Answer:
[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]
Step-by-step explanation:
[tex]\alpha \text{ and } \beta \text{ in Quadrant I}[/tex]
[tex]$\tan(\alpha)=\frac{1}{7} \text{ and } \sin(\beta)=\frac{1}{\sqrt{10}}=\frac{\sqrt{10} }{10} $[/tex]
Using Pythagorean Identities:
[tex]\boxed{\sin^2(\theta)+\cos^2(\theta)=1} \text{ and } \boxed{1+\tan^2(\theta)=\sec^2(\theta)}[/tex]
[tex]$\left(\frac{\sqrt{10} }{10} \right)^2+\cos^2(\beta)=1 \Longrightarrow \cos(\beta)=\sqrt{1-\frac{10}{100}} =\sqrt{\frac{90}{100}}=\frac{3\sqrt{10}}{10}$[/tex]
[tex]\text{Note: } \cos(\beta) \text{ is positive because the angle is in the first qudrant}[/tex]
[tex]$1+\left(\frac{1 }{7} \right)^2=\frac{1}{\cos^2(\alpha)} \Longrightarrow 1+\frac{1}{49}=\frac{1}{\cos^2(\alpha)} \Longrightarrow \frac{50}{49} =\frac{1}{\cos^2(\alpha)} $[/tex]
[tex]$\Longrightarrow \frac{49}{50}=\cos^2(\alpha) \Longrightarrow \cos(\alpha)=\sqrt{\frac{49}{50} } =\frac{7\sqrt{2}}{10}$[/tex]
[tex]\text{Now let's find }\sin(\alpha)[/tex]
[tex]$\sin^2(\alpha)+\left(\frac{7\sqrt{2} }{10}\right)^2=1 \Longrightarrow \sin^2(\alpha) +\frac{49}{50}=1 \Longrightarrow \sin(\alpha)=\sqrt{1-\frac{49}{50}} = \frac{\sqrt{2}}{10}$[/tex]
The sum Identity is:
[tex]\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)[/tex]
I will just follow what the question asks.
[tex]\text{Find the value of }\alpha+2\beta[/tex]
[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]
[tex]\text{I will first calculate }\cos(2\beta)[/tex]
[tex]$\cos(2\beta)=\frac{1-\tan^2(\beta)}{1+\tan^2(\beta)} =\frac{1-(\frac{1}{7})^2 }{1+(\frac{1}{7})^2}=\frac{24}{25}$[/tex]
[tex]\text{Now }\sin(2\beta)[/tex]
[tex]$\sin(2\beta)=2\sin(\beta)\cos(\beta)=2 \cdot \frac{\sqrt{10} }{10}\cdot \frac{3\sqrt{10} }{10} = \frac{3}{5} $[/tex]
Now we can perform the sum identity:
[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]
[tex]$\sin(\alpha + 2\beta)=\frac{\sqrt{2}}{10}\cdot \frac{24}{25} +\frac{3}{5} \cdot \frac{7\sqrt{2} }{10} = \frac{129\sqrt{2}}{250}$[/tex]
But we are not done yet! You want
[tex]\alpha + 2\beta[/tex] and not [tex]\sin(\alpha + 2\beta)[/tex]
You actually want the
[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]
Answer:
ok bye guy................
HELP ME PLEASE Given that the universal set is all real numbers, write the complement of set A. Set A: {Irrational numbers}
Answer: The complement is Q, the set of the rational numbers.
Step-by-step explanation:
Ok, here we can use the fact that the set of all the real numbers is equal to the union of the set of the rational numbers and the set of the irrational numbers. (Remember that Q, the rational numbers, also does include the set of the integer numbers))
Then, if the universal set is R, we have that the universal set is:
R = Q + I
Where Q = set of rational numbers and I = set of irrational numbers.
Then, the complement of the set A = I = irrational numbers, is equal to:
R - I = Q + I - I = Q
Then the set of the rational numbers is the complement of the set A.
A homeowner measured the voltage supplied to his home on 41 random days, and the average (mean) value is volts. 128.5 Choose the correct answer below. A. The given value is a for the because the data collected represent a . statistic year population B. The given value is a for the because the data collected represent a . statistic year sample C. The given value is a for the because the data collected represent a . parameter year sample D. The given value is a for the because the data collected represent a .
Answer:
B. The given value is a for the because the data collected represent a . statistic year sample
Step-by-step explanation:
A population is the total of similar items that are of interest to the researcher.
Since the researcher cannot measure each of these items he chooses a part of it to measure. This part of the population is called a sample.
A good sample is representative of the larger population. Deduction made from the sample is used to represent the whole population.
In this scenario the population is the whole year, and the sample is 41 days.
So the mean derived from the sample is statistic of sample from the year.
This can be used to make deductions about the whole year.
Plz help!
i Cant answer it
Answer: (4,90)
Step-by-step explanation:
In a coordinate pair, the first number represents the x-axis and the second represents the y-axis.
Hope it helps <3
Answer:
C (4,90)
Step-by-step explanation:
In the graph, the point P is on 4 along the x-axis,
and 90 on the y-axis,
therefore making it's coordinates (4, 90).
Hope this helped! :)
p=E/x+Y express x in terms of p,e and y
Answer:
x = E/(p - y)
Step-by-step explanation:
p - y = e/x
x(p-y) = e
x = e/(p-y)
Answer:
Hey there!
p=e/x+y
p-y=e/x
x(p-y)=e
x=e/(p-y)
Hope this helps :)
What the answer now now
Answer:
The area of the triangle is [tex]346.0\ mm^2[/tex]
Step-by-step explanation:
Given
Triangle VWU
Required
Determine the Area of the Triangle
First, we'll solve for the third angle
Angles in a triangle when added equals 180; So
[tex]36 + 24 + <V = 180[/tex]
[tex]60 + <V = 180[/tex]
[tex]<V = 180 - 60[/tex]
[tex]<V = 120[/tex]
Next is to determine the length of VW using Sine Law which goes thus
[tex]\frac{VW}{Sin24} = \frac{34}{Sin36}[/tex] (Because 24 degrees is the angle opposite side VW)
Multiply both sides by Sin24
[tex]SIn24 * \frac{VW}{Sin24} = \frac{34}{Sin36} * Sin24[/tex]
[tex]VW = \frac{34}{Sin36} * Sin24[/tex]
[tex]VW = \frac{34}{0.5878} * 0.4067[/tex]
[tex]VW = 23.5 mm[/tex] (Approximated)
At this stage, we have two known sides and two known angles;
The Area can be calculated as the 1/2 * the products of two sides * Sin of the angle between the two sides
Considering VW and VU
VW = 23.5 (Calculated);
VU = 34 (Given)
The angle between these two sides is 120 (Calculated);
Hence;
[tex]Area = \frac{1}{2} * 23.5 * 34 * Sin120[/tex]
[tex]Area = \frac{1}{2} * 23.5 * 34 * 0.8660[/tex]
[tex]Area = \frac{1}{2} * 691.934[/tex]
[tex]Area = 346.0 mm^2[/tex]
Hence, the area of the triangle is [tex]346.0\ mm^2[/tex]
PLSSSSS HELPPPPP Subtract 6/7-3/x
Answer:
[tex]\huge\boxed{\dfrac{6}{7}-\dfrac{3}{x}=\dfrac{6x-21}{7x}}[/tex]
Step-by-step explanation:
[tex]\dfrac{6}{7}-\dfrac{3}{x}=\dfrac{(6)(x)}{(7)(x)}-\dfrac{(7)(3)}{(7)(x)}=\dfrac{6x}{7x}-\dfrac{21}{7x}=\dfrac{6x-21}{7x}[/tex]
A point with coordinates (a, b) is plotted on a coordinated plane. The values of a and b can be any positive or negative integer.
What must be true about the point ( a, b)?
A) It is flipped across the
y- axis from the original point
B) it is flipped across the
x-axis from the original point
C) it is in the quadrant diagonal to the original point
D) it is in the same quadrant as the original point, but in a different location
Answer:
I think it's x-axis.
Step-by-step explanation:
but me could me wrong
Answer:
The correct answer to this question would be C.
Step-by-step explanation:
took the test. Hope this helps!
30 points **please help quadratic relations - will give brainlist to first one who answers
Answer:
See attached figure with table filled in.
Step-by-step explanation:
Answer:
[tex]\boxed{\mathrm{view \: attachment }}[/tex]
Step-by-step explanation:
Vertex is the highest or lowest point of a parabola.
Axis of symmetry is the line that cuts the parabola in half.
y-intercept is the point where the parabola touches the y-axis.
The maximum or minimum values are the highest or lowest values the parabola can reach.
x-intercepts are the points where the parabola touches the x-axis.
A cylinder has radius r and height h. A. How many times greater is the surface area of a cylinder when both dimensions are multiplied by a factor of 2? 3? 5? 10? B. Describe the pattern in part (a).
Answer: A. Factor 2 => 4x greater
Factor 3 => 9x greater
Factor 5 => 25x greater
Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:
A = 2.π.r.h
A cylinder of radius r and height h has area:
[tex]A_{1}[/tex] = 2πrh
If multiply both dimensions by a factor of 2:
[tex]A_{2}[/tex] = 2.π.2r.2h
[tex]A_{2}[/tex] = 8πrh
Comparing [tex]A_{1}[/tex] to [tex]A_{2}[/tex] :
[tex]\frac{A_{2}}{A_{1}}[/tex] = [tex]\frac{8.\pi.rh}{2.\pi.rh}[/tex] = 4
Doubling radius and height creates a surface area of a cylinder 4 times greater.
By factor 3:
[tex]A_{3} = 2.\pi.3r.3h[/tex]
[tex]A_{3} = 18.\pi.r.h[/tex]
Comparing areas:
[tex]\frac{A_{3}}{A_{1}}[/tex] = [tex]\frac{18.\pi.r.h}{2.\pi.r.h}[/tex] = 9
Multiplying by 3, gives an area 9 times bigger.
By factor 5:
[tex]A_{5} = 2.\pi.5r.5h[/tex]
[tex]A_{5} = 50.\pi.r.h[/tex]
Comparing:
[tex]\frac{A_{5}}{A_{1}}[/tex] = [tex]\frac{50.\pi.r.h}{2.\pi.r.h}[/tex] = 25
The new area is 25 times greater.
B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.
find the value of a and explain
Answer:
D
Step-by-step explanation:
The triangle is an isosceles triangle which means that two sides are the same, A is the same size of the equal side so A is D.
Answer:
The answer is D.
1) Suppose f(x) = x2 and g(x) = |x|. Then the composites (fog)(x) = |x|2 = x2 and (gof)(x) = |x2| = x2 are both differentiable at x = 0 even though g itself is not differentiable at x = 0. Does this contradict the chain rule? Explain.
Answer:
This contradict of the chain rule.
Step-by-step explanation:
The given functions are
[tex]f(x)=x^2[/tex]
[tex]g(x)=|x|[/tex]
It is given that,
[tex](f\circ g)(x)=|x|^2=x^2[/tex]
[tex](g\circ f)(x)=|x^2|=x^2[/tex]
According to chin rule,
[tex](f\circ g)(c)=f(g(c))=f'(g(c)g'(c)[/tex]
It means, [tex](f\circ g)(c)[/tex] is differentiable if f(g(c)) and g(c) is differentiable at x=c.
Here g(x) is not differentiable at x=0 but both compositions are differentiable, which is a contradiction of the chain rule
Which of the following represents the factorization of the polynomial below?
2x2 +11x +5
Answer:
(2x + 1)(x + 5)
Step-by-step explanation:
2x² + 11x + 5 =
= 2x² + 10x + x + 5
= 2x(x + 5) + (x + 5)
= (2x + 1)(x + 5)
HELP!!
According to the graph, what is the value of the constant in the equation below?
Answer:
The answer is option BStep-by-step explanation:
To find the constant in the equation pick any values of x and y and substitute it into the equation
First make constant the subject
constant = height × width
From the question
Using
height = 30
width = 2
We have
constant = 30 × 2 = 60
Again
Using
height = 12
width = 5
constant = 12 × 5 = 60
Since the constant is the same for any values used
constant = 60Hope this helps you
Long Division of x^3-3x^2-10x+24 ÷x-2
Answer:
see explanation
Step-by-step explanation:
x - 2 | x² - x - 12
------------------------
x³ - 3x² - 10x + 24
x³ - 2x² ↓ ↓ ← subtract terms from terms above
--------------------------
- x² - 10x + 24
- x² + 2x ↓ ← subtract terms from terms above
----------------------------
- 12x + 24
- 12x + 24 ← subtract terms from above terms
----------------------------
0 ← remainder
Since remainder is zero then (x - 2) is a factor
and quotient = x² - x - 12 , thus
x³ - 3x² - 10x + 24 = (x - 2)(x² - x - 12) = (x - 2)(x - 4)(x + 3)
ratio
simplify
4x:9=7:3
Answer:
4x:9=7:3 can be written as
[tex] \frac{4x}{9} = \frac{7}{3} [/tex]
Cross multiply
We have
4x(3) = 9 × 7
12x = 63
Divide both sides by 12
[tex]x = \frac{21}{4} \: \: \: \: \: or \: \: \: 5 \frac{1}{4} [/tex]
Hope this helps you
Answer:
[tex]\boxed{x=\frac{21}{4}}[/tex]
Step-by-step explanation:
[tex]4x:9=7:3[/tex]
Turn ratios to fractions.
[tex]\frac{4x}{9} =\frac{7}{3}[/tex]
Cross multiplication.
[tex]4x \times 3 = 9 \times 7[/tex]
Simplify.
[tex]12x=63[/tex]
Divide both sides by 12.
[tex]x=\frac{63}{12}[/tex]
[tex]x=\frac{21}{4}[/tex]
Eight of your friends came to your house to watch a movie. Three-fourths of your friends stayed overnight. How many friends stayed?
Answer:
6 friends
Step-by-step explanation:
8 friends came to watch the movie.
3/4 of them stayed overnight.
The number of people that stayed overnight will be the product of 3/4 by 8:
3/4 * 8 = 24 / 4 = 6
6 friends stayed overnight.
Answer:
6 friends because the three fourths are gone
Step-by-step explanation:
Which is a diagonal through the interior of the cube? Side A H Side B E Side C H Side F G
Answer:
Option (A)
Step-by-step explanation:
Every cube has 8 vertices and 6 faces.
Cube shown in the picture attached,
Diagonal through interior of the given cube will be the segments joining the vertices A-H, G-B, C-F and D-E.
Therefore, from the given options diagonal of the interior of the cube will be Side AH.
Option A will be the answer.
Answer:
the awnser is A
Step-by-step explanation:
i took a quiz
How many solutions are there to |x|=-8
Answer:No solution
Step-by-step explanation:An absolute value equation cannot equal a negative number
What is the equation of the line of best fit for the following data? Round the
slope and yintercept of the line to three decimal places.
Need help ASAP!!
Answer:
The second choice should be the best fit line.
Hi! Can I have some help on this math question...
Question C please!
Please explain it as I am very confused!
15 Points
- Thanks!
Answer:
β = 22.5°
Step-by-step explanation:
In a triangle, the sum of interior angles must add up to 180°.
Since the angle marked with corners is equal to 90°, we can write an equation to solve for β.
3β + β + 90° = 180°
4β = 180° - 90°
4β = 90°
β = 90° / 4
β = 22.5°
Answer:
T is equal to R
Hope this helps.....
Evaluate 7m + 2n - 8p/n for m = –4, n = 2, and p = 1.5.
Answer:
-30
Step-by-step explanation:
7m + 2n - 8p/n
Let m = –4, n = 2, and p = 1.5
7(-4) + 2 ( 2) -8*(1.5)/2
-28 + 4 - 4*1.5
-28+ 4 - 6
-30
Answer:
-30
Step-by-step explanation:
Hey there!
Well given,
m = -4
n = 2
p = 1.5
We need to plug those number into,
7m + 2n - 8p/n
7(-4) + 2(2) - 8(1.5)/(2)
-28 + 4 - 12/2
-28 + 4 - 6
-24 - 6
-30
Hope this helps :)
If events A and B are independent, what must be true?
P(A|B) = P(B)
P(A|B) = P(A)
P(A) = P(B)
P(A|B) = P(B|A)
Answer:
P(A|B) = P(A)
Step-by-step explanation:
If events A and B are independent, then we have:
P(A) x P(B) = P(A⋂B)
As the conditional probability formula states:
P(A⋂B) = P(A|B) x P(B) = P(B|A) x P(A)
=> P(A) x P(B) = P(A|B) x P(B) = P(B|A) x P(A)
or
P(A) = P(A|B)
or
P(B) = P(B|A)
Answer:
B
Step-by-step explanation:
Please answer this question now
Answer:
y = 9.1
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}[/tex]
[tex]\frac{\text{SinW}}{\text{w}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{SinX}}{\text{x}}[/tex]
Since m∠W + m∠X + m∠Y = 180°
m∠W + 58° + 106° = 180°
m∠W = 180° - 164°
m∠W = 16°
[tex]\frac{\text{Sin16}}{\text{w}}=\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}[/tex]
[tex]\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}[/tex]
y = [tex]\frac{8\times (\text{Sin106})}{\text{SIn58}}[/tex]
y = 9.068
y ≈ 9.1
What is the simplified form of 5x-9x
Answer:
-4x
Step-by-step explanation:
5x - 9x
Factor out x
x( 5-9)
x ( -4)
-4x
please help Evaluate 5 - (3/2) to the 3 power A.) 13/8 B.) 9.5 C.) 18.5 D.) 2197/8
Answer: THE ANSWER IS A
Step-by-step explanation:
5-(3/2)^3
=13/8
im a math god
Someone please help! Thank you
Answer:
110
Step-by-step explanation:
the sum of straight angle is 180
the sum of angle of triangle=180
angle E=180-120=60
triangle BDE: <B=180-60-90=30
<B in triangle ACB=180-(130+30)=20)
in traingle ACB: <A = 180-(90+20)=70
angle x=180-70=110 degrees
James determined that these two expressions were equivalent expressions using the values of y=4 and yu 6. Which
statements are true? Check all that apply
7x+4 and 3x+5+4x-1
When - 2. both expressions have a value of 18.
The expressions are only equivalent for X-4 and X- 6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When - 0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if X-
Answer with explanation:
Two or more Algebraic expressions are said to be equivalent, if both the expression produces same numerical value , when variable in the expressions are replaced by any Real number.
The two expressions are
1. 7 x +4
2. 3 x +5 +4 x =1
Adding and subtracting Variables and constants
→7 x +5=1
→7 x +5-1
→7 x +4
→ When x=2,
7 x + 4 =7×2+4
=14 +4
=18
So, Both the expression has same value =18.
→So, by the definition of equivalent expression, when ,you substitute , x by any real number the two expression are equivalent.
Correct options among the given statement about the expressions are:
1.When x = 2, both expressions have a value of 18.
2.The expressions have equivalent values for any value of x.
3.The expressions have equivalent values if x = 8.
In the lab, Charmaine has two solutions that contain alcohol and is mixing them with each other. Solution A is 12% alcohol and Solution B is 40% alcohol. She uses 800 milliliters of Solution A. How many milliliters of Solution B does she use, if the resulting mixture is a 32% alcohol solution
Answer: Charmaine wil use 2000 mL of solution B
Step-by-step explanation: Suppose that volume of solution B for the mixture is J.
Volume of solution A used is [tex]V_{A}[/tex] = 0.12*800
Volume of solution B used is [tex]V_{B}[/tex] = 0.4*J
Volume Total is V = 800 + J
0.12*800 + 0.4*J = 0.32(800 + J)
96 + 0.4J = 256 + 0.32J
0.08J = 160
J = 2000
Volume of solution B is 2000mL or 2L.
Mary earns $28,000 a year. One week she grossed $658.00. She had sold $1673.19 worth of merchandise. what is the rate of her commission?
Answer:
Her commission rate is 7.44%
Step-by-step explanation:
The parameters given are;
The amount Mary earns annually = $28,000
The amount Mary grossed during a week = $658.00
The amount Mary had sold during the week to make the amount grossed during the week = $1673.19
Given that Mary makes $28,000 per year
Therefore;
The amount Mary earns per week = Amount earned per year/52
The amount Mary earns per week = $28,000/52 = $538.46
The amount extra she made on commission = $658.00- $538.46= $119.54
The commission rate = Commission earned/(Amount of merchandise sold)×100
The commission rate = 119.54/1673.19 × 100 = 7.14%
Her commission rate = 7.44%
I promise I will mark as brainiest
There are 18 rectangles inside the playing field. And if you include the fence around the field, that makes 19.