"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 please its timed
Answers
Answer:
15
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
2² + 6(3) - 7
Step 2: Evaluate exponents
4 + 6(3) - 7
Step 3: Evaluate parenthesis (multiply)
4 + 18 - 7
Step 4: Add
22 - 7
Step 5: Subtract
15
(5x+2)/8=x/6 what value will make it true??
Answers
Answer:
-6/11 =x
Step-by-step explanation:
We can use cross products to solve
(5x+2)/8=x/6
6 ( 5x+2) = 8x
Distribute
30x + 12 = 8x
Subtract 30x from each side
30x -30x +12 = 8x - 30x
12 = -22x
Divide each side by -22
12/-22 = -22x/-22
-6/11 =x
PLEASE HELP!!! URGENT
Answers
Answer:
scale factor = ratio of corresponding side= 0p/xy = 4/10= 2/5
∠x = 58
∠y= 180-49-58= 73
Step-by-step explanation:
What is the equation shown in standard form of the line shown on the graph?
O x = 4
O y = 4
O x - y = 4
Answers
Answer:
[tex]y = 4[/tex]
Step-by-step explanation:
Because no matter what value x is, y is always 4
Write the ratio in simplest form for area of pool/ area of yard
Answers
Answer:
Option (C)
Step-by-step explanation:
From the map attached,
Area of the rectangular yard = length × width
Length of the yard = 10 units
Width of the yard = 8 units
Area = 10 × 8
= 80 square yards
Since, pool is a composite figure of two rectangles,
Therefore, area of the pool = Area of large segment + Area of the small pool
= (5 × 6) + (3 × 3)
= 30 + 9
= 39 square units
Ratio of Area of the pool and area of yard = [tex]\frac{39}{80}[/tex]
Therefore, Option (C) will be the answer.
1 7/8 x 10/7 x 4 I need help answering this its confusing
Answers
Answer: 75/7
Step-by-step explanation:
Concept:
Multiplication in fraction is the numerator times numerator and denominator times denominator, and if possible, you can simplify the numerator and denominator by eliminating common factor.
Solve:
1 7/8= 15/8
1 7/8 × 10/7 × 4
=15/8 × 10/7 × 4
=150/56 × 4
=600/56
=75/7
There are 1,044 apartments in Baldwin County this year, which is approximately an 8.1% increase from last
year. How many apartments were there in Baldwin County last year?
Answers
Answer:
~966 apartments
Step-by-step explanation:
[tex]\frac{1044}{1.081}[/tex]
A merchant mixed 10 lb of a cinnamon tea with 2 lb of spice tea. The 12-pound mixture cost $13. A second mixture included 16 lb of the cinnamon tea and 8 lb of the spice tea. The 24-pound mixture cost $28. Find the cost per pound of the cinnamon tea and of the spice tea.
Answers
Step-by-step explanation:
Let's say c is the price of cinnamon tea, and s is the price of spice tea.
10c + 2s = 13
16c + 8s = 28
Divide the second equation by 4:
4c + 2s = 7
Subtract from the first equation:
6c = 6
c = 1
Use any equation to find s.
s = 1.5
Therefore, the cinnamon tea costs $1 per pound and the spice tea costs $1.50 per pound.
The circumference of a circle is 16Pi ft what is the radius
Answers
Answer:
Given circumference (C) = 16
Radius =
C =
2π
2.5464790894703
Diameter =
C =
π
5.0929581789407
Area =
C2 =
4π
20.371832715763
Step-by-step explanation:
We've all seen circles before. They have this perfectly round shape.
Every circle has a center, which is a point that lies exactly at the... well... center of the circle. A circle is a shape where the distance from the center to the edge of the circle is always the same. In order to calculate the radius, you need the circumferance or the diameter.
Answer:
Pi is a number that is approximated by 3.14, or 22/7. It is the ratio of the circumference to the diameter of any circle. This ratio can be rearranged to find circumference of a circle by multiplying pi times diameter
Step-by-step explanation:
Maggie's brother is 10 years younger than three times her age. The sum of their ages is 50. How old is Maggie?
Maggie is _____ Years old
Answers
Answer:
9
Step-by-step explanation:
Please see the picture attached!
I hope this helps! If it does, a brainliest would be much appreciated :)
Determine the 18th term of the sequence 3,9,27,...
Answers
Answer:
[tex]x_{18}=387420489[/tex]
Step-by-step explanation:
So we have the sequence:
3, 9, 27...
First, note that this is a geometric sequence because each subsequent term not increasing linearly.
To find the 18th term, we can write an explicit formula.
The standard explicit formula for a geometric sequence is:
[tex]x_n=a(r)^{n-1}[/tex]
Where a is the initial term, r is the common ratio, and n is the nth term.
From the sequence, we can see that the initial term a is 3. The common ratio is 3 since each subsequent term is 3 times the previous term. So, substitute:
[tex]x_n=3(3)^{n-1}[/tex]
To find the 18th term, substitute 18 for n. So:
[tex]x_{18}=3(3)^{18-1}[/tex]
Subtract:
[tex]x_{18}=3(3)^{17}[/tex]
Evaluate:
[tex]x_{18}=3(129140163)[/tex]
Multiply:
[tex]x_{18}=387420489[/tex]
And we're done!
Which of the numbers 8,9, or 10 is the solution to 70=8-x
Answers
Answer:
Step-by-step explanation:
Add x to both sides.
70 +x = 8
Subtract 70 from both sides.
x = 8 - 70
x = - 62
None of the answers fit.
Which of the following equations are dimensionally consistent?
(a) x=1/2at2,
(b) t=v/x,
(c) t=(2x/a)1/2
Answers
Answer:
A. x = 1/2at²
Step-by-step explanation:
Among the equations, the equation that is dimensionally consistent is x=1/2at² where;
x is the distance in meters (dimension is length (L))
a is the acceleration in m/s² (dimension is L/T²)
t is the time in seconds (s) (dimension of time is T)
Substituting the dimensions into the formula to check if we are going to arrive at the dimension for distance;
1/2at² = 1/2(L/T²)T²
= 1/2× L/T² × T²
= 1/2 × L
Since L which is the resulting dimension is the dimension for distance (x), this means that the equation x = 1/2at² is dimensionally consistent.
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions.
Online Content: Site 1
How can right triangles be similar based on their angles?
Answers
Answer:
a right triangle has at lease on 90 degree angle
Step-by-step explanation:
Answer:
By the Side-Angle-Side Similarity Theorem (SASS), if two sides of a triangle are in proportion with the corresponding sides of another triangle, and the included angles are congruent, then the triangles are similar.
Step-by-step explanation:
i got 100% on edg. hope this helps!
enter an inequality that represents the graph
PLEASE HELP QILL GIVE BRAINLIEST
Answers
-6(3 + x) + 2(3x + 5) = 0
Answers
Answer:
No solution
Step-by-step explanation:
Step 1: Write equation
-6(3 + x) + 2(3x + 5) = 0
Step 2: Solve for x
Distribute: -18 - 6x + 6x + 10 = 0
Combine like terms: -8 ≠ 0
∴ No solution
No answer
Step-by-step explanation:
-6(3+x) Multiply -6 by 3=-18. -18+-6x 2(3x+5) 6x+10
(-18+-6x) + (10+6x) = (-8 = 0).
ax + b = c for x. is what I want to know
Answers
Answer:
[tex]x=\frac{c-b}{a}[/tex]
Step-by-step explanation:
[tex]ax+b=c\\\\ax+b-b=c-b\\\\ax=c-b\\\\\frac{1}{a}(ax)=\frac{1}{a}(c-b) \\\\x=\frac{c-b}{a}[/tex]
The perimeter of a rectangular flower bed is 68 feet. Find the dimensions of the flower bed if the length is 2 less than three times the width.
Answers
Answer:
Step-by-step explanation:
Perimeter of the rectangular flour = 2(Length+Width)
P = 2(L+W)... 1
If if the length is 2 less than three times the width, then L = 3W - 2.... 2
Substitute equation 2 into 1;
P =2(3W-2+W)
68 = 2(4W-2)
68 = 8W-4
8W = 68+4
8W = 72
W = 72/8
W = 9 feet
Since L = 3W-2
L = 3(9)-2
L = 27-2
L = 25
The length is 25ft and the width is 9ft
Which figure is described below?
Answers
Answer:
Answer option "A" : line.
Step-by-step explanation:
The trace formed by the collection of all points equidistant from (-5, -6) and (-5, 7) describe a horizontal line with equation y = 1/2.
Therefore the answer option "A" is the correct one.
If 15 books cost $90, what is the unit price?
Answers
Answer:
$6/ book
Step-by-step explanation:
Unit price = Total cost/ total number of items
= 90/15
=$6 per book
explanation: 6*15 is 90
The selling price for a classic speedboat is $12,000. what was the speedboats original price if it is currently selling for $2,000 less than two times its original price?
Answers
Answer:
$7,000
Step-by-step explanation:
Let [tex]x[/tex] equal the original price.
[tex]12,000+2000=2x[/tex]
Combine like terms.
[tex]14,000=2x[/tex]
Divide by the coefficient of [tex]x[/tex], which in this case is [tex]2.[/tex]
[tex]7,000=x[/tex]
If you like the variable on the left, rewrite:
[tex]x=7,000[/tex]
What is the solution of the following quadratic inequality?
9x – x2 > 18
(3, 6)
[3, 6]
(−∞, 3) ∪ (6, ∞)
(−∞, 3] ∪ [6, ∞)
Answers
Answer:
(3,6)
Step-by-step explanation:
well it's parentheses because it is not equal to.
and it shouldn't have infinity signs because they both have stopping points
Answer: A
(3, 6)
Step-by-step explanation:
Find the equation of the line that is perpendicular to -x+2y=11 and passes through the point (6,-5).
Answers
Step-by-step explanation:
m=-2
y+5=2(x-6)
y+5=2x-12
y=2x-17
Answer:
Step-by-step explanation:
2y = x + 11
y = 1/2x + 11/2
perp. -2
y + 5 = -2(x - 6)
y + 5 = -2x + 12
y = -2x + 7
Rewrite 0.011 as a fraction in lowest terms
Answers
Answer:
11/1000
Step-by-step explanation:
and did not copy i swear
Answer:
11/1000 or 10/500
Step-by-step explanation:
I need help with this question
Answers
x = (1056.5 - 470)/ 69
Explanation:
First you would need to find how much money was charged for labor, so you needed to subtract 470 from the total.
Second, once you find the amount charged for labor, you would need to divide the hourly rate by that number. That would give you the number hours.
In order to isolate the variable term in the equation 6 – 2x = –3 using the subtraction property of equality, which number should be subtracted from both sides of the equation?
–3
–2
3
6
Answers
hope this helps
B = 6/13 Y +12 Solve for y
Answers
Answer:
y = (13/6)(b - 12)
Step-by-step explanation:
b = 6/13 y + 12
Subtract 12 from both sides.
b - 12 = 6/13 y
Multiply both sides by 13/6.
(13/6)(b - 12) = y
y = (13/6)(b - 12)
HELLLLLLLLPPPP PLEEEAAASSSSSSEEEEEE
Answers
Answer:
1 and 8 , and 4 and 8 are congruent
The rest are supplementary
Step-by-step explanation:
A shopper paid 11/100 of a dollar for 1/16 of a kilogram of nails. What was the rate in dollars per
kilograms?
Answers
Answer:
[tex]Rate = \$1.76/kg[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{16}kg[/tex] of nails costs [tex]\$ \frac{11}{100}[/tex]
Required
Determine the rate
The rate, in this case, will be calculated as:
[tex]Rate = \frac{amount}{weight}[/tex]
[tex]Rate = \frac{\frac{11}{100}}{\frac{1}{16}}[/tex]
This gives
[tex]Rate = \frac{11}{100}/\frac{1}{16}[/tex]
[tex]Rate = \frac{11}{100} * 16[/tex]
[tex]Rate = \frac{176}{100}[/tex]
[tex]Rate = \$1.76/kg[/tex]
Answer:
Answer:
Step-by-step explanation:
Given
of nails costs
Required
Determine the rate
The rate, in this case, will be calculated as:
This gives
Step-by-step explanation:
What number is 40% of 30?
Input only whole numbers.
Numerical Answers Expected!
Answer for Blank 1:
Answers
Answer:
12
Step-by-step explanation:
40/100*30
=12
Answer:
12..
Step-by-step explanation:
off topic but broski i think we're in the same school program?