cot(θ) = cos(θ)/sin(θ)
So if both cot(θ) and cos(θ) are negative, that means sin(θ) must be positive.
Recall that
cot²(θ) + 1 = csc²(θ) = 1/sin²(θ)
so that
sin²(θ) = 1/(cot²(θ) + 1)
sin(θ) = 1 / √(cot²(θ) + 1)
Plug in cot(θ) = -2 and solve for sin(θ) :
sin(θ) = 1 / √((-2)² + 1)
sin(θ) = 1/√(5)
which two cards show reflection, rotation, or translation?
Answer:
1 & 4
Step-by-step explanation:
because 3 & 5 is a reflection, 2 & 6 is a translation.
A print shop borrows $5700 from a credit union for 193 days. The credit union charges simple interest at an annual rate of 12% for this loan. Assume 1/365 each day is
of a year. Answer each part below.
Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
The amount borrowed by the print shop: $5700
Time for which loan is taken: 193 days
Rate of interest: 12%
Day in terms of year is given by: 1/365
The formula for simple interest:
Simple interest = P*R*T/100
where P = principal amount invested
R = rate of interest
T = time in years
Solving the question using the formula we have:
Simple interest = (5700*12*193)/(100*365)
= 13201200/36500
= 361.67 or $362
Interest that will be owed after 193 days will be $362
Amount owed after 193 days will be $5700 + $362 = $6062
Although a part of your question is missing, you might refer to this full question: A print shop borrows $5700 from a credit union for 193 days. The credit union charges simple interest at an annual rate of 12% for this loan. Assume 1/365 each day of a year. Find the interest that will be owed after 193 days. If no payments are made on the loan find the amount owed after 193 days.
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Find x. (Hint: Draw an auxiliary line.)
The angle x will be 98 ⁰
What are alternate interior angle ?
An alternate interior angle is one formed on the inside side of two parallel lines and opposite on the outer side of the transversal when those two parallel lines are intersected by a transversal and they are equal.
Alternate angles between a transverse and parallel lines are equal .
Let the lines are AB and CD and let us draw a transverse line HI parallel to AB and CD, then the angle FEI will be 62 degree as alternate interior angle are equal. and also angle EPC will be supplementary angle of 144 degree that is 36 degree thus forming angle GEI to be 36 degree also as shown in figure below :
Now calculating angle x :
x = 62+ 36
x = 98 ⁰
Therefore, the angle x will be 98 ⁰
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14a - (2a +9)=2/3 (12a-18)
Answer: a=-0.75
Step-by-step explanation:
14a - (2a +9)=2/3 (12a-18)
14a - 2a -9=2/3 * 6(2a-3)
12a-9=2*6/3 (2a-3)
12a-9=2*2(2a-3)
12a-9=4(2a-3)
12a-9=8a-12
4a-9=-12
4a=-3
a=-3/4
a=-0.75
What is the equation of the line?
y=-12+1
Oy=2x-1
O y=-2z+1
Oy=-z-1
Answer:
y = -1/2 x + 1.
Step-by-step explanation:
The slope is -1/2.
The y intercept is at y = 1
So, it's
y = -1/2 x + 1.
Bonjour,
Quelqu'un pourrait m’aider svp.
a-/ |-5-10| = 15 ; |-2√2-√12|=2√3+√12 ; |-π-4π|=5π
A triangle has two sides of lengths 4 and 7. What value could the length of
the third side be? Check all that apply.
A. 9
B. 5
C. 17
D. 7
E. 3
F.' 11
SULMIT
A=9, B=5 and D=7 are the correct options.
In the *Geometry*, a *triangle* is a closed 2-dimensional figure with 3 angles, 3 sides and 3 vertices. Triangles are considered as a *polygon* with the least number of sides.
a,b and c are the sides of a triangle if it satisfies:
a<b+c , b<a+c and c<b+a
Here, a=4 and b=7
We have to find c
i.e. all those c which satisfies:
4<7+c , 7<4+c and c<4+7=11
AAAAAA. 9 it is true
B.5 it is true
C.17 This is clearly false, since it doesn't satisfies inequality third.
D.7 it is true
EE. 3 it is not true since it doesn't satisfies second inequality.
F.11 This is clearly false, since it doesn't satisfies inequality third
Hence, The correct answer of the given question is A,B and D.
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Pls help I’m not very smart
Answer:
Blank 1: 97
Blank 2: 73
Step-by-step explanation:
This equation is shown on a straight line, which equals 180.
We can start by adding the two equations which together are equal to 180.
15x + 2 + 10x + 3 = 180
We can simplify it to 25x + 5 = 180
Now we can subtract 5 from both sides to get
25x = 175
Then we can divide both sides by 25 to get x = 7
Now we can plug in x for both angles
Angle RQS is 15x + 2, so 15*7=95 and the +2 is 97.
Angle TQS is 10x + 3 so 10*7=79 and the + 3 is 73
:D
Can yall help me with this
Answer:
8 feet
Step-by-step explanation:
Since it is 2 inches and 1 inch is equal to 4 feet, you just multiply 2 inches by 4 feet which will give you 8 feet.
Hope that helps
Given negative four and one sixth times negative three and fifteen hundredths, determine the product.
The resulting product of the expression is 13 1/8
Product of fractionsFractions are written as a ratio of two integers
Given the following expression
-4 1/6 * -3 15/100
Convert to improper fraction to have:
-25/6 * -315/100
-1/6 * -315/4
315/24
13 1/8
Hence the resulting product of the expression is 13 1/8
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The circumference is 25 ft I have to find what X is for my radius
R= -4x-5
The value of x based on the information given about the circumference is 2.24.
How to illustrate the information?It should be noted that the circumference is calculated as:
= 2πr
where
π = 3.142
r = radius = 4x - 5.
Circumference = 25
Therefore, circumference = 2πr.
(2 × 3.142)(4x - 5) = 25
6.284(4x - 5) = 25.
25.136x - 31.42 = 25
Collect like terms
25.136x = 25 + 31.42
25.136x = 56.42
x = 56.42 / 25.136
x = 2.24
Therefore, the value of x based on the information given about the circumference is 2.24.
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Please answer the 2 question in photo [ Brainliest + easy points ]
your friend says that you can write any equation in slope-intercept form. is your friend correct? explain.
Answer:
almost.
Step-by-step explanation:
You can write almost every linear equation in slope-intercept form.
Slope-intercept form is:
y = mx + b
So every line except a vertical line can be written in the form y=mx+b.
This form cannot be used when m is undefined.
Prove the following inequality.
The proof of the inequality → (a + b)²/2 ≥ 2ab, is given below -
We have the following inequality -
(a + b)²/2 ≥ 2ab
We have to prove it.
What is inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
According to the question, we have -
Inequality -
(a + b)²/2 ≥ 2ab
Proof -
Starting from the inequality - (a - b)² ≥ 0
(a - b)² ≥ 0
a² + b² - 2ab ≥ 0
a² + b² - 2ab + 2ab ≥ 2ab
a² + b² ≥ 2ab
Add - 2ab on both sides, we get -
a² + b² + 2ab ≥ 4ab
(a + b)² ≥ 4ab
Divide both sides by 2, we get -
(a + b)²/2 ≥ 2ab
Hence Proved.
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to determine her blood sugar level, charlotte divides up her day into three parts: morning, afternoon, and evening. she then measures her blood sugar level at 3 randomly selected times during each part of the day.
According to the given statement this is a type of stratified sampling.
What is a Stratified random sampling?Stratified random sampling is often when researchers want to know about different subgroups or based on the entire population being studied. For instance, if one is interested in differences between groups based on race, gender, or gender.
Briefing:she measures her blood sugar level at 3 randomly selected times during each part of the day.
Stratified is defined as taking samples from a group that has been partitioned or divided into multiple pieces.The lady has organized her day into three sections here: morning, afternoon, and evening.This is a method for randomly selecting a sample from a population. therefore, charlotte took 3 random sample from each part of the day.So,
This is a type of stratified sampling.
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I understand that the question you are looking for is :
To determine her blood sugar level, charlotte divides up her day into three parts: morning, afternoon, and evening. She then measures her blood sugar level at 3 randomly selected times during each part of the day.
What type of sampling is used?
the shorter leg of a right triangle is 8 less than the hypotenuse. the longer leg is one less than the hypotenuse. find the perimeter
The perimeter of the right triangle is 30 units.
How to find the perimeter of a right triangle?The shorter leg of the right triangle is 8 less than the hypotenuse. The longer leg is one less than the hypotenuse.
Let's break the information into smaller chunk.
The shorter leg of a right triangle is 8 less than the hypotenuse.
The longer leg is one less than the hypotenuse.
The hypotenuse is the longest side of a right triangle.
Therefore,
let
the hypotenuse = x
short leg = x - 8
long leg = x - 1
Applying Pythagorean theorem in the given right triangle.
c² = a² + b²
where
c = hypotenusea and b are the other legs.(x - 1)² + (x - 8)² = x²
(x - 1)(x - 1) + (x - 8)(x - 8) = x²
x² - x - x + 1 + x² - 8x - 8x + 64 = x²
2x² - 18x + 65 = x²
x² - 18x + 65 = 0
(x - 13)(x - 5) = 0
Therefore,
x = 5 and x = 13
13² - 5² = a²
169 - 25 = a²
a = √144
a = 12
So, the hypotenuse is 13, the shorter leg is 5 and the longer leg is 12.
perimeter of the right triangle = 13 + 5 + 12 = 30
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A pool measuring 18 meters by 20 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the
path combined is 1520 square meters, what is the width of the path?
18
20
20+ 2x
18+2x
By solving a quadratic equation we can see that the width of the path measures 20 meters.
How to find the width of the path?
We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:
A = 18m*20m = 360 m^2
Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:
(18m + 2x) and (20m + 2x)
And its area is given by:
(18m + 2x)*(20m + 2x)
And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):
(18 + 2x)*(20 + 2x) = 1520
360 + 4x^2 + 76x = 1520
Now we just need to solve that quadratic equation:
4x^2 + 76x - 1520 + 360 = 0
4x^2 + 76x - 1160 = 0
The solutions are:
x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)
x = (-76 ± 156)/4
We only care for the positive solution, which gives:
x = (-76 + 156)/4 = 20
We conclude that the width of the path measures 20 meters.
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ar travels on a straight, level road. (a) Starting from rest, the car is going 38 ft/s (26 mi/h) at the end of 4.5 s. What is the car's average acceleration in ft/s²?
The car's average acceleration is 8.44 ft/s².
Acceleration is defined as the rate of change of velocity per unit time. It is usually denoted by the letter a.
Here, we are given that a car travels on a straight road. Starting from rest, the car is going at 38 ft/s (26 mi/h) at the end of 4.5 s.
Acceleration of an object can be calculated using the given formula-
acceleration = velocity/ time
Here, the velocity of the car will be 38 ft/s
and the time is equal to 4.5 seconds.
Thus, putting these formulas in the equation, we get-
acceleration of the car = 38/ 4.5
= 380/ 45
= 8.44
Thus, the car's average acceleration is 8.44 ft/s².
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Darius designed a billboard. The
billboard is 480 inches long by 144
inches high. Darius uses a
computer to design the billboard.
Determine the height for the
computer design that maintains
the same scale and has a length of
12 inches.
20 +? =100 ÷ 4
Help
Answer:
5
Step-by-step explanation:
Both answers equal 25.
HEY I NEED HELP ASAP CAN YOU HELP? WILL GIVE BRAINLYIST
show your work or explain your reasoning in mathematical terms. Be specific. Draw a picture if you need to.
Question:
Abdul wants to put a rug in a square room that has an area of 775 square feet. He wants to leave a 3-foot border of bare floor on each side. What are the dimensions of the rug rounded to the nearest hundredth?
The dimensions of the rug which Abdul would use in discuss as described in the task content are; 21.84 ft by 21.84 ft.
What are the dimensions of the rug rounded to the nearest hundredth?It follows from the task content that the dimensions of the rug which Abdul would use in the room in discuss are to be determined.
Since the room Abdul wants to put a rug on is; 775 ft² and the room is a square room.
It follows that all sides of the room are equal and the length of each side can be determined as;
s = √Area; since Area = s².
s = √775
s = 27.839 ft.
Hence, the dimensions of the room is; 27.839 ft by 27.839 ft.
However, since he wants to leave a 3-foot border of bare floor on each side, it follows that the dimensions of the rug on each axis would be;
= 27.839 - 3 -3 = 21.839 ft on all sides.
Consequently, the dimensions of the rug rounded to the nearest hundredth are; 21.84 ft by 21.84 ft.
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There is quite literally not one moment where I was taught this that I remember answer correctly for 69 points. Answer choices are 15, 20, 23, 25, and 18.
It should be noted that based on the information given, the square root of 225 will be A. 15.
What is the square root?It should be noted that a number y such that y² = x, or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, since 4² = 16, 4 and -4 are the square roots of 16.
It should be noted that in this case, the square root of 225 will be:
= ✓225
= 15
Therefore, it should be noted that based on the information given, the square root of 225 will be 15.
In conclusion, based on the information, the correct option is A.
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Enlarge triangle A by scale factor 1.5 with centre (0,2)
Scale factor 1.5
Let O (0,2) as the centre of enlargement
A (0, 0)
B (-2, 0)
C (-2, 4)
Step 1:
First draw lines from point O through A, B and C, as shown in the image attached below
Step 2:
Measure the length O A and multiply it by 1.5 to get the distance from O of the image point A';
<=> O A' = 1.5 × O A.
<=> OA' = 1.5 * [tex]\sqrt{2^2}[/tex]
<=> OA' = 1.5*2
<=> OA' = 3
Mark the point A' on the diagram
Step 3:
The images B' and C' can then be marked in a similar way and the enlarged triangle A' B' C' can then be drawn.
OB' = 1.5OB
<=> OB' = 1.5 *[tex]\sqrt{( 2^2+2^2}[/tex]
<=> OB' = 1.5*2[tex]\sqrt{2}[/tex]
<=> OB' = 3[tex]\sqrt{2[/tex]
OC' = 1.5*[tex]\sqrt{2^2+2^2}[/tex]
<=> OC' = 1.5*2[tex]\sqrt{2[/tex]
<=> OC' = 3[tex]\sqrt{2}[/tex]
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Get 15 points and 1 Thanks if ur answer is correct.
Answer:
1 3/4
Step-by-step explanation:
OK but what if brainliest instead
Answer:1 3/4
Step-by-step explanati
find f(-2)
i need help
Answer:
f(-2) = -1
Step-by-step explanation:
wwwwwwwwwwww
Answer: f(-2) = 5
Step-by-step explanation: In this piecewise function, when x is less than -1, the equation is -3x-1. -2 is less than -1 so we use the first equation. -3(-2)-1= 6-1 = 5.
Translate abc with coordinates a(3,4) b(7,7) c( 8,1) 6 units left 7 units down
Answers:
A ' = (-3, -3)
B ' = (1, 0)
C ' = (2, -6)
=====================================================
Explanation:
To translate 6 units to the left, we subtract 6 from each x coordinate.
For point A, we have x = 3 become 3-6 = -3 as the new x coordinate.
Point A also goes down 7 units, in which we subtract 7 from the y coordinate. So the y coordinate of point A, which is 4, becomes 4-7 = -3 as the new y coordinate.
This is how we can write out the work shown for moving point A
[tex](\text{x},\text{y})\to(\text{x}-6,\text{y}-7)\\\\(3,4)\to(3-6,4-7)\\\\(3,4)\to(-3,-3)[/tex]
Point A is at (3,4) and moves to A ' which is at (-3, -3)
Do similar steps for points B and C to get the answers shown above.
find the indicated value for the given function. f(4) =|2x-7|
Answer: 1
I did this problem a couple times and got 1 every time
3. Select all the equations that match the diagram.
X+5\x+5\x+5
a.
x+5=18
b. 18÷3=x+5
C. 3(x+5)= 18
d. x+5=-18
e. 3x+5= 18
The equations that match the diagram are 18 ÷ 3 = x + 5 and 3(x + 5) = 18
How to select all the equations that match the diagram?The given parameters are
Expression = x+5\x+5\x+5
Value = 18
The above means that
Expression = Value
So, we have
x + 5 + x + 5 + x + 5 = 18
Evaluate the sum
So, we have
3x + 15 = 18
Factor out 3
So, we have
3(x + 5) = 18
Divide both sides by 3
So, we have
x + 5 = 18 ÷ 3
Hence, the equations that match the diagram are 18 ÷ 3 = x + 5 and 3(x + 5) = 18
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( 2x+7) - (2x - 4) please help me with this answer because it is in big ideas math
Answer:
11
Step-by-step explanation:
You want to simplify (2x+7) - (2x - 4).
Distributive propertyThe distributive property tells you the factor outside parentheses applies to every term inside parentheses. It is used for the purpose of removing parentheses.
(2x+7) - (2x - 4) = 2x +7 -(2x) -(-4) = 2x +7 -2x +4
Like termsTerms that have the same variable (or product of variables) are "like terms." Their coefficients can be combined. (This is another use of the distributive property.)
2x +7 -2x +4 = 2x -2x +7 +4 = (2 -2)x +(7 +4) = 0x +11
= 11 . . . . simplified form of the given expression
Find the measure of ∠ b ?
Answer:
38 degrees
Step-by-step explanation:
Angle 38 and b are the same.