The values of the sine and tangent of the angle are √2 / 2 and - 1. By using inverse trigonometric functions, the value of angle is 135° (3π / 4).
How to find the values of other trigonometric functions and the angle behind themAccording to the statement, the cosine of the angle is in the second quadrant and therefore the value of the sine must be positive and the value of the tangent must be negative. Then, the value of the sine is found by the fundamental formula:
sin θ = √(1 - cos² θ)
sin θ = √[1 - (- √2 / 2)²]
sin θ = √(1 - 1 / 2)
sin θ = √(1 / 2)
sin θ = √2 / 2
And the value of the tangent:
tan θ = sin θ / cos θ
tan θ = (√2 / 2) / (- √2 / 2)
tan θ = - 1
By using inverse trigonometric functions, we find that the value of angle is 135° (3π / 4).
To learn more on trigonometric functions: https://brainly.com/question/14746686
#SPJ1
The diameter of Jupiter at its equator is approximately 1.43 x 10 to the 5th power kilometers. Write this number in standard notation. An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.000439 meters. Write this number in scientific notation.
The conversions to standard and scientific notation will result into-
D (Jupiter) = 143000 Km
λ (Wavelength) = 4.39 x [tex]10^{-4}[/tex] meters.
We have diameter of Jupiter and radiation of a wavelength.
We have to write them in standard notation and scientific notation.
What is Scientific Notation ?Scientific notation is a way of writing very large or very small numbers in the powers of 10.
According to the question -
D = 1.43 x [tex]10^{5}[/tex] Km
In standard notation -
D = 143000 Km
and
λ = 0.000439
In scientific notation -
λ = 4.39 x [tex]10^{-4}[/tex] meters
Hence, the conversions to standard and scientific notation will result into-
D (Jupiter) = 143000 Km
λ (Wavelength) = 4.39 x [tex]10^{-4}[/tex] meters
To solve more questions on Standard and Scientific notation, visit the link below-
https://brainly.com/question/24601907
#SPJ1
I’m so confused! Can someone please help.
For the given kite DCBA, the value of AD as 22 units and CB as 30 units.
We know that the two longer sides and the two shorter sides of the kite are equal to each other.
So, we get that:
AD = CD
Substituting the values, we get that:
11 y - 22 = 7 y - 6
11 y - 7 y = 22 - 6
4 y = 16
y = 16 / 4
y = 4
AD = 11 y - 22 = 44 - 22 = 22 units
AB = BC
Substituting the values, we get that:
3 x + 12 = 5 x
5 x - 3 x = 12
2 x = 12
x = 12 / 2
x = 6
CB = 5 x = 30 units
Therefore, we get that, for the given kite DCBA, the value of AD as 22 units and CB as 30 units.
Learn more about kite here:
https://brainly.com/question/23279609
#SPJ9
1. A restaurant has three pieces of apple pie, five pieces
of cherry pie, and four pieces of pumpkin pie in its
dessert case. How many ways are there to arrange the
pies in a line? (note every pie is a unique work of art).
there are a total of 7983360 way of arrangements of the pies.
As we are provided we three pieces of apple pie, five pieces of cherry pie, and four pieces of pumpkin pie, in total 12 pies
So total combination will be
12! = 1*2*3*4*5*6*7*8*9*10*11*12
= 479001600
In the event that there was 1 pie, at that point it would be fair 1 in its line. If we had 2 pies A and B, at that point we have 2 combinations AB and BA. Adding a 3rd pie C would multiply those combinations by 3, ABC, ACB, BAC, BCA, CAB, and CBA. If each pie piece may be a unique work of craftsmanship at that point 12! is the proper amount of combinations. On the off chance that you need combinations that disregard setups where for illustration two cherry pie pieces are compatible, meaning you want uniqueness at that point you divide 12! by 5 at that point by 3 and after that by 4.
Usually 12! / (5*3*4) = 7983360 exceptionally interesting combinations.
To know more about combination refer to the link https://brainly.com/question/28720645?referrer=searchResults.
#SPJ9
Which expression has the greatest value?
O 24+ 16 ÷ 4
O (24+16) ÷ 4
O 24 ÷ 4+2
O 24 ÷ (4+2) PLS HELP
Answer:
24 +16÷4=00
(24+16)÷4=00
24÷(4+2)=42
!! NEED HELP ASAP !! 35 POINTS!! Which shapes are similar to shape A?
The shapes which are similar to shape A are the shape in pink color, the shape in blue color inside the square and the shape in voilet color inside the square.
From the given figure, we can find the similar shapes
From shape A to shape in pink color, the translation is rotation about the origin at 90° counterclockwise.
From shape A to shape the shape in blue color inside the square, the translation is diminishment with the scale factor 0.5 and opposite rotation about an origin 90° clockwise.
From shape A to the shape in voilet color inside the square, the translation is enlargement with the scale factor 1.5 and opposite.
What is a scale factor?Shapes in various dimensions are scaled using the scale factor. In geometry, we study a variety of two- and three-dimensional geometrical shapes. A measurement for similar figures that appear the same but have distinct scales or measures is the scale factor.
To learn more about the similar shape visit:
brainly.com/question/24214480.
#SPJ9
Suppose you make hot chocolate. It's too hot to drink, so you put it in the freezer to cool it off. If the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit, what will the temperature of the hot chocolate be after 4 minutes? (k = 0.12)
307.05
272.33
132.56
117.57
If the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit the temperature of the hot chocolate be after 4 minutes is: 117.57.
Temperature of the hot chocolateGiven:
k=0.12
Original or initial temperature=190 degrees Fahrenheit
Freezer temperature = 0 degrees Fahrenheit
Using Newton's Law of cooling to find the temperature of the hot chocolate
Temperature (t)= Temperature of surrounding environment T1 +(initial temperature of object T0-Temperature of surrounding environment T1)e-^kt
Hence,
T(t)=0+(190-0)e^-0.12t
T(t)=190e^-0.12t
Where t=4
T(t)=190e^-0.12(4)
T(t)=190e^-0.48
T(t)=117.5688
T(t)=117.57 (Approximately)
Therefore if the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit the temperature of the hot chocolate be after 4 minutes is: 117.57.
Learn more about Temperature of the hot chocolate here: https://brainly.com/question/14578298
#SPJ1
In the diagram below, m/CAD = 47°, m/CAB = 77° and
m/ADB = 105°. Find m/B.
Step
1
2
3
try
Angle
m/CAD = 47°
m/CAB = 77°
(hover here to see on figure)
m/ADB = 105°
m/
B
O
Select a Reason
105°
Reason
Given
Given
Given
C
47°
A
(
4) m∠BAD=30° (angle subtraction postulate)
5) m∠B=45° (sum of angles in a triangle)
x:4|x-3|-6<10. what is the missing number
Answer: -1<x<7
Step-by-step explanation:
4|x-3|-6<10
4|x-3|-6+6<10+6
4|x-3|<16
4|x-3|/4<16/4
|x-3|<4
x-3<4
x<7
x-3>-4
x>-1
-1<x<7
During track practice any walks three minutes for every eight minutes of running at this rate how many minutes will she walk in a total if she runs 32 minutes
How to write three hundred eight and sixty thousandths in decimal number
Answer: 308.0006
Step-by-step explanation:
Select the correct answer.
What is the y-intercept of f(x) = 3x+2?
O A.
(9,0)
O B.
(0,9)
O C.
(0,-9)
O D. (9,-9)
Answer:
y = 2
Please go through my explanation.
Step-by-step explanation:
If y = 3x + 2
then y intercept is the value of y when x = 0
At x = 0
y = 3 x 0 + 2
y = 0 + 2
y = 2
I have attached a graph to prove this
Note
It does not fit any of the answer choices. Maybe the answer choices are incorrect or the equation is incorrect.
The y intercept from the answer choices should be either (0, 9) or (0, -9) since x has to be 0 to get the y intercept
If y-intercept is to be 9, the equation should be y = 3x + 9
If y-intercept is to be -9, the equation should be y = 3x -9
You may wish to explain to the teacher about this if you are absolutely sure that the equation and answer choices are correct
Hope that helps in some small way
A point on the y-axis known as an intercept is where the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses.
A line's slope and intercept give information on its steepness and the point at which it crosses an axis, respectively.
We have,
f(x) = 3x + 2
To find the y intercept put x= 0 we get
y = 3x +2
y= 3(0)+ 2
y= 0+ 2
y= 2
Thus, the y intercept is (0, 2).
Learn more about Intercept here:
https://brainly.com/question/14180189
#SPJ5
Anna and Connor are in different math classes in NYC. Anna's teacher is always giving exams with 30 questions on them, while Connor's teacher gives more frequent exams with 24 questions on them. Anna's teacher also gives 3 projects. Even though two classes take different number of exams, the teachers told them the they will have the same total number of exam questions this year. What is the minimum amount of exam questions Anna and Connor will expect this year?
Layla has $680 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $319.28. She buys 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94. She plans to spend some or all of the money she has left to buy new biking outfits for $77.02 each.
The inequality that can be used to determine "x", the maximum number of outfits that Layla can purchase while staying within her budget is [tex][680\geq (371.90+77.02x)][/tex].
As per the question statement, Layla has a budget of $680 to spend at a bicycle store for some new gear and biking outfits, and she buys a new bicycle for $319.28, 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94.
We are required to express the inequality that can be used to determine "x", the maximum number of outfits that Layla can purchase while staying within her budget if a new biking outfit costs $77.02
First, let us calculate the total spending Layla has already done before going for new biking outfits, which is $319.28 on bicycle, 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94, summed up as [tex][319.28+(4.90*3)+37.94]=(319.28+14.7+37.94)=371.92[/tex]
And supposing that she buys "x" new biking outfits, of $77.02 each, the total spending has to be equal to, or less than $680, i.e.,
[tex][680\geq (371.90+77.02x)][/tex]
Hence, the inequality that can be used to determine "x", the maximum number of outfits that Layla can purchase while staying within her budget is [tex][680\geq (371.90+77.02x)][/tex].
Inequality: In mathematics, an inequality is a relation which makes comparison between two inequal numbers or other mathematical expressions.To learn more about Inequality, click on the link below.
https://brainly.com/question/20383699
#SPJ1
SOLVE this equation.
0.5r+5=r-8
Answer:
r = 26
Step-by-step explanation:
Let's solve the problem,
→ 0.5r + 5 = r - 8
→ r - 0.5r = 5 + 8
→ 0.5r = 13
→ r = 13/0.5
→ [ r = 26 ]
So, the value of r is 26.
y = 3x - 1 on a graph
Answer:
See explanation
Step-by-step explanation:
One of the band members, Darius, wants to explore the waters of the Great Barrier Reef. Darius is currently -5 feet from the surface of the water and plans to explore a shipwreck that is at -75 feet from the surface. If he moves at a rate of -8 feet per minute, how many minutes does it take Darius to reach the shipwreck?
The number of minutes it takes Darius to reach the shipwreck is 8.75 minutes
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the number of minutes it takes Darius to reach the shipwreck?The given parameters are
Initial position = -5 feet
Rate = -8 feet per minute
Final position = - 75 feet
The linear equation of this situation is
Final position (y) = Initial position + Rate * Time (x)
So, we have
-75 = -5 -8x
This gives
-8x = -70
Divide both sides by -8
x = 8.75
Hence. the number of minutes it takes Darius to reach the shipwreck is 8.75 minutes
Read more about linear equations at
https://brainly.com/question/14323743
#SPJ1
(y + 2)² when y=-7, z = 19
Answer:
Step-by-step explanation:
if y=-7 you can plug it in the equation[tex]=(-7+2)^{2} \\=(-5)^{2} \\=25[/tex]The area of a triangle is 75 square units with a scale factor of 1 to 4 Find the area of the preimage preimage
The area of the pre-image is 300 square units
Area of triangleA triangle is a 2D shape that has a 3 sides and angles. The formula for calculating the area is expressed as;
Area= 1/2 * bh
where
b is the base of the triangle
h is the height of the triangle
Given the following parameters
Area of triangle = 75 square inches
If the area is increased with with a scale factor of 1 to 4, then
Area of pre-image = 4 * 75
Area of pre-image = 300 square units
Hence the area of the pre-image is 300 square units
Learn more on scaling here: https://brainly.com/question/25324744
#SPJ1
5. Look at the model and fill in each blank with the correct answer.
bigger
smaller
?
5526
3496
?
(a) The smaller number is
(b) The difference between the two numbers is
(c) The sum of the two numbers is_
The smaller number is 3496
The difference between the two numbers is 2030
The sum of the two numbers is 9022
Given no.
5526,3496
The difference between the two numbers is 5526-3496=2030
The sum of the two numbers is 5526+3496=9022
The process of combining two or more objects is known as addition. The procedure of determining the sum of two or more integers in mathematics is known as addition. It is a basic mathematical operation that we all employ on a daily basis. When we work with money, compute our shopping bills, or calculate the time, we employ addition frequently.
Addition is a mathematical procedure that is used to add numbers. The sum of the provided numbers is the outcome of adding the supplied numbers. For instance, if we add 2 and 3, (2 + 3), the result is 5. We used the addition function on two integers, 2 and 3, to produce the sum, 5.
To learn more about Addition from the given link:
https://brainly.com/question/14092461
#SPJ9
Megan wants to purchase 2
1/2
pounds of chocolate pretzels for lunch this week. If each pound cost $3.48, how much will she
spend on pretzels?
PLEASE WORK OUT ANSWER
Answer: $8.70
Step-by-step explanation: $3.48 x 2 for the 2 pounds. You divide 3.48/2 to get the half pound. 3.48 x 2 = 6.96. 3.48/2=1.74. 1.74 + 6.96 = $8.70
Answer:
Step-by-step explanation:
$3.48 x 2 for the 2 pounds. You divide 3.48/2 to get the half pound. 3.48 x 2 = 6.96. 3.48/2=1.74. 1.74 + 6.96 = $8.70
HELP ILL MARK AS BRAINliEST
Answer: it's A.12 \ 3 =4 if worrg do D.16\4=4 i hop this help's you
i did this one long time ago it was ether one so ya i forgotten it sorry
What is three subtracted by 4/7
Answer:
2.42
Step-by-step explanation:
3 - 4/7 = 2.42
3 - 8/14 = 2.42
3 - 0.57 = 2.42
3 - 57.1 = 2.42
Breaking things down like this will make it easier to solve and get you answers faster!
Which fraction is equivalent to 3/7?
Answer:
6/14,9/21
Step-by-step explanation:
those two are equavalent to 3/7
24 over 80 equivalent
The equivalent expression of 24 over 80 is 3/10
How to determine the equivalent?The expression is given as
24 over 80
Rewrite the expression properly
So, we have
24/80
Divide the numerator and the denominator by 8
So, we have
3/10
Hence, the equivalent expression of 24 over 80 is 3/10
Read more about equivalent expression at
https://brainly.com/question/2972832
#SPJ1
Why is there one decimal in 0.25x0.4
Answer:
this is since the decimal point moves
Step-by-step explanation:
forget about the decimal point for right now
025
04
-------
0
8
20
0
0
0
+
-----
100
now there are 3 numbers behind the decimal points (2,5,and 4) so put the decimal point where 3 numbers are behind it.
.100 or .1
find the volume of cylinder with radius 15mm and height 63mm
4. The top rung of a ladder is 18 inches long. The lengths of the rungs increase one-half inch uniformly from the top to the bottom. What is the length of the tenth rung from the top?
The top rung of a ladder is 18 inches long, lengths of the rungs increase one-half inch uniformly from the top to the bottom. The length of the ladder after 10th rung from the top is 33inches.
What is the function of a ladder and their uses?A ladder is a piece of gear used for climbing up or down objects that consists of repeating bars or steps (rungs) between two upright lengths of metal, wood, or rope.
In the industry, step ladders are most frequently used. This ladder is unique since it may be used in any location. This is due to the fact that it may be utilized without needing to lean against any kind of support because it is self-supportable. This ladder can therefore be used in the middle of a room or in other places without support.
Step ladders are incredibly practical to have throughout the house, particularly in the kitchen. Simply said, this ladder is a miniature ladder that you can use to access higher objects. When purchasing this ladder, storage space is not a concern because step stools are made to fold up.
Given,
Top rung =18 inches
Length increases = 1.5inches
Therefore, after 10th rung length= (1.5*10)+18 inches= 33 inches
To know more about ladder visit: https://brainly.com/question/28636911
#SPJ9
Suppose that the width of a certain rectangle is 1 inch more than one-fourth of its length. The perimeter of the rectangle is 52 inches. Find the
length
width
The length of the rectangle is 82.4 inches and the width of the rectangle is 21.6 inches.
Let the length of the rectangle be x inches.
So, the width of the rectangle will be:
Width = 1 / 4 x + 1 inches.
Now, the perimeter = 52 inches.
Now, the formula for the perimeter is:
P = 2 (l + b)
Substituting the values in the formula, we get that:
52 = 2 ( x + 1 / 4 x + 1)
104 = 5 / 4 x + 1
103 = 5 / 4 x
x = 103 × 4 / 5
x = 82.4 inches.
Length = 82.4 inches
Width = 1 / 4 x + 1 = 21.6 inches.
Therefore, we get that, the length of the rectangle is 82.4 inches and the width of the rectangle is 21.6 inches.
Learn more about rectangle here:
https://brainly.com/question/25292087
#SPJ9
During a giveaway, every fourth customer gets a coupon and every tenth customer gets a free item. If 60 customers participate, how many get both the coupon and free item? A. 2 people B. 10 people C. 20 people D. 3 people
For which value of x is line l parallel to line m?
X=
The value of x should be 20 for the line l to be parallel to the line m
What are parallel lines?Parallel lines are those lines that are equidistant from each other and never meet.
Parallel lines cut by a transversal, forms different angle relationship like alternate angles, corresponding angles, etc.
Therefore, for the line l to be parallel to the line m, the angles formed are corresponding angles.
Corresponding angles are equal.
Therefore,
3x - 20 = 2x + 10
3x - 2x = 10 + 20
x = 20
Therefore, the value of x should be 20 for the line l to be parallel to the line m.
learn more on parallel lines here: https://brainly.com/question/7849620
#SPJ1
