What is the value of angle x rounded to the nearest whole number

What Is The Value Of Angle X Rounded To The Nearest Whole Number

Answers

Answer 1

Answer:

  x ≈ 42°

Step-by-step explanation:

Label the vertices of the quadrilateral shown at the upper left in you diagram A, B, C, and D, starting at the lower left. Label the center point X. Then the red line is CX and the lower two line segments are CD and DA. (A, C, D, and X are not coplanar.)

Angle D of triangle ACD is the interior angle of a regular pentagon, so measures 108°. That means angle ACD measures (180° -108°)/2 = 36°. If we label the midpoint of segment AC point Y, then the length of segment CY is ...

  CY = CD·cos(36°)

Now triangle BCD is an equilateral triangle, so segment CX will have a length corresponding to the altitude of that triangle, CD·√3/2. Shifting our focus to the triangle AXC, we find that angle XCY will satisfy the relation ...

  cos(XCY) = CY/CX = CD·cos(36°)/(CD·√3/2) = (2/)√3·cos(36°)

Angle x is the exterior angle of triangle AXC that is opposite the two equal interior angles XCY and XAY. Hence its value is double that of angle XCY.

  angle x = 2·arccos((2/√3)·cos(36°)) ≈ 2·20.905° ≈ 41.81°

  angle x ≈ 42°

_____

Comment on the angle

The icosahedron is the only Platonic solid with a dihedral angle more than 120°. It is about 138.19°, the supplement to angle x.

Comment on point labels

It may help to label the points in the 3-d version of the figure. Then you can see that segment AC is a line through the interior space of the icosahedron.


Related Questions

simplify 4x2 + 8x - 11x + 6 - 5x2 + 2​

Answers

Answer:

[tex]\boxed{\bold{-5x+8}}[/tex]

Step-by-step explanation:

Combine Similar Elements: [tex]\bold{8x-11x=-3x}[/tex]

[tex]\bold{4\cdot \:2x-3x+6-5\cdot \:2x+2}[/tex]

Multiply: [tex]\bold{4\cdot \:2=8}[/tex]

[tex]\bold{8x-3x+6-10x+2}[/tex]

Group Like Terms

[tex]\bold{8x-3x-10x+6+2}[/tex]

Combine Similar Elements: [tex]\bold{8x-3x-10x=-5x}[/tex]

[tex]\bold{-5x+6+2}[/tex]

Add Numbers: [tex]\bold{6+2=8}[/tex]

[tex]\bold{-5x+8}[/tex]

To simplify the expression, combine like terms resulting in -1[tex]x^2[/tex] - 8x + 8.

To simplify the given algebraic expression, we need to combine like terms. The terms in the expression are: 4[tex]x^2[/tex], 8x, -11x, 6, -5[tex]x^2[/tex], and 2. Combining the [tex]x^2[/tex] terms and the x terms separately, we get:

[tex]4x^2 - 5x^2 = -1x^2[/tex]

8x - 11x - 5x = -8x

Finally, we add the constant terms: 6 + 2 = 8.

Putting it all together, the simplified version of the expression is: -1[tex]x^2[/tex] - 8x + 8.

7.
Cirrus clouds form more than 6,000 meters above Earth. Write an inequality to represent H, the height, in
meters, of cirrus clouds.
Enter your answer in the space provided. Enter only your inequality

Answers

Answer:

h > 6000

Step-by-step explanation:

Let h be the height of the Cirrus clouds in the inequality.

h > 6000

This states that  h  is greater than  6000

HELP ME PLZ
*****************

Answers

think it’s 6.5 hours

52.08 ÷ 3 =
A) 16.18
B) 16.36
C) 17.18
D) 17.36

Answers

Hey there!

52.08 ÷ 3 = 17.36

The correct answer is D

Hope this helps you!

God bless ❤️

xXxGolferGirlxXx

If BC=6.7, CD=6.2, and AD=13.3, find AB to the nearest tenth

Answers

Answer:

14.4

Step-by-step explanation:

AB / BC = AD/CD

AB/6.7 = 13.3 / 6.2

AB = 13.3 * 6.7 / 6.2

AB = 14.4

Answer:

The answer is 14.4 units.(option A)

Step-by-step explanation:

Angles BAC and CAD are equal.

We can solve this by using the proportional relation.

[tex]\frac{AB}{BC} =\frac{AD}{CD}[/tex]

Let AB be = x

So, [tex]\frac{x}{BC} =\frac{AD}{CD}[/tex]

[tex]\frac{x}{6.7} =\frac{13.3}{6.2}[/tex]

[tex]\frac{x}{6.7} =2.145[/tex]

[tex]x=6.7\times2.145[/tex] = 14.37 units

And rounding to nearest tenth, we get 14.4 units.

Which quantity is proportional to 65⁄5? Check all that are true. 13⁄1 260⁄10 195⁄15 130⁄15 130⁄10

Answers

Answer:

[tex]\frac{13}{1}[/tex]

[tex]\frac{195}{15}[/tex]

[tex]\frac{130}{10}[/tex]

Step-by-step explanation:

we have the ratio

[tex]\frac{65}{5}[/tex]

step 1

Divide both sides (numerator and denominator) by 5

[tex]\frac{65/5}{5/5}=\frac{13}{1}[/tex]

therefore

[tex]\frac{13}{1}[/tex] is proportional to [tex]\frac{65}{5}[/tex]

step 2

Multiply both sides (numerator and denominator) by 3

[tex]\frac{65*3}{5*3}=\frac{195}{15}[/tex]

therefore

[tex]\frac{195}{15}[/tex] is proportional to [tex]\frac{65}{5}[/tex]

step 3

Multiply both sides (numerator and denominator) by 2

[tex]\frac{65*2}{5*2}=\frac{130}{10}[/tex]

therefore

[tex]\frac{130}{10}[/tex] is proportional to [tex]\frac{65}{5}[/tex]

Which answer describes the function f(x)=2x^3-x^2

Odd
Even
Neither

Answers

it is neither, it cannot be raised to a power unless it is 0 or 1 :)

The function is neither an odd function nor an even function

The function is given as:

f(x)=2x^3-x^2

Calculate f(-x)

f(-x)= 2(-x)^3 - (-x)^2

f(-x)= -2x^3 - x^2

Calculate -f(x)

-f(x)= -2x^3 + x^2

From the above computation,

f(x), f(-x) and -f(x) are not equal

Hence, the function is neither an odd function nor an even function

Read more about functions at:

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Suppose Y varies directlly With x. If y= 6 when x=2 find x when y= 12

Answers

Answer:

The value of x = 4 when the value of y = 12

Step-by-step explanation:

∵ y α x ⇒ it is direct variation

- It means y increase when x increase

∴ y = kx ⇒ where k is a constant

- To find the value of k we will substitute the values of x

  and y in the equation above

- If y = 6 when x = 2

∴ 6 = k(2) ⇒ divide two sides by 2

∴ k = 3

∴ y = 3x ⇒ equation of variation

- To find the value of x when y = 12

- Substitute the value of y in the equation of variation

∴ 12 = 3x ⇒ divide both sides by 3

∴ x = 4

* The value of x = 4 when the value of y = 12

Answer: x=4

Step-by-step explanation:

By definition, the direct variation eqution has the following form:

[tex]y=kx[/tex]

Where k is the constant.

Therefore, if If [tex]y=6[/tex] when [tex]x=2[/tex], you can calculate k as following:

-Substitute values.

- Solve for k.

Then:

 [tex]6=k(2)\\k=3[/tex]

Then, when [tex]y=12[/tex], you can calculate the value of x as it is shown below:

-Substitute values.

- Solve for x.

Then:

[tex]12=3x\\x=4[/tex]

A park in the shape of a right triangle is surrounded by three streets. The park is 120 feet along Park Street and 95 feet along Water Street. What is the area of the park?

Answers

Area of a triangle

1/2×b×h

=1/2×120×95

=60×95

=5700

Answer

5700 ft.

Answer:

5700 ft

Step-by-step explanation:

What is the volume of this cube?


Enter your answer as a decimal in this box.

Answers

it would be 25.2 hope this helps

What is the following sum? 4(5 sqrt x^2y)+3(5 sqrt x^2y) PLEASE HELP IM TIMED

Answers

Answer: [tex]35\sqrt{x^2y}[/tex]

Step-by-step explanation:

To solve this exercise  you must apply the proccedure shown below:

- Apply multiplication, as following:

[tex]4(5\sqrt{x^2y})+3(5\sqrt{x^2y})=20\sqrt{x^2y}+15\sqrt{x^2y}[/tex]

- As you can see, the index of the radical in the first term is 2 and the index of the radical in the second term is also 2.

- You can observe that the radicands are the same.

- Therefoe, as the index of the first radical is equal to the index of the second radical and the radicands are the same, you can make the addition. Then, you obtain:

[tex]35\sqrt{x^2y}[/tex]

THE ANSWER IS C all the other people are wrong because they don’t even got the answer choices. 7(5sqrt ^2y)

Point O is the center of the circle. What is the value of X?
Answer options: 64, 54, 34, 44.

Answers

Answer:

34°

Step-by-step explanation:

The angle made when a tangent and a radius intersect=90°

Therefore angle OQP =90°

The triangle made by the two radii is isosceles ( base angles are equal) hence angle POQ=180-2(62)

=56°

The right triangle  OPQ can hence be solved as follows

angle POQ=56°

angle OQP=90°

angle x=180-(56+90)=34° as all the interior angles of any triangle add up to 180°

what is the shortest time it takes to collect a container of water

Answers

Around 35-45 minutes, but it depends on the size of the container.

The shortest time it takes to collect a container of water is 45 minutes.

What is Box plot?

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.

We have given the box plot which shows the amount water collect in how many minutes.

The box plot gives the following information

Minimum value = 45

Median = 48

Lower Quartile = 53

Upper Quartile = 56

Maximum = 64

So, the shortest time is given by minimum value which is 45 minutes.

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the functuion of g(x)= 2x-3 is compressed horizontally to form f(x). which of the following could be the equation of f(x) ?

A.f(x)=1/3x-1
B.f(x)=x+12
C.f(x)=-2x+1
D.f(x)=4x-3

Answers

Answer:

Please see attached graph for further understading of the solution.

To easily solve this problem, we can graph each of the functions and compare them to the original one.

g(x)= 2x-3

An horizontal compression implies a greater slope for the line. This means that the graph of f(x), must reach higher values faster.

Based on the image, the answer is option D

Two positive numbers have a sum of 8 and their product is equal to the larger number plus 10

Answers

Answer:

There are 2 sets of numbers that work...

x = 3, y = 5

and

x = 6, y = 2

Step-by-step explanation:

Let x be one number, and let y be the other number.  We have 2 equations...

x + y = 8    (two positive numbers have a sum of 8)

xy = y + 10   (their product is equal to the larger number plus 10)

solve the first equation for y, and substitute that into the second equation...

y = 8 - x

  x(8 - x) = 8 - x + 10

now solve for x...

  8x - x² = 18 - x  

This is a quadratic, so get everything to one side so it's equal to zero...

   -x² + 9x - 18 = 0   (add x and subtract 18 from both sides)

Now solve for x...

     x² - 9x + 18 = 0    (divide both sides by -1)

         (x - 6)(x - 3) = 0    (factor)

so

x - 6 =  0  becomes   x = 6    (add 6 to both sides)

and

x - 3 = 0  becomes x = 3      (add 3 to both sides

If x is 3, then y = 5     (3 + 5 is 8, and 3(5) = 5 + 10, both equations hold up)

If x is 6, then y = 2    (6 + 2 is 8, and 6(2) = 2 + 10, both equation hold up)

   

What is question 3? Please help me

Answers

It would be answer choice (B) :D

Answer:

See below.

Step-by-step explanation:

Problem  A

I have no tool that will draw this easily but I can direct you to do it.

Draw 4 bricks separated by 3 spaces on the top row of bricks. They should be going horizontally. Draw 9 bricks going vertically. They should not touch the bricks in the first row.Draw 4 bricks going horizontally separated by 3 spaces just like the ones drawn in step one.

Problem B

The general formula for the number of  bricks in any pattern (n) is

4n + 1 where n is the pattern number. Try some values.

n =3  

4n + 1

4*3 + 2

13

n = 4 which is the one you just drew

4n + 1

4*4 + 1

16 + 1

17

n = 8

4n + 1

4*8 + 1

32 + 1

33

Problem C

4n + 1 = 49           Formula

4n -1 = 49 - 1         Subtract 1 from both sides

4n = 48                 Divide by 4

4n/4 = 48/4

n = 12                    Answer

Pattern 12 will have 49 bricks

Problem D

The general formula we have been using all along is the answer.

4n + 1

solve by factoring square roots x^2 -49=0​

Answers

Answer:

X=7

Step-by-step explanation:

X = SQRT(49)

X = 7

Best regards

A standard coffee mug has a capacity of 16 fluid ounces. If Anni needs to fill 26 mugs with coffee, how many total quarts of coffee does she need?

Answers

13 quarts of coffee

Answer:

13 quarts

Step-by-step explanation:

1 quart = 32 ounces

mug = 16 ounces = 1/2 quart

26 * 1/2 = 13

Can someone please answer the chart part please?? ASAP!!

Answers

When x=0, that’s the y-intercept. So in this case the y-intercept would be (0,2)

write the equation 4x+y=7 in slope intercept form​

Answers

Final answer:

The equation 4x + y = 7 can be rewritten in slope-intercept form as y = -4x + 7, where -4 is the slope and 7 is the y-intercept. This format makes it easier to graph the line as it directly gives us the slope and y-intercept.

Explanation:

To rewrite the equation 4x + y = 7 in slope-intercept form (y=mx+b), we need to solve for y. This equation can be transformed by subtracting 4x from both sides, resulting in y = -4x + 7. Here, -4 is the slope (m) and 7 is the y-intercept (b).

In comparison, if we look at the given graphic (Figure A1), we see another equation where the slope or 'm' is 3 and the y-intercept 'b' is 9. This slope and y-intercept gives us the equation y = 3x + 9. Thus, it can be seen that y = mx + b format helps to better understand the geometry of a linear equation on a graph, with 'm' indicating the slope and 'b' being the y-intercept.

Learn more about Slope-Intercept Form here:

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Use formula I=prt to solve:

Steve borrowed 450$ for 3 years the yearly interest rate was 13%. How much interest did he owe at the end of 3 years?

Answers

Answer: $175.50

Step-by-step explanation: Since you are given the formula, your next step is to put your information into it.

I = PRT

I = 450 x .13 x 3

Now to solve for it:

I = $175.50

What is the length of the side labeled x cm?

Answers

Answer:

The length of side [tex]x[/tex] is 4.9 cm

Step-by-step explanation:

The first thing we need to do is find the third angle using the angle sum theorem.

The angle sum theorem states that the sum of the interior angles of a triangle is always 180°. A + B + C = 180°

Let's call our missing angle A, so

A + 41° + 62° = 180°

A + 103° = 180°

A = 180° - 103°

A = 77°

Now we can use the rule of sines to find side [tex]x[/tex]:

[tex]\frac{x}{sin(41)} =\frac{14}{sin(77)}[/tex]

[tex]x=\frac{14sin(41)}{sin(77)}[/tex]

[tex]x=9.4[/tex]

We can conclude that the correct answer is 9.4 cm

Rewrite 11/35 and 3/10 so they have common denominator

Answers

Final answer:

To rewrite 11/35 and 3/10 with a common denominator, find the LCD, which is 70 and it will result in 22/70 and 21/70.

Explanation:

To rewrite the fractions 11/35 and 3/10 so they have a common denominator, we need to find the Least Common Denominator (LCD) for both fractions. The denominators are 35 and 10. Prime factorizing 35, we get 5 and 7. Prime factorizing 10, we get 2 and 5.

The LCD for both will therefore be the product of these prime factors taken at the highest power that appears in each, which is 2 * 5 * 7 = 70. To rewrite the fractions, we multiply the numerator and the denominator of each fraction by any factors needed to reach the LCD.

For 11/35 to have 70 as its denominator, we observe that 35 already has the factor 7 and 5, hence it only needs to be multiplied by 2. So, 11/35 = 11 * 2 / 35 * 2 = 22/70.

For 3/10 to have 70 as its denominator, we see that 10 has the factor 2 and 5, so it needs to be multiplied by 7. Therefore, 3/10 = 3 * 7 / 10 * 7 = 21/70.

Now both fractions have the same denominator of 70, which is 22/70 and 21/70 respectively.

What number am I ???

Answers

Answer:

17

Step-by-step explanation:

Since the number has only 2 factors it must be a prime number

A prime number has 2 factors 1 and itself

Since the difference between the factors is 16 then

17 - 1 = 16 and so the number is 17 with factors 1 and 17

Add polynomial expressions

Answers

[tex]12 {g}^{2} + 4g - 1[/tex]

Answer:

[tex]12g^2 + 4g - 1[/tex]

Step-by-step explanation:

Hello!

We can add the two polynomials vertically.

Add[tex]10g^2 + 3g - 10\\\underline{+( 2g^2 + g + 9)}[/tex]

[tex]10g^2 + 3g - 10\\\underline{+( 2g^2 + g + 9)}\\12g^2 + 4g - 1[/tex]

The simplified form is  [tex]12g^2 + 4g - 1[/tex].

orlando has a bag of 37 apples and a bag of 29 apples he can bake 6 apples in a pan how many pans can orlando make. plzzzzzzz i need help now and thx​

Answers

the answer is 11 trays

16 =2/3 f equals what

Answers

Answer:

The answer is f = 24

Step-by-step explanation:

In order to find this, multiply both sides by 3/2

16 = 2/3f

24 = f

f=24


16 = (2/3)*f // - (2/3)*f

16-((2/3)*f) = 0

(-2/3)*f+16 = 0

16-2/3*f = 0 // - 16

-2/3*f = -16 // : -2/3

f = -16/(-2/3)

f = 24

Find the measure of a central angle that intercepts an arc of 3 inches in a circle whose radius is 8 inches.

0.375 rad
1.05 rad
2.3 rad

Answers

Answer:

option (A)

central angle = 0.375 rad

Step-by-step explanation:

Given in the question,

radius of the circle = 8 inches

arc of the circle = 3 inches

To find,

measure of a central angle

Central angles are subtended by an arc between those two points.

Formula to use:

    s = (r) (θ)

where r = radius

           s = arc length

           θ = angle in radians

Plug in the values in the equation

3 = (8) (θ)θ = 3/8 0.375 rad

Answer:

.375 rad

Step-by-step explanation:

Using the equation w=v/r

w=3/8

w=.375

Look at the following math problems. 10 + 2 = 12 12 − 2 = 10 What are these operations called?

Answers

Answer:

i think it might be fact families

Step-by-step explanation:

this is because they use the 3 same #rrs

Answer: Inverse Operations

Step-by-step explanation:

From the years 1988 through 1996 Steffi Graf won the annual U.S open tennis championships five times and Wimbledon seven times what percent or both tournaments combined during those 9 years was Steffi Graf the women’s champion?

Answers

Answer:

66.67%

Step-by-step explanation:

If there is 1 US open tennis championship and 1 Wimbledon per year, there are a total of 9 US open and 9 wimbledon from 1988 to 1998. So in total there are 18 championships.

Steffi Graf won 5 US open and 7 Wimbledons = 12

Essentially we want to know, 12 is what percent of 18? We can solve this by:

[tex]\frac{12}{18}*100=66.67[/tex]

Hence, 66.67% won

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