The triangle below is equilateral. Find the length of side x in simplest radical form with a rational denominator.
Answers
Answer:
x = √30
Step-by-step explanation:
For an equilateral triangle, the measure of the angle at each vertex is 60 degrees
Thus, the angle 60 faces the side measure x
Also, the given length is adjacent to the angle 60 measure
Mathematically, the trigonometric ratio that links the adjacent and the opposite is the tan
The tan is the ratio of the opposite to the adjacent
Thus;
Tan 60 = x/ root 10
x = root 10 * tan 60
x √(10 * √(3
x = √30
The length of [tex]x[/tex] is required.
The length of [tex]x[/tex] is [tex]\sqrt{30}\ \text{units}[/tex]
In an equilateral triangle the altitude divides the side into halves.
So, the hypotenuse will be [tex]\sqrt{10}+\sqrt{10}=2\sqrt{10}[/tex]
From the Pythagoras theorem we have
[tex]x^2+(\sqrt{10})^2=(2\sqrt{10})^2\\\Rightarrow x=\sqrt{(2\sqrt{10})^2-(\sqrt{10})^2}\\\Rightarrow x=\sqrt{30}[/tex]
The length of [tex]x[/tex] is [tex]\sqrt{30}\ \text{units}[/tex]
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Related Questions
Christopher the barber did 8 haircuts. One of the 8 was a walk-in. Express the amount
of walk-ins as a percent.
Answers
Use the graph to write a linear function that relates Y toX
Answers
x-y=xy
2-1=1
Y=1
An adult ticket costs £4.
A child ticket costs £3.
Hina spends £47 on cinema tickets.
She buys 8 adults tickets.
Work out how many child tickets she buys.
Answers
8*4=32
47-32= 15
15/3= 5
MARKING BRAINLIEST ..Please
Answers
Answer:
B
Step-by-step explanation:
Have a good day :)
Answer: I think D.
Step-by-step explanation:
help plzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answers
Answer:
I think I just posted that last time. Check my timeline
Javier built a skateboard ramp by elevating one end of an 8-foot piece of plywood so that it makes a 20 degree angle with the ground.
Answers
Answer:
2.74feet
Step-by-step explanation:
Since we are not told what to find, we can find the height of the plywood
Given the following
length of ramp = 8feet
angle of elevation = 20degrees
Required
Height of the plywood
Using the SOH CAH TOA identity
Sin theta = opposite/hypotenuse
Sin 20 = H/8
H = 8sin20
H = 8(0.3420)
H = 2.74 feet
Hence the height of the plywood is 2.74feet
It’s about solving systems of equations...
Answers
Answer:
(-1,-1)
Step-by-step explanation:
Which of the following is a dilation?
Answers
Answer:
A) image is being doubled in size in A
Step-by-step explanation:
B and C are rotations
D is a translation
Complete the equation of the line through (3,-1)(3,−1)left parenthesis, 3, comma, minus, 1, right parenthesis and (4,7)(4,7)left parenthesis, 4, comma, 7, right parenthesis.
Answers
Answer: [tex]y=8x-25[/tex]
Step-by-step explanation:
Given
Line passes through [tex](3,-1)\ \text{ and}\ (4,7)[/tex]
Equation of line when it passes through two points [tex](x_1,y_1),(x_2,y_2)[/tex]
[tex]\Rightarrow \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y-y_1}{x-x_1}[/tex]
Insert the values
[tex]\Rightarrow \dfrac{7+1}{4-3}=\dfrac{y+1}{x-3}\\\\\Rightarrow \dfrac{8}{1}=\dfrac{y+1}{x-3}\\\\\Rightarrow 8x-24=y+1\\\Rightarrow y=8x-25[/tex]
Answer:
8x-25
Step-by-step explanation:
:O thats ez
Match the cube roots and square roots with their values.
V4
327
64
364
49
31,000
2
10
3
4
8
7
Answers
10= cube root of 1000
3= cube root of 27
4= cube root of 64
8= sqrt 64
7= sqrt 49
Which choice is equivalent to the quotient shown here when x2 0?
Answers
Answer:
Option A.
Step-by-step explanation:
√18x÷√32
√18x/√32
√18x/32
√9x/16
9 and 16 are perfect squares
=3√x/4.
Option A
The price of an item yesterday was $130. Today, the price rose to $351. Find the percentage increase.
please help and I will mark you braniest!
Answers
Answer: The percentage increase is 170%
Step-by-step explanation:
Increase= $351 - $130
Increase= 221
Percent increase = 221/ 130
Percent increase= 170%
I'm not sure if I'm right, but I hope that this helped:)
Answer:
170%
Step-by-step explanation:
130 = 100%
65 = 50%
13 = 10%
351 - 130 = 221 (doesnt count)
221 - 130 = 91
91 - 65 = 26
26 - (13 + 13) = 0
100 + 50 + 20 = 170%
For any number, y
Add one third of the number
Then subtract _____________ of the result.
The answer is y
Answers
Answer:
y/3
Step-by-step explanation:
According to the conditions :
y + y/3 - x = y
y + y/3 - y = x
(3y + y - 3y )/3 = x
y/3 = x
Answer:
[tex]\frac{3}{12}[/tex]
Step-by-step explanation:
Create an equation and solve for x:
[tex]y + \frac{1}{3} y = \frac{4}{3} y\\\frac{4}{3}y - x(\frac{4}{3}y) = y\\x = \frac{3}{12}[/tex]
Tatum walks her dog 2/3 of a mile every day after school how many miles does she walk her dog in 5 days
Answers
Answer:
i think it is 3 miles but dunno
Step-by-step explanation:
PLS HELP ASAP!!
50 POINTS!
Answers
Answer:
135Step-by-step explanation:
3³· (12 - 2) ÷ 2 = 3³ · 10 ÷ 2 = 27 · 10 ÷ 2 = 270 ÷ 2 = 135
1) Bruce L. Sprouts had to take a loan worth $5,000.
The loan has a 3.5% interest rate.
He has to pay the loan off in 6 years.
A) How much will he have to pay for the interest?
B) How much will he have to pay total? Please answer fast show your work you will be marked as brain
Answers
Answer:
A) $1,050
B) $6,050
Step-by-step explanation:
We solve using the Simple Interest formula
Simple Interest (I) = Principal × Rate × Time
From that above question, we have the parameters
Principal = $5000
Rate = 3.5 % = 0.035
Time = 6 years
A) How much will he have to pay for the interest?
Hence,
Interest = $5,000 × 0.035 × 6
= $1,050
Therefore, the amount of interest he will have to pay is $1,050
B) How much will he have to pay total?
The amount he will have to pay in contact =
Principal + Interest paid on loan
= $5,000 + $1,050
= $6,050
There are 4 portable classrooms at Glynn High School. Four teachers will be assigned to the rooms. In how many ways can these assignments be made?
Answers
Answer:
24
Step-by-step explanation:
In the first classroom, there are 4 possibilities of teachers to be assigned.
In the second classroom, 1 teacher has already been assigned, so there are 3 possibilities.
In the third classroom, 2 teachers have already been assigned, so there are only 2 possibilities.
Finally, there is only 1 possible teacher for the fourth classroom, since 3 teachers have already been assigned to other classrooms.
We can find the total number of possibilities using the product rule.
N = 4 × 3 × 2 × 1 = 24
What is the equation of the line that passes through the point (-4, 2) and has a slope of -5/4?
Answers
Answer:
y = -5/4 x - 3 is the slope-intercept form
5x + 4y = -12 is the standard form
Step-by-step explanation:
Use the point-slope form: [tex]y - y_{1} = m(x - x_{1})[/tex]
[tex](x_{1}, y_{1})[/tex] = (-4, 2)
y - 2 = -5/4(x + 4) Multiply by 4 to remove the fraction
4y - 8 = -5(x + 4)
4y - 8 = -5x - 20
4y = -5x - 12
y = -5/4 x - 3 is the slope-intercept form
5x + 4y = -12 is the standard form
THIS IS AREA OF CIRCLES PLS HELPP
Answers
Answer:
3 ft
Step-by-step explanation:
You are given the area, and the area formula, and you can set them equal to each other:
pi r^2 = 9 pi
Divide by pi on both sides:
r^2 = 9
Find the square root of both sides to get:
r = 3 feet
Answer:
r = 3 ft.
Step-by-step explanation:
In order to solve this problem, you need to substitute the information given into the equation and solve for r. The problem tells us that the area of the circle is 9π ft². We can use this value and substitute it into the equation.
9π = πr²
⇒ 9 = r²
⇒ 3 = r
Therefore, the radius of the circle is 3 ft.
Find the MEDIAN of the data set. (Hint: the numbers must be in order first!) 40 76 40 63 47 57 49 55 50 53
Answers
Given:
The data set is:
40, 76, 40, 63, 47, 57, 49, 55, 50, 53
To find:
The median of the given data set.
Solution:
We have,
40, 76, 40, 63, 47, 57, 49, 55, 50, 53
Arrange the data values in ascending order.
40, 40, 47, 49, 50, 53, 55, 57, 63, 76
Here, the number of observations is 10 which is an even number. So, the median is:
[tex]Median=\dfrac{(\dfrac{n}{2})\text{th term}+(\dfrac{n}{2}+1)\text{th term}}{2}[/tex]
Putting n=10, we get
[tex]Median=\dfrac{(\dfrac{10}{2})\text{th term}+(\dfrac{10}{2}+1)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{5\text{th term}+6\text{th term}}{2}[/tex]
From the arranged terms, it is clear that the the 5th term is 50 and the 6th term is 53.
[tex]Median=\dfrac{50+53}{2}[/tex]
[tex]Median=\dfrac{103}{2}[/tex]
[tex]Median=51.5[/tex]
Therefore, the median of the given data set is 51.5.
First correct response gets brainliest
Answers
Answer:
x = 13
Step-by-step explanation:
This question is based on Secant Secant theorem.
Secant Secant theorem gives us the following formula:
(AB + BD)AB = (AC + CE).AC
From the above question we have the following parameters
AB = 5
BD = x
AC = 7.5
CE = 4.5
Hence,
(AB + BD)AB = (AC + CE).AC
(5 + x)5 = (7.5 + 4.5)7.5
25 + 5x = 90
Collect like terms
5x = 90 - 25
5x = 65
x = 65/5
x = 13
If you were trying to prove that a shape had all four sides congruent, which formula
would you be using?
A. Slope Formula
B. Distance Formula
C. Quadratic Formula
D. Midpoint Formula
Answers
Select ALL the expressions that are equivalent to -4(8x-3)
A) -20X
B) 4(3-8x)
C) -32x-12
D) 2(-16x+6)
E) 5-9(8x-3)
Answers
Answer:
dddddStep-by-step explanation:
PLS HELP ASAP...A triangle has side lengths of (10m-5) centimeters, (6m-2) centimeters, and (8n+4) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
1. 12n+16m−7
2. 16m+8n−3
3. 12n+5m+4
4. 12n+9m
Answers
Answer:
perimeter = 10m - 5 + 6m - 2 + 8n + 4
= 16m -7 + 8n + 4
16m + 8n -3
option 2
The expression represents the perimeter of the triangle will be 16m + 8n - 3. Then the correct option is B.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The sum of all the sides of the triangle will be known as the perimeter of the triangle.
A triangle has side lengths of (10m - 5) centimeters, (6m - 2) centimeters, and (8n + 4) centimeters.
The expression represents the perimeter of the triangle will be
P = (10m - 5) + (8n + 4) + (6m - 2)
P = 16m + 8n - 3
The expression represents the perimeter of the triangle will be 16m + 8n - 3. Then the correct option is B.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ2
The length of a rectangle is 8feet less than the width. The perimeter is 64 feet. Find the length and the width
Answers
Answer:
Length = 4 feet
Width = 4 feet
Step-by-step explanation:
The perimeter of a rectangle formula = 2L + 2W
Where L = Length
W = Width
The length of a rectangle is 8feet less than the width.
Hence,
L = 8 - W
The perimeter is 64 feet.
Hence,
64 = 2(8 - W) × 2W
64 =( 16 - 2W )2W
64 = -4W² + 32W
4W² - 32W + 64 = 0
Factorise
4W² - 16W - 16W + 64 = 0
4W (W - 4) - 16(W - 4) = 0
W - 4 = 0
W = 4
Width = 4
Solving for L
L = 8 - W
L = 8 - 4
L = 4
Therefore,
Length = 4 feet
Width = 4 feet
Jose has a bag of 6 blue marbles, 3 white marbles, and 8 black marbles. What is the probability that he pulls a blue marble out of the bag?
Answers
6+3+8= 17
Then, to find the probability you put the number of marbles which you want to find the probability of being pulled out on top of the fraction and make it out of 17
6/17
The diameter of a circle is 19 ft. Find the circumference to the nearest tenth.
Answers
Answer:
Half of 19 = 9.5(new radius)
2 x 3.4 x 9.5 = 64.6 ft is your answer.
Formula of circumference:
2 x 3.14(pi or 22/7 depending on what they tell you to use for pi) x radius(half of diameter or given radius)
Answer:
C = 59.7
Step-by-step explanation:
The formula for the circumference of a circle is C = 2πr
R = radius
The radius is the half of a diameter, so 19/2 is 9.5.
C = 2π(9.5)
C = 59.69026041
9 Sam earns $54 275 in a year.
He pays no income tax on the first $8200.
He pays 18% income tax on everything he earns over $8200.
a Work out how much income tax he pays.
b Work out what percentage of his income he pays in tax.
c If the income tax rate is increased to 21%, how much more tax will Sam pay?
Answers
Answer:
See all three answers below
Step-by-step explanation:
Given data
Amount Earned= $54275
Income Tax= 18%
a Work out how much income tax he pays.
Amount of income tax
=18/100*54275
=0.18*54275
=$9769.5
b Work out what percentage of his income he pays in tax.
=9769.5/54275*100
=0.18*100
=18%
c. If the income tax rate is increased to 21%, how much more tax will Sam pay?
=21/100*54275
=0.21*54275
=$11397.75
Can someone give me the anwers I don’t understand it
Answers
3. Mrs Naidoo wants to buy a new kitchen cabinet on which she can place her new
microwave. Mrs Naidoo notices one advertised for R3 999,00. She decides to
save until she has enough cash to pay for the kitchen cabinet. She uses her
December bonus of R2 900,00 to deposit into her savings account where she
is offered 3,5% p.a. compound interest.
Determine if Mrs Naidoo will be able to afford the kitchen cabinet a year later if she
adds R960,00 to the saved amount.
please help
Answers
Answer:
thats about like ummm 69?
Step-by-step explanation: