By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.
How to simplify a trigonometric expression
In this question we must apply trigonometric rules to simplify a given number, in which case we can take advantage of this expression:
[tex]\sin \frac{\theta}{2} = \sqrt{\frac{1 - \cos \theta}{2} }[/tex]
If we know that [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex], then the rewritten expression is:
x = sin 85°
By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.
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can someone please help meee
Answer:
-3/5
Step-by-step explanation:
put down the 5,0 and 0,3 then simply start at the 5,0 and count up how many boxes it takes to get to the three then count left how many boxes it takes to get to 0 so...3/5. then look at the line. its going down which means it is negative. so the slope is -3/5
Answer:
y is 3 and x is
Step-by-step explanation:
A comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of _______.
A comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of a rate
What is a rate?
A rate is known as the quantity measured with respect to another measured quantity. It refers to the comparison of a part to a whole.
It is also the measure of a part with respect to a whole or a proportion.
Therefore, a comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of a rate
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Find the equation of the parabola with its focus at (6,2) and its directrix y = 0.
What is the value of the element in row 1, column 1 of matrix x? [4 y 0 1] x= [y 4]
The value of the element in row 1, column 1 of matrix x is; y.
What is the value of the element in row 1, column 1 of matrix x?According to the task content, it follows that matrix x is defined as; x= [y 4].
In essence, it follows that the matrix x contains one row and 2 columns. Therefore, the element in row 1, column 1 of matrix x is; y.
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Answer: A
Step-by-step explanation:
A segment that intersects a circle in two points is called a ________________.
hii guys please answer this question
if two -1 and 2 are two zeroes of the polynomial 2x3- x2 - 5x - 2, find its third zero
Answer:
-1/2
Step-by-step explanation:
Zeros of a polynomial function are its x-intercepts, the values of x that make the polynomial zero. Each zero x=p corresponds to a linear factor (x-p) of the polynomial.
Monic polynomialA monic polynomial is one that has a leading coefficient of 1. For a monic polynomial of degree n, the coefficient of the term of degree n-1 is the opposite of the sum of all of the zeros. The constant term of any odd-degree monic polynomial is the opposite of the product of the zeros.
The given polynomial can be made monic by dividing by its leading coefficient:
(2x^3 -x^2 -5x -2)/2 = x^3 -(1/2)x^2 -(5/2)x -1
Sum of zerosThe given polynomial has degree 3, so we're interested in the coefficient of the x^2 term. That coefficient is -1/2, so the sum of zeros will be ...
sum of zeros = -(-1/2) = 1/2
If z represents the third zero, then we have the sum ...
1/2 = -1 +2 +z
z = -1/2 . . . . . . subtract 1 from both sides
The third zero is -1/2.
Product of zerosThe given polynomial is of odd degree, so the product of the zeros is the opposite of the constant.
(-1)(2)(z) = -(-1)
z = 1/(-2) = -1/2 . . . . . divide by the coefficient of z
The third zero is -1/2.
GraphOf course, a graph will show all of the (real) zeros. The attached graph from a graphing calculator shows the third zero is -1/2.
7. Holly plays pool on Sundays. She pays $6.50 for admission and $3.50 for
each round she plays. Which expression can be used to determine how
much she pays if she plays x rounds of pool?
Answer:
3.50x+6.50=y
Step-by-step explanation:
Describe three ways to determine the measure of segment YZ.
Triangle X Y Z is shown. Angle X Y Z is a right angle and angle Z X Y is 30 degrees. The length of hypotenuse X Z is 50 meters.
Step-by-step explanation:
tan 30 degre = perpendicular /base
I wrote the rule than you can easily find hope this help you
Using 3 different methods, we can find that YZ = 25m
The complete image of a triangle is attached with the answer below.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations
sin(θ) = (opposite cathetus)/H
cos(θ) =(adjacent cathetus)/H
tan(θ) =(opposite cathetus)/(adjacent cathetus)
Now, in the given image we can see that:
θ = 30°
H = 50m
XY = adjacent cathetus
YZ = opposite cathetus.
We want to find YZ, so with the known things, we can use the first relation:
Sin 30 = YZ / 50
YZ = 50 x Sin30 = 25 meters
Now let's try another way.
We know that the sum of the internal angles of a triangle is always equal to 180°
In a triangle rectangle, we always have an angle equal to 90°.
Then the missing angle for our triangle can be computed from:
Z + 90° + 30° = 180°
Z = 180° - 90° - 30° = 60°
From this angle, the side YZ is the adjacent cathetus, then we can use the second trigonometric relation:
Cos 60 = YZ / 50
YZ = 50 x Cos 60 = 25 meters
Third way.
Whit the same angle we could find the side XY, the opposite cathetus, with:
Sin 60 = XY / 50
XY = 50Sin 60 = 43.3 meters
Now that we know one of the catheti, we can use the last trigonometric relation
tan 60 = XZ / YZ = 43.3 / YZ
YZ = 43.3 / tan 60 = 25 meters
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Solve the system of equations using the elimination method. 1.Solve {x + 3y = -15
{-3x + 2y = 23
Step 1- Multiply the equations to make the coefficients
match in either the x- or y-variable.
Step2- After you multiply, add or subtract the two equations.
Step 3- Then solve for the variables that is left.
The solution is ( , )?
check the solution in both original equations by using algebra
An equation is formed of two equal expressions. The solution is (-9,-2).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the equation x + 3y = -15 and -3x + 2y = 23,
Step 1- Multiply the equations to make the coefficients match in either the x- or y-variable.
x + 3y = -15
3x + 9y = -45
Step2- After you multiply, add or subtract the two equations.
3x + 9y -3x + 2y = -45 + 23
Step 3- Then solve for the variables that is left.
11y = -22
y = -2
Step4- Substitute the value of y in any one of equations to solve for x.
x + 3(-2) = -15
x - 6 = -15
x = -9
Hence, The solution is (-9,-2).
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Distribute and simplify these radicals.
[tex]\sqrt{12} times(-1+\sqrt{5} )[/tex]
Answer:
[tex]-2\sqrt{3} +2\sqrt{15}[/tex]
Step-by-step explanation:
When we simplify this equation, we have to multiply the numbers outside the parenthesis with the the numbers inside the parenthesis. In this equation, we have to multiply [tex]\sqrt{12}[/tex] by [tex]-1[/tex] , getting the answer of [tex]-\sqrt{12}[/tex], which can be further simplified into [tex]-2\sqrt{3}[/tex]. Next, looking at [tex]\sqrt{12}[/tex] × [tex]\sqrt{5}[/tex], we get [tex]\sqrt{60}[/tex], which can also be simplified further into [tex]2\sqrt{15}[/tex]. Now, adding up these two numbers get [tex]-2\sqrt{3} +2\sqrt{15}[/tex].
Help me show your work
The value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
The value of x that will satisfy this condition can be found by simplifying the given inequality. Therefore, The given inequality can be simplified as,
4x + 1 - 1 ≥ -8
4x ≥ -8
x ≥ -2
Hence, the value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.
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can someone please help and explain its due in a littleee
The slope of the given equation of the straight line is - 5/4.
We know that the direction of a line is defined by its slope. The slope is calculated by dividing the difference between the y-coordinates of two points on a line by the difference between their x-coordinates.
Here the equation of the line is
y = - (5/4)x - 1.
At x = 0, y = -(5/4) × 0 - 1 = -1
and at x = 4, y = -(5/4) × 4 - 1 = - 5 - 1 = -6
Now the slope = (-6 - (-1))/(4 - 0) = (-6 + 1)/4 = - 5/4
Therefore the slope of the given equation of the straight line is - 5/4.
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Which is precisely defined using the undefined terms point and plane?
O circle
O line segment
O perpendicular lines
O ray
Answer:
Option A: circle
Step-by-step explanation:
A circle is a set of points in a plane that are equidistant from a common center point.
Find the base of an isosceles triangle whose area is 60 cm² and the length of one of its equal sides is 13 cm.
Answer:
Base = 24 cm or 10cm
Step-by-step explanation:
REMEMBER:
An isosceles triangle ABC with base BC = ‘b' & height AD = ‘h' & its equal sides =13 cm & area = 60 cm²
Using the formulas
[tex]A=\frac{bh_b}{2}[/tex]
[tex]h_b=\sqrt{a^2-\frac{b^2}{4} }[/tex]
There are 2 solutions for [tex]b[/tex]
[tex]b=2\sqrt{2} \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2+\sqrt{13^4-4*60^2} } }[/tex] ≈ [tex]10cm[/tex][tex]b=2\sqrt{2} \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2-\sqrt{13^4-4*60^2} } }=24cm[/tex]
Less complex:
Area of a triangle = 1/2 * b * h = 60
=> h = 120/b
In right triangle ABD
13² = h² + b² /4 ( by Pythagoras law)
=>169 = 120²/b² + b²/4
=>676 b² = 57600 + b^4
=> b^4 - 676 b² + 57600 = 0
=> b² = 676 +- √(676² - 4*57600) / 2
=> b²= 676 +- √(226576) /2
=> b² = (676 +- 476 )/2
=> b² = 1152/2 , 200 /2
=> b² = 576 , 100
=> b = 24, 10
So, Base = 24 cm or 10cm
If Scott started by asking 3 friends to sponsor him and each of those friends asked
three friends, how many sponsors would he have on the 4th week
Answer:
336 sponsers
Step-by-step explanation:
3＋(3×3)
=3+9
=12
for the 4th week：
12×7=84
84×4=336
Given: f(a)= a³ +a and g(a) = a -1 Find: (fog)(a)
Answer:
(fog)(a) = a³ - 3a² + 4a - 2
= (a - 1)×(a² - 2a + 2)
Step-by-step explanation:
Given :
g(a) = a -1
f(a)= a³ +a
…………………………
(fog)(a) = f(g(a)))
= g(a)³ + g(a)
= (a - 1)³ + (a - 1)
= (a³ - 3a² + 3a - 1) + (a - 1)
= a³ - 3a² + 3a - 1 + a - 1
= a³ - 3a² + 3a + a - 1 - 1
= a³ - 3a² + 4a - 2
Second method :
(fog)(a) = f(g(a)))
= f(a - 1)
= (a - 1)³ + (a - 1)
= (a - 1)×[(a - 1)² + 1]
= (a - 1)×[a² - 2a + 1 + 1]
= (a - 1)×(a² - 2a + 2)
can someone please help mee
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Domain = [-2, 1)[/tex]
[tex]\qquad \tt \rightarrow \:Range = [0 , 4][/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Domain = All possible values of x for which f(x) is defined
[ generally the extension of function in x - direction ]
Range = All possible values of f(x)
[ generally the extension of function in y - direction ]
[tex] \large\textsf{For the given graph : } [/tex]
[tex]\qquad \tt \rightarrow \: domain = [ - 2,1)[/tex]
[tex]\qquad \tt \rightarrow \: range= [ 0,4][/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
find the value of c so that (x+1) is a factor of the polynomial p(x). p(x)=5x^4+7x^3-2x^2-3x+c
Answer:
C=1
Step-by-step explanation:
5x^4+7x^3-2x^2-3x+1 / (x+1)
-1/ 5 7 -2 -3 1
5 2 -4 1 0
Remainder of 0 indicates that x=-1 is a solution.
All the edges of the object in the diagram are equal in length. The object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges. What is the shape of the cross-section resulting from the cut?
The shape of the cross-section resulting from the cut is rhombus.
What is a rhombus?A rhombus simply means a shape that has opposite sides to be parallel and the sides are equal.
Given:
object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges.
Edges of the object in the diagram are equal in length and that the object is cut by a vertical plane containing A and B.
Hence, the shape of the cross-section resulting from the cut is a rhombus.
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GIVING 100 POINTS PLEASE HELP!! Consider the expression 3+(−4)−2−(−1). answer these three questions.
How many balloons should you add? How many should you remove?
How many weights should you add? How many should you remove?
What is the final answer?
Answer:
Step-by-step explanation:
12 becuase you have to read the equasion and do the problem
factorise 3 squared+ 5x +12
factorise 3 squared+ 5x +12
15.95 to the nearest cent
Step-by-step explanation:
95 95 branded to the nearest 10 with the number line
deter determine the two constructive multiples of 10 that bracket 95
9 is between 90 and 100
asteroid on the number line 95 is the midpoint between the 90 and 100
therefore 95 rounding to the nearest 10 is equal to 100
I need these answers ASAP would be very grateful for these if you would like to help me out I would appreciate it and give a good amount of points!
Answer:
5. c = 8pi cm
6. c = 18pi ft
7. c = 8.6pi in
8. c = 11/2pi m
Step-by-step explanation:
The circumference of a circle can be easily found using the formula: c = [tex]\pi[/tex]d, where the diameter is d.
Now you just plug your numbers into the formula!
5. c = pi x d
c = 8pi cm
6. This one gives you the radius instead of the diameter. All you need to do now is to double the radius to find the diameter.
9 ft x 2 = 18 ft
Now, it follows the formula.
c = pi x d
c = 18pi ft
7. c = pi x d
c = 8.6pi in
8. c = pi x d
c = pi x 2(2 3/4m) - Note that this is a mixed fraction. To be able to multiply it, you need to convert it to an improper fraction.
c = pi x 2(11/4)
c = pi x 11/2
c = 11/2pi m
:)
Philippa threw some darts. Her minimum score was 5 and
her maximum score was 53. What was the range of her
scores?
Min = 5
Max = 53
Range = ?
can someone do this i sent a ss with it aswell
Answer:
the answer is 6
Step-by-step explanation:
1. 3x+4=22
2. subtract 4 from both sides
3x+4=22
-4=22
-4
3. rewrite the equation 3x=18
4. divide 3 from both sides
3x/3=18/3
hint: 3x/3 cancels out so you just have x
5. divide 18 by 3
6.x=6
Four complex numbers form the vertices of a square in the complex plane. Three of the numbers are $-19 32i,$ $-5 12i,$ and $-22 15i$. What is the fourth number
If the three numbers of a square in the complex plane are [tex]-19+32i,-5+12i and -22+15i[/tex] , then the fourth complex number [tex]-2+19i[/tex].
Given [tex]-19+32i,-5+12i and -22+15i[/tex] are three numbers.
Complex numbers are those numbers which extends the real numbers with an imaginary i. In this [tex]i^{2}=-1[/tex]. Major complex numbers are in the form a+ bi where a and b are real numbers.
let the fourth complex numbers be [tex]x+yi[/tex]. Then according to question;
=[tex](-22+15i)-(-5+12i)[/tex]
=(cos π/2+i sin π/2) [tex](x+yi)-(-5+12i)[/tex]
[tex]-17+3i=-y+12[/tex][tex]+(x+5)i[/tex]
Now solving for x and y by equating both sides.
x=-2 and y=29
Put the value of x and y in [tex]x+yi[/tex]
Z=-2+29i
Hence if the three numbers which forms vertices of a square are [tex]-19+32i,-5+12i,-22+25i[/tex] then the fourth complex numbers be [tex]-2+29i[/tex].
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The function h(x) is a transformation of the square root parent function,
f(x)=√x. What function is h(x)?
-5
5
-5-
h(x)
f(x)
K
I
5
The function h(x) is a transformation of the square root parent function,
f(x)=√x. The function is h(x) A: √x+5.
What is Transformations?Transformations come in the form;
y =√(x-h) +k,
where h is responsible for left-right movements, and k is responsible for up-down movements.
From the graph, we can see that f(x) is simply the parent square root function, √x.
To translate a function right by p units and up by q units, the function becomes
g(x) = f(x -p) +q
(p, q) = (5, 0)
To get h(x), there is a translation of 5 units to the left, which can be represented by a value of h = -5.
h(x) = f(x + 5) +0
h(x) = √(x+ 5)
Hence, The function h(x) is a transformation of the square root parent function, f(x)=√x. The function is h(x) A: √x+5.
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An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of s 46° e to a location in the sea. it then flies 483 miles from the sea at a bearing of s 55° w to another location. finally, the aircraft flies straight back from the second location to its base. what is the total distance it flies, rounded to the nearest mile? 2 vertical lines. top, point a (airport), point c below are marked on left line. point b marked on middle of right line. abc makes triangle. ab as c equals 5.5. bc as a equals 4.83. interior angle a 46 degrees. exterior angle b 55 degrees. a. 550 miles b. 1,033 miles c. 1,583 miles d. 1,692 miles e. 2,210 miles
The total distance it flies, rounded to the nearest mile is: d. 1,692 miles .
Total distanceFirst distance= 550 miles (given)
Second distance=483 miles (given)
Now let find the third distance
Let x represent the third distance
Hence:
x/sin79 = 550/sin55
x= 659.1
Now let calculate the total distance
Total distance=550+483+659.1
Total distance= 1692.1
Total distance= 1692 miles (rounded)
Therefore the correct option is d.
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Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 polnts)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Horizontal and Vertical translations can transform f(x) to g(x).
Equations to transform f(x) to g(x) are: g(x) = f(x) + k, and g(x) = f(x + k).
In vertical translation k = 18, and horizontal translation k = 6.
SolutionEquations of the two st. lines
Select two points on the line f(x) viz. (1,2), (2,5).
The equation of the line f(x) is
[tex]\frac{y-2}{x-1} = \frac{5-2}{2-1} \Rightarrow \mathbf{y=3x-1}.[/tex]
Select two points on the line g(x) viz. (-5,2), (-4,5).
The equation of the line g(x) is
[tex]\frac{y-2}{x+5} = \frac{5-2}{-4+5} \Rightarrow \mathbf{y=3x+17}.[/tex]
Ways to transform
The two lines, f(x) and g(x), are parallel to each other so their orientation w.r.t. each other is not changed. f(x), thus, can be translated to obtain g(x).
The translation of f(x) can be done in two ways: Vertical translation, and Horizontal translation.
Horizontal translation
f(x) can be translated horizontally to obtain g(x) by the relation of type g(x) = f(x + k).
Using the above relation for the two lines,
3x + 17 = 3(x + k) -1 ⇒ k = 6.
The horizontal translation relation is g(x) = f(x + 6).
Vertical translation
Vertical translation can be done with the relation g(x) = f(x) + k.
Using the above relation for the two lines,
3x + 17 = 3x - 1 + k ⇒ k = 18.
The vertical translation relation is g(x) = f(x) + 18.
The two transformation relations are: g(x) = f(x + 6), and g(x) = f(x) + 18.
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How do you use the additive inverse to evaluate an expression that uses subtraction ?
To use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive
What is additive inverse?Additive inverse is simply changing the sign of a number and then adding it to the original number to get an answer that is equal to 0.
The additive inverse of a number is another number
The additive inverse of number 3 is - 3
For an expression that uses subtraction, to use the additive inverse, change the sign of the number to positive
Thus, to use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive
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