Answer:
[tex]4\cos x\cos (4x)\cos (2x)[/tex]
Step-by-step explanation:
Given: [tex]cosx + cos3x + cos5x + cos7x[/tex]
To convert: the given sum into product
Solution:
Use formula: [tex]\cos A+\cos B=2\cos \left ( \frac{A+B}{2} \right )\cos \left ( \frac{A-B}{2} \right )[/tex]
[tex]cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos (2x)\cos (-x)+2\cos (6x)\cos (-x)\\=2\cos (2x)\cos (x)+2\cos (6x)\cos (x)\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ][/tex]
[tex]cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]\\=2\cos x\left [2 \cos \left ( \frac{2x+6x}{2} \right )\cos \left ( \frac{2x-6x}{2} \right ) \right ]\\=2\cos x\left [ 2\cos (4x) \cos (-2x) \right ]\\=4\cos x\cos (4x)\cos (2x)[/tex]
What is the volume of the following triangular prism?
5 cm
15 cm
4 cm
cubic centimeters. You must submit your neat and organized work once you have submitted the test.
Write only the number.
10 points need fast
Answer:
[tex]V=150cm^3[/tex]
Step-by-step explanation:
First we need to find area of the triangle with a base of 4 cm and a height of 5cm, and then multiply that by the length of the prism of 15cm.
The area of the triangle is given by the formula:
[tex]A_T=\frac{bh}{2}[/tex]
where b is the base: [tex]b=4cm[/tex] and h is the height: [tex]h=5cm[/tex]
thus, in this case we have:
[tex]A_T=\frac{(4cm)(5cm)}{2}\\ \\A_T=\frac{20cm^2}{2} \\\\A_T=10cm^2[/tex]
And now, the volume will be the area of the triangle multiplied by the length [tex]l=15cm[/tex] of the prism:
[tex]V=A_T*l[/tex]
Substituting the known values:
[tex]V=10cm^2*15cm\\V=150cm^3[/tex]
The volume in cubic centimeters is 150.
What is the name given to integers that cannot be factored
Answer:
irreducible
Step-by-step explanation:
A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial .
Answer:
prime numbers
Step-by-step explanation:
prime numbers are only divisible by themselves and one, hence why they are not factor-able.
Can anyone please help me with this geometry question?
The height of a parallelogram is three times its base. If the area of the parallelogram is 675 square inches, find its base and height.
Which of these choices are correct?
b = 25 in & h = 75 in
b = 75 in & h = 225 in
b = 45 in & h = 135 in
b = 25 in & h = 12.5 in
Answer:
Step-by-step explanation:
let base be x and height be 3x
we know area of parallelogram is
base*height
ie x*3x=675
3x^2=675
x^2=675/3
x^2=225
x= square root of 225
x=15
therefore base =15
height = 45
Matthew obtained a balloon mortgage but was late on a few payments during
the period of the loan. Which of the following is an unlikely option for him
once the balloon payment becomes due?
A. Sell the home
B. Refinance the balloon payment
C. Foreclosure
D. Pay balloon payment in full
Answer:
The answer is C. Forclosure
Answer:
Refinance the balloon payment
Step-by-step explanation:
AP3X
pls be quick i feel stupid not knowing the answer
Answer:
584!
Step-by-step explanation:
Let's see. There is a missing side. Let's call that x. However, we know what the other sides are!
This is how we do it.
We know the largest side's length., 172.
Since we know the other sides, we can subtract their length from 172.
172-57-51-31=33
x=33
So now add the sides!
54+31+66+172+57+30+33+19+51+71\
584!
suppose an experiment is rolling a dice and tossing a coin . list the elements of the sample space.
Answer:
S = {1H,2H,3H,4H,5H,6H,1T,2T,3T,4T,5T,6T}
Step-by-step explanation:
A sample space is the set of all outcomes that may come. It consists of all the values that may result in result of an experiment.
In the given problem, we have to find the sample space of rolling a dice and flipping a coin
As the dice has 6 sides and coin has 2 sides
The number of outcomes are: 6*2 = 12
The outcome of dice can either be with heads of coin or tails of coin.
The sample space will be:
S = {1H,2H,3H,4H,5H,6H,1T,2T,3T,4T,5T,6T}
Keywords: Sample Space
3) The sum and the difference of the LCM and GCD of two numbers are 312 and 264 respectively. Find the numbers if their sum is 168.
Answer:
The numbers are 72 and 96.
Step-by-step explanation:
LCM + GCF = 312
LCM - GCF = 264
2*LCM = 576
LCM = 576/2 = 288
HCF = 312–288 = 24
The product of two numbers = HCF*LCM
Let the numbers be x and (168-x)
x(168-x) = 24*288 = 6912
x^2–168x+6912 = 0
x = [168 +(168^2 -4*6912)^0.5]/2
= [168 +(28224–27648)^0.5]/2
= [168 + 576^0.5]/2
= (168+24}/2
= 192/2
= 96 and the other number is 168–96 = 72.
What is the probability the spinner does NOT land on green? Assume it cannot land on the line between two colors.
A) 20%:
B) 40%
C) 60%
D) 80%
Answer:
4/5 which is 80%
Step-by-step explanation:
there is a total of 5 which means that the probability to not land on green is 4/5
which in decimal form is .8
which in percent is 80%
what is the sum of the interior angles of a polygon shown below?
Answer: The sum of the interior angles of a polygon shown in the picture is [tex]540^{\circ}[/tex].
Step-by-step explanation:
The given polygon is a regular pentagon having 5 sides.
The sum of the interior angles of a regular polygon is given by :-
[tex](n-2)\times180^{\circ}[/tex], wherer n= number of sides of the regular polygon.
Since it has 5 sides, then the sum of the interior angles of a polygon would be
[tex](5-2)\times180^{\circ}\\\\=3\times180^{\circ}\\\\=540^{\circ}[/tex]
Hence, the sum of the interior angles of a polygon shown in the picture is [tex]540^{\circ}[/tex].
(05.06)Which interval on the graph could be described as linear decreasing?
7.
6-
5-
D
B
4.
с
3
A
2.
13
А
ОА
Ов
Ос
OD
Oml fellow FLVS student here, it would be C.:)
Explanation: I got it right lol
In the given graph, interval C could be described as linear decreasing.
What is an interval?"An interval is a set of real numbers that contains all real numbers lying between any two numbers of the set."
In the given graph,
A is the interval(0, 2) where the graph is linear increasing.
B is the interval(2, 4) where the graph is constant.
C is the interval(4, 5) where the graph is linear decreasing.
D is the interval(5, 8) where the graph is linear increasing.
Therefore, the required interval is C.
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MS. Winkler surveyed her students in just one class with 30 students to see how many siblings each of them had. Here are the results
Only child: 5
1 sibling: 7
2 siblings: 13
3 or more siblings: 5
If she were to survey all 140 of her students, predict how many total have just 1 sibling. (Round to the nearest whole number)
Answer choices:
a)33
b)30
c)42
d)2
I need you to show your work for each problem
1-5
Answers:
2-7286.67-735-12Please see the attached picture for full solution
Hope it helps...
Good luck on your assignment
Simply the equation 3i(2-11i)
Answer:
6i + 33
Step-by-step explanation:
3i * ( 2 - 11i) = 6i - 33 [tex]i^{2}[/tex]
[tex]i^{2} = -1[/tex]
6i - 33 [tex]i^{2}[/tex] = 6i - 33 * (-1) = 6i + 33
Answer:
6i+33
Step-by-step explanation:
What is the factored form of this polynomial?
X2 + 5x-36
OA. (x+ 4)(x+ 9)
OB. (x-4)(x-9)
O C. (x-4)(x+ 9)
O D. (x - 5)(x+ 8)
Hey There!
x² + 5x - 36
First step is to find out the two numbers when multiplied results to 36 & when subtracted results to 5. Um..Let's think for a lil bit.....Yeah! you got it :) The numbers are 9 and 4!---- x²+ ( 9 - 4)x - 36
Distribute x :---- x² + 9x - 4x - 36
Take the common :---- x ( x + 9 ) - 4 (x + 9 )
---- ( x - 4 ) ( x + 9 )
Yayyy! We got our answer :) The right answer is of Option C [ ( x - 4 ) ( x + 9 ) ]~KEEP EXPLORING! < 3
Which belongs to which? Will mark brainliest
Is this right or wrong?Tell me if I need to change my answer.
Answer:
Yes you are correct
Step-by-step explanation:
You have 180 feet of fence to make a rectangular pen. What are the
dimensions of the rectangle with the maximum area?(include explanation or step-by-step)
Answer:
45 x 45 = 2025
Step-by-step explanation:
On a coordinate plane, 2 triangles are shown. The first triangle has points A (negative 2, 1), C (negative 4, 1), and B (negative 3, 4). The second triangle has points A prime (1, negative 2), B prime (4, negative 3), and C prime (1, negative 4).
What is the rule for the reflection?
ry=x(x, y) → (–y, –x)
ry=–x(x, y) → (–y, –x)
ry=x(x, y) → (y, x)
ry=–x(x, y) → (y, x)
Answer:
R(y=x) = (x, y) → (y, x)
Step-by-step explanation:
The coordinates of A are (-2, 1).
The coordinates of A' are (1, -2).
Clearly, the values have been swapped in accordance with ...
(x, y) → (y, x)
This is the result of a reflection across the line y = x. Hence the rule and its name are ...
R(y=x) = (x, y) → (y, x)
Answer:
R(y=x) = (x, y) → (y, x)
Step-by-step explanation:
egd2020
1. A school has 400 students. They all come to school by bus, and each bus carries the same number of students. How many students might there be on each bus? PS the number of buses is 100
Answer:
4, I believe
Step-by-step explanation:
400 students
100 buses
400/100=4
Answer:
4
Step-by-step explanation:
There are 400 students, and 100 buses, so number of student in each bus= 400/100
= 4
What is the surface area
Answer:it is the yellow part
Step-by-step explanation:
because the yellow face is touching the floor
Answer:
Surface area: A=496
Volume: V=640
Step-by-step explanation:
Shape: Rectangle Prism
Solved for volume
Formula for volume: L*W*H
Formula for surface area: 2(wl+hl+hw)
To calculate the volume
1: First calculate the width, height, and the length. Which is Length: 16ft Width: 8ft Height: 5ft.
Answer for volume: V=640
To calculate the surface area:
1: Use the formula wl+hl+hw. So plus the length, width and the height which is. Height: ft Width: 8ft Length: 16ft.
Answer for surface area: A=496
Hope this helps.
f(0)=g(0)
f(-2)=g(-2)
f(0)=g(-2)
f(-2)=g(0)
Answer:
F(-2)=G(-2)
Step-by-step explanation:
Which statement is true? The function is only increasing when x ≥ −8. The function is only increasing when x ≥ 0. The function is always decreasing. The function is always increasing.
Answer:
THE FUNCTION IS ALWAYS INCREASING.
Complete question: The graph of f(x)= power of 3√x + 8 is shown.
Step-by-step explanation:
See attachment for the missing graph.
when x = -16 ; y = -2
when x = -12 ; y = -1.5
when x = -8 ; y = 0
when x = -6 ; y = 1.25
when x = 0 ; y = 2
when x = 6 ; y = 2.5
As the value of x increases, so does the value of y. Thus, the function is always increasing.
Answer:
D
Step-by-step explanation:
find points of discontinuity y=x-8/x^2+6x-7
Answer:
Step-by-step explanation:
You'll need to use parentheses here to remove ambiguity regarding what's in your denominators:
x - 8 x - 8
y = ------------------ = -----------------
x^2 + 6x - 7 (x + 7)(x - 1)
This last result becomes undefined at x = -7 and x = 1, and thus its graph is discontinuous at those x- values.
The points of discontinuity is x = -7, x = 1
Use parentheses to remove ambiguity considering the denominators
[tex]y=x-8/x^{2} +6x-7[/tex]
= x-8 ÷ (x+7)(x-1)
The result becomes undefined at x = -7
and x = 1,
thus its graph is discontinuous at those x values.
Therefore the points of discontinuity is x =-7 and x = 1.
Learn more about discontinuity points, refer:
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Zero
Undefined
Positive
Negative ?
Answer:
Zero
Step-by-step explanation:
The line is a straight line going across the x axis so there is no change in y so there is no slope because slope is the change of y.
help PLEASE
urgent...
Answer:
C!
Step-by-step explanation:
It appears that all choices have the 1st part the same, so we are looking at domains. I recommend drawing the functions without the domain limitations. We know that the linear function is closed so it's inequality is either [tex]\geq[/tex] or [tex]\leq[/tex]. So eliminate B and D. Since the quadratic function continues to the left the inequality sign should be <. So the answer is C
Triangle DEF has vertex coordinates D(0, -3), E(-1,0), and F(-2,-1). It is
reflected across the y-axis. What are the coordinates of D'EF?
The coordinates of D'E'F' after reflection are,
D' = (0, - 3)
E' = (1, 0)
F' = (2, - 1)
We have to given that,
Triangle DEF has vertex coordinates D(0, -3), E(-1,0), and F(-2,-1).
Here, Triangle DEF is reflected across the y-axis.
The rule for a reflection over the y -axis is,
(x, y) → (- x, y)
Hence, the coordinates of D'E'F' after reflection is,
D' = (0, - 3)
E' = (- (- 1), 0) = (1, 0)
F' = (- (- 2), (- 1)) = (2, - 1)
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Please help The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
Answer:
The full steel bead tire would weigh 1.5432358353 pounds, or about 1.8. The lighter wheel weighs 1.5432358353 pounds, or about 1.5. Together they weigh 3.086471671, or about 3.1 pounds.
2 Points
Which of the following appear in the diagram below?
Check all that apply.
Y
x
O A. _XYZ
OB. ZX
OC. YX
OD. _ZXY
SUBMI
Answer:
D and B
Step-by-step explanation:
hope this is correct!
The following appears in the diagram below are:
XZ and XY and ∠ZXY.
Options B, C, and D are the correct answer.
What is an angle?In mathematics and geometry, an angle is a measure of the amount of rotation or turn between two lines or line segments that meet at a common endpoint, called the vertex of the angle.
Angles are typically measured in degrees (°) or radians (rad).
A full rotation around a point is 360 degrees or 2π radians.
We have,
An angle is a measure of the amount of rotation or turn between two lines or line segments that meet at a common endpoint, called the vertex of the angle.
Arc length is the distance along the curve of a circle or any other curved shape. It is defined as the length of the portion of the circumference of a circle or a portion of a curve between two endpoints, measured along the arc of the curve.
From the diagram,
XZ and XY are arc lengths.
∠ZXY is an angle.
Thus,
The following appears in the diagram below are:
XZ and XY and ∠ZXY.
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The measure of central angle MNL is π radians, and the measure of the entire circle is 2π radians. The ratio of the measure of the central angle to the entire circle measure is . The area of the entire circle is π units2. The area of the sector is π units2.
Answer:
The answer is "The calculated ratio of the central angle to the entire circle is 1:2".
Step-by-step explanation:
Let,
MNL angle [tex]= \pi[/tex]
So, the entire circle is [tex]= 2\pi[/tex]
The ratio of the central angle to the entire circle is:
[tex]\Rightarrow \frac{\pi}{2\pi}\\\\\Rightarrow \frac{1}{2}\\\\[/tex]
Hence, the calculated ratio is = 1:2.
A spinner has four equal sections, with one letter from the word "MATH" in each section.
Type your response in each blank below.
1. You spin the spinner 20 times. About how many times do you expect it will land on A?
2. You spin the spinner 80 times. About how many times do you expect it will land on something other than A?
Explain your reasoning.
Answer:
1. 5 times
2. 60 times
Step-by-step explanation:
there is only one a so its 1/4 times 20 and 4 because that is the total
20/4= 5
there is 3 because there is letters that are not a
3/4 times 80
240/4
1. The number of times expected that should be landed on A should be 5 times.
2. The number of times expected should be 60 times.
Calculation of the number of times:1. Since A spinner has four equal sections, with one letter from the word "MATH" in each section.
So, here the number of times should be
= [tex]20\div 4[/tex]
= 5
2. The number of times should be
[tex]= 3/4 \times 80\\\\= 240\div 4[/tex]
= 60
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