Answer:
l = 2cosΘ p = see attachment
Step-by-step explanation:
√2+√2+2cos 4Θ
√2+√2(1 + cos 4Θ)
√2 + √2(2 cos² 2Θ)
√2 + √4 cos² 2Θ cos 2Θ = 2 cos²Θ - 1
√2 + 2cos 2Θ
√2(1 + cos 2Θ)
√4cos²Θ
2cosΘ
Answer:
Step-by-step explanation:
I'm only going to do the first one, because the tangent problem is going to give us both night mares.
Start with cos(4*theta), There are various places on the internet which solves this, so I won't bother. Basically it comes down to using cos(2*theta).
cos(4theta) = 8*cos^4(theta) - 8*cos^2 (theta) + 1
2*cos(4*theta) = 16*cos^4(theta) - 16cos^2(theta) + 2
2 + 2cos(4*theta) = 16cos^4(theta) - 16cos^2(theta) + 4
(2 + 2cos(4*theta) = (4 cos^2(theta) - 2 )^2
sqrt(2 + 2cos(4theta) = 4cos^2(theta) - 2
=====================================
sqrt(2 + 4cos^2(theta) -2 ) = sqrt( 4 cos^2(theta) = 2 cos(theta) = RHS
*PLEASE ANSWER, NEED HELP* Find the surface area of the rectangular prism below.
Answer:
461.02
Step-by-step explanation:
2 × ( (12.3 × 4.3) + (12.3 × 10.7) + (4.3 × 10.7)) = 461.02 m^2
Answer:
461.02 M^2
Step-by-step explanation:
A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
SA = 2lw+2lh+2hw
2LW = 105.78 M^2 ( 52.89* 2 )
L= 12.3 M^2 , W = 4.3 M^2
LW = 52.89 M^2
2LH = 263.22 ( 131.61 * 2 )
L = 12.3 M^2 , H = 10.7 M^2
LH = 131.61 M^2
2HW = 92.02 ( 46.01 * 2 )
H = 10.7 M^2 , W = 4.3 M^2
HW = 46.01 M^2
SA = 2lw+2lh+2hw
SA = 105.78 M^2+ 263.22 M^2 + 92.02 M^2
SA = 461.02 M^2
please help me immediately
Answer:
756
Step-by-step explanation:
In the last question the volume of the tank was 168 m³
so to find the cost multiply 168 and 4.5
168*4.5 =756it will cost 756
Answer:
756
Step-by-step explanation:
168 x 4.5 = 756
5. You are constructing a railing to place on a ramp for your handicapped grandmother. You have been given a 12-ft rail and 5 posts to support the railing. The posts are equally spaced under the rail and the first and last posts are positioned at each end of the rail. The ramp rises at an angle of 12°. a. What part(s) will represent the transversal(s)? b. In order to make the posts parallel, what angles must they form with the transversal? c. What angle would they form with the ramp? d. Which angles would be alternate interior, alternate exterior, corresponding, and consecutive interior? Explain your reasoning. e. What do you know about each of these angles? f. How far apart will the posts be?
Answer:
a. The railing is transversal to the posts
b. In order to make the posts parallel, the angle between the posts and the transversal should be = 78°
c. The angle between the post and the ramp is 102° as we reach the post from the bottom and 102° and 78° immediately after the post
d. 1) Alternate interior angles = 78° and 102°
2) Alternate exterior angles = 102°
3) Corresponding angles = 78° and 102° depending on the side of from which we approach the post
4) Consecutive interior = 78° and 102° depending on the side of from which we approach the post
e. The interior angles are supplementary
f. Horizontal spacing between posts = 2.93 ft.
Spacing between posts along the length of the railing = 3 ft. spacing
Step-by-step explanation:
a. A transversal is a line crossing two or more parallel lines which are in a plane at different points
Therefore, the railing is transversal to the posts
b. Whereby the ramp rises at an angle of 12°, the railing, which is the transversal is therefore inclined at 12° to the horizontal and the posts which will be vertical erect will be at 90° to the horizontal
Therefore, in order to make the posts parallel, the angle between the posts and the transversal should be 90° - 12° = 78° for each post to railing.
c. The angle between the post and the ramp before the post as we ascend the ramp is therefore, 180 - 78 = 102° and 78° after the post
d. The alternate interior angles lie on the opposite sides of the transversal = 78° on one side and 102° on the other (Sum of angles on a straight line) which are the angles on the transversal
The alternate exterior angles lie on the exterior opposite sides of the transversal = 102°
Corresponding angles are the angles located in the corresponding positions on the transversal = 78° on one side and 102°as we cross the post (Sum of angles on a straight line)
Consecutive interior angles are the angles that are located on the same part of the transversal = 78° and 102° (Sum of consecutive interior angles of parallelogram = 180°
e. For the posts to be parallel, the consecutive interior angles should be supplementary or equal to 180°
f. Whereby we have a 12-ft rail inclined at 12°, we have;
Horizontal distance covered by the rail = 12 × cos(12) = 11.74 ft
Since we have 5 posts, there 4 equal spaces between them which gives
Spaces between posts = 11.74/4 = 2.93 ft. horizontally and 3 ft. spacing between each post along the railing.
please help me immediately
Answer:
112 m³
Step-by-step explanation:
Let's calculate first the voulume of the tank
the volume of thi tank is given by :
V = l*w*h l is the length w is the width h is the heightso the volume is :
V = 4*12*3.5V=168 m³Multiply by 2/3 to get the volume of the water
V' = 168*(2/3) V' = 112 m³Answer:
112 m^3
Step-by-step explanation:
V = l x w x h
V = 4 x 12 x 3.5
V = 168 m^3
V = 168 x (2/3)
V = 112 m^3
Use the graph to find the value of y = sin q for the value of q.
Answer:
c
Step-by-step explanation:
A =3x2+4x+1,B=5x2−3x+8,C=4x2−7x−3, find the value of B + C –A.
Answer:
6x^2 - 14x + 4.
Step-by-step explanation:
5x^2 - 3x + 8 + 4x^2 - 7x - 3 - (3x^2 + 4x + 1)
= 5x^2 - 3x + 8 + 4x^2 - 7x - 3 - 3x^2 - 4x - 1
= 6x^2 - 14x + 4.
What is 10^4 in standard notation
Answer:
10,000
Step-by-step explanation:
Standard notation is just the normal way of writing things. 10 x 10 x 10 x 10 = 10,000.
The graph of the function, f(x) = 3x2 + x + 2, opens and has a value.
Answer:
Opens down
Has a maximum value
x2 + 4y2 = 36
The major axis runs along:
O y = 4x
x-axis
y-axis
Answer:
The x-axis.
Step-by-step explanation:
This is an ellipse.
In standard form it s x^2/36 + y^2/9 = 0.
When y = 0, x = +/- 6 and when x = 0, y = +/- 3 so the minor axis has length 6 and the major axis has length 12 and runs along the x-axis.
How many houses have an area less than 100^2m?
Answer:
4
Step-by-step explanation:
Each bar represents a range in area. The first bar represents the number of houses with an area of more than 50 but less than 100. It's height is 4, so there are 4 of those houses.
The time it takes to drive from Orangeville to the Vaughan Mills Mall is normally distributed with a mean of 52 minutes and standard deviation of 5 minutes. What intervals could you estimate, using the knowledge from this activity that do not include the mean as a max or min? For example, is an interval we could estimate? However, it includes the mean as the maximum of the interval. Another example is as an example of a probability interval that we know from this activity, but it includes the mean as the minimum.
Given:
Mean of 52 minutes and a standard deviation of 5 minutes.
Solution:
According to the empirical rule: For the normal distribution, all of the data will fall within three standard deviations of the mean.
1: 68% of the data will fall within the first standard deviation from the mean.
2: 95% of the data fall within two standard deviations.
3: 99.7% of the data fall within three standard deviations.
[tex]3SD =99.7\%=\mu\pm3\sigma\\[/tex]
Therefore, the 7 intervals and their probabilities are:
1. [tex]1SD=0.68=P(47<x<57)[/tex]
2. [tex]0.95=P(42<x<62)[/tex]
3. [tex]0.997=P(37<x<67)[/tex]
4.[tex]13.5\%=P(42<x<47)[/tex]
5.[tex]13.5\%=P(57<x<62)[/tex]
6. [tex]2.35\%=P(37<x<42)[/tex]
7.[tex]2.35\%=P(62<x<67)[/tex]
What is the degree measure of an interior angle of a regular pentagon?
Answer:
it is 540 degrees.
Step-by-step explanation:
Answer:
108°
Step-by-step explanation:
Sum of interior angle of any polygon = (n - 2 )*180
Here, n = number of sides
Sum of interior angle of regular pentagon = ( 5 - 2)*180 = 3*180 = 540°
In regular pentagon all the angles are congruent.
Interior angle of regular pentagon = 540/5
= 108°
Please hurry!!!
The fraction bars represent which equation?
A fraction bar is labeled 1. Underneath the bar, 4 boxes are labeled 1/4. Underneath the 4 boxes, boxes are labeled 1/8. 6 of those boxes are circled.
A. 1/4 ÷ 1/8 = 6
B. 3/4 ÷ 1/8 = 6/8
C. 1/4 ÷ 1/8 = 6/8
D. 3/4 ÷ 1/8 = 6
Answer:
Answer- 3/4 divided by 1/8 = 6/8
solve each equation for 0 x 360 sqrt 2 cosx+1=0 please hurry
Answer:
[tex]120\º \text{ and } 240\º[/tex]
or in radians:
[tex]$\frac{2\pi }{3} \text{ and } \frac{4\pi }{3}$[/tex]
Step-by-step explanation:
From the way you wrote, you want to solve the equation
[tex]\sqrt {2 \cos(x)+1}=0[/tex] for [tex]0 \leq x < 360\º[/tex], or in radians [tex][0, 2\pi)[/tex]
[tex]\sqrt {2 \cos(x)+1}=0[/tex]
Square both sides
[tex]2 \cos(x) +1= 0[/tex]
[tex]2\cos(x)=-1[/tex]
[tex]$\cos(x)=-\frac{1}{2} $[/tex]
In the Unit Circle, considering one revolution (interval [tex][0, 2\pi)[/tex]),
the values where [tex]$\cos(x)=-\frac{1}{2} $[/tex] are in Quadrant II and III.
Once
[tex]$\cos(x)= \frac{1}{2} \text{ for } x = 60\º \text{ in the Quadrant I}$[/tex]
The values where
[tex]$\cos(x)=-\frac{1}{2} $[/tex] are 120º and 240º.
Answer:
C on edge
Step-by-step explanation:
When you simplify,
10!/(10 - 3)!-3
is equal to:?
Answer:
120
Step-by-step explanation:
expand and calculate
10x9x8x7!/(10-3)!x3!
10x9x8x7!/7!x3!
reduce
10x9x8x7!/7!x3!
10x9x8/3!
Calculate the product
10x9x8/3!
Now Cacluate the factorial
720/3!
720/6
reduce
120
Answer: 120
Step-by-step explanation:
Find the distance between the $x$-intercept and the $y$-intercept of the graph of the equation $3x - 7y = 21$
Answer:
√58 or 7.62
Step-by-step explanation:
x-intercept = (7, 0)
y-intercept = (0, -3)
distance = √(-3 - 0)² + (0 - 7)² = √58 or 7.62
helppp plzzzzzz help me right now plz i need help
Answer:
the third one is the correct answer
Proportions in similar triangles: Find the value of X.
If someone would be kind enough to explain how to do this :)
Answer:
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication, and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Step-by-step explanation:
order the following values from least to greatest: 22.4, -28, 27, -17
Answer:
asDawas
Step-by-step explanation:
sadasda
Answer: -28, -17, 22.4, 27
hope this helps
Solve the following equations and inequalities showing all work.
18.1/2(x - 5) + 1 = 2x +4
19.3-x>-3
20. - x = 12
21. -2 = 8
22. –1 + 3 = 3 +
5
23.4 - (5x + 6) = 18 - 3x
24.-6x + 24 = 4x - 15(x-3)
25.4(x – 3) 12 =(x-3)
26. (15x 2) (-2) = x + 4
Answer:
See the answers in the pics
Step-by-step explanation:
Srry, I didn't quite understood the last two equations
but I hope that from now on you will know how to solve equations and inequalities like this ;]
Answer:
LLLLLLLLLLLLLl
Step-by-step explanation:
A five question multiple choice quiz has five choices for each answer. Use the random number table provided, with 0’s representing incorrect answers, and 1’s representing correct answers to answer the following question: What is the experimental probability of correctly guessing at random exaclty three correct answers? PLS HELP ME
Answer:
9/20 (or) 45% (or) .45 (however your teacher wants it expressed)
Step-by-step explanation:
There are 20 experiments and 9 of them have three ones and two zeros.
9/20
What is the Value of X??? Will give brainliest
Answer:
x = 65
Step-by-step explanation:
50 + 2x = 180
2x = 130
x = 65
Hope this helps)))
Answer:
65 degrees
Step-by-step explanation:
break apart the image into 2 sets of 2 lines and a transversal. Doing that you can see that 2x and 50 degrees are supplementary due to corresponding angles. 50 degrees+2x=180 degrees. Using ALgebra you can solve to find that x equals 65 degrees, which brings you to your answer
simplify the expression
[tex]8p + 10 + - 2p - 1 + 10[/tex]
Answer:
6p+19
Step-by-step explanation:
combine like terms:
8p+10+-2p+-1+10
(8p+-2p)+(10+-1+10)
6p+19
HOPE THIS HELPS!!!!!!:)
Question 8 of 10
What is the value of X?
50°
100"
O.
A. 50°
B. 150°
ОО
C. 1000
D. 30°
Answer:
30 degrees
Step-by-step explanation:
100+50=150
180-150=30
All triangles equal 180 degrees, so if the other angles equal 150 than the third angle equals 30 degrees.
QUICK!! 18x^2+21x-60=0 pls give me the steps as well
Answer:
[tex]x1 = - \frac{5}{2} [/tex][tex]x2 = \frac{4}{3} [/tex]
Step-by-step explanation:
[tex]18 {x}^{2} + 21x - 60 = 0[/tex]
Divide both sides of the equation by 3
[tex]6 {x}^{2} + 7x - 20 = 0[/tex]
Write 7x as a difference
[tex]6 {x}^{2} + 15x - 8x - 20 = 0[/tex]
Factor out 3x from the expression
[tex]3x(2x + 5) - 8x - 20 = 0[/tex]
Factor out -4 from the expression
[tex]3x(2x + 5) - 4(2x + 5) = 0[/tex]
Factor out 2x + 5 from the expression
[tex](2x + 5)(3x - 4) = 0[/tex]
When the product of factors equals 0 , at least one factor is 0
[tex]2x + 5 = 0[/tex]
[tex]3x - 4 = 0[/tex]
Solve the equation for X
[tex]2x + 5 = 0[/tex]
Move constant to R.H.S and change its sign
[tex]2x = 0 - 5[/tex]
Calculate the difference
[tex]2x = - 5[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{ - 5}{2} [/tex]
Calculate
[tex]x 1= - \frac{5}{2} [/tex]
Again,
[tex]3x - 4 = 0[/tex]
Move constant to RHS and change its sign
[tex]3x = 0 + 4[/tex]
Calculate the sum
[tex]3x = 4[/tex]
divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{4}{3} [/tex]
Calculate
[tex]x 2= \frac{4}{3} [/tex]
Hope this helps..
Best regards!!
Answer:
39x+58
Step-by-step explanation:
18x 2+21x-60=0
pick the like terms together
18x+21x=39x
60-2=58
=39x+58
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answer:
3 > x
Step-by-step explanation:
–2(5 – 4x) < 6x – 4
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: divide each side by by -2, remembering to flip the inequality
-6/-2 > -2/-2
3 > x
Answer:
x < 3
Step-by-step explanation:
−2(5−4x)<6x−4
Use the distributive property to multiply −2 by 5−4x.
−10+8x<6x−4
Subtract 6x from both sides.
−10+8x−6x<−4
Combine 8x and −6x to get 2x.
−10+2x<−4
Add 10 to both sides.
2x<−4+10
Add −4 and 10 to get 6.
2x<6
Divide both sides by 2. Since 2 is >0, the inequality direction remains the same.
x= 6/2
Divide 6 by 2 to get 3.
x= 3
X< 3
Mark me as brainliest
Leah wants to carpet a room that is 12 feet wide and 15 feet long. Carpeting is sold by the square yard. Find the length and width of the room in yards. Then find the number of square yards needed to carpet the room.
Answer:
length: 5 yd
width: 4 yd
area: 20 yd^2
Step-by-step explanation:
1 yd = 3 ft
15 ft * (1 yd)/(3 ft) = 5 yd
12 ft * (1 yd)/(3 ft) = 4 yd
A = LW
A = 5 yd * 4 yd = 20 yd^2
Answer:
20 yd²
Step-by-step explanation:
1 yd = 3 ft =>
=>w = 12ft×yd/3ft = 4 yd
=> l = 15ft×yd/3ft = 5 yd
A = l × w
= 5yd × 4yd
= 20 yd²
Carver is trying to reproduce a scale drawing where every 3 in. will be equal to 2 feet. How long should Carver make the red line, in feet?
Answer:
6 ft
Step-by-step explanation:
Since the red line is 9 feet long, and we know that [tex]3\cdot3 = 9[/tex], we can note that 3 inches goes into 9 inches 3 times.
Now that we are making the red line increase by 2 feet for every 3 inches, we can multiply the values.
2 feet × 3 times = 6 feet
So Carver should make the red line 6 feet long.
Hope this helped!
Answer:
6ft
Step-by-step explanation:
If the scale is 3in:2ft then every 3 inches is equal to 2 feet. 9in can be divided into 3 3in sections and after the sections are scaled 3 2t sections which in all are equal to 6ft.
The following table shows the number of animal crackers in each kid's lunch box. Find the median number of animal crackers.
Answer:
4
Step-by-step explanation:
2 2 3 5 7 7 (order from least to greatest)
3+5=8(find the most middle number,if there are two numbers you add both and then divide by 2)
8÷2
4
Hi there!! (✿◕‿◕)
⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐
First, you have to put the numbers from least to greatest.
2, 2, 3, 5, 7, 7
Then, you have to find the middle number.
2, 2, 3, 5, 7, 7
3 and 5 and both in the middle so, you add them both and divide them by 2.
3+5 = 8
8/2 = 4
4 is the median.
Hope this helped!! ٩(◕‿◕。)۶
Find the amplitude of the sine curve shown below. a. 3 b. p c. 1.5 d. 6
Answer:
Amplitude = 3
Step-by-step explanation:
Given
The sine curve above
Required
Determine the amplitude
To determine the amplitude of a sine curve, we have to calculate the distance between the horizontal line of the curve and the top or bottom of the function
Using the top of the curve as a point of reference;
Amplitude = Top of curve - Horizontal Line.
The horizontal line is always at point 0
From the graph above, the top of the curve is at point 3
Hence,
Amplitude = 3 - 0
Amplitude = 3