Answer:
x = 4[tex]\sqrt{3}[/tex] , y = 8[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The ratio of the sides of a 30- 60- 90 triangle are
x : x[tex]\sqrt{3}[/tex] : 2x
From the diagram
x[tex]\sqrt{3}[/tex] = 12 ( divide both sides by [tex]\sqrt{3}[/tex] )
x = [tex]\frac{12}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ( rationalising the denominator )
= [tex]\frac{12\sqrt{3} }{3}[/tex]
x = 4[tex]\sqrt{3}[/tex]
Then
y = 2x = 2 × 4[tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex]
The approximate values of x and y are 4√3 and 8√3, respectively.
Given is a right triangle with base = x and the hypotenuse = y and the perpendicular side is 12, the acute angle between the base and the perpendicular side is 60°.
We need to find the value of x and y,
So, to find the value of x and y, we will use the concept of trigonometric ratios,
So, we know,
Sin = perpendicular / hypotenuse
Cos = base / hypotenuse
Tan = perpendicular / base
Let's denote the acute angle between the base and the perpendicular side as θ.
Angle θ = 60°
Using the sine ratio, we can write:
Sin(60°) = 12 / y
√3/2 = 12 / y
Cross-multiplying, we get:
√3 × y = 2 × 12
√3 × y = 24
y = 24 / √3
y = 8√3
To find the value of x, we can use the cosine ratio.
Cos(60°) = x / y
1/2 = x / 8√3
Cross-multiplying, we get:
2x = 8√3
x = 4√3
Hence, the value of x and y are:
x = 4√3
y = 8√3
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pls help i need to finish this !!
Answer:
a
Step-by-step explanation:
it's non-linear
Step-by-step explanation:
the functions linear because as x increases by 4, y is increasing by 12 at a constant rate
what is a fraction between 1/31 and 1/22?
__________
Step-by-step explanation:
Q = { 1/31 < x < 1/22 }
Q = { 1/30, 1/29, 1/28, 1/27, 1/26, 1/25, 1/24, 1/23 }
#mathisfun
What is the midpoint of the segment shown below?
10
O A. (-1,-1)
(-11, 0)
O B. (-2, -3)
O C. (-1, -3)
- 10
10
(9,-1)
- 10
D. (-2, -1)
Answer:
(-1,-0.5)
Step-by-step explanation:
Find the solution to this problem by using the midpoint formula which is (x1+x2/2,y1+y2/2) plug in the values of y and x to get -11+9/2+0-1/2. simplify to get the solution of (-1,-0.5)
ef is the median of trapezoid abcd (please explain the answer im so confused lol)
Step-by-step explanation:
Okay, so...
The Median of a trapezoid is directly in the middle. For some weird mathimatical reason you won't ever need to know unless it's on an exam or you become a math major, its midsegment is the average of the top length and the bottom length.
In other words,
EF = ( BC + AD ) / 2
So for part 1, we can use that equation to find x.
[tex]EF = ( BC + AD ) / 2[/tex]
Insert known equations.[tex]4x-18=[(x+12)+(3x-4)]/2[/tex]
Simplify within parentheses.[tex]4x-18=[x+12+3x-4]/2[/tex]
[tex]4x-18=[x+3x+12-4]/2[/tex]
Add.[tex]4x-18=[4x+8]/2[/tex]
Divide.[tex]4x-18=2x+4[/tex]
Simplify.[tex](4x-2x) +(-18+18)=(2x-2x)+(4+18)[/tex]
[tex]2x=22[/tex]
Divide both sides by 2.[tex]x=11[/tex]
Part 2 is a lot easier now. All we have to do is plug in 11 for x.
[tex]BC =x+12[/tex]
[tex]BC = 11+12[/tex]
[tex]BC = 23[/tex]
-
[tex]AD = 4x-18[/tex]
[tex]AD = 4(11)-18[/tex]
[tex]AD = 44-18[/tex]
[tex]AD = 26[/tex]
-
[tex]EF = 3x-4[/tex]
[tex]EF = 3(11)-4[/tex]
[tex]EF = 33-4[/tex]
[tex]EF = 29[/tex]
Answer:
Part I: x = 11
Part II:
BC = 23AD = 26EF = 29to use the Pythagorean theorem, we need
a. right triangle with 2 known angles and 1 side
b. right triangle with 2 known angles
c. right triangle with 1 known side and 1 known angle
d. right triangle with 2 known sides
Answer:
sfygyisfislsiyitiyjhjs hjgks6skyk
Step-by-step explanation:
jzsisfyisyistoisisoootsFind the measure of one interior angle for the following regular polygon
What is the measure of
Answer:
try D
Step-by-step explanation:
Which number is rational?
A. -3 1/2
B. sqrt 5
C. Pi
D. 9.23157 ...
Answer:D
Step-by-step explanation:
Solve: 3w + 2 = 20 Write a real world problem that this equation represents.
Step-by-step explanation:
3w + 2 = 20
-2 -2
------------------
3w = 18
---- ----
3 3
w = 6
You and your 2 friends have 20 fruits in total and your friend's mother gave you and your friends two more.
Hope this helped.
Equation – 3w + 2 = 20
Solution :3w + 2 = 20Transpose 2 to the right hand side of the given equation
3w = 20 - 2Now, simplify the right hand side
3w = 18Cross multiply
w = 18/3 w = 6Hence, the solution of the equation is 6
The sum of 2 consecutive integers 117 what are the integers
Answer:
58,59
Step-by-step explanation:
Let x be the first integer
x+1 be the next consecutive integer
x + x+1 = 117
2x+1 = 117
2x +1-1 =117-1
2x = 116
2x/2 = 116/2
x = 58
x+1 = 59
Find the perimeter of the following figure.
Answer:
10 meters
Step-by-step explanation:
Perimeter= 3+3+2+2
=10
Have a nice day:)
what is value of y and x if 3x+2y=2 and 2x+3y=4
We need to form a system of equations:
3x + 2y = 2
2x + 3y = 4
Now, we can multiply the first equation by 2, and the second equation by 3, to even out the coefficients by the variables (to make them the same thing).
6x + 4y = 4
6x + 9y = 12
Next, we can subtract the second equation from the first. We get:
0x - 5y = -8
Then this becomes:
-5y = -8
÷-1 ÷-1
5y = 8
÷5 ÷5
y = 1.6
Substitute 1.6 for y in one of the equations:
2x + 3(1.6) = 4
2x + 4.6 = 4
2x = -0.6
÷2 ÷2
x = -0.3
Answer: [tex]\Large \boldsymbol{(-0,4 \ \ ; \ \ 1,6)}[/tex]
Step-by-step explanation:
[tex]\displaystyle \Large \boldsymbol{} - \left \{ {{3x+2y=2} \ \ |\times3\atop {2x+3y=4}\ \ |\times2} \right. => \\\\\\\ 9x-4x+6y\!\!\!\!\!\!\diagup-6y\!\!\!\!\!\!\diagup=6-8 \\\\5x=-2 \\\\x=-0,4 \ \ ; \ \ y=(2+1,2):2 =1,6[/tex]
What is the domain of the function graphed below?
Answer:
(-2,4] and [7,α)
Step-by-step explanation:
the domain is open at -2 but closed at 4 and also closed at 7 but open till infinity..
The domain of the given function is (-2,4] U [7, ∞), which is the correct option (B).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
f(x) = x²+1 if (-2,0]
This the sub-function define between the interval (-2,0].
f(x) = -1 if (0, 4]
This the sub-function define between the interval (0, 4].
f(x) = -(x-7)² if [7, ∞)
This the sub-function define between the interval [7, ∞).
Thus, the domain of the given function is (-2,4] U [7, ∞).
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lvan earned $8 each time he walks his neighbor's dog. he already walked the dog 5 times.
How many more times does her need to walk the dog to earn enough money to buy a game that costs $88
__? more times
what function equation is represented by the graph?
Answer:
maybe f(x)= -2/3 x + 1 since it goes down two times or up two times and three times to the left or right depending where you wanna go i don't know how to explain but maybe this might help
5. Find the measure of x and and the angle measure.
(3x - 15)
(2x + 7)
Answer:
here's the answer to your question
If you can show the work please its due in 1 hour 15 points and marking brainliest.
Answer:
[tex]a) \: \: 7x[/tex]
[tex]b) \: \: 12 {x}^{2} - 5x[/tex]
[tex]c) \: \: - 3x + 4[/tex]
Step-by-step explanation:
[tex]a) \: \: 4x+7x−3x−x \\ 11x−3x−x \\ 8x−x \\ 7x[/tex]
[tex]b) \: \: 7 {x}^{2} −6x+5 {x}^{2} +x \\ 12 {x}^{2} −6x+x \\ 12 {x}^{2} - 5x[/tex]
[tex]c) \: \: 9−4x−5+x \\ −4x+4+x \\ −3x+4[/tex]
Hope it is helpful....5. PLEASE HELP ME
Write the equation in standard form. Then factor the left side of the equation.
2x2 + 7x = 15
A. (2x – 3)(x + 5) = 0
B. (2x + 3)(x + 5) = 0
C. (2x + 5)(x – 3) = 0
D. (2x – 5)(x + 3) = 0
Answer:
7x=11
Step-by-step explanation:
do it
Find the value of x in the figure.
X= _
Answer:
x=35
Step-by-step explanation:
For a polygon with n sides, the sum of its interior angles is equal to
(n-2) * 180
Here, there are 6 sides, so the sum of this polygon's interior angles is equal to (6-2)* 180 = 720
Therefore, the sum of the interior angles is 720. We can add them up to get
(4x-5) + 117 + (3x-3) + (3x+6) + 118 + 4x-3
= 14x +230 = 720
subtract 230 from both sides to isolate the x and its coefficint
14x = 490
divide both sides by 14 to get x
x=35
Can u help solve this
Answer:
Sure:)! the answer is-487.5
Step-by-step explanation:
1.3x3xr^31.3x3=3.93.9r^3r=55x5x5=1253.9x125=487.5As said in the problem pie=3 as determined in the problem. Hence, the answer is 487.5
Hope this helps :)!
Step-by-step explanation:
[tex]volume = \frac{4}{3} \pi \: {r}^{3} \\ = here\pi = 3 \\ then \: v = \frac{4}{3} \times 3 \times {5}^{3} \\ = 4 \times 125 \\ = 500 {in}^{3} \\ thank \: you[/tex]
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 247 cubic units.
What is the height of the cylinder?
O 2 units
O 4 units
O 6 units
O 8 units
The height of the cylinder is 6 units.
What is cylinder?A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
Given that, the height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24π cubic units.
Volume = π × radius² × height
Let the height of 3x then the radius will be x,
24π = π × x² × 3x
24 = 3x³
x = ∛8
x = 2
Therefore, height = 6
Hence, the height of the cylinder is 6 units.
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2. Given the function f : x -> |x+8|, find the possible values of x when the image is 3.
Answer:
f (x)=11
Step-by-step explanation:
f (x)= x + 8
f (3)= (3 +8)
=f(x) =11
**replace the x with a variable which is 3
The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = x2 + 1 and g(x) = 3x.
Find f − g.
A.
x2 + 3x + 1
B.
x2 + 3x
C.
3x3 + 3x + 1
D.
x2 − 3x + 1
Answer:
D
Step-by-step explanation:
(f-g)(x) = x^2+1-3x= x^2-3x+1
If MN = 5, NO = 13, then LM = (Blank 1). (Round your answer to one decimal place, as necessary.)
Answer:
8.1 = LM
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
13 * 5 = LM^2
65 = LM^2
sqrt(65) = LM
8.06225 = LM
To one decimal place
8.1 = LM
If d= the number of dogs ,which variable expression represents the phase below? The sun of the number of dogs and the 6 cats
Answer:
d + 6
Step-by-step explanation:
Given that :
Number of dogs = d
The sum of the number of the number of dogs and 6 cats is :
This is a straightforward question :
We take the sum of d and 6
Hence, we have
d + 6
Plssssss help!!! On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles, find the total distance traveled in the two days.
The total distance traveled in two days would be 380 miles.
Let's see how we calculate the distance.
Distance is calculated by multiplying speed with time. So,D = S * TS = D ÷ TGiven that,
Speed on first day = 40 mph
Since,
Speed = Distance/Time
∵ 40 = [tex]d_{1}[/tex]/[tex]T_{1}[/tex] ...(i)
Speed on the second day = 60 mph
Distance traveled = [tex]d_{1}[/tex] - 20
Time taken = [tex]T_{1}[/tex] - 2
Since,
Speed = Distance/Time
∵ 60 = ([tex]d_{1}[/tex] - 20)/ ([tex]T_{1}[/tex] - 2) ...(ii)
As we know,
Total distance = [tex]d_{1} + d_{2}[/tex]
= [tex]d_{1}[/tex] + [tex](d_{1} - 20)[/tex]
= 2[tex]d_{1}[/tex] - 20 ...(iii)
From (i), we can deduce that,
[tex]d_{1}[/tex] = 40[tex]T_{1}[/tex]
[tex]T_{1}[/tex] = [tex]d_{1}[/tex]/40
Now, by putting the values of [tex]d_{1}[/tex] and [tex]T_{1}[/tex] in equation (ii), we get
60 = ([tex]d_{1}[/tex] - 20)/ ([tex]T_{1}[/tex] - 2)
⇒ [tex]d_{1}[/tex] - 20 = 60([tex]T_{1}[/tex] - 2)
⇒ [tex]d_{1}[/tex] - 20 = 60[tex]T_{1}[/tex] - 120
⇒ [tex]d_{1}[/tex] - 20 = 60 * (
⇒ [tex]d_{1}[/tex] = 3
⇒ [tex]d_{1}[/tex] - 3
⇒ - [tex]d_{1}[/tex]/2 = -100
∵ [tex]d_{1}[/tex] = 200
By substituting the value of [tex]d_{1}[/tex] in equation (iii),
Total distance = 2[tex]d_{1}[/tex] - 20
= 2(200) - 20
= 400 - 20
= 380 miles
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The center of the circle whose equation is (x + 2)² + (y - 3)² = 25 is (2, -3) (2, 3) (-2, 3)
Step-by-step explanation:
We know that if (h,k) is the center of any circle and whose radius is = r then its equation is :
[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
Given, the equation of circle
[tex] {(x + 2)}^{2} + (y - 3) ^{2} = 25 = {5}^{2} [/tex]
By comparing, we will get,
h = -2
k = 3
So, center of the circle is ( -2,3)
[tex]\large \green{ \: \: \: \: \boxed{\boxed{\begin{array}{cc} \bf\:Mark\\\bf\:me\:as\\\bf brainliest \end{array}}}} \\ [/tex]
Answer:
-2;3
Step-by-step explanation:
we have a formular
(x-a)^2 +(y-b)^2=c
the center of the cirlce is (a;b)
so in this case it's (-2;3)
Consider triangle GHJ in the figure below.
please help :)
Answer:
The picture isnt really showing for me
Step-by-step explanation:
It's either me or the picture.
Step 1: Subtract 3 from both sides of the inequality. Step 2: __________ Step 3: Divide both sides of the inequality by the coefficient of x.
Answer:
Hence the correct answer is Add 8x to both sides of the inequality.
Step-by-step explanation:
Step 1: Subtract 3 from both sides of the inequality.
Step 2: Add 8x to both sides of the inequality.
Step 3: Divide both sides of the inequality by the coefficient of x.
The inequality
5 - 8x < 2x + 3.
sin(2x-pi/2)=sin pi/3