If a = 3 sqrt(3) in the right triangle shown, what is the value of b?
Answers
Note: Consider the below figure attached with this question.
Given:
[tex]a=3\sqrt{3}[/tex]
To find:
The value of b.
Solution:
In a right angled triangle,
[tex]\tan \theta = \dfrac{Perpendicular}{Base}[/tex]
For the given right angled triangle,
[tex]\tan \theta = \dfrac{a}{b}[/tex]
[tex]\tan (30^\circ) = \dfrac{3\sqrt{3}}{b}[/tex]
[tex]\dfrac{1}{\sqrt{3}} = \dfrac{3\sqrt{3}}{b}[/tex]
On cross multiplication, we get
[tex]1\times b=3\sqrt{3}\times \sqrt{3}[/tex]
[tex]b=3(3)[/tex]
[tex]b=9[/tex]
Therefore, the value of b is 9.
Related Questions
Karen performs a transformation on parallelogram ABCD that is plotted on a coordinate grid to form parallelogram A'B'C'D'. The image of
each point is shown in the table below.
Image
Original
Point
| A(-4,-1)
B (-7,-6)
C (-14, -6)
D(-11, -1)
(1.-4)
(6.-7)
(6.-14)
(1.-11)
Which best describes the transformation Karen performed?
A.reflection over the y-axis
B.dilation of scale factor
-1/4
C.counterclockwise rotation of 90 degrees about origin
D.translation of 5 units to the right and 3 units down
Answers
Answer:
its c
Step-by-step explanation:
took the test
Karen performed a transformation of (C) counterclockwise rotation of 90 degrees about origin
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90° counterclockwise about the origin, the new point is at A'(-y, x).
Parallelogram ABCD has vertices at A(-4,-1) , B (-7,-6) , C (-14, -6) , D(-11, -1), if it is rotated 90° counterclockwise about the origin, the new point would be at A'(1.-4) , B'(6.-7), C'(6.-14) , D'(1.-11)
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what is the scientific notation for 92100
Answers
Answer:
9.21*10^4
Step-by-step explanation:
Identify the line of symmetry.
line q
line p
line r
Answers
Answer:
Line r
Step-by-step explanation:
I took the Test
Which of the following sets of numbers could represent the three sides of a right
triangle?
Answers
Answer:
(45,60,75)
Step-by-step explanation:
Because 45^2 + 60^2 = 75^2
5625 = 5625
There are 10 seniors and 15 juniors in a gym class. What is the ratio of seniors to total students?
Answers
Answer:
for every 2 seniors there are 3 juniors or 2:3
The ratio of seniors to total students will be 2: 5.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
There are 10 seniors and 15 juniors in a gym class.
The total number of students will be given as,
Total students = 10 + 15
Total students = 25
Then the ratio of seniors to total students will be given as,
Ratio = Seniors / Total student
Ratio = 10 / 25
Ratio = 2 / 5
The ratio of seniors to total students will be 2: 5.
More about the ratio and the proportion link is given below.
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YOU GET 60 POINTS!! Ronald rents a car from Cheap Rent-a-Car for $25 plus $0.05 per mile. Dixon rents a car from Great Cars for $40 plus $0.03 per mile. How many miles must they both drive for their rental fees to be the same?
Answers
Answer:
750 miles
Step-by-step explanation:
25+0.05x=40+0.03x
0.02x=15
x=750
So I just need help.
Answers
Answer:
a = 100 + 45t
Step-by-step explanation:
$100 is a one time addition so it will be a constant
100
$15 is added three times a month, so $45 a month
t stands for months as shown in the question
100 + 15(3)t
100 + 45t
John and his best friend found some money. They split the money evenly, each getting $14. How much money did they find?
Answers
Answer:
$28
Step-by-step explanation:
John and his best friend each got $14, so in total there are $14+$14=$28.
Answer:
$28
Step-by-step explanation:
If they split the money evenly then both of them got half.
So, multiply 14 by 2 to find the answer:
(14)(2) = 28
John and his best friend found a total of $28.
I hope this helps!!
- Kay :)
1. Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with
the origin as the center of dilation using the rule (x, y) - (x, y) to create pentagon
M'N'P'Q'R'. Which statement is true?
Answers
Answer:
B
Step-by-step explanation:
if its less than 1 it shrinks
The correct statement is; Pentagon M’N’P’Q’R is smaller than pentagon MNPQR because the scale factor is smaller than 1.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
If a polygon is dilated by a scale factor = k
Rule to be followed as;
(x, y) → (kx, ky)
Here, k = Scale factor
If 0 < k < 1, size of the image will be reduced.
Similarly, k > 1, size of the image will be enlarged.
We are given that Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.
Rule used for the transformation,
(x, y) → (1/4x, 1/4y)
Here, the scale factor through which MNPQR has been dilated is 1/4.
Since, scale factor is between zero and 1/4, size of M'N'P'Q'R' will be reduced.
Therefore, the size of pentagon M'N'P'Q'R' will be 1/4 smaller than pentagon MNPQR.
Option (2) is the answer.
Learn more about scale factors here :
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Which of the following correctly shows the next two terms after −40 in the pattern?
−10, 20, −40
Answers
Answer/ explanation: -10 for sure :)
The next two terms after -40 in this pattern are 60 and -160.
What is arithmetic Progression?The difference between every two subsequent words in a sequence is the same; this is known as an arithmetic progression (AP). An equation for the previous block of the AP may be derived from this kind of development. For instance, the sequence 2, 6, 10, 14,... is a mathematical progression (AP) because it fits a pattern where every other number is acquired by adding 4 to the respective period.
The given data is,
-10, 20, -40
From -10 to 20 it is multiplied by 2 with a positive sign, and from 20 to -40 it is multiplied by 2 with a negative sign. Similarly, the next two numbers are 80 and -160.
To know more about reasoning:
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Someone help!
Three customers have accounts owing money. The table shows the account balances.
Which customer owes the least amount of money?
Customer Balance
M. Palmer –$56.72
B. Leftwich –$74.19
R. Jordan –$54.31
M. Palmer
B. Leftwich
R. Jordan
Answers
jordan owes the least amount of money
Sara missed 7 of 184 school days this year. Approximately what percent of school days was Sara present?
A. 4%
B. 96%
C. 177%
D. 7%
Answers
Answer:
B. 96%
Step-by-step explanation:
Sara only missed 7 days of 184 days this year meaning 184 - 7 = 177 and
177 is how many days she attended school, so to figure out percentage take the number of days she attended school and divide by the total amount of days in this year which is 184: 177/184 = 0.96195652173
then multiply by 100 to get percentage so approximately 96%.
Simplify the complex fraction shown below: 1/4 over 10/9
Answers
Answer:
9/40 or 0.225
Step-by-step explanation:
Find the value of x 105,160,110,105,115
Answers
Answer:
dzxfchgjvhkbjl
Step-by-step explanation:
given a piece wise
function f(x)={2x,x<1 5, x=1
Answers
The area of a rectangle is 15 square inches. What wil be the area, in square inches, of the rectangle after it is dilated by a
scale factor of 2?
Answers
Answer:
60 inches²
Step-by-step explanation:
Unit test
May someone help me out on this question?
Answers
Answer:
y = 2 for x < 0
x for 0 ≤ x < 3
3 for x ≥ 3
Step-by-step explanation:
From the graph attached,
Equation of line (1),
y = 2
Where x < 0
Let the equation of line (2) is,
y = mx + b
y-intercept 'b' = 0 [line (2) passes through origin]
Slope of the line 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{3}{3}[/tex]
= 1
Therefore, equation of line (2) will be,
y = x
where 0 ≤ x < 3
Equation of line (3) will be,
y = 3
Where x ≥ 3
Therefore, piecewise linear function will be,
y = 2 for x < 0
x for 0 ≤ x < 3
3 for x ≥ 3
which is an equation for the line passing through the points (-3,3) and (6,9)
Answers
Answer:
y=2/3x +5
hope this helps
Answer:
[tex] \red{ \boxed{ \bold{2x - 3y + 15=0}}}[/tex]
Explanation
[tex] slope \:of \:the\: required\:\: line \implies\\\frac{9-6}{6-(-3)}=\frac{6}{9} [/tex]
[tex] equation \:of \:the\: required\:\: line\implies\:\\y - 3 = \frac{6}{9} (x + 3)[/tex]
[tex] \implies \: 9y - 27 = 6x + 18[/tex]
[tex] \implies \: 6x - 9y + 45=0[/tex]
[tex] \implies\:2x-3y+15=0[/tex]
Hence the equation of the line is
[tex] \green{ \boxed{ \bold{2x - 3y + 15=0}}}[/tex]
5+3w+3-w combine like terms to simplify
Answers
Answer:
8 + 2w
Step-by-step explanation:
⇒ Change all signs to addition (subtraction is the same as adding a negative):
5 + 3w + 3 + -w
⇒ Since the expression is now all addition, you can rearrange them in any order. So group the terms together by their type:
5 + 3 + 3w + -w
⇒ Simplify:
8 + 2w
Answer: 8 + 2w
Hope this helps! :)
Simplify.
9/3x + 4+ 2x
Answers
Answer:
5x+4
Step-by-step explanation:
__Na2O + __ H2O → __NaOH
Answers
Answer:
Na20+H20 -> 2NaOH
Step-by-step explanation:
Plzz help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
12.50
Step-by-step explanation:
i think
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idk this please help me
Answers
Answer:
Pretty sure it is c
Step-by-step explanation:
r = 4 in., θ = 11 rad; find s
Answers
Answer:
The arc length s = 44 inches
Step-by-step explanation:
We are given:
r = 4 in
Ф = 11 radians
We need to find s
The formula used is: [tex]s=r\theta[/tex]
where s represents arc length, r is radius and Ф is angle in radians
Putting values and finding s
[tex]s=r\theta[/tex]
Put r = 4 and Ф = 11
[tex]s=4\times 11\\s=44[/tex]
So, the arc length s = 44 inches
What is the image point of (9,4) after a translation left 5 units and up 1 unit?
Answers
Answer:
(4,5)
Explanation: 9-5=4, 4+1=5
Tyler's mom purchased a savings bond for Tyler. One year after it was purchased, the value of the savings bond was $156. If the value of the savings bond increases by 4% after one year, what was the value of the bond when Tyler's mom purchased it?]
Answers
Answer:
$149.76
Step-by-step explanation:
please help and explain i’ll mark brainliest!! worth a lot of points too
Answers
nth term (math) asap please.
Answers
Answer:
Just do minus two, and you will get 27-100=-73
Step-by-step explanation:
Help needed. 30 points to complete the table and do the second part.
Answers
Answer:
-4,-6,-8,-10
Step-by-step explanation:
I am not so sure though.
Given the conditional statement: "If it is Wednesday, then Kayden doesn't
have baseball practice." What is the hypothesis of this statement? *
Answers
Answer:
if it's wednesday
Step-by-step explanation: