"Find y". I got this wrong and want to understand why and how to do the problem. Can someone please help?
Answers
Answer:
[tex]y=\frac{15\sqrt{3} }{4}[/tex]
Step-by-step explanation:
Well what you have here are two right triangles within another right triangles created by an altitude. This results in 3 similar triangles (see attached for reference)
As a result , using the properties of similar triangles, and taking ratios of their sides of the medium triangle and the largest triangle, we can form the following relationship:
[tex]\frac{b}{z}=\frac{y}{x} = \frac{z}{a+b}[/tex] (we know that a+b = 15), hence the equation becomes:
[tex]\frac{b}{z}=\frac{y}{x} = \frac{z}{15}[/tex] ----------eq 1
If we consider the largest triangle, we will see that
cos 30° = z / 15
but from our special angles (see second attachment) we know that cos 30° = (√3)/2
hence
(√3)/2 = z / 15
z = (15√3) / 2 --------eq 2
from the same largest triangle, we will also see that
sin 30° = x / 15
similarly from our special angles, we know that sin 30° = 1/2
hence,
1/2 = x/15
x = 15/2 --------eq 3
now that we have values for x and z, we can neglect the first term of equation 1 and form an equality with x, y and z
[tex]\frac{y}{x} = \frac{z}{15}[/tex]
[tex]y = x\frac{z}{15}[/tex] (substituting the values for x and z that we found above)
y = (15/2) · [ (15√3) / 2] / 15
y = (15√3) / 4
[tex]y=\frac{15\sqrt{3} }{4}[/tex]
Related Questions
Help! ASAP!!!
Use the map shown below to find the distance between cities A and B to the nearest tenth.
Answers
Answer:
7.2 units
Step-by-step explanation:
Coordinates of city A = (0, 0)
Coordinates of city B = (6, 4)
Use the distance formula to find the distance between the two cities as follows:
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] A(0, 0) = (x_1, y_1) [/tex]
[tex] B(6, 4) = (x_2, y_2) [/tex]
Plug in the values into the formula
[tex] AB = \sqrt{(6 - 0)^2 + (4 - 0)^2} [/tex]
[tex] AB = \sqrt{(6)^2 + (4)^2} [/tex]
[tex] AB = \sqrt{36 + 16} = \sqrt{52} [/tex]
[tex] AB = 7.2 [/tex] (nearest tenth)
A line passes through point (-6, -1) and is parallel to the equation y2x-5.
What's the equation of the line?
Answers
Answer:
Step-by-step explanation:
Which statements about opposites are true?
Answers
Answer:
The opposite of a negative number is always positive.
Step-by-step explanation:
Answer:
Opposites always have the same absoulute value.
Step-by-step explanation:
^^^^ I don't fully know what type of question you are asking but here is my answer ^^^^
6x + 8 = 62 slove for x
Answers
Answer:
4.428571429
Step-by-step explanation:
You have to do 8+6 then 62 divided by 14 and then thats what your x equals.
Answer:
x=9
Step-by-step explanation:
start with
6x+8=62
subtract 8 from each side
6x=54
divide each side by 6
x=9
PLEASE ANSWER FAST
Find the square root of 16.
O a
-4
Ob
4
Ос
+4
Od
-8
Answers
Answer:
the square root of 16 is 4
Given C=n+15, determine the value of C when n=4
Answers
Answer:
19
Step-by-step explanation:
If N=4 and the problem is C= N+15 that means you add 4 to 15 and then get 19 which will be your answer for C. You can also check this by subtracting 19-15 or 19-4!!! I hope this helps!!! Have a great day whom ever you are
the sum of 3 numbers is 114. the second number is 4 times the third the third number is 6 more than the first
Answers
Answer:
let the three numbers be x,y,z
X= z-6
Y= 4z
Z= z
Step-by-step explanation:
X+Y+Z=114
hence
=z-6+4z+z=114
=collect like times. X= 20-6=14
= z+4z+z=114+6. Y= 20*4=80
=6z=120. . Z= 20
z=20
Answer:
14 + 20 + 80 = 114
Step-by-step explanation:
Let's begin by representing our 1st number as x.
Then our 2nd number is said to be 6 more than the 1st number, which we can represent as x + 6.
Lastly, our 3rd number is said to be 4 times the 2nd number, which we can represent as 4(x + 6).
Now can write our equation to express the sum of these three numbers as 114 and then solve for x to find the values of these three numbers:
x + (x + 6) + 4(x + 6) = 114
x + x + 6 + 4x + 24 = 114
6x + 30 = 114
6x = 114 - 30
6x = 84
x = 84/6 = 14 (1st number)
x + 6 = 14 + 6 = 20 (2nd number)
4(x + 6) = 4(20) = 80 (3rd number)
We can check our answers by adding these numbers up to see if their sum is 114:
14 + 20 + 80 = 114
34 + 80 = 114
114 = 114
Their sum is 114, so we are confident that our three numbers are correct.
-Hope this helps
PLS MARK ME BRAINLIEST
The circumference of a circle is 16Pi ft
Answers
Area of the circle: 64π ft²
Radius of circle: 8 ft
The circumference formula: C = d · π
We can plug in the values we know.
16π = d · π; We can cancel out the π, as it is on both sides.
d = 16ft; r = 8ft
The area formula: A = πr²
A = 64π ft²
A line has a slope of 2 and passes through the point ( -1, 3). Write an equation in slope intercept form
Answers
Answer:
y=2x+5
Step-by-step explanation:
The equation of a line in slope intercept form is written as: y=mx +b where m is the slope and b is the y-intercept.
Taking point (-1,3) , m= 2 and imaginary point on the line, (x,y) then ;
m=change is y-coordinates/change in x-coordinate
m=Δy/Δx
m=y-3/x--1
2= y-3 / x+1
2(x+1) = y-3
2x +2 =y-3
2x=y-3-2
2x=y-5
y=2x+5 is the equation.
Answer:b
Step-by-step explanation:
Which number is equivalent to 4/5?
A. 25
100
B. 0.2
O C.
16
100
D. 0.8
PLEASE HELP ASAP
Answers
Answer:
D) 0.8
Step-by-step explanation:
To get this answer, divid 4 by 5! 4 divided by 5 is equivalent to 0.8!
A 34 inch baseball bat is resting 6 inches from the base of a play house as shown how far up on the Playhouse is a baseball bat resting round to the nearest 10th
Answers
Convert 2.42 to percent
Answers
Answer:
242%
Step-by-step explanation:
Answer:
242%
Step-by-step explanation:
Whole numbers are a 100% each, so there's 200%. Tenths are 10% every tenth, so 40%, and hundredths are 1% every hundredth, so 2%.
200+40+2=242%
If it was helpful, could you plz consider giving me brainliest?
Find an equation for the line with the given properties. Express the equation in slope-intercept form.
Slope = 3; containing the point (5,-4)
What is the equation of the line?
y =
Answers
Answer:
y = 3x - 19
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Define variables
Slope m = 3
Random point (5, -4)
Step 2: Plug in known variables
y = 3x + b
Step 3: Find b
-4 = 3(5) + b
-4 = 15 + b
b = -19
Step 4: Write linear equation
y = 3x - 19
What type of angle is angle M? A. Acute B. Obtuse C. Straight or D. right
Answers
Step-by-step explanation:
acute angle is a tiny angle obtuse is a wide 180 straight is just a straight line and a right angle is a right angle which equals 90 degrees
Answer:
Acute angle refers to angle less than 90
Obtuse angle refers to angle greater than 90 but less than 180
straight line angle is equal to 180
right angle is equal to 90
I am in 9th grade,if you have 889,865x999,786 what doe it equal also yes i am not in virtual school and teacher will not let me use a calculatar
Answers
Answer:
889674568890
Step-by-step explanation:
I used a calculator :)
4. Solve x -- 7 = 25.
A 18
B 32
Answers
Answer:
B
Step-by-step explanation:
b okay it b good
jwnsndm
skskxkmxxmcmc
jsjdkdjxkxxkxi
16. Find the values of x and y. (2y + 5) (5x - 17) (3x – 11)º
Answers
Answer:
x = 26
y = 9
Step-by-step explanation:
(5x - 17)° + (3x - 11)° = 180° (angles in a straight line)
Solve for x
5x - 17 + 3x - 11 = 180
Collect like terms
5x + 3x - 17 - 11 = 180
8x - 28 = 180
Add 28 to both sides
8x = 180 + 28
8x = 208
Divide both sides by 8
x = 208/8
x = 26
Also:
(2y + 5)° + 90° + (3x - 11)° = 180° (angles on a straight line)
Plug in the value of x and solve for y
2y + 5 + 90 + 3(26) - 11 = 180
2y + 5 + 90 + 78 - 11 = 180
Collect like terms
2y + 162 = 180
Subtract 162 from both sides
2y = 180 - 162
2y = 18
y = 9 (dividing both sides by 2)
Find a − b when a = −7 and b = 11.
Answers
Answer:
-18
Explanation:
a - b
a = -7
b = 11
Insert -7 for 'a' and 11 for 'b'
-7 - 11
= -18
Which statement about the graph is true? 7 6 5 2 3 2 1 1 2 3 4 5 6 7 8 x O The graph shows a proportional relationship because it is a line, and the difference between each point is the same. The graph shows a proportional relationship because it is a line, and each x-value isha multiple of 2. O The graph does not show a proportional relationship because each point written as a ratio gives a different value.
Answers
Answer:
I think but it can also be the first one
The graph shows a proportional relationship because it is a line, and each x-value isha multiple of 2.
HLEP MEE!!!!
Solve for Y!
Answers
Answer:
y = 10
Step-by-step explanation:
120 + 6y = 180
6y = 60
y = 10
Answer:
y = 10
Step-by-step explanation:
6y + 120 = 180
6y = 60
y = 10
Determine whether the given segments have the same length. Drag and drop each number
into the correct box to complete the justification of your answer. BC and EF
Answers
Answer:
Step-by-step explanation:
Length of a segment between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Coordinates of extreme ends of BC and EF are,
B(1, 4), C(3, -2), E(-3, -2) and F(-1, 1)
Length of BC = [tex]\sqrt{(1-3)^2+(4+2)^2}[/tex]
= [tex]\sqrt{4+36}[/tex]
= [tex]2\sqrt{10}[/tex] ≈ 6.32 units
Length of EF = [tex]\sqrt{(-3+1)^2+(-2-1)^2}[/tex]
= [tex]\sqrt{4+9}[/tex]
= [tex]\sqrt{13}[/tex] ≈ 3.61 units
The length of BC is 6.32. The length of EF is 3.61.So, BC and EF don't have the same length.
The maximum speed that an X43A plane can reach is 7,500 miles per hour. At this speed, how many feet
can the X43A travel in 1 second? (1 mile = 5,280 feet)
Answers
Answer:
11000 feet/secondsStep-by-step explanation:
This problem requires that we convert from miles per hour to feet per seconds
Given that the speed of the X43A plane is 7500 mph
and that 1 mile = 5,280 feet)
[tex]=\frac{7500miles}{h} *\frac{5280 feet}{mile} \frac{1hour}{3600 seconds} \\\\=\frac{7500*5280}{3600} \\\\=\frac{396*10^5}{3600} \\\\=11000 feet/seconds\\\\=11*10^3feet/seconds\\\\[/tex]
Therefore the speed of the X43A plane in feet per second is 11000
y/-5=1/10
Enter your answer as a reduced fraction.
Answers
Answer:
1/2
Step-by-step explanation:
y/-5=1/10
multiply -5 on both sides
y/-5 x -5 - cancels
1/10 x -5/1
1/10 x -50/10 = 5/10 = 1/2
so then its y=1/2
-4 1/2 divided by (-2 2/3
Answers
Answer:
1 11/16
Step-by-step explanation:
Answer:
1 11/16
Step-by-step explanation:
Convert mixed numbers into improper fractions:
-4 1/2
Step 1: whole number x denominator + numerator
-4 x 2 + 1 = -9
Step 2: write that number over your original denominator
-9/2
Step 3: repeat for other fraction
-2 2/3
-2 x 3 + 2 = -8
-8/3
Step 4: copy, dot, flip
-9/2 × -3/8
Step 5: solve
27/16
Step 6: convert back to mixed number
1 11/16
*note* Negative x negative = positive
what is 5 1/12 -3 5/12?
Answers
Answer:
the answer is -5/6 hope this helps
If 2x=4(5−2x), then x =
Answers
Answer:
here's your answer
hope this helped you
please mark as the the brainliest(ㆁωㆁ)
Step-by-step explanation:
2x=4(5-2x)2x=20-8x2x+8x=2010x=20x=21.) (-18, -20) (18, 16)
2.) (-7, 14) (-11, 4)
3.) (-5, -4) (3, 9)
4.) (13, -8) (-9, -1)
Answers
1.) (-18, -20) (18, 16)
m= 1
2.) (-7, 14) (-11, 4)
m= 5/2
3.) (-5, -4) (3, 9)
m= 13/8
4.) (13, -8) (-9, -1)
m= -7/22
What is the difference?
77 – 43.6 =
A. 23.3
B. 33.4
O C. 34.6
OD. 44.1
Answers
Answer:
B. 33.4
Step-by-step explanation:
77 - 43.6 = 33.4
You’re just subtracting them
HELP PLEASE
If y varies directly with x and y = 26 when x = 8, write the equation that represents this direct variation relationship
Oy - 4x + 13
Oy=13x +4
Answers
Answer: y= 13 over 4x
Step-by-step explanation: trust me king
Simplify.
4−16÷4+42
Item 5
Simplify.
4−16÷4+42
Answers
Answer:
42
Step-by-step explanation:
16 dividied by 4 is 4
4 minus 4 is 0
and 0 plus 42 is 42
Answer:
45
Step-by-step explanation:
4-16÷4+42
12÷4+42
3+42
45