Step-by-step explanation:
arccos(sin(5π/4))
= arccos(sin(-π/4))
= arccos(-√2/2)
= 3π/4.
The value of trigonometric function arccos(sin(5π/4)), π/4
What is trigonometry?Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.
There are 6 commonly used functions in trigonometry with their name and abbreviations-
sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)
First, we can use the trigonometric identity sin(θ) = cos(π/2 - θ) to rewrite this expression:
sin(5π/4) = cos(π/2 - 5π/4)
Next, we can use the fact that cos(x) is an increasing function on the interval [0, π], so cos(x) is unique on this interval for each value of x.
This means that the inverse cosine function, arccos, is also unique on the interval [0, π].
Therefore, we can conclude that:
0 ≤ π/2 - 5π/4 ≤ π
arccos(sin(5π/4)) = π/2 - 5π/4 = π/4.
So the answer is π/4 in radians.
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The sum of two numbers is 8. The difference between the two numbers is 2. What are the numbers? x + y = 8 x - y = 2 *Use the tables to list the possibilities
Answer:
x=5 y=3
Step-by-step explanation:
x+y=8 1
x-y=2 2
x+y=8
y=8-x
substitute into 2
x-(8-x)=2
x-8+x=2
2x=10
x=5
substitute x into 1
5+y=8
y=3
5+3=8
5-3=2
What is two thirds minus one fifth?
Answer:
7/15
Step-by-step explanation:
First, we have to make the bottom part the same:
2/3 - 1/5 = 10/15 - 3/15
10 - 3 = 7 = 7/15
A box in the shape of a cube has a side length of 1 1/2 feet. What is the volume of the box?
Answer:
Step-by-step explanation:
V cube=s^3, where is the side of the cube
1 1/2ft=3/2 ft
V=(3/2)^3=27/8 ft^3=3 3/8 ft^3
V=3.375 ft^3
An aquarium costs $85
plus $2 per fish. Write an equation to
find the cost c of an aquarium plus
any number of fish f. Make a table to
find the cost of an aquarium plus 3, 4,
5, or 6 fish.
Answer:
C=85+2x
Step-by-step explanation:
c=85+2(3) -- $91
c=85+2(4) -- $93
c=85+2(5) -- $95
c=85+2(6) -- $97
what expression is equivalent to −24x+72?
Answer choices:
1. 24(x+72)
2. 24(x+3)
3. −24(x−72)
4. −24(x−3)
Step-by-step explanation:
the answer is 4. you factor the equation since 24.
Find the value of x.
Z
Y
11x – 10
80°
W
X
Answer: I think the value of x is 20 but im not sure
Step-by-step explanation:
no explanation here
Which of the following is the solution set of the given equation?
(x-3)-2(x+6)=5
Answer:
the answer is x=-20 there you go
Answer: x = - 20 Hope I Helped!!
Step-by-step explanation:
Distribute
Eliminate Redundant Parentheses
Subtract The Numbers
Combine Like Terms
Add 15 to both sides of the equation!!!
help me plz this is my last question finally! will mark brainliest
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
On the left triangle, the shorter side is labeled 4 inches and the longer side is labeled 10 inches. On the right triangle, the shorter side is labeled x inches and the longer side is labeled 20 inches.
The two triangles above are similar. Find the value of x. Be sure to explain your steps.
Answer:
8
Step-by-step explanation:
We are dealing with similaraty and similar shapes length are in proportion so we are going to set up an proportion.
Length of left triangle small side/ Length of left triangle long side= length of right triangle small side/length of right triangle long side
4/10=x/20
Cross multiply: 10x=80
x=8
Answer:
x = 8 inchesStep-by-step explanation:
As the triangles are similar, their corresponding sides will have same ratio:
left short side /right short side = left long side / right long sideor simpler
s₁/s₂ = l₁/l₂Substitute values to find the missing one:
4/x = 10/204/x = 1/2x = 4*2x = 8The missing side is 8 inches long
Factor the quadratic expression completely.
2x2 + 7x + 3
Answer:
(2x+1)(x+3)
Step-by-step explanation:
just remember to put a ^ when you do this 2x2 put it like this 2x^2
an you welcome and plz give me brainiest
Jill is buying new appliances. The cost of the dishwasher is $459 and the cost of the microwave is $289. What is the total price including the sales tax of 7%?
Answer:
$800.36
Step-by-step explanation:
429+289=748
7% of 748= 52.36
748 + 52.36=800.36
The total price of the dishwasher and microwave after the sales tax of 7% will be $800.36.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Jill is buying new appliances.
The cost of the dishwasher is $459 and the cost of the microwave is $289.
The total amount of the dishwasher and microwave will be
Total amount = 459 + 289
Total amount = $748
Then the price of the dishwasher and microwave after the sales tax of 7% will be
Total price = 7% of $748
Total price = 1.07 x $748
Total price = $800.36
Then the total price of the dishwasher and microwave after the sales tax of 7% will be $800.36.
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How does hiphop use energy as a element of dance PLEASE ANSWER
Answer:
Energy can happen with movement. Dance requires a bunch of movement.
dancing is the use of force, tension, and weight.
HEELP ASAP
1. Evaluate the following algebraic expression: 8h ÷ 12 when h=3
Step-by-step explanation:
3h ÷ 12
= but this is wt I know❤️
Answer:
8 (3) /12 = 24/12, 24/12= 2
The solution set of 2(x+4) -5 =-4 is *
-5
3
5
-4
Step-by-step explanation:
2(x+4)-5=-4
2x+8-5=-4
2x=-4-8+5
2x=-12+5
2x=-7
x=-7/2
Round to the nearest hundredths place.
226.671
Answer:
200.000 because it's lower than 250
Step-by-step explanation:
pls give brainly
Answer:
226.67 is the answer
i need help with this !!!!
Line I is parallel to line m. If the measure of <6 is 75, what is the measure of <3
Answer:
m∠3 = 105°
Step-by-step explanation:
Line 'l' is parallel to line 'm' and a transversal is intersecting these parallel lines at two distinct points.
m∠3 + m∠6 = 180° [Consecutive interior angles]
Since, ∠6 = 75° [Given]
m∠3 + 75° = 180°
m∠3 = 180 - 75
= 105°
Therefore, measure of ∠3 is 105°.
In the given diagram, the measure of ∠3 is 105°
From the question,
We are to determine the measure of ∠3
In the diagram, ∠3 and ∠6 are consecutive interior angles
NOTE:
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary
That is,
∠3 + ∠6 = 180°
From the given information,
∠6 = 75°
Then, we can write that
∠3 + 75° = 180°
∠3 = 180° - 75°
∠3 = 105°
Hence, the measure of ∠3 is 105°
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help plz i dont undertand
Answers:
x = 4AB = 36BC = 36AC = 36All three sides are 36 units long.
===========================================================
Explanation:
Triangle ABC is equilateral, so all three sides are the same length.
Pick any two of those sides, set them equal to each other, and solve for x
AB = BC
8x+4 = 11x-8
8x-11x = -8-4
-3x = -12
x = -12/(-3)
x = 4
Use this x value to find each side. We should get the same value (if not, then an error occurred in solving for x).
AB = 8x+4 = 8*4+4 = 32+4 = 36BC = 11x-8 = 11*4-8 = 44-8 = 36AC = 9x = 9*4 = 36We get the same value for the three side lengths, so this confirms we have the correct x value.
Base = 147cm2
Volume= 1323
What is the height ?
The height of the rectangular prism will be 9 cm.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H.
Then the volume of the prism is given as
V = L x W x H
We know that the product of the length and width will be known as the base area.
Then the volume of the rectangular prism will be
V = A x H
Base area = 147 cm²
Volume = 1323 cm³
Then the height of the rectangular prism will be
1323 = 147H
H = 9 cm
The height of the rectangular prism will be 9 cm.
The complete question is attached below.
More about the volume of the rectangular prism link is given below.
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graph the solution to the inequality on the number line. please help me
Answer:
Step-by-step explanation:
The ratio : y is 3:1
Which of the following statements is correct?
A x is 3/4 of y
B y is 1/3 of x
c x is 1/3 of y
D y is 1/4 of x
Answer:
y is 1/3 of x
Step-by-step explanation:
x:y is 3:1
mathematically, we have this as;
x/y = 3/1
x = 3y
or y = x/3
So the correct answer is that y is 1/3 of x
Mr. Johnson buys 5 bottles of lemonade for the school picnic. He buys four 28
ounce bottles and one 64-ounce bottle. Using rounding to the nearest ten, about
how much lemonade does Mr. Johnson buy in all?
A. 360 ounces
B. 180 ounces
C. 90 ounces
D. 190 ounces
Landen's front lawn measures 20 feet by 80 feet. He counts to find that there are
120 blades of grass per square inch. How many blades of grass are in the entire
lawn?
Answer:
[tex]27,648,000[/tex]
Step-by-step explanation:
The area of a rectangle is given by [tex]l\cdot w[/tex]. Landen's 20 feet by 80 feet front lawn therefore has an area of [tex]20\cdot 80 = \fbox{$1600\: \mathrm{ft^2}$}[/tex].
He counts there are 120 blades of grass per square inch. There are [tex]12^2=144[/tex] square inches in one square foot.
Therefore, his lawn has an area of [tex]1600\: \mathrm{ft^2}\cdot \frac{144\:\mathrm{in^2}}{1\:\mathrm{ft^2}}=230,400\:\mathrm{in^2}[/tex].
Thus, there are [tex]230,400\:\mathrm{in^2}\cdot 120=\fbox{$27,648,000$}[/tex] blades of grass in the entire lawn.
If you could help I would really appreciate it, but if not that’s fine. Thank you.
Answer:
Its 3x-5
Step-by-step explanation:
Can someone help me with this?
Graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7).
Use the Polygon tool to graph the quadrilateral by connecting all its vertices.
Here is a link to another brainly question that has the picture of my problem I just need a good answer for it and QUICK! 30 points https://brainly.com/question/12339482?exp=25-1
Answer:
Step-by-step explanation:
Point (-7,-2) is the center of dilation. The scale factor is 2.
If point A has coordinates (-3,-2), then its image point H has coordinates (1,-2).
If point B has coordinates (-6,2), then its image point E has coordinates (-5,6).
If point C has coordinates (-4,3), then its image point F has coordinates (-1,8).
If point D has coordinates (-1,1), then its image point G has coordinates (5,4).
Need help i suck at mathh
What is the value of x^2 – 3 when the value of x is 4?
Answer: the value is 13
Step-by-step explanation:
we simply substitute the letter for the number 4.
4^2 - 3
16 - 3
13
Answer:
13
Step-by-step explanation:
Which plant is the furthest below the surface
of the water?
A. sea grass
B. green seaweed
C. mangrove
D. red algae
Answer: The answer is seagrass
Step-by-step explanation: I did it and got it right
Suppose that Omar's marginal utility for cups of coffee is constant at 1.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 10 for the first doughnut he eats, 9 for the second doughnut he eats, 8 for the third he eats, and so on (that is declining 1 unit for each additional doughnut consumed). Suppose that coffee costs $1.00 per cup and doughnuts $1.00 each, and Omar has a budget that he can spend only on doughnuts and coffee. How large would his budget need to be before he would spend a dollar on coffee?
Answer:
$6.5
Step-by-step explanation:
The marginal utility per dollar of a commodity is obtained by:
Marginal utility of coffee = 5.5
Price of coffee = $1
The marginal utility of doughnut declines by 1 per additional unit of donut consumed :
10 / 1, 9 /1..... 1/1
Therefore , before a dollar can be spent on coffee, then the marginal. Utility of coffee should be greater than doughnut.
5.5 doughnuts will be purchased, at this time marginal utility of doughnut will be 5.5/1, the 6th doughnut will have a marginal utility of 5 which is less than that of coffee.
Cost of 5.5 donuts = $5.5
Cost of coffee = $1
Total = $(5.5 + 1) = $6.5