Write an equation in standard form for a line that passes through (2, 2) and (0, -3).

Answers

Answer:

y=(5/2)x-3

Step-by-step explanation:

slope of the line=(y2-y1)/(x2-x1)=(-3-2)/(0-2)=5/2

use any point to get the line:

y-(-3)=(5/2)(x-0)

y=(5/2)x-3

Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. 2 4 6 8 10 12 14 amount of sugar (mg) 60 80 100 120 140 160 180 200 Frequency What is the sample size for this data set

Answers

Answer:

The sample size for the data set = 56

Step-by-step explanation:

The sample size or number of individuals (n) is gotten from a histogram by summing up the total frequencies of occurrences.

In this example, the frequencies are: 2 4 6 8 10 12 14

Therefore, the sample size (n) is calculated as follows:

n = 2 + 4 + 6 + 8 + 10 + 12 + 14 = 56

Therefore the sample size for the data set = 56

The sample size for the data set = 56

Given that,

Data was collected for a sample of organic snacks.

The calculation is as follows:

= 2 + 4 + 6 + 8 + 10 + 12 + 14

= 56

Learn more: https://brainly.com/question/15622851?referrer=searchResults

Simplify ^36 - ^16 =

Answers

Answer:

[tex]x^{36}-x^{16}[/tex] is already at its simplest form

Step-by-step explanation:

You cannot factor or GCF anything out of it, and you cannot just subtract exponents. Therefore, it is simplified already.

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