find the length of side x in simplest radical form with a rational denominator.
Answers
Answer:
[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
In all 30-60-90 triangles, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle. Since the side opposite to the 30 degree angle is marked as 3, the value of [tex]x[/tex] must be [tex]\boxed{3\sqrt{3}}[/tex].
Alternatively, we can use basic trig. for a right triangle to solve. In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. Thus, we have:
[tex]\tan 60^{\circ}=\frac{x}{3},\\x=3\tan 60^{\circ}=\boxed{3\sqrt{3}}[/tex]
Answer:
Step-by-step explanation:
The tangent of a 60 degree angle = Sin(60) / Cos(60)
Sin(60) = Square root (3) / 2
Cos(60) = 1/2
Tan(60) = √3 / 2 // 1/2 Invert the denominator and multiply
Tan(60) = √3/2 * 2/1
Tan(60) = √3
Tan(theta) = opposite / adjacent
Tan(theta) = x/3 in this case
Tan(60) = √3 = x/3
x = 3*√3
Related Questions
Hellpp and thanks!!
Answers
Answer:
c = 4n
Step-by-step explanation:
Find measure of angles B, E, D and C and the length of BC.
Triangle ABC ~ Triangle DEF. Measure of angle A = 30 degrees and measure of angle F = 65 degrees. AB=20, DE = 35, EF= 28.
Answers
Answer:
< B = 180-30-65=85°
< E = 85°
< D = 30°
< C = 65°
BC = 20/35 × 28 = 16
Answer:
<D = 30
< C = 65
<B = <E = 85
16 = BC
Step-by-step explanation:
ABC ~ Triangle DEF
<A = <D = 30
< C = <F = 65
Since they are similar triangles
A+ C + B = 180 since the angles of a triangle = 180
30+65+B =180
95+ B = 180
<B = 180 -95 = 85
<B = <E = 85
The triangles are similar so the sides are proportional
AB BC
---- = ---------
DE EF
20 BC
---- = ---------
35 28
Using cross products
20*28 = 35 BC
Divide each side by 35
20*28/35 = 35/35 BC
16 = BC
......................
Answers
Answer:
Value of opposite ∠2 = 120°
Step-by-step explanation:
Given question:
Quadrilateral inscribed in a circle
Value of ∠1 = 60°
Find:
Value of opposite ∠2
Computation:
In Quadrilateral inscribed in a circle, sum of opposite angle is 180
So,
Value of ∠1 + Value of ∠2 = 180°
60 + Value of ∠2 = 180
Value of ∠2 = 180 - 60
Value of ∠2 = 120
Value of opposite ∠2 = 120°
(5x-3)=(3x+27) I dont understand
Answers
Answer:
x = 15
Step-by-step explanation:
(5x-3)=(3x+27)
Subtract 3x from each side
(5x-3x-3)=(3x-3x+27)
2x-3 = 27
Add 3 to each side
2x-3+3 = 27+3
2x= 30
Divide by 2
2x/2 = 30/2
x = 15
Consider the function and its inverse.
f(x) = x2 + 4 and f-1(x) = -x - 4
When comparing the functions using the equations, which conclusion can be made?
The domain of f(x) is restricted to x 20, and the domain of f'(x) is restricted to x2 0.
The domain of f(x) is restricted to x 20, and the domain off(x) is restricted to xs 0.
O The domain of f(x) is restricted to x s 0, and the domain off'(x) is restricted to x2 4.
O The domain of f(x) is restricted to x s 0, and the domain off'(x) is restricted to x s 4.
Answers
Step-by-step explanation:
it might be the last one
may it helped u
find out the area and perimeter of circle of radius 7cm
Answers
Answer:
Step-by-step explanation:
radius, r = 7 cm
[tex]Area = \pi r^2 = \pi \times 7^2 = 49 \pi = 153.94 \ cm^2\\\\Perimeter = 2 \pi r = 2 \pi \times 7 = 43.98 \ cm[/tex]
Find the area of the triangle defined by the coordinates (-3,-4), (-7.0), and (-3, 4).
Answers
i think D is the answer 16
The graph of a linear function passes through the
points (2, 11) and (6,21).
Write an equation for the function.
Use the number pad to enter numbers in the boxes.
y me
| x2 +
Answers
Answer:
y = 5/2x + 6
Step-by-step explanation:
Find the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{11-21}{2-6}\\\\m=\frac{-10}{-4}\\\\m=\frac{5}{2}[/tex]
Use point-slope form to find the equation in slope-intercept form:
[tex]y-y_1=m(x-x_1)\\\\y-11=\frac{5}{2} (x-2)\\\\y-11=\frac{5}{2}x-5\\\\y=\frac{5}{2}x+6[/tex]
The equation of the line for the function will be y = 5/2x + 6.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the graph of a linear function passes through points (2, 11) and (6,21).
Slope = ( 21 - 11 ) / ( 6 - 2 )
Slope = 10 / 4
Slope = 5 / 2
The y-intercept will be calculated as:-
y = mx + c
y = ( 5 / 2 )x + c
11 = ( 5 / 2 ) x 2 + c
c = 11 - 5
c = 6
The equation of the line will be:-
y = mx + c
y = (5/2)x + 6
To know more about an equation of the line follow
https://brainly.com/question/18831322
#SPJ2
Answer my this question too uregent
Answers
Answer:
The correct answer is D.
A, B, and C are incorrect. <3
Hope this helps!
- Madeline
The rest wrong
Hope this helped you
Why would the answer be 3.?
Answers
Answer: Cause why not?
Step-by-step explanation:
[tex]3(4x-1)=-2x+19+8x-4[/tex]
First combine like terms:
[tex]3(4x-1)=(-2x+8x)+(19-4)\\\\3(4x-1)=6x+15[/tex]
Now distributive property
[tex](3)(4x)-(3)(1)=6x+15\\12x-3=15+6x[/tex]
Additive Property of Equality
[tex]12x-3+3=15+6x+3\\12x=18+6x[/tex]
Subtractive Property of Equality
[tex]12x-6x=18+6x-6x\\6x=18[/tex]
And finally Division Property of Equality
[tex]\frac{6x}{6} =\frac{18}{6} \\x=3[/tex]
In 24 games, Jamie has 48 scoring attempts. Which unit rate describes Jamie's scoring attempts? A) 1/2 of a scoring attempt per game. B) 2 scoring attempts per game. C) 24 scoring attempts per game. D) 72 scoring attempts per game
Answers
Answer:
The answer is B) 2 scoring attempts per game.
What scale factor, as a percent, was applied to create the copy?
A. 50%
B. 75%
C. 125%
D. 150%
Answers
I’m sorry if it wrong
Have a nice day
A market sells cucumber for 1.20 the cost of each cucumber is the same
Answers
Answer:
Step-by-step explanation:
Let the number of cucumber = x
And the cost of the cucumber = y
Cost of the cucumber will be directly proportional to the number of cucumbers.
y ∝ x
y = kx [Here, k = proportionality constant]
Since, market sells 3 cucumbers for $1.2
1.2 = k(3)
k = 0.4
Therefore, equation for this situation will be,
y = 0.4x
Part A
If x = 1,
y = 0.4(1)
= 0.4
For x = 2,
y = 0.4(2)
= 0.8
For x = 3,
y = 0.4(3)
= 1.2
Number of cucumbers Cost($)
1 0.4
2 0.8
3 1.2
Part B
Equation representing relation between number of cucumbers and the cost will be,
y = 0.40x [Option A]
PLEASE HELP MEEEEEE PLEASE I need HELP. thank you I love you
Answers
Answer:
b
Step-by-step explanation:
<ABC refers just to angle B. Angle B is on the opposite side of 98 therefore we would have to divide it by two. 98 divided by 2 is 49
Peter flips a standard coin twice What is the probability that the coin lands on tails both times?
А. 1/4
B. 2
C. 1
D. 1/2
PLEASE ANSWER FASTTT
Answers
answer:
the answer is going to be ½
Complete the table for the given rule.
Rule:y= 4/1 x+1y
Answers
Answer: 2, 3, 4
Step-by-step explanation:
In the table graph provided, you will a column that has "x" as it's title. Under x, 4, 8, and 12 should listed. You figure out the answers for y by inputting the x value into the rule: y = 1/4x + 1.
For y = 1/4(4) + 1, you would multiply 1/4 by 4 and since the fours eliminate one another, you would get 1. Now, you would do 1 + 1, which equals 2. For y = 1/4(8) + 1, you would multiply 1/4 by 8 and since four and eight share the number four as their greatest common factor, four would be eliminated and eight would be reduced to 2. Now, you would do 2 + 1, which equals 3.For y = 1/4(12) + 1, you would multiply 1/4 by 12 and since four and twelve share the number four as their greatest common factor, four would be eliminated and twelve would be reduced to 3. Now, you would do 3 + 1, which equals 4.
How do you factor the quadratic equation 3x^2 + 8x + 3 to find the roots?
Answers
Answer:
Step-by-step explanation:
Hope this helps u!!
Hope this helps!
The perpendicular of a right angled triangle measures 3m, the area of the triangle 6 sq. m. What are the lengths of the other two sides of the triangle?
Answers
Answer:
the length of the other sides are
4 m and 5 m
Step-by-step explanation:
the area of right triangle = ½× b x h = 6
let b = 3m => h= 2×6/ 3 = 4m
and the hypotenuse = √3²+4²=√25= 5m
Answer:
5m and 4m
Step-by-step explanation:
(area of a right angle triangle)=1/2×b×h
let b = 3m
1/2×6×2=6×2=12/3=4m
and it's hypotenuse= 3
[tex]3 { }^{2} + 4 {}^{2} = \sqrt{25 {}^{2} } [/tex]
= 5m
Which is an equation of a direct proportion?
A: y=16x+6
B: y=6x
C: y=6x−6
D: y=6x
Answers
Answer:
B) y=6x
Step-by-step explanation:
Find the area of the circle.
Answers
Answer:
153.86
Step-by-step explanation:
So first off, what is the formula for finding area of a circle?
Its [tex]\pi r^{2}[/tex]
We know that r(radius), is the distance from one point of the circle to its center.
In this case it is 7.
Note that in other cases, you might see a line going strait through the middle of the circle.
This is the diamater, and is 2x the radius. If you see the diamater, divide it in half, and you will find radius.
Now, back to the problem.
We know our radius is 7, so lets plug that into [tex]\pi r^{2}[/tex]:
[tex]\pi *7^{2}[/tex]
=
[tex]\pi *49[/tex]
=
153.93
So tecnically, this test is wrong. THe actual answer is .07 bigger than what they give.
However, it is the only possible answer, so it is correct.
Answer:
153.86
Hope this helps!
The road leading to the top of a hill has an angle of elevation of 23 degrees. The hill is 120 feet high. What is the length of the road to the top of the hill?
Answers
Answer:
2760
Step-by-step explanation:
23 multiply by 120
=2760
I really need help❤️
Answers
Answer:
about (-3,1.5)
Step-by-step explanation:
Hope this helps!
the mean of three number is 15. if 2 of the numbers are 18 and 16 what is the third number
Answers
Answer:
The third number is 11
Step-by-step explanation:
First, you multiply 15 by 3 to get the sum(45) and then you add 18 and 16 to get 34. Lastly, you will minus 45 and 34 and your answer will be 11.
resuelve la siguiente ecuación polinómica
Answers
Answer:
This question cannot be solved.
Step-by-step explanation:
because they have different
What is the measure of the sides of a square with an area of 49 inches
Someone please answer fast ❤️
Answers
Answer:
7 inches
Step-by-step explanation:
area of square=l^2
49=l^2
[tex]\sqrt{49[/tex]=l
7=l
therefore the sides of a triangle is 7 inches.
Answer:
7
Step-by-step explanation:
So to find this you know a square has 4 equal sides. The area is 49, and area is side length multiplied by side length. So what number multiplied by itself is 49? 7 x 7=49!
What is the value of y?
O A. 36°
O B. 72°
C. 54°
O D. 1080
Answers
sorry but can u show a picture of y?
Answer:
but where is que plz show your que
the choices are
[tex] \frac{4}{25} [/tex]
[tex] - \frac{2}{5} [/tex]
[tex] - \frac{4}{25} [/tex]
[tex] \frac{2}{5} [/tex]
Answers
Answer:
option b) -2/5
Step-by-step explanation:
Using the rule :
[tex]\sqrt[3]{a^3} = (a^3)^{\frac{1}{3}} = a[/tex]
[tex]\sqrt[n]{-x} = - \sqrt[n]{x} , if \ n \ is \ odd[/tex]
[tex]\sqrt[3]{-\frac{8}{125}} = \sqrt[3]{-\frac{2 \times 2 \times 2}{5 \times 5 \times 5}} = -\frac{2}{5}[/tex]
Answer:
[tex]\sqrt[3]{-\frac{8}{125} }[/tex]
[tex]-\sqrt[3]{2^3} /\sqrt[3]{5^3}[/tex][tex]-2/\sqrt[3]{5^3}[/tex][tex]-\frac{2}{5}[/tex]So, your answer is B) - 2/5
-----------------------------
hope it helps...
have a great day!!
explain fully please
Answers
Answer:
whats the question..........
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is of a mile long. On Monday, Selma ran the loop in of an hour. What is Selma's unit rate in miles per hour for Monday's run?
Answers
Answer:
4.5 miles per hour
Step-by-step explanation:
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is 3/4 of a mile long. On Monday, Selma ran the loop in 1/6 of an hour. What is Selma's unit rate in miles per hour for Monday's run?
Distance = 3/4 of a mile
Time taken on Monday = 1/6 of an hour.
What is Selma's unit rate in miles per hour for Monday's run?
Unit rate in miles per hour for Monday's run = distance ÷ time taken
= 3/4 ÷ 1/6
= 3/4 × 6/1
= (3 * 6) / (4 * 1)
= 18/4
= 4.5 miles per hour
Unit rate in miles per hour for Monday's run = 4.5 miles per hour
plzz help me with the correct ans find x
Answers
Answer:
15
Step-by-step explanation:
Since, triangle ABC is the enlargement of triangle XYZ.
[tex] \therefore \triangle ABC \sim \triangle XYZ[/tex]
So, corresponding sides of both the triangles would be in proportion.
[tex] \therefore \frac{x}{6}=\frac{25}{10}[/tex]
[tex] \therefore x= \frac{6\times 25}{10}[/tex]
[tex] \therefore x =\frac{150}{10}[/tex]
[tex] \therefore x = 15[/tex]
