The diagonal of an isosceles trapezoid with angle to the base is equal to 30. Find the length of the height of the trapezoid if it is known that the midline of this trapezoid is equal to 8 cm.

Answers

Answer 1

Answer:

4.62 cm to nearest hundredth.

Step-by-step explanation:

If the parallel sides are x and y then:

x + y = 2*8 = 16

x + y = 16

If we drop a perpendicular line from one of the upper points on the trapezoid we have the height.  Let the upper point be C and the point on the base be A. Let the point on right of the base be B.

AC is the height of the trapezoid.  AB is the baseline of the triangle CAB.

In triangle CAB the angle B is 30 degrees.

As this is a 30-60-90 degree triangle

AC/AB = 1/√3 so AC = AB/ √3.

As the trapezoid is isosceles:

AB = x + 0.5(y - x)

AB = 0.5x + 0.5y

So AC = 1 /√3 (0.5x + 0.5y)

           = 1 /√3 (0.5x + 0.5(16 - x))   (Substituting for x)

            = 1 /√3 (0.5x + 8 - 0.5x)

             =8 / √3    

.              = 4.6188 cm


Related Questions

Which expression is NOT equivalent to the others?
14^2 x 12^2 x 12^1
14^2 x 12^3
14 x 14 x 12 x 12 x 12
14^1 x 14^1x 12^2 + 12^1

Answers

The last one is different . The last one is adding the 12s

Jake has $120 to spend for a party. Juice costs $8. Pizza costs $12. Write the standard equ.
how much juice and pizza Jake can buy?

Answers

Answer:

$8x + $12y = $120

Step-by-step explanation:

x = amount of juice

y = amount of pizza

$120 = his total money

Help me plzzzzzzzzzzzzz

Answers

Answer: It is D

Step-by-step explanation:

Amy was scheduled for 12 intervals this week. One her first interval, she had a technical issue that prevented her from working for 15 minutes. This issue was reported to a diagnosed by Arise Technical Support, in which they issued an individual Waiver. Amy also looked at her schedule wrong, and computer missed three intervals in a row. What was her CA%

Answers

Based on the total of intervals vs the number of intervals Amy attended her CA percentage is 75%

What is the CA percentage?

The CA percentage measures the commitment of an employee to be logged in during the intervals that were assigned to him/her to work.

In this way, the CA percentage is equal to 100% if the employee worked as scheduled. Moreover, this percentage can be affected by factors such as:

Technical issues.Human errors.

In the case of Amy, there is a total of 12 intervals and it is known:

She had a technical issue that prevented her from working, but this was reported so it is unlikely this is considered in her CA.She missed three intervals because she looked at her schedule wrong.

Based on this information, let's calculate her CA:

12 intervals = 100%9 intervals =  x

x = 9 x 100 / 12x = 900 / 12x = 75%

Learn more about percentage in: https://brainly.com/question/8011401

Need help

Every week a company provides fruit for its office employees. They can choose from among five kinds of fruit. What is the probability distribution for the 30 pieces of fruit, in the order listed?

Answers

Answer:

it is A bacause the fractions for that one are correct

Step-by-step explanation:

Find the area and perimeter of a square whose side length is
2x+3

Answers

Answer:

Area = 4x^2 + 12x + 9

Perimeter = 8x + 12

Step-by-step explanation:

answer pls having problem in this

Answers

[tex]\dfrac{\sqrt[3]{343}}{\sqrt[3]{-343}}=\dfrac{\sqrt[3]{343}}{-\sqrt[3]{343}}=-1[/tex]

Write the percent as fraction or mixed number in simplest form 34%

Answers

Answer: 34/100

Step-by-step explanation:

it is 34% out of 100, so it is 34/100. Reduced is 17/50

If x + 2 and x - 3 are factors of the following polynomial, then find the values of a and b. F(x) = x^2 + ax^2- 7x + b

Answers

[tex]\text{Given that,}\\\\f(x) = x^3+ax^2-7x+b \\\\\text{Since}~ (x+2)~ \text{and}~ (x-3)~ \text{are factors of f(x),}\\\\f(-2) = 0 ~ \text{and}~ f(3)=0\\\\\\ \text{Now,}\\\\f(-2)=0\\\\\ \implies (-2)^3+a(-2)^2-7(-2)+b =0\\\\\implies -8 +4a +14+b =0\\\\\implies 4a +b +6 =0~~~....(i)\\\\\\f(3) = 0\\\\\implies 3^3+a(3^2) -7(3) +b =0\\\\\implies 27 +9a -21 +b =0\\\\\implies 9a +b +6 =0~~....(ii)\\\\\\(ii)-(i):\\\\9a+b+6 - 4a-b - 6 = 0\\\\\implies 5a =0\\\\\implies a = 0\\[/tex]

[tex]\text{Substitute a=0 in equation (i):}\\\\4(0) +b +6 =0\\\\\implies b+6 =0\\\\\implies b =-6\\\\\text{Hence, a = 0 and}~ b =-6[/tex]

30=2y+16 simplify your answer as much as possible

Answers

Answer:

y=7

Step-by-step explanation:

please help
meeeeeeeeeeeeeeee

Answers

Answer:

C 43

Step-by-step explanation:

happy holidays

Answer:

Since the two triangles are similar, the two medians AC and FH are in proportion. The proportionality rate is [tex]k=\frac{48}8=6[/tex]. That is the same ratio of the sides., so AD is k times the corresponding side FG, or [tex]\overline {AD} = k\overline{FG} = 6\times 9 = 63[/tex]

The age melat five times older than the age of hana.In ten years time the ratio of the age of hana to melat is 5:9. find the present age of hana and melat?

Answers

Answer:

carbon take x(1)+4(-2)=0

x(1)-8=0

x(1)=8

x=8

comparing freezers

Maria compares two freezers.

Freezer A is 8 feet long, 4 feet wide, and 2 feet high.

Freezer B is 6 feet long, 4 feet wide, and 3 feet high.

correctly complete the statement : Freezer _ has _ more cubic feet than Freezer _ .

Answers

Answer:

Freezer B has 8 more cubic feet than Freezer A.

Step-by-step explanation:

Volume of Freezer A = 8 * 4 * 2 = 64 ft^3.

Volume of Freezer B = 6 * 4 * 3 = 72 ft^3.

72 - 64 = 8 ft^3.

Answer:

Freezer B has 8 more cubic feet than Freezer A.

Step-by-step explanation:

find the value of x {0<x<(π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 ​

Answers

In attachment I have answered this problem.

The value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 ​is x = π/4.

Since cos x /(cosec x + 1) + cos x /(cosec x - 1) = 2 ​

Taking the L.C.M (cosecx + 1)(cosecx - 1), we have

[cosx(cosecx - 1) + cosx(cosecx + 1)]/(cosecx + 1)(cosecx - 1) = 2

[cosxcosecx - cosx + cosxcosecx + cosx]/(cosec²x - 1²) = 2

[cosx/sinx - cosx + cosx/sinx + cosx]/(cosec²x - 1²) = 2

[cotx - cosx + cotx + cosx]/(cosec²x - 1) = 2

collecting like terms, we have

[cotx + cotx + cosx - cosx ]/(cosec²x - 1) = 2

[2cotx + 0]/(cosec²x - 1) = 2

2cotx/(cosec²x - 1) = 2

cotx/(cosec²x - 1) = 1

Since cot²x + 1 = cosec²x ⇒ cot²x = cosec²x - 1

So, cotx/(cosec²x - 1) = 1

cotx/cot²x = 1

1/cotx = 1

tanx = 1

Taking inverse tan of both sides, we have

x = tan⁻¹(1)

x = 45°

x = 45 × π/180

x = π/4

So, the value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 ​is x = π/4.

Learn more about trigonometric equations here:

https://brainly.com/question/24371132

50 POINTS FOR EACH PERSON PLSSSSS HELP!!!!!

∫[tex]x^{\frac{3}{2} }[/tex]㏑(x) dx

Answers

Answer:

Look at images below ^^

Step-by-step explanation:

I'm not sure if they are correct, since I'm not there yet. But I hope it's correct.

What percent of 111 is 94?

Answers

Answer:

I’d say 84.68%

Solve the system of equations -6x-y=-16 and -6x-5y=-8 by combining equations

Answers

Answer:

[tex]\left \{ {{y=-2} \atop {x=3}} \right.[/tex]

Step-by-step explanation:

[tex]\left \{ {{-6x - y = -16} \atop {-6x - 5y = -8}} \right. <=> \left \{ {{4y= -8} \atop {-6x-5y =-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5y=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5*(-2)=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x=-18}} \right. <=> \left \{ {{y=-2} \atop {x=3}} \right.[/tex]

16. Write an equation for the line that is parallel to the given line and passes through the given
(1 point)
point
y = 3x+7; (2, 10)

A. Y=3x + 11

B. y = 3x + 4

C. y=-3x+4

D. y=(-1/3)x+ 4

Answers

Answer:

Step-by-step explanation:

Parallel lines have identical slopes

y = 3x + b

add in the desired point

10 = 3(2) + b

b = 4

B.  y = 3x + 4

Please answer the file question.

Answers

WT is 63 units long. Work on paper.

Answer:

WT = 63

Step-by-step explanation:

Given Δ SDE is similar to Δ SWT then the ratio of corresponding sides are in proportion, that is

[tex]\frac{WT}{DE}[/tex] = [tex]\frac{ST}{SE}[/tex] , substitute values

[tex]\frac{5x+3}{56}[/tex] = [tex]\frac{4x-3}{40}[/tex] ( cross- multiply )

56(4x - 3) = 40(5x + 3) ← distribute parenthesis on both sides

224x - 168 = 200x + 120 ( subtract 200x from both sides )

24x - 168 = 120 ( add 168 to both sides )

24x = 288 ( divide both sides by 24 )

x = 12

Then

WT = 5x + 3 = 5(12) + 3 = 60 + 3 = 63

Which of the following equations has only one solution? A. x^2 -8 x + 16 = 0 B. x(x - 1) = 8 C. x^2 = 16

Answers

[tex]\\\\\\x^2 -8x +16 = 0\\\\\implies x^2 - 2(4) + 4^2 =0\\\\\implies (x-4)^2 =0\\\\\implies x -4 =0\\\\\implies x =4\\\\\text{This equation has only one solution.}[/tex]

What is the GCF of 9y and 12y?

Answers

The greatest common factor is 3y.

9 - 1,3,9
12 -1,3,4,12

There is a y in both terms.

So, 3y is the greatest common factor.

The data table represents the distance between a well-known lighthouse and a cruise ship over time. The cruise ship is travelling at uniform speed. Which equation represents the distance (y) from the lighthouse, based on the number of hours (x)? Number of Hours Distance from Lighthouse (in oceanic miles) 2 53 4 95.5 6 138 8 180.5 10 223 12 265.5 14 308 16 350.5 A. y = 42.5x + 10.5 B. y = 10.5x + 32 C. y = 21.25x + 10.5 D. y = 12.25x + 28.5 E. y = 12.5x + 10.5

Answers

Answer:

ddd

Step-by-step explanation:

PrOblem 1: Find the slope of the line containing the points: (3,-5) and (-1, -2)
Problem 2: Find the x and y intercepts of the line: 2x – 3y = 12
Problem 3: Graph the line x-4y=8

Answers

Answer:

1) -3/4

2) (6, 0), (0, -4)

3) connect (0,-2) and (8,0) together

Step-by-step explanation:

1) (-2) - (-5) / (-1) - 3 = -3/4

2) x = 0 -3y=12 y = -4, y= 0 2x =  12 x = 6, x intercept = (6, 0) y intercept = (0, -4)

3) x - 4y = 8 this could be written as y = x/4 - 2 and y intercept is (0, -2) and x intercept is (8, 0) so connect these points together and make a line

#1

m=y2-y1/x2-x1m=-2+5/-1-3m=3/-4

#2

Inetercept form x/a+y/b=1

2x-3y=122/12x-3/12y=12/12x/6-y/4=1

x inetercept at 6 and y intercect at -4

#3

Graph attached

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)

Answers

Answer:

Try this on for size

Step-by-step explanation:

The set-up cost for a machine that attaches snaps on clothing is $1,100. After set-up,
it costs $0.12 for each snap to be attached. A newer machine has come out that has
a set-up cost of $1,520. With the new machine, it only costs $0.09 for each snap to
be attached. How many snaps would the company have to attach to make the
purchase of the newer machine worthwhile?

Answers

Answer:

14,001

Step-by-step explanation:

old machine: 1,100+.12x

new machine: 1,520+.09x

if you plug in 14,000 for x, you get

old machine: 2,780

new machine: 2,780

therefore, you need 1 over 14,000 for it to be worth it because

if you plug in 14,001 for x, you get

old machine: 2,780.12

new machine: 2,780.09

which makes the new machine $.03 cheaper at this point (and the more snaps attached, the more the new machine will be worth it)

hope this helps!

Which equation best matches the scenario below?

The total cost t is proportional to the number n of items purchased at a constant price of $4.

A) 4t = n
B) t = 4n
C) t = n ÷ 4
D) 4t = 4n

Answers

Answer:

Definetly t = 4n

A line that includes the point (0, -2) has a slope of 1. What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y=1x-2

Step-by-step explanation:

Well this one is already given

When x=0, it's the y intercept

and it gives the slope, so we got it :D

Answer:

y=x-2

Step-by-step explanation:

y-y1=m(x-x1)

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

y+2=1(x)

y+2=x

y=x-2

x+3x+3y+3z=21
Find the value of X.​

Answers

Answer:

[tex] x = \frac{21 - 3y - 3z}{4} [/tex]

Step-by-step explanation:

Question:-To find value of x

Equation:-x + 3x + 3y + 3z = 21

Solution:-

=> x + 3x + 3y + 3z = 21

[On adding like terms x and 3x]

=> 4x + 3y + 3z = 21

[On subtracting both sides with 3y]

=> 4x + 3y + 3z - 3y = 21 - 3y

[On Simplification]

=> 4x + 3z = 21 - 3y

[On subtracting both sides with 3z]

=> 4x + 3z - 3z = 21 - 3y - 3z

[On Simplification]

=> 4x = 21 - 3y - 3z

[On dividing both sides with 4]

[tex] = > \frac{4x}{4} = \frac{21 - 3y - 3z}{4} [/tex]

[On Simplification]

[tex] = > x = \frac{21 - 3y - 3z}{4} (ans)[/tex]

Given :

x + 3x + 3y + 3z = 21

To Find :

The value of x

Solution :

[tex]\qquad { \dashrightarrow \: { \sf{x + 3x + 3y + 3z = 21}}}[/tex]

Adding the like terms :

[tex]\qquad { \dashrightarrow \: { \sf{4x + 3y + 3z = 21}}}[/tex]

Transposing 3y to the other side which then becomes negative :

[tex]\qquad { \dashrightarrow \: { \sf{4x + 3z = 21 - 3y}}}[/tex]

Now, Transposing 3z to the other side which then becomes negative :

[tex]\qquad { \dashrightarrow \: { \sf{4x = 21 - 3y - 3z}}}[/tex]

Dividing both sides by 4 :

[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{4x}{4} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]

[tex]\qquad { \dashrightarrow \: { \sf{{x} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]

Therefore, the value of x = 21 – 3y – 3z/4

Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign. HELP MEEE ASAPPPP ILL GIVE BRAINLIEST!!!!!!

Answers

Answer:

y > - x - 4

Step-by-step explanation:

1) Find the equation of the line

2) The equation of the line is y = - x - 4

3) Identify where the graph is shaded

4) It is shaded above and to the right of the line

5) This means that it is more positive/ greater than the unshaded areas

6) Switch the = sign to > to signify the inequality

7) All done!

Step-by-step explanation:

the delimiter line is going through the points (-4, 0) and (0, -4).

the line function

y = mx + b

m is the slope of the line, b is the y-intercept (the y value when x = 0).

the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to another.

so, for the 2 found points :

x changes by +4 (from -4 to 0)

y changes by -4 (from 0 to -4).

the slope m is then

-4/+4 = -1

and the y-intercept is -4 (as explained).

so, the line is

y = -x - 4

and the graphic says that all values greater than our equal to the line values are valid, so

y >= -x - 4

please help tysm ill mark brainliest

Answers

Answer:

use pemdas(order of the operations)and you'll get the answer 27!!

Step-by-step explanation:

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