Answers
Answer:
A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Step-by-step explanation:
Given : Triangle 90 -45 -45 .
To find : What is cos 45.
Solution : We have given
Triangle 90 -45 -45
Hypotenuse = √2 ,
Adjacent side to 45 degree = 1 .
By the trigonometric ratio : cosine is the ratio of the adjacent side to angle to the hypotenuse .
Cos ( theta) = [tex]\frac{Adjacent}{hypotenuse}[/tex].
Plug the values Hypotenuse = √2 , Adjacent side to 45 degree = 1 .
Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Therefore, A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
The cosine of 45° is √2 / 2.
In a triangle with angles of 90°, 45°, and 45°, we can use the trigonometric functions to find the ratios of the sides.
In this case, we want to find the cosine of 45°.
The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.
In the given triangle, the adjacent side to the 45° angle is 1, and the hypotenuse is √2.
Using the formula for cosine, we have:
cos 45° = adjacent side / hypotenuse
Substituting the values, we get:
cos 45° = 1 / √2
To rationalize the denominator, we multiply both the numerator and denominator by √2:
cos 45° = (1 / √2) * (√2 / √2) = √2 / 2
Therefore, the cosine of 45° is √2 / 2.
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Related Questions
Someone please help me?
Answers
AP = BP
3x-4 = 2x +12
subtract 2x from each side:
x-4 = 12
add 4 to each side:
x = 16
now we know x, replace x with 16 in the equation for AP:
AP = 3(16) -4
AP = 48 -4
AP = 44 meters
(evaluating expressions) what is the value of the expression 2½x + 3⅔y if x = 4 and y = 3? * 21
Answers
10 + 11 = 21
Craig is designing a new cylinder-shaped can for a pet food company. He wants the height of the can to be 40 mm and the radius of the can to be 1 3/8 times the height of the can. He models the can on a coordinate grid as a rectangle in the first quadrant that will be rotated around the y-axis to create the 3-dimensional can. What will be the diameter of the can?
Answers
h = 40 mm
The radius of the can is given by:
r = (1 3/8) * h
Substituting values:
r = (1 3/8) * 40
r = 55 mm
Therefore, the diameter of the can is:
d = 2 * r
d = 2 * 55
d = 110 mm
Answer:
The diameter of the can will be:
d = 110 mm
A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.2%). what is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?
Answers
If p is the point estimator;
Then,
Minimum range = p - Error
Maximum range = p + Error
Solving one of the two expressions,
0.011 = p - 0.0105 => p = 0.011+0.0105 = 0.0215 = 2.15%
Answer:
Read more on Brainly.com - https://brainly.com/question/9975138#read more Error = 1/2(Maximum range - Minimum range) = 1/2(3.2-1.1) = % = 0.0105If p is the point estimator; Then, Minimum range = p - Error Maximum range = p + Error Solving one of the two expressions,0.011 = p - 0.0105 => p = 0.011+0.0105 = 0.0215 = 2.15%
Step-by-step explanation:
Miguel’s teacher asked him to color 4/8 of his grid. He must use 3 colors: red, blue, and green. There must be more green sections than red sections. how can Miguel color the sections of his grid to follow all the rules.
Answers
2x-14y= -16 solve for x ..
Answers
2x = -16 + 14y
Now divide both sides of the equation by 2.
x = -8 + 7y
Since we cannot simplify this equation any further,, the correct answer will be that x = -8 + 7y.
Let me know if you have any further questions.
:)
2x - 14y = -16
Move all the terms without the variable on the other side of the equation. Add 14y to both sides of the equation.
2x = -16 + 14y
Divide both sides by 2.
x = -8 + 7y is your answer.
Which of the following are exterior angles ? Check all that Apply NEED ASAP
Answers
Answer:
∠2 , ∠3 , ∠5 ,∠6 are exterior angles
Step-by-step explanation:
Given : Figure.
To find : Which of the following are exterior angles.
Solution : We have given a figure with angle 1 ,2, 3,4,5,6.
Exterior angle : An angle which lies outside the closed figure.
We can see ∠1 and ∠4 area lies in closed figure.
But all other angle ∠2 , ∠3 , ∠5 ,∠6 are lies outside so, these are the exterior angles.
Therefore, ∠2 , ∠3 , ∠5 ,∠6 are exterior angles
Answer:
5. 6. and 2
Step-by-step explanation:
All exterior ANGLES that are still connected to the triangle. 3 Is not an angle on Triangle 1. It is its own triangle, as well as a point.
Michelle will be 72 years old in eighteen years. How old is Michelle now?
Answers
72-18=54
Graph the equations to solve the system Y equals 1/3 X +6 and why equals 1/3 X +4
Answers
y = (1/3) x + 6
y = (1/3) x + 4
We note that both lines have the same slope in this case given by:
m = 1/3
Therefore, the lines are parallel. As they are parallel, they are not cut at any point.
Thus, the system of equations has no solution.
Answer:
The system has no solution (parallel lines)
Following the formula: y=mx+b,
where:
m= slope
b=y-intercept
As observed in the given equations, they have the same slope which is equal to 1/3 but each have different y-intercept which is 6 and 4.
Note that two lines are parallel if their slopes are equal and they have different y-intercepts.
Upon graphing, it had seen that the two functions are parallel.
See attached picture for the graph.
An acrobat was launched toward a water tank, with an upward velocity of 48 feet per second. The launch point was 32 feet below the water level in the tank. Use the quadratic equation 0 = -16t2 + 48t – 32 to find how much time, t, it took for her to reach the water level in the tank.
Answers
Answer:
1 or 2 seconds
Step-by-step explanation:
Math papa
Answer:
B. 1 or 2 seconds
Step-by-step explanation:
ttm
Today an exercise equipment store took 15% off the price of a treadmill, and for the next 2 days, it will take 15% off the previous day's price. If the price of the treadmill yesterday was $4000, what will be the price of the treadmill 2 days from now? (5 points: Part I – 1 point; Part II – 1 point; Part III – 1 point; Part IV – 2 points)
Answers
You should use 85% (100% - 15%) as the part you will pay for a quicker calculation.
$4000 x 0.85 = $3400 (after the first day)
$3400 x 0.85 = $2890 (after the second day)
$2890 x 0.85 = $2456.50 (after third day)
If the price of the treadmill yesterday was $4000, what will be the price of the treadmill 2 days from now? I interpreted this as the discount would be applied for 3 days.
A total of 589 tickets were sold for a play. They were either adult tickets or student tickets. There are 61 fewer student tickets sold than adult tickets. How many adult tickets were sold?
HELLLPP ASAPPP
Answers
Student Tickets: 264
You can get this by setting adult tickets equal to x and student tickets equal to x - 61. Then you can set equal to 589 and solve for x.
Reduce the fraction to lowest terms. 38x^2yz^2/ -19 yz^2z^3
Answers
A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. one flower is chosen at random and given to a woman. another flower is then chosen at random and given to a different woman. what is the probability that both flowers are pink roses?
Answers
Answer:
Step-by-step explanation:
The probability that the first flower is a pink rose is 4 /15.
The probability that the second flower is a pink rose is 3 /14 .
Therefore, the probability that both flowers are pink roses is
4 /15 · 3 /14 = 0.057
Peaches varied directly as apples. when there were 40 peaches, there were 120 apples. how many apples went with 500 peaches?
Answers
let the number of peaches be p and that of apples be a
hence
p=ka
where
k is constant of proportionality given by:
k=p/a
when:
p=40, a=120
thus
k=40/120=1/3
thus the equation will be:
p=1/3a
thus the number of apples where there are 500 peaches will be:
500=1/3a
multiplying both sides by 3 we get:
500×3=1/3a×3
a=1500
The volume of a right rectangular prism is 573.3 cm³. The length of the right rectangular prism is 7.35 cm and the height is 16.25 cm. What is the width of the right rectangular prism? Enter your answer in the box.
Answers
Answer:
4.8
Step-by-step explanation:
A school play cost $1,200 to produce. if tickets sold for $5 each, the profit, p, made on the play by selling x tickets is given by the equation shown. p=5x−1,200 what is the slope of the line representing this equation?
Answers
Slope is always the number attached to x.
The slope of the line representing this equation will be;
⇒ $5
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The tickets sold for $5 each, the profit, p, made on the play by selling x tickets is given by the equation shown,
⇒ p = 5x - 1,200
Now,
We know that;
The slope - intercept form of an equation is,
y = mx + c
Where, 'm' is slope of the line and 'c' is y - intercept.
Here, The equation is,
⇒ p = 5x - 1200
By comparing, we get;
⇒ Slope (m) = 5
Thus, The slope of the line representing this equation = 5
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If the reserve rate is 6% and a bank receives a deposit of $14,000, how much of the $14,000 is the bank free to loan out?
Answers
Apex said $13160 was the right answer
The bank must keep 6% of the $14,000 deposit as a reserve, which amounts to $840. Therefore, it is free to loan out the remaining $13,160.
If the reserve rate is 6% and a bank receives a deposit of $14,000, the bank is required to keep 6% of that deposit as reserves. To calculate the amount the bank needs to keep in reserves, we multiply the total deposit by the reserve rate:
Reserve amount = Total deposit x Reserve rate
Reserve amount = $14,000 x 0.06 = $840
Now, to find out how much the bank is free to loan out, we subtract the reserve amount from the total deposit:
Amount available for loans = Total deposit - Reserve amount
Amount available for loans = $14,000 - $840 = $13,160
The bank can loan out $13,160 of the initial $14,000 deposit.
What percent of 51 is is 40?
Answers
WILL MARK BRAINLIEST! PLEASE HELP
In triangle PQR, mP= 43, PQ=7.5 and PR= 8.4. What is mR to the nearest degree?
A. 64
B. 52
C. 41
D. 60
In triangle ABC mA=43, mB=62 and BC=22 in. What is AB to the nearest tenth of an inch?
A. 28.5
B. 15.6
C. 14.1
D.31.2
thank you.
Answers
we know that
the law of cosines establishes that
c²=a²+b²-2*a*b*cos C
in this problem
c=QR
a=PQ=7.5
b=PR=8.4
C=angle P=43°
c²=a²+b²-2*a*b*cos C----> c²=7.5²+8.4²-2*7.5*8.4*cos 43°
c²=34.66--------> c=5.89
QR=5.9
applying the law of sines
7.5/sin R=5.9/sin 43-----> 7.5*sin 43=5.9*sin R---> sin R=7.5*sin 43/5.9
sin R=0.8669---------> R=arc sin (0.8669)----> R=60.11°----> R=60°
the answer Part 1) is the option
D. 60
Part 2) In triangle ABC mA=43, mB=62 and BC=22 in. What is AB to the nearest tenth of an inch?
we know that
∠C=180-(62+43)-----> ∠C=75°
Applying the law of sines
22/sin 43=AB/sin 75------> AB=22*sin 75/ sin 43-----> AB=31.16 in
AB=31.2 in
the answer Part 2) is
D.31.2
What is the eleventh term in the sequence 17, 24, 31, 38…?
Answers
What is the area of a circle with a radius of 13 millimeters?
(Use 3.14 for Pi.)
Answers
The area of a circle with a radius of 13 millimeters is calculated using the formula πr², which equals 530.66 mm².
Explanation:The area of a circle is calculated using the formula πr², where 'r' represents the radius of the circle and 'π' (Pi) is a mathematical constant approximately equal to 3.14. When you have a circle with a radius of 13 millimeters, you would substitute 13 into the formula in place of 'r'.
So, the calculation for this circle's area becomes π*(13)² = 3.14 * 169. When you calculate this, you get 530.66 mm². Therefore, the area of a circle with a radius of 13 millimeters is 530.66 mm².
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answer these questions. Number 1 and number 2.
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2) A cone, the top right one, is being formed by the rotation.
Robin says that polynomials are closed under division. Brad adamantly disagrees. Who is correct? Justify your answer.
Answers
Polynomials do not include negative exponents; this means there can be no variables in the denominator. If two polynomials do not divide evenly, the remainder is written as a fraction with the divisor (which can include a variable) in the denominator. This is not a polynomial.
A translation is applied to the rectangle formed by the points A(−2, 6) , B(2, 6) , C(2, 4) , and D(−2, 4) . The image is the rectangle that has vertices A′(1, 6) , B′(5, 6) , C′(5, 4) and D′(1, 4) . Select the phrase from the drop-down menu to correctly describe the translation. The rectangle was translated .
Answers
You can just move one of the points to see how it moved.
Answer:
The answer is 3 units to the right.
Step-by-step explanation:
A rectangle has a length that is 3 times the width. Use the formula P = 2l +2w to determine the length if the perimeter is 32 and the width is 4 a. 12 c. 32 b. 8 d. 4
Answers
Let the lenght be 3x because it is 3 times the width
P = 2L + 2W
32= 2(3X)+2(4) Combine like terms
32 = 6x+ 8 solve for x
24=6x divide
x= 4
Answer: D
The chord AB is a diameter of O. True or false.
Answers
Answer:
False.
Step-by-step explanation:
We have been given a graph and a statement. We are asked to determine whether the given statement is true or false.
Statement: The chord AB is a diameter of O.
We know that diameter of a circle is a chord that passes through the center of the circle.
Upon looking at our given graph, we can see that chord AB doesn't pass through the center at point 'o', therefore, AB is not a diameter of circle O.
Therefore, the given statement is false.
Answer: False
Step-by-step explanation:
I just got it right on the quiz
How do I do this? Please help
Answers
so on chord FH you have 3.5 and 4.8
multiply those: 3.5 x 4.8 = 16.8
so now chord GI needs to equal 16.8
to find Y divide 16.8 by 2.4
y = 16.8 / 2.4 = 7
y = 7
A line passes through (-7, -5) and (-5, 4). a. Write an equation gor the line in point-slope form. b. Rewrite the equation in standard form using integers.
A. Y-5=9/2(x+7);-9x+2u=-53
B. Y+5=9/2(x-7);-9x+2y=53
C. Y+5=9/2(x+7);-9x+2y=53
D. Y+7=9/2(x+5);-9x+2y=31
Answers
[tex]\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=\cfrac{9}{2}[x-(-7)] \\\\\\ \boxed{y+5=\cfrac{9}{2}(x+7)}\implies y+5=\cfrac{9}{2}x+\cfrac{63}{2}\impliedby \begin{array}{llll} \textit{and now we multiply}\\ \textit{both sides by }\stackrel{LCD}{2} \end{array} \\\\\\ 2y+10=9x+63\implies \boxed{\stackrel{\textit{standard form}}{-9x+2y=53}}[/tex]
just a quick note, multiplying both sides by the LCD, whatever it may be, simply gets rid of the denominators.
Two apples and three peaches cost $1.65. three apples and two peaches cost $1.60. what is the cost of one peach
Answers
From the two statements we can create the following system of equations:
2a + 3p = 1.65
3a + 2p = 1.60
Since we want to know the cost of a peach, let's eliminate the "a" terms by creating opposites. The LCM for 2 and 3 is 6 so I will multiply the top equation by 3 and the bottom equation by -2. This will create opposites to cancel "a" terms.
3(2a + 3p = 1.65) → 6a + 9p = 4.95
-2(3a + 2p = 1.60) → -6a - 4p = -3.20
The result of adding → 5p = 1.75
The result of ÷ 5 → p = .35
This means one peach cost .35 or 35 cents
Number of apples = a
Number of peaches = p
Two apples and three peaches cost $1.65
⇒2a + 3p = 1.65
Three apples and two peaches cost $1.60
⇒3a + 2p = 1.60
System Equations :
[tex]\begin{cases}&2a + 3p = 1.65 ---- (1) \\&3a + 2p = 1.60 ---- (2)\end{cases}[/tex]
[tex]\begin{cases}&\text{Equation (1}) \times3: 6a + 9p = 4.95 ---- (1a) \\&\text{Equation (2}) \times2: 6a + 4p = 3.20 ---- (2a)\end{cases}[/tex]
Equation (1a) - (2a) :
[tex] \begin{aligned} &5p = 1.75 \\&p = 0.35&\end{aligned} [/tex]
Answer: $0.35