expresa como monomio Cos7x +Sen5x Sen2x
plis lo necesito urgente
Answer:
El monomio equivalente es [tex]\cos 5x \cdot \cos 2x[/tex].
Step-by-step explanation:
Un monomio es una entidad algebraica consistente en un componente, el polinomio dado puede ser transformado mediante el uso de la siguientes propiedades trigonométricas:
[tex]\cos (\alpha + \beta) = \cos \alpha \cdot \cos \beta - \sin \alpha \cdot \sin \beta[/tex]
Es decir:
[tex]\cos 7x + \sin 5x \cdot \sin 2x[/tex] Dado
[tex]\cos (5x+2x) + \sin 5x\cdot \sin 2x[/tex]
[tex]\cos 5x \cdot \cos 2x - \sin 5x \cdot \sin 2x + \sin 5x \cdot \sin 2x[/tex]
[tex]\cos 5x \cdot \cos 2x[/tex]
El monomio equivalente es [tex]\cos 5x \cdot \cos 2x[/tex].
7.
2
a)
An open rectangular box measuring 28 cm by 20 cm
by 12 cm internally is made of woodcm thick. Find:
the capacity of the box in litres,
the volume of wood used in making the box,
the mass of the box if the density of the wood used is
1.25 g/cm3
b)
c)
J
28 82
Answer:
1. Capacity of the box in Litres: 7.917L≈8L
2. Volume of wood used in making the box: 1197cm^3
3. The mass of the box: 1496.25g/cm^3
Step-by-step explanation:
1. 29×21×13=7917cm^3
7917cm^3 → 7.917dm^3→7.917L≈8L
2. Outside Volume: 29×21×13=7917cm^3
Inside Volume: 28×20×13=6720cm^3
7917-6720=1197cm^3
3. 1197×1.25=1496.25g/cm^3
Solve: -7 < 2x+5 < 7
Answer:
[tex] - 6 < x < 1[/tex]
Step-by-step explanation:
first things first:
[tex] - 7 < 2x + 5 \\ - 7 - 5 < 2x + 5 - 5 \\ - 12 < 2x \\ - 6 < x[/tex]
now:
[tex]2x + 5 < 7 \\ 2x + 5 - 5 < 7 - 5 \\ 2x < 2 \\ x < 1 [/tex]
now the intersection is:
[tex] - 6 < x < 1[/tex]
If α and β are the zeroes of the polynomial 2x2 + 3x – 7, then find a polynomial whose zeroes are and .
Answer:
[tex]\frac{-\sqrt{65} - 3 }{4}, \frac{\sqrt{65} + 3}{4}[/tex]
Step-by-step explanation:
Since we cannot factor the expression, we must use quadratic formula: [tex]x = \frac{-b +/-\sqrt{b^2 - 4ac} }{2a}[/tex]
Plug in a for 2, b for 3, and c for -7 and you should find your roots.
In a certain company, all employees are either beta employees or standard employees. In this company, 25% of the beta employees and 17% of the standard employees participate in the voluntary equity program. Let S be the number of standard employees. If there are 600 employees total, what is the value of S?
In addition to the question, the following conditions must be met:
(1) M > 100
(2) more than 130 employees participate in the voluntary equity program
Answer:
Value of A is 200
Step-by-step explanation:
In this scenario when we divide 100 by the percentage of each employee category we will get a proportion that the number of employees must obey.
This is illustrated below:
For Beta employees 100/25= 4
So the number of employees that are Beta must be divisible by 4
For Standard employees 100/17 = 5.882
Since fractions of employees cannot be obtained, in this case the number of employees must be a multiple of 100
Total employees are 600
The various combinations are:
1. Beta employees 500 and Standard employees 100
Survey participants= (0.25 * 500) + (0.17 * 100) = 142
Number of participants is okay as it is >130 but does not satisfy Standard employees being >100
2. Beta employees are 300 and Standard employees are 300
Survey participants = (0.25 * 300) + (0.17 * 300) = 126
This does not satisfy condition of survey participants >130
3. Beta employees 400 and Standard employees 200
Survey participants = (0.25 * 400) + (0.17 * 200) = 134
This satisfies conditions of >130 survey participants and Standard employees >100
So correct value of S is 200
BRAINLIEST ANSWER
Which trigonometric ratio is correct for triangle DEF? (Hint: Use
Pythagorean Theorem first)
Sin(D)= 24/7
Tan(D)= 24/25
Cos(E)= 24/25
Sin(E)= 7/24
Answer:
/25 is the trigonometric
tan=24
Answer:
cos(e) sin(e) is the he correct ratio
This box has the same length, width, and height as the two tennis balls. Which expression gives the volume of the empty space encircling the tennis balls inside the box?
Formala : Times bottom row with side row with the height.
Example: A box has the same length, width, and height as two tennis balls.
Times the bottom row with side row with the height.
100
b)
2. Write the following decimals as common fractions in their simplest forms
a) 0,8
b) 0,03
Answer:
4/5, 3/100
Step-by-step explanation
Let's look at 0.8 first.
0.8 is 8/10, but there's some more.
Let's divide 8 / 2. It is 4.
and, 10 / 2 is 5.
so, 0.8's simplest form is 4/5.
and, 0.03's simmplest fraction is easy.
It is 3/100, cuz 3 is a prime number and 3's integer is only 1 and 3.
Hope this helps!
The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62.
The probability that any postcard posted in Portugal on Friday is delivered to the UK within a week is 0.41.
Anna is on holiday in Portugal.
She posts 15 postcards to the UK on Monday.
How many of her postcards can she expect to be delivered within a week?
(2 marks)
Answer:
You can expect at least 9 of her postcards to arrive within a week
To find that, we multiply the number of postcards by the probability
15 x 0.62 = 9.3
Hope this helps
Good Luck
f(x)=x^2 what is g(x) PLEASE HELP FAST :)))) THANKS IN ADVANCE!!! YOU'RE THE BEST
Answer:
g(x) = -x² - 3
Step-by-step explanation:
You want to mirror f(x), hence the minus sign.
Then you want to translate it 3 down, hence the -3.
Answer:
g(x) = -x² - 3
Step-by-step explanation:
f(x) is x², so g(x) will be negative because it is on the opposite side of the plane.
g(x) will be -x², it cross the y-intercept at (0, -3)
g(x) = -x² - 3
The length of the smaller rectangle at the right is 1 inch less than twice its width. Both the dimensions of the larger rectangle are 2 inches longer than the smaller rectangle. The area of the shaded region is 86 square inches. What is the area of the larger rectangle? PLEASE its important
Answer: 464 square inches is the area of the larger rectangle.
Step-by-step explanation: Assuming that the shaded area is the part of the large rectangle outside the small rectangle, you can set up dimensions from the information given.
The small rectangle's Area = w (2w -1) which is 2w² -w
The large rectangle's Area = (w + 2)(2w + 1) which is 2w² + 5w +2
Now figure out the equation for the "shaded area" (probably outside the small rectangle) 2w² + 5w +2 -(2w² -w) = 86 (The 2w² terms cancel)
6w + 2 = 86, so 6w = 84, w=14
Substitute 14 for w in the dimensions of the large rectangle: (w + 2)(2w + 1)
(14+2)(2[14] + 1) = Area
16 × 29 = 464
(I think I deserve Brainliest for figuring this out, but I see the question has been red-flagged, so We'll see!)
Find the solution of the following simultaneous inequalities: x - 7 –1
Answer:
x-8
Step-by-step explanation:
You add the -7 and -1 and then put the x in front of your answer.
Answer: x-8
Step-by-step explanation:
x-7-1
-7-1=-8
x-8
Which is a better deal? Three movie tickets for 18 dollars or 8 movie tickets for 42 dollars? How do you know? How much money do you save per ticket with the better deal?
Answer:
$42 for 8 tickets
Step-by-step explanation:
To tell which is the better deal you need to find out how much each ticket costs per scenario
$18 for 3 tickets you will need to do 18/3 which will give you $6 a ticket
$42 for 8 tickets you will need to do 42/8 which will give you $5.25 a ticket
$42 option is cheaper per ticket so it is therefore the better option.
Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).
f(x) = -4(x − 8)2 + 3
g(x) = 3x2 + 12x + 15
(graph attatched= h(x) )
Answer:
1. x=8 is the line of symmetry for f(x) = -4(x − 8)2 + 3
2. x=-2 is the line of symmetry of g(x) = 3x2 + 12x + 15
3. x=3 is the line of symmetry of h(x), shown in the graph.
Step-by-step explanation:
To find the line of symmetry of a vertical parabola (second degree polynomial), find the value of x that sets the squared term to zero. This is a vertical line passing through the vertex of the second degree function.
1. f(x) = -4(x − 8)2 + 3
setting x=8 will give f(8) = 3, so x=8 is the line of symmetry
2. g(x) = 3x2 + 12x + 15
here, we need to complete the squares,
g(x) = 3x2 + 12x + 15
g(x) = 3(x^2+4x+5)
g(x) = 3(x^2 + 2(2x) +4 +1)
g(x) = 3((x+2)^2 +1)
So setting x=-2 will anihilate or cancel the squared term, therefore
x= -2 is the line of symmetry.
3. the curven shown in graph,
we see that the vertex is at x=3, so x=3 is the line of symmetry.
The axes of symmetry of the functions f(x), g(x), and h(x) will be x = 8, x = -2, and x = 3, respectively.
What is the axis of symmetry?Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.
Three capabilities are given underneath: f(x), g(x), and h(x).
f(x) = -4(x − 8)² + 3
The axis of symmetry of the function f(x) will be given as,
x − 8 = 0
x = 8
g(x) = 3x² + 12x + 15
Convert the expression into a vertex form.
g(x) = 3x² + 12x + 15
g(x) = 3(x² + 4x + 5)
g(x) = 3(x² + 4x + 4) + 3
g(x) = 3(x + 2)² + 3
The axis of symmetry of the function g(x) will be given as,
x + 2 = 0
x = −2
From the graph, the axis of symmetry of the function h(x) will be given as,
x = 3
More about the axis of the symmetry link is given below.
https://brainly.com/question/22495480
#SPJ2
Riley has a farm on a rectangular piece of land that is 200200200 meters wide. This area is divided into two parts: A square area where she grows avocados (whose side is the same as the length of the farm), and the remaining area where she lives.
Every week, Riley spends \$3$3dollar sign, 3 per square meter on the area where she lives, and earns \$7$7dollar sign, 7 per square meter from the area where she grows avocados. That way, she manages to save some money every week.
Write an inequality that models the situation. Use lll to represent the length of Riley's farm.
Answer:
The inequality that models the situation for her to have money to save is
7L² > 3(200L - L²)
On simplifying and solving,
L > 60 meters
Step-by-step explanation:
The length of her farm = L meters
The farm where she grows avocados is of square dimension
Area of the farm = L × L = L²
The piece of land is 200 m wide.
Total area of the piece of land = 200 × L = (200L) m²
If the area of her farm = L²
Area of the side where she lives will be
(Total area of the land) - (Area of the farm)
= (200L - L²)
= L(200 - L)
Every week, Riley spends $3 per square meter on the area where she lives, and earns $7 per square meter from the area where she grows avocados.
Total amount she earns from the side she grows the avocados = 7 × L² = 7L²
Total amount she spends on the side where she lives = 3 × (200L - L²) = 3(200L - L²)
For her to save money, the amount she earns must be greater than the amount she spends, hence the inequality had to be
(Amount she earns) > (Amount she spends)
7L² > 3(200L - L²)
To simplify,
7L² > 3L(200 - L)
Since L is always positive, we can divide both sides by L
7L > 3(200 - L)
7L > 600 - 3L
10L > 600
L > 60 meters
Hope this Helps!!!
Answer:
Answer is in attached image.
Intersecting chords form a pair of supplementary, vertical angles. True or false. WILL GIVE BRAINLIEST.
Answer:
False
Step-by-step explanation:
Yes, they do give vertical angles, which by definition means opposite angles created by intersecting lines. BUT, these angles are not supplementary, as they don't always complete eachother. If they were supplementary, they would not be vertical angles. Instead, they create CONGRUENT veritcal angles.
Hope this helped!
The statement is False which is intersecting chords do not form a pair of supplementary and vertical angles.
What is the chord of the circle?A chord of a circle is defined as the line segment whose both endpoints of that line are on the circumference of the circle.
What is the vertical angle?Vertical Angles are the angles formed facing opposite to each other when two lines intersect each other.
What is the supplementary angle?Supplementary angles are the adjacent angles whose sum is 180° and together form a straight line.
So, here when two intersecting chords of the circle intersect each other at a point, they form two pairs of vertical angles, and according to the theorem of vertical angle, vertical angles are congruent.
As vertical angles are opposite to each other, so they can't be adjacent and can not form always 180° by adding their values and do not make straight line together.
But Intersecting chords of the circle can form a pair of congruent vertical angles.
So the given statement: Intersecting chords of a circle form a pair of supplementary, vertical angles is False.
Learn more about supplementary angles
here: https://brainly.com/question/12919120
#SPJ2
please help easy time table consumer math <3
I need help badly please
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the SUBTRACTION.
so here we are going to use the BODMAS Rule,
Answer is -11
Answer:
Step-by-step explanation:
Can do skmeone help me
A triangle has angles that measure 107°, 20°, and 53°. What kind of triangle is it?
Answer:
Scalene triangle
Step-by-step explanation:
Let's first cancel out the obvious.
This is not a equilateral triangle because the angles are not equal.
Now if you draw out the triangle, you can see that the triangle is a little weird. Not at all a equilateral triangle.
It's also not a iscosles because no two angles are the same.
Thus we end up with scalene triangle.
Hope this helps!
4. Find the height of a cylinder whose radius is 7cm and the total surface area is 968 sq.cm
(1 Point)
17cm
16cm
15cm
14cm
(its an emergency the due date is about to finish so let's make it quick)
Answer:
Height of the cylinder = 15
Step-by-step explanation:
According to the question, TSA=968
TSA of cylinder=2π r (r+h2*22 / 7*7 (7+h) = 968
2*22 (7+h) = 968
(7+h) = 968/44
7+h=22
h = 22-7
= 15 cm
Can anyone help me with this question
Answer:
Step-by-step explanation:
Like your other question, let's break it down systematically
6x + 9y - 9(6x - 3y + 8z)
Use the distributive property
6x + 9y - 9(6x - 3y + 8z)
6x + 9y - 54x - 27y + 72z
Match like terms
6x - 54x = -48x
9y - 27y = -18y
72z - 48x - 18y
Which step is the same in the construction of parallel lines and the construction of a perpendicular line to a point off a line?
Answer:
Both types of lines are built on the same plane although they meet different objectives for which they are built.
Step-by-step explanation:
The difference is that in the case of parallel lines they will never cross and in the case of perpendicular lines if they cross each other, which can give rise to the formation of right angles to each other.
An incomplete distribution is given below:Variable You are given that the median value is 70 and the total number of items is 200. Using the median formula fill up the frequencies.
Answer:
The missing frequencies are x = 8 and y = 43.
Step-by-step explanation:
Median Value =70
Then the median Class =60-80
Let the missing frequencies be x and y.
Given: Total Frequncy = 200 , Median = 46
[tex]\left|\begin{array}{c|ccccccc}Value&0-20&20-40&40-60&60-80&80-100&100-120&120-140\\Frequency&12&30&x&66&y&27&14\\$Cumu.Freq&12&42&42+x&108+x&108+x+y&135+x+y&149+x+y\end{array}\right|[/tex]
From the table
[tex]\sum f_i =149+x+y[/tex]
Here, n = 200
n/2 = 100
Lower Class Boundary of the median class, l=60
Frequency of the median class(f) =66
Cumulative Frequency before the median class, f=42+x
Class Width, h=10
[tex]Median = l + \dfrac{\dfrac{n}{2} - c.f }{f} \times h[/tex]
[tex]70 = 60+ \dfrac{100- 42+x }{66}\times 10\\70 = 60+ \dfrac{58+x }{66}\times 10\\70-60=\dfrac{58+x }{66}\times 10\\10*66=10(58+x)\\58+x=66\\x=66-58\\x=8[/tex]
200=149+x+y
200=149+8+y
y=200-(149+8)
y=43
Hence, the missing frequencies are x = 8 and y = 43.
When a bus service reduces fares, a particular trip from New York City to Albany, New York, is very popular. A small bus can carry four passengers. The time between calls for tickets is exponentially distributed with a mean of 30 minutes. Assume that each caller orders one ticket. What is the probability that the bus is filled in less than 3 hours from the time of the fare reduction
The probability that the bus is filled in less than 3 hours from the time of the fare reduction is 0.8488
Let the time for calls for tickets is denoted by x.
The time between calls for tickets is exponentially distributed, with a mean of 30 minutes.
[tex]X \sim Exp(\lambda = \frac{1}{30})[/tex]
A small bus can carry four passengers. We have to find the probability that the bus is filled in less than 3 hours from the time of the fare reduction.
That means there are more than 4 passengers in less than 180 minutes (3 hours).
Let N be the number of seats filled in 3 hours.
Then,
[tex]N \sim Poisson(\lambda t)[/tex]
Or,
[tex]N \sim Poisson(\frac{1}{30} \times180)[/tex]
[tex]N \sim Poisson(6)[/tex]
Then the required probability is:
[tex]P(N\geq 4) = 1 - P(N < 4)[/tex] --------(1)
PDF for Poisson random variable with parameter λ is give by:
[tex]P(X =x) = \dfrac{{e^{-{\lambda}} {\lambda}^x}}{x!}[/tex]
Then for the variable N
P(N<4) = P(N=0)+P(N=1)+P(N=2)+P(N=3)
[tex]P(N < 4) = \dfrac{{e^{-{6}} {6}^3}}{3!} +\dfrac{{e^{-{6}} {6}^2}}{2!} +\dfrac{{e^{-{6}}{6}^1}}{1!}+\dfrac{{e^{-{6}} {6}^0}}{0!}[/tex]
On solving the above:
P(N<4) =0.0892+ 0.0446+0.0149+0.0025
P(N<4)= 0.1512
Substitute this value in (1)
P(N≥4) =1-0.1512
P(N≥4) =1-0.1512
P(N≥4) =0.08488
Hence, the required probability is 0.8488.
Learn more about probability here:
https://brainly.com/question/32117953
#SPJ4
find 1st - 4th term and then the 10th term for:
A: rule is n^2+3
B: rule is 2n^2
Answer:
A
n^2+3
1. 1^2+3= 4
2. 2^2+3= 7
3. 3^2+3= 12
4. 4^2+3= 19
5. 10^2+3= 103
B
2n^2
1. 2*1^2=2
2. 2*2^2= 8
3. 2*3^2= 18
4. 2*4^2= 32
5. 2*10^2= 200
Answer:
see below
Step-by-step explanation:
n^2+3
n=1: 1^2+3 = 1+3 =4
n=2: 2^2+3 = 4+3 =7
n=3: 3^2+3 = 9+3 =12
n=4: 4^2+3 = 16+3 =19
n=10: 10^2+3 = 100+3 =103
2n^2
n=1: 2*1^2 = 2*1 =2
n=2: 2*2^2 = 2*4 =8
n=3: 2*3^2 = 2*9 =18
n=4: 2*4^2 = 2*16 =32
n=10: 2*10^2 = 2*100 =200
Use the identity below to complete the tasks:
23 - 63 = (a - b)(a² + ab + b2)
When using the identity for the difference of two
cubes to factor 64x8 - 27
a=
b =
Answer:
a is 2q^2r
b is 3s^2t
the expression factored is...
(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)
Step-by-step explanation:
Which of the following are identities?
1. x2 + 2xy + y2 = (x + y)2
II. 2x + 2 = 2(x + 1)
III. O + a = a
Answer:
The answer is 2 because they are similar it is just that the one at the side is factorised
Combine the like terms to create an equivalent expression: r+(-5r)
Answer:
-4r
Step-by-step explanation:
r + -5r
Factor out r
r( 1-5)
r(-4)
-4r
Please help me find the area of this shape
Answer:
44+50 =94 in²
Step-by-step explanation:
Trapezoid
A= 1/2h(b1+b2)
A= 1/2*4(7+15)
A=1/2*4(22)
A=44
Rectangle
A=l*w
A=5*10
A=50
44+50 =94 in²
30 Points!! Vivian is at a fair in Coachella Valley, California. Much of the valley lies below sea level. Vivian has brought along an altimeter to measure her elevation at different places in the valley. Vivian’s first ride was on the Ferris wheel. When she sat on the wheel at its lowest point, her altimeter read -9.6 feet. When she reached the top of the wheel, her altimeter read 12.3 feet.
Is the change in Vivian's elevation from the bottom of the Ferris wheel to the top a positive number or a negative number? Why?
Answer:
Its a postive number
Step-by-step explanation:
If you look it says she is at sea leveal wicth is 0 and she is going up 12.3 feet so its postive.
The change in elevation from the bottom of the Ferris wheel to the top is 21.9 feet, which is a positive number.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, the lowest point of the Ferris wheel is -9.6 feet, and the highest point is 12.3.
The change in elevation from the bottom of the Ferris wheel to the top of the Ferris wheel is,
12.3 - (-9.6)
=12.3 + 9.6
= 21.9
Hence, the change in elevation from the bottom of the Ferris wheel to the top is 21.9 feet, which is a positive number.
To learn more about subtraction, click here:
https://brainly.com/question/2346316
#SPJ5