sin (60° - 20)°
sin (40°)
Explanation:Note that:
sin(A - B) = sinAcosB - cosAsinB
The given trigonometric expression is:
sin 60° cos 20° - cos 60° sin 20°
Applying the addition rule of trigonometry written above:
sin 60° cos 20° - cos 60° sin 20° = sin(60° - 20°)
This can also be written as sin (40°)
please help bless you !
Answer:
A = 20, therfore B = 180
Step-by-step explanation:
Technically it's 17 but that is a really awkward scale so I had to round up. This really annoys me because if there was one more box you could had the scale 15 and it would've looked so much nicer but unfortunate you're short one
can someone help me please
Sam made a 70% on his test. If there were 80 questions on the test, how many did he get right?
Answer: He got 56 questions right.
Step-by-step explanation:
Answer:
Sam got 56 questions correct.
Step-by-step explanation:
If there were 80 questions on the test, sam got 56 correct in order to get a 70%.
To find this, you must find 70 percent of 80 questions. You first must turn 70% into a decimal, making it 0.70. You multiply this decimal by the 80 questions on the test. You then get 56. Meaning they got 56 right. I hope this helps!
Does that look right or am I supposed to multiply and get 52.7
Answer: multiply to get 52.7
Step-by-step explanation: scale factor enlargement means the number they give you (6.2) the new size.
in this case would be 8.5 times 6.2
I hope this helps!
the equation of a line in the point-slope form is shown below. y-9=1/5(x-2)
what is the slope of this line?
A. 2
B. 1/9
C. 5
D. 1/5
Answer:
D) 1/5
Step-by-step explanation:
Point - slope form:
y - y1 = m(x -x1)
y - 9 = 1/5(x - 2)
Write the simple linear regression equation for miles per gallon as the response variable and weight as the predictor variable. How might the car rental company use this model
The simple linear regression equation for miles per gallon as the response variable and weight as the predictor variable is
M = \(\beta\)0 + \(\beta\)1W + ε
The car rental company can use this model to determine the effect of weight (of the car) on miles per gallon.
Given: To write a simple linear regression equation with Miles per gallon as the response variable and weight as the predictor variable.
What is simple linear regression?
Simple linear regression is used to estimate the relationship between two quantitative variables.
Let's say "Miles per gallon" is represented as M and
"Weight" be represented as W
The simple linear regression equation is :
M = \(\beta\)0 + \(\beta\)1W + ε
where,
M is Miles per gallon, the response variable also known as the dependent variable shows a predicted value for any given value of the independent variable W.\(\beta\)0 is the intercept, the predicted value of M when W is 0\(\beta\)1 is the regression coefficient - how much we expect M to change as W increases.W is the predictor variable also known as the independent variable ( the variable that is influencing M )ε is the error of the estimate, or how much variation there is in our estimate of the regression coefficient.How might the car rental company use this model?
The car rental company might use the regression model to determine the
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Help! Geometry building blocks
Answer:
XY = 11 centimeters
Step-by-step explanation:
Given info:
WZ = 28cm
Y is the midpoint of XZ
What are we asked to find:
XY
Solve:
WZ is the sum sum of WX + XY + YZ
The variable is a
We know that WZ is 28, and values for WX, XY, and YZ are given as expression
So:
28 = (a + 1) + (2a + 1) + (2a + 1)
Combine like terms:
28 = 5a + 3
Solve for a:
28 - 3 = 5a + 3 - 3
25 = 5a
25 ÷ 5 = 5a ÷ 5
5 = a
Now that we solved for a, we can simply plug a in for the expression (2a + 1)
(2a + 1) =
(2*5 + 1) =
(10 + 1) = 11
XY in centimeters is 11
-Chetan K
Please answer this question asap
An isoline that connects all points of highest mean temperature on a world map is called Group of answer choices the thermal equator. the temperature range line. the highest mean temperature isoline. an isobar.
An isoline that connects all points of highest mean temperature on a world map is called the highest mean temperature isoline.
An isoline is a line on a map that connects points of equal value for a particular variable. In this case, the isoline connects all points of the highest mean temperature, indicating regions with the highest average temperatures.
Therefore, it is referred to as the "highest mean temperature isoline." The other options mentioned are not specifically related to the concept described.
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Someone please helppp
Answer:
112
Step-by-step explanation:
A quadratic can be written in the form
ax^2 +bx +c
-3x^2 +4x+8
a = -3 b = 4 c = 8
the discriminant is
b^2 -4ac
(4)^2 - 4(-3) (8)
16+96
112
Answer:
112
Step-by-step explanation:
Discriminant = b² - 4ac
Substitute the values for the variables.
\((4)^2-4(-3)(8)\\16-4(-24)\\16-(-96)\\16+96\\112\)
Decrease the number 724,062.58 by 100,000
Answer:
624,062.58 is your answer :)
Step-by-step explanation:
A greengrocer buys 20 cases of oranges at a cost of $15 per case. Each case contains 10 kg of oranges. If he sells the oranges at $4/kg, how many kilograms must he sell before he makes a profit? If he sells all the oranges what will be his profit?
Answer:greengrocer should Dell 17 kg before profit. 500$ profit
Step-by-step explanation:
what fraction is eqivilant to 500%
Answer:
5/1
Step-by-step explanation:
Answer:
5/1
Step-by-step explanation:
What is the value of L-1.1)?
Answer:
-2
Step-by-step explanation:
The floor function returns the largest integer not greater than the function's argument. The largest integer less than or equal to -1.1 is -2.
A soccer field is a rectangle 100 meters wide and 130
meters long. The coach asks players to run from one
corner to the other corner diagonally across. What is
the distance diagonally? Round to the nearest
TENTHS place.
a.83.1 meters
b.164.0 meters
c.26900 meters
with steps please (: <3
Answer: b.164.0 meters
Step-by-step explanation:
The frequency vibrations for a certain guitar string When is blood can be determined by the equation below, Where F is the number of vibration per second and T is measured in pounds.If the frequency of the vibrations is 600 vibrations per second, How many pounds of tantrums was used to plug the string? F = 200sqrt(T)
Answer:
9 poundsStep-by-step explanation:
Given the frequency vibrations for a certain guitar string modeled by the equation
F = 200√T where:
T is amount of tantrums in pounds
If the frequency of the vibrations is 600 vibrations per second, the amount of pounds in tantrums will be gotten by substituting F = 600 into the equation and calculating T as shown:
600 = 200√T
Divide both sides by 200
600/200 = 200√T /200
3 = √T
Square both sides
3² = (√T)²
9 = T
T = 9
Hence 9 pounds of tantrum was used to plug the string
Convert these polar coordinates to rectangular coordinates. Make sure to show your work.
a.) (2, 3pi/2)
b.) (1, 5pi/6)
The rectangular coordinates of the polar coordinates are as follows:-
a) x = 0 and y = ( -2 )
b) x = ( -√3/2 ) and y = 1
How to convert these polar coordinates to rectangular coordinates?To convert these polar coordinates to rectangular coordinates, we calculate the following,
a) ( 2, 3π/2 ) :
r=2 ; θ = 3π/2
x = r * cosθ
x = 2 * cos( 3π/2 )
x = 2 * 0
Therefore, x = 0
y = r * sinθ
y = 2 * sin( 3π/2 )
y = 2 * ( -1 )
Therefore, y = ( -2 )
b) ( 1, 5π/6 ) :
r = 1 ; θ = 5π/6
x = r * cosθ
x = 1 * cos( 5π/6 )
x = 1 * ( -√3/2 )
Therefore, x = ( -√3/2 )
y = r * sinθ
y = 2 * sin( 5π/6 )
y = 2 * ( 1/2 )
Therefore, y = 1
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Find the coordinates of the point 3/10 of the way from A to B.
The coordinates of the point 3/10 of the way between A and B are (-19/15, 1/5).
What is defined as the section formula?The Section formula is used in coordinate geometry to find the ratio of a line segment divided by a point, either internally or externally. It determines the centroid, incenter, and excenters of a triangle.Let P be the point that is 3/10 of a way from A to B. This means that it divides P in the ratio 3:10 = AP/PB = 3/10.
To find the coordinates, use the internal division formula, which is given as:
x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Where,
(x₁, y₁) = A(-3, -5)
(x₂, y₂) = B(12, 4)
m = 3 and n = 10.
Substitute the values to find the x and y coordinates of point P.
y = (3×4 + 10(-5))/(3 +10)
On solving;
y = -19/15
Solve for x coordinates;
y = (3(12) + 10(-3)/(3 +10)
on solving;
y = 1/5
Therefore, the coordinates of the point 3/10 a way from A and B is (-19/15, 1/5).
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If one interior in a polygon is 140 degrees, how many sides does it have
\(\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =140 \end{cases}\implies n(140)=180(n-2) \\\\\\ 140n=180n-360\implies 140n+360=180n \\\\\\ 360=40n\implies \cfrac{360}{40}=n\implies 9=n\)
Last questions guys !! Go on my page for more chances for brainliest !!
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Can I have Brainllest? Please I need It?
Your teacher asked your class to describe a real world situation in which a y-intercept is 100 and the slope is 5. Your partner gave the following description: My younger brother originally had 100 small building blocks, but he has lost 5 of them every month since. What mistake did your partner make?
Answer:
He should have said that his small brother had 100 small building bricks, but lost 5 in total now.
110°
х
z
у
Find the unknown angle measures
Answer:
x = z = 70°
y = 110°
Step-by-step explanation:
From the diagram, we have 4 angles;
To find y;
110° and y are vertically opposite angles so they are equal.
So, y = 110°
Also, y and x lie on a straight line. Sum of angles on a straight line is 180°;
y + x = 180
110 + x = 180
x = 180-110 = 70°
Also, x and z are vertically opposite angles and they are equal;
x = z = 70°
y = 110°
(b) Fatima starts a phone call at 18:32 The phone call finishes at 19:16
Work out the length of the phone call.
4(x+15) = 2(2x+25) has how many solutions?
Answer: There are no solutions.
Step-by-step explanation: Hope this help :D
Today only, a suit is being sold at a 15% discount. The sale price is $391.
What was the price yesterday?
Answer:
$460.
Step-by-step explanation:
\(Percentage\ change = (\frac{Original\ Price\ - Discounted\ Price}{Original\ Price})100\\\\15=(\frac{x-391}{x})100\\\\15x=(x-391)100 \\\\15x/100=x-391\\0.15x=x-391\\391=x-0.15x\\391=0.85x\\391/0.85=x\\460=x\\\)
So the price yesterday was $460
A security car is parked 25 ft from a movie theater. Find at what speed the reflection of the security strobe lights is moving along the wall of the movie theater when the reflection is 30 ft from the car. The strobe lights are rotating with the speed 2 revolutions per second.
Answer:
v=20π ft/s
Step-by-step explanation:
Given:
Distance from the security car to the movie theater, D=25 ft
Distance of the reflection from the car, d=30 ft
Speed of rotation of the strobe lights, 2 rev/s
To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.
We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.
ω=2πf
=> ω=2π(2)
=> ω=4π rad/s
The distance between the security car and the reflection on the wall of the theater is...
r=30-25= 5 ft
The speed of reflection is given as (this is the linear velocity)...
v=ωr
Plug our know values into the equation.
v=ωr
=> v=(4π)(5)
∴ v=20π ft/s
Thus, the problem is solved.
The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.
To solve this problem, we can use the concept of related rates. Let's consider the following variables:
x: Distance between the security car and the movie theater wall
y: Distance between the reflection of the security strobe lights and the security car
θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights
We are given:
x = 25 ft (constant)
y = 30 ft (changing)
θ = 2 revolutions per second (constant)
We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.
Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:
x^2 + y^2 = z^2
Differentiating both sides of the equation with respect to time (t), we get:
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.
Plugging in the known values, we have:
2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)
Simplifying the equation, we find:
60(dy/dt) = 120π
Dividing both sides by 60, we get:
dy/dt = 2π ft/s
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Picture below has question/answer choices!!
The statements that is true about the similarity of the two triangles the option D
D. ΔMNO and ΔJKL are not similar triangles
What are similar triangles?Similar triangles are triangles which have proportional corresponding sides
The parameters in the question are;
The length of segment MN = 20
Length of segment NO = 12
Length of segment OM = 25
Measure of angle ∠O = 56°
Length of segment LJ =- 15
Length of segment JK = 12
Length of segment KL = 9
Measure of angle ∠L = 56°
Two triangles are similar if the ratio of two sides on one triangle are proportional to two sides of another triangle, and the included angle between the two sides are congruent
The included angle between sides ON and MO on triangle MNO is congruent to the included angle between segment LK and JL in triangle JKL
However, the ratio of the sides LK to ON and JL to MO are;
9/12 ≠ 15/25
Therefore, the triangles are not similar
The correct option is option D
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A local cell phone company off ers two different calling plans. In the fi rst plan, you pay a monthly fee of $30 and $.35 per minute. In the second plan you pay a monthly fee of $99 and $.05 per minute
a. Write a system of equations showing the two calling plans.
b. When is it better to use the fi rst calling plan?
c. When is it better to use the second calling plan?
d. How much does it cost when the calling plans are equal?
How much will alice pay for carpet that costs $3.00 per square foot? alice will pay $ for the carpet.
To calculate how much Alice will pay for the carpet, we need to know the area of the carpet in square feet. Without that information, it is not possible to provide the exact amount Alice will pay.
The cost of the carpet is given as $3.00 per square foot. To determine the total amount Alice will pay, we need to know the area of the carpet. The formula to calculate the total cost is given by multiplying the cost per square foot by the area of the carpet:
Total cost = Cost per square foot × Area of the carpet
Without the area of the carpet being provided, we cannot calculate the exact amount Alice will pay. The cost per square foot only gives us the rate at which the carpet is priced, but it does not provide information about the size of the carpet. Once we have the area in square feet, we can multiply it by the cost per square foot to determine the total cost that Alice will pay for the carpet.
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Discuss the applicability of Rolles theorem for the function
\(f(x) = log \frac{ {x}^{2} + ab}{x(a + b) } \\ \)
on the interval [a, b] where a > 0.
Explain the steps properly.
The Rolle’s theorem is applicable for the given function f(x) = log((x² + ab) / x(a + b)) on the interval [a, b] where a > 0.
Rolle’s theorem is one of the significant aspects of differential calculus. Rolle’s theorem is relevant when we need to calculate the value of c which makes the derivative of the function zero.
The following is the applicability of Rolle’s theorem for the given function f(x) = log((x² + ab) / x(a + b)):Rolles theorem can be defined as if a function is continuous on a closed interval and differentiable on the open interval and if the function's value at the two endpoints of the closed interval is the same, there exists at least one point on the open interval such that the derivative of the function at that point is zero.
Let's prove the Rolle's theorem for the given function f(x).Given function f(x) = log((x² + ab) / x(a + b))
Now we will check the conditions of Rolle's theorem:
Condition 1: Given function is continuous on the closed interval [a, b] as it is a composition of continuous functions. Hence condition 1 is satisfied.
Condition 2: Given function is differentiable on the open interval (a, b) as it is a composition of differentiable functions. Hence condition 2 is satisfied.
Condition 3: f(a) = f(b).f(a) = log(((a² + ab) / a(a + b)))f(b) = log(((b² + ab) / b(a + b)))
By solving the above equations we get f(a) = f(b)
Hence all the conditions of Rolle's theorem are satisfied.
Hence we can say that there exists at least one point "c" on the open interval (a, b) such that the derivative of the function f(x) at that point is zero.
Conclusion:Thus we can say that the Rolle’s theorem is applicable for the given function f(x) = log((x² + ab) / x(a + b)) on the interval [a, b] where a > 0.
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