Find the length of side x in simplest radical form with a rational denominator.
60
X
5
30
Answers
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
Sin 30 = 5/x
Sin 30 = 1/2
x = 10
The length of the side x is 10.
What are trigonometric identities?
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
The length of side x can be calculated using the trigonometric identities.
We know that,
Sin x = Perpendicular / Hypotenuse
Sin 30 = 5 / x
1/2 = 5/x
Multiply 2 on both sides.
1= 10/x
x = 10
Thus,
The length of the side x is 10.
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A) 1/2x-6=-2x-1
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substitute the equations into this to get 1/2x-6= -2x-1
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Write the point-slope form of an equation of the line through the points (-4, 7) and (5, -3).
A. y−5=−109(x+3)
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D. y+4=−109(x−7)
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Multiplying StartFraction 3 Over StartRoot 17 EndRoot minus StartRoot 2 EndRoot EndFraction by which fraction will produce an equivalent fraction with a rational denominator?
Answers
Answer:
(√17 + √2)/(√17 + √2)Step-by-step explanation:
You need to determine the conjugate of the denominator.
√17 - √2 has conjugate of √17 + √2, when multiplied the product is going to be a rational number:
(√17 - √2)/(√17 + √2) = 17 - 2 = 15Therefore correct choice is B or second from the top:
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Step-by-step explanation:
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Solve the expression (w - z)²
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which triangles are congruent in the figure
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Answer:
Step-by-step explanation:
The two triangles that are congruent are ABE and CBD by SSS.
P+45267=87012 evaluate
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p+45267=87012
We move all terms to the left:
p+45267-(87012)=0
We add all the numbers together, and all the variables
p-41745=0
We move all terms containing p to the left, all other terms to the right
p=41745
FIND THE MEASURE OF ANGLE 2 PLEASE HELP ASAP!
Answers
Answer:
We know that the figure has a symmetry
angle 1 = angle 2
angle 1 =180°-(18°+90°) = 180° - 108°=72°
Therefore, angle 2 =72°.
Can someone help me with this i will give brainliest please!
Answers
Answer:
(-1, -3)Step-by-step explanation:
Given system:
4x - 2y = 22x + y = - 51) Solving the second equation for y:
2x + y = - 5 ⇒y = -5 - 2x2) Substituting y into the first equation:
4x - 2y = 2 ⇒4x - 2( -5 - 2x) = 2Correct option is a)3) Solving for x:
4x - 2( -5 - 2x) = 24x + 10 + 4x = 28x = 2 - 108x = -8x = -14) Solving for y:
y = -5 - 2xy = -5 - 2(-1) = -5 + 2 = -3y = -35) Ordered pair is:
(x, y) = (-1, -3)Answer:
Step-by-step explanation:
Explain what method is used to solve problems involving scale drawings.
A. Use a proportion
B. Make an educated guess
C. Get a ruler or tape measure and measure the distance
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Which equation is equivalent to 1/5x - 3 = 2/3
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C : 3x-45=10
D : 5x-45=3
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Is -8 a rational number
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Answer:
yes
Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Two sides of a triangle have the same length. The third side measures 6 m less than twice the common length. The perimeter of the triangle is 14 m. What are the lengths of the three sides?
What is the length of the two sides that have the same length?
Answers
Answer: 5
Step-by-step explanation:
x = common side length
2x + (2x - 6) = 14
4x - 6 = 14
4x = 20
x = 5
BC -
Round your answer to the nearest hundredth.
B
?
35
A
с
2.
Answers
Answer:
BC ≈ 1.40
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA [Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Identify
Angle θ = 35°
Opposite Leg BC = x
Adjacent Leg AC = 2
Step 2: Solve for x
Substitute [Tangent]: tan35° = x/2Isolate x: 2tan35° = xRewrite: x = 2tan35°Evaluate: x = 1.40042Round: x ≈ 1.40Tangent (Angle) = Opposite side / adjacent side
Tangent(35) = BC/2
Multiply both sides by 2:
BC = 2 x Tangent(35)
BC = 1.40042
Rounded to nearest hundredth: BC = 1.40
Prove: The square of a number that is
one more than a multiple of 3 is also one
more than a multiple of 3.
n +
(3n + 1)2 = [ ? ]n? +
1([ ]n2 +
=
)n) +
- 1 more than a multiple of 3
Answers
Let 3n + 1 denote the "number" in question. The claim is that
(3n + 1)² = 3m + 1
for some integer m.
Now,
(3n + 1)² = (3n)² + 2 (3n) + 1²
… = 9n² + 6n + 1
… = 3n (3n + 2) + 1
… = 3m + 1
where we take m = n (3n + 2).
Please help at answer least one question please number it!!
Answers
I think so
Answer:
1. 88
2. -17
3. -10
4. -16
5. -14
6. 44
7. -76
8. 18
Step-by-step explanation:
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Here's a graph of a linear function. Write the equation that describes that function.
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Answer:
2/3x + 1
Step-by-step explanation:
The y-intercept is 1. you can see that when x increases three, y increases 2.
Find the measures of the numbered angles of the parallelogram.
Answers
Answer:
1=40
2=140
3=40
Step-by-step explanation:
We know on side
140 and side 2 are equal
1 and 3 are equal
So since 140 and 2 are equal
140*2=280
360 degrees total in any 4 sided shape
360-280=80
80/2=40
What is the standard deviation of this data set?
12, 14, 9, 11, 10, 15, 16, 12, 7, 14
Answers
Answer:
The standard deviation is 2.6832815729997
Step-by-step explanation:
SD^2=(12-12)^2+...+(14-12)^2/10
SD^2=72/10
SD^2=7.2
SD=squeare root of 7.2
SD=2.6832815729997
A rectangle has an area of 82 ft2. What is
the length if the width is 10 ft?
Answers
Answer:
187
Step-by-step explanation:
Arthur has a box which contains 6 black balls and n (n ≥ 2) white balls, then at random, he takes 3 balls from the box. If the probability of taking any ball is the same and Pₙ is the probability of taking 1 black ball and 2 white balls, what is the largest possible value for Pₙ?
Answers
Answer:
11/68 or 0.1618Step-by-step explanation:
Balls
Black - 6White - nOptions of getting 3 balls
1. White, black, black2. Black, white, black3. Black, black, whiteProbability P(n) in each option
1. WBB
P(w) = 6/(n + 6)P(b1) = n/(n + 6 - 1) = n/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 1)P(n) =
P(w)P(b1)(P(b2) = 6/(n+6) × n/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)2. BWB
P(b1) = n/(n + 6)P(w) = 6/(n + 6 - 1) = 6/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 4)P(n) =
P(b1)P(w)(P(b2) = n/(n+6) × 6/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)3. BBW
P(b1) = n/(n + 6)P(b2) = (n - 1)/(n + 6 - 1) = (n - 1)/(n + 5)P(w) = 6/(n + 5 - 1) = 6/(n + 4)P(n) =
P(b1)P(b2)(P(w) = n/(n+6) × (n - 1)/(n + 5) × 6/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)Final equation is same for each case:
P(n) = 6n(n - 1) / (n + 6)(n + 5)(n + 4)The easy way to find the maximum is to try the numbers or graph.
Both of the methods give the maximum integer n = 11 or n = 12
See attached graph
At both values n we get P(n):
P(11) = 6*11*10 / 15*16*17 = 11/68 = 0.1618 (rounded)P(12) = 6*12*11 / 16*17*18 = 11/68 = 0.1618 (rounded)help me please!!!!!!
Answers
==========================================================
Explanation:
Recall that sine is the ratio of opposite over hypotenuse.
For angle C, the opposite side is AB = 24 as this leg is furthest as possible from angle C. The hypotenuse is always opposite the 90 degree angle.
So,
sin(angle) = opposite/hypotenuse
sin(C) = AB/AC
sin(C) = 24/40
sin(C) = (8*3)/(8*5)
sin(C) = 3/5
If you want to find the measure of angle C, then you apply the arcsine rule to both sides. Inverse sine is the same as arcsine.
Answer:
Step-by-step explanation:
Solution
Here,
H=40
P=32
B=24
Now,
sinC=p/h
=32/40
=4/5
Where, 4 is perpendicular and 5 is hypotenuse.
Hope it helped you.
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the target temperature for a laboratory is 71° f. it can vary by up to 3°. if t is the temperature in the laboratory, which of the following inequalities represents this situation?
Answers
Answer:
|t-71| < 3
Step-by-step explanation:
The inequalities represents this situation is | t - 71 | < 3 .
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size
According to the question
The target temperature for a laboratory = 71° f.
it can vary by up to 3°. (highest limit)
the temperature in the laboratory represented by t
Now,
inequalities represents this situation is
| t - 71 | < 3
Hence, the inequalities represents this situation is | t - 71 | < 3
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The altitude of a helicopter increases 1000 feet every 4 minutes .what is the unit rate change (feet per minute) of the altitude.(there’s no picture)
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Answer:
250
Step-by-step explanation:
divide 1000 by 4 and you will get the unit rate
Give the ratio for sine (e) in decimal form to 4 digits.
13
11
5
Answers
.0147
I am a jedi master
John has a rectangular field that is 12 meters by 6 meters, if he wants to divide the field into 8 sections, what would the area per section be?
Answers
Answer:
9 Meters Squared
Step-by-step explanation:
First multiply 6 by 12 to find the area of the whole field:
[tex]6*12=72[/tex]
Then divide that area by 8:
72/8=9
So:
9 meters squared