I need help with the solutions for 19,20,21 thank you
Answer:
GIVEN :-
Coordinates of points are :-
(-5 , 12)(2 , 8)(3 , -6)TO FIND :-
All the trigonometric values of given pointsFACTS TO KNOW BEFORE SOLVING :-
It's important to know that :-
In 1st quadrant (0° to 90°) , all the trigonometric values are positive .In 2nd quadrant (90° to 180°) , except sin & cosec , rest all trigonometric values are negative.In 3rd quadrant (180° to 270°) , except tan & cot , rest all trigonometric values are negative.In 4th quadrant (270° to 360°) , except cos & sec , rest all all trigonometric values are negative.SOLUTION :-
Q1)
Plot (-5,12) on the cartesian plane and name it 'A'Drop a perpendicular to x-axis from 'A' and name the point 'B' where the perpendicular meets x-axis.Join the point A with the origin 'O'.You'll notice a right-angled ΔABO formed (∠B = 90°) in the 2nd quadrant of the plane whose :-
length of perpendicular of triangle (AB) = 12 unitslength of base of triangle (OB) = 5 unitslength of hypotenuse (OA) = 13 unitsLet the angle between OA & positive x-axis be θ.
⇒ ∠AOB = 180 - θ
So ,
[tex]\sin (AOB) = \sin(180 - \theta) = \sin \theta = \frac{12}{13}[/tex][tex]\cos(AOB) = \cos (180 - \theta) = -\cos \theta = -\frac{5}{13}[/tex][tex]\tan(AOB) = \tan(180 - \theta) = -tan \theta = -\frac{12}{5}[/tex][tex]\csc(AOB) = \csc(180 - \theta) = \csc \theta = \frac{1}{\sin \theta} = \frac{13}{12}[/tex][tex]\sec(AOB) = \sec(180 - \theta) = -\sec \theta = -\frac{1}{\cos \theta} = -\frac{13}{5}[/tex][tex]\cot(AOB) = \cot(180 - \theta) = -\cot \theta = -\frac{1}{\tan \theta} = -\frac{5}{12}[/tex]Q2)
Plot (2,8) on the cartesian plane and name it 'A'Drop a perpendicular to x-axis from 'A' and name the point 'B' where the perpendicular meets x-axis.Join the point A with the origin 'O'.You'll notice a right-angled ΔABO formed (∠B = 90°) in the 1st quadrant of the plane whose :-
length of perpendicular of triangle (AB) = 8 unitslength of base of triangle (OB) = 2 unitslength of hypotenuse (OA) = 2√17 unitsLet the angle between OA & positive x-axis be θ.
⇒ ∠AOB = θ
So ,
[tex]\sin(AOB) = \sin \theta = \frac{8}{2\sqrt{17} } = \frac{4}{\sqrt{17} }[/tex][tex]\cos(AOB) = \cos \theta = \frac{2}{2\sqrt{17}} = \frac{1}{\sqrt{17}}[/tex][tex]\tan(AOB) = \tan \theta = \frac{8}{2} = 4[/tex][tex]\csc(AOB) = \csc \theta = \frac{1}{\sin \theta} = \frac{\sqrt{17}}{4}[/tex][tex]\sec(AOB) = \sec \theta = \frac{1}{\cos \theta} = \sqrt{17}[/tex][tex]\cot (AOB) = \cot \theta = \frac{1}{\tan \theta} = \frac{1}{4}[/tex]Q3)
Plot (3,-6) on the cartesian plane and name it 'A'Drop a perpendicular to x-axis from 'A' and name the point 'B' where the perpendicular meets x-axis.Join the point A with the origin 'O'.You'll notice a right-angled ΔABO formed (∠B = 90°) in the 4th quadrant of the plane whose :-
length of perpendicular of triangle (AB) = 6 unitslength of base of triangle (OB) = 3 unitslength of hypotenuse (OA) = 3√5 unitsLet the angle between OA & positive x-axis be θ . [Assume it in counterclockwise direction].
⇒ ∠AOB = 360 - θ
So ,
[tex]\sin(AOB) = \sin(360 -\theta) = -\sin \theta = -\frac{6}{3\sqrt{5} } = -\frac{2}{\sqrt{5} }[/tex][tex]\cos(AOB) = \cos(360 - \theta) = \cos \theta = \frac{3}{3\sqrt{5} } = \frac{1}{\sqrt{5} }[/tex][tex]\tan(AOB) = \tan(360 - \theta) = -tan \theta = -\frac{6}{3} = -2[/tex][tex]\csc(AOB) = \csc(360 - \theta) = -\csc \theta = -\frac{1}{\sin \theta} = -\frac{\sqrt{5} }{2}[/tex][tex]\sec(AOB) =\sec (360 - \theta) = \sec \theta = \frac{1}{\cos \theta} = \sqrt{5}[/tex][tex]\cot(AOB) = \cot(360 - \theta) = -\cot \theta = -\frac{1}{\tan \theta} = -\frac{1}{2}[/tex]i’m so confused.. a little help?
Answer:
Triangle has a greater perimeter.
Step-by-step explanation:
Triangle perimeter = 21cm
Add the sides.
Square perimeter = 16cm
Add the sides (since it's a square the sides are the same.)
24. Identify the center and radius of the circle given the equation (x +15)2 + (7 - 9)2 = 25 .
a. Center: (-15, 9), Radius: 5
b. Center: (15, -9), Radius: 25
c. Center: (-15, -9) Radius: 5
d. Center: (15,9) Radius: 25
Answer:
a. Center: (-15, 9), Radius: 5
Step-by-step explanation:
Equation of a circle:
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this question, we have that:
[tex](x + 15)^2 + (y - 9)^2 = 25[/tex]
Comparing both equations:
[tex]x - x_0 = x + 15[/tex]
[tex]x_0 = -15[/tex]
And
[tex]y - y_0 = y - 9[/tex]
[tex]y_0 = 9[/tex]
The center is [tex](-15,9)[/tex].
For the radius:
[tex]r^2 = 25[/tex]
[tex]r = \sqrt{25} = 5[/tex]
The correct answer is given by option a.
LINK=REPORT
(4^2)^3=
A. 4^5
B. 4^6
C. 8^5
D. 16^5
(5^2)(5^3)=
A. 5^5
B. 5^6
C. 10^5
D. 25^5
(3^4)(3^5)=
A. 3^9
B. 9^9
C. 3^20
D. 6^20
Which is equivalent to 2^3•2^-5?
A. 2^-15
B. 2^-8
C. 2^-2
D. 2^2
If you answer all four of them and they are right I will give brainliest!
Answer:
a) 4^6
b) 5^5
c)3^9
d)2^-2
Step-by-step explanation:
When raising a number to a power and then to another power, you can multiply the exponents.
When multiplying numbers with the same base to different exponents, you can add the exponents.
G = B. What is the length of CD?
CD = ___
Answer:
10
Step-by-step explanation:
Since G = B (and 284 + 76 = 360), then FE = CD
PLEASE HELP!!!
You buy a car thats $11,800. The expected depreciation of the car is 35% per year.
Part A- what is the car worth each year it depreciates from the previous year?
Part B - Find the depreciated value of the car after 6 years.
YOU CAN ANSWER EITHER. BOTH WOULD BE NICE. PLEASE HELP.
Answer:
Part a- after one year of depreciation the car would value $7475
part b: the car would be worth $-12650
Step-by-step explanation:
not sure if its correct but that's what I got
selecting a marble from a bag containing 50 marbles and 45 orange marbles
Find the missing dimension.
Answer:
1.66
Step-by-step explanation:
a = b*h
5.833 = 5*h
5.833/5 = h
1.166 = h
------------------------------------------
check work:
b*h = a
5 * 1.166 = 5.833
True
Answer:
1.66
Step-by-step explanation:
I did this already in my math class
The measures of the interior angles of a pentagon are 2x + 15, 3x, 3x + 5, 4x + 10, and 5x. What is the measure of the largest angle for this pentagon?
130
140
160
150
Answer:
i think 140
Step-by-step explanation:
even tho this one old
A pentagon's largest internal angle is 150 degrees.
What is a pentagons?The geometric shape known as a pentagon has five sides and five angles. Penta here means five, and gon means angle. One of the different kinds of polygons is the pentagon. A regular pentagon's internal angles add up to 540 degrees.
Given, The measures of the interior angles of a pentagon are 2x + 15, 3x, 3x + 5, 4x + 10, and 5x. Since the sum of all the interior angles of the pentagon is 540 degrees. Hence
2x + 15 + 3x + 3x + 5 + 4x + 10 + 5x = 540
17x + 30 = 540
17x = 510
x = 30
All five angles of the pentagon are 75, 90, 95, 130, and 150.
Therefore, the biggest interior angle of a pentagon is 150 degrees.
Learn more about the pentagons here:
https://brainly.com/question/27476
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The demon drop at cedar point in Ohio takes riders to the top of a tower and drops them 60 feet. A function that approximates this ride is h = 16^2 + 64x - 60, where h is the height in feet t
Completion of question:
The Demon Drop at Cedar point in Ohio takes riders to the top of the tower and drops them 60 feet. A function that approximates this ride is h=-16^t2 + 64t + 60 where h is the height in feet and t is the time in seconds. About how many seconds does it take for riders to drop to the ground?
Answer:
4.78 s
Step-by-step explanation:
Given the equation :
h = - 16^t2 + 64t + 60
Using the quadratic formula ; where
a = - 16 ; b = 64 ; c = 60
Dropping to the ground, h = 0
16^t2 + 64t - 60 = 0
-b ± (√b²- 4ac) / 2a
-64 ± (√64²- 4(-16)(60)) / 2(-16)
-64 ± (√7936) / - 32
(-64 ± 89.08) / - 32
(-64 + 89.08) / - 32 = - 0.783 OR
(-64 - 89.08) / - 32 = 4.78
Reject the negative
t = 0.783 seconds
What is 75.4 in expanded form
Answer: 75.4 =
70
+ 5
+ 0.4
Step-by-step explanation:
Hope this helps :)
Hundred Metal Spheres with a radius of 4cm each are melted. The melted solution is filled into a cube with a base area of 16cm x 10cm. Find the height of the cube filled with solution.
Answer:
Height = 167.47 cm
Step-by-step explanation:
volume of one sphere = 4/3πr³ = 4/3(3.14)(4³) = 267.9467 cm³
267.9467 cm³ x 100 spheres = 26794.67 cm³
volume of cube = L x W x H
26794.67 = 16 x 10 x H
H = 167.47 cm
HELP ASAPP!!
Distribute:
3(-2x + 9)
Answer:
-6x+27
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
-6x+27
Step-by-step explanation:
3(-2x + 9)
-6x+27
two-thirds of the quantity 63 less than y
Answer:
y - 2/3 * 63 or y - 42
Step-by-step explanation:
two-thirds of the quantity 63: 2/3 * 63
two-thirds of the quantity 63 less than y: y - 2/3 * 63 = y - 42
Rectangle F'G'H'I' is a translation of rectangle FGHI. Write the translation rule.
A book which was bought for Rs.100 was sold at Ra.90 what will be the loss percent?
Answer:
10% or 1%
Step-by-step explanation:
i swear u better not remove this
Whats the area?????????????
Answer:
The simplest (and most commonly used) area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
Step-by-step explanation:
An architect is creating a scale drawing of a school computer lab. The length of the lab is 32 feet and the width of the lab is 48 feet. If each 16 feet of the lab equals 2 centimeters on a scale drawing, which of the following drawings is the scale drawing of the computer lab?
Answer:
The answer is B
Step-by-step explanation:
Length:
32ft. / 16ft. = 2
2 x 2cm. = 4 cm.
Width:
48ft. / 16ft. = 3
3 x 2cm. = 6cm
Answer:
b
Step-by-step explanation:
Can anyone here help me out?
Answer:
A)15x+30=weekly income
B)8 hours
Step-by-step explanation:
15x+30= weekly income
The 15 multiplies because it says per hour
The 30 is constant because she only earns it once (per week)
15x+30=150
minus 30 from both sides
15x=120
divide by 15
x=8
Helpppppppppppppppp meeeeeeeeeeee plssssssssssssssssss
Answer:
A: NO
B: YES
C: NO
D: NO
Step-by-step explanation:
An indoor running track is 200 meters in length. During a 3,000-meter race, runners must complete 15 laps of the track. An electronic timing device records the time it takes each runner to complete a lap for every lap in the race. These are called lap times. The histogram below displays the lap times for Stefano, a runner in the 3,000-meter race.
A histogram titled Stefano apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis and frequency on the y-axis. 32 to 33, 1; 34 to 35, 1; 36 to 37, 1; 37 to 38, 4; 38 to 39, 5; 39 to 40, 1; 40 to 41, 2.
Which of the following is a true statement based on the histogram?
There were no lap times between 35 and 36 seconds.
There were six laps with times less than 37 seconds.
There were three laps with times greater than 38 seconds.
The interval from 37 to 38 seconds saw the most lap times.
Answer:
Person above me is wrong lol
If we're looking at the same graph, it's actually (A).
There should be a gap between 35-36.
There were no lap times between 35 and 36 seconds.
ED2021
The following is a true statement based on the histogram
There were no lap times between 35 and 36 seconds.
The correct option is (A).
What is Histogram?A histogram is a graphical representation that organizes a group of data points into user-specified ranges.
An indoor running track is 200 meters in length.
As, a 3,000-meter race, runners must complete 15 laps of the track.
As, there were no data for interval 35-36 seconds. There should be a gap between 35-36.
So, there were no lap times between 35 and 36 seconds.
There were six laps with times less than 37 seconds is false.
There were three laps with times greater than 38 seconds, is also false.
The interval from 37 to 38 seconds saw the most lap times, most lap time is 38-39.
Learn more about histogram here:
https://brainly.com/question/16819077
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2x 3 +5x 2 +x−5 is divided by x+1x+1
Answer:1
Step-by-step explanation:
Find the solution(s) to the system of equations. Select all that apply.
y=x-4
y = 2x- 5
Answer:
Y
Step-by-step explanation:
find the exact value of tan A in simplest radical form
Answer:
tan A = 20/21
Step-by-step explanation:
tan Θ = opp/adj
tan A = 20/21
An education reform lobby is compiling data on the state of education in the United States. In their research they looked at the percent of people who graduate high school in 10 different states. The data are provided below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the sample standard deviation and the sample variance. Round your answers to one decimal place.
Answer:
Following are the responses to the given question:
Step-by-step explanation:
Let the missing value:
[tex]77.1 \\\\82.9 \\\\90\\\\91.3\\\\81.9\\\\83.3\\\\84.9\\\\82.5\\\\84.6[/tex]
Using the statistical software to calculate the output which can be defined as follows:
Summarizing the statistics:
[tex]Column \ \ \ \ \ \ \ a \ \ \ \ \ \ \ Mean \ \ \ \ \ \ \ Variance \ \ \ \ \ \ \ Std.\ \ der.\\\\ Data \ \ \ \ \ \ \ \ \ \ \ 10 \ \ \ \ \ \ \ 84.11 \ \ \ \ \ \ \ \ \ 16.432111 \ \ \ \ \ \ \ 4.053654[/tex]
From the above output:
[tex]Standard \ deviation\ S = 4.1\\\\Variance \ S^2= 16.4[/tex]
HELP im behinds on math and need help with this
Answer:
261.7 mm³
Step-by-step explanation:
the volume= ⅓×3.14×5²×10
= ⅓× 785
= 261.7 mm³
1. Three people went to lunch at a buffet restaurant that charges $9.99 per
person for food.
• Each drink is an additional $1.99.
• Sales tax is 8.5%.
• Each person orders a drink, food, and leaves a $1.50 tip.
How much was their total lunch bill?
A $14.50
B. $35.94
C. $39.99
D. $43.49
Choosing a tuna turkey or cheese sandwich on wheat or white bread with a side of potato chips corn chips or baked potatoes
Answer:
Cheese sandwich on white bread and a side of potato chips
Step-by-step explanation:
If the price is increasing at a rate of 2 dollars per month when the price is 10 dollars, find the rate of change of the demand.
Answer:
The demand reduces by $7.12 per month
Step-by-step explanation:
Given
[tex]p\to price[/tex]
[tex]x \to demand[/tex]
[tex]2x^2+5xp+50p^2=24800.[/tex]
[tex]p =10; \frac{dp}{dt} = 2[/tex]
Required
Determine the rate of change of demand
We have:
[tex]2x^2+5xp+50p^2=24800.[/tex]
Differentiate with respect to time
[tex]4x\frac{dx}{dt} + 5x\frac{dp}{dt} + 5p\frac{dx}{dt} + 100p\frac{dp}{dt} = 0[/tex]
Collect like terms
[tex]4x\frac{dx}{dt} + 5p\frac{dx}{dt} = -5x\frac{dp}{dt} - 100p\frac{dp}{dt}[/tex]
Factorize
[tex]\frac{dx}{dt}(4x + 5p) = -5(x + 20p)\frac{dp}{dt}[/tex]
Solve for dx/dt
[tex]\frac{dx}{dt} = -\frac{5(x + 20p)}{4x + 5p}\cdot \frac{dp}{dt}[/tex]
Given that: [tex]2x^2+5xp+50p^2=24800.[/tex] and [tex]p = 10[/tex]
Solve for x
[tex]2x^2 + 5x * 10 + 50 * 10^2 = 24800[/tex]
[tex]2x^2 + 50x + 5000 = 24800[/tex]
Equate to 0
[tex]2x^2 + 50x + 5000 - 24800 =0[/tex]
[tex]2x^2 + 50x -19800 =0[/tex]
Using a quadratic calculator, we have:
[tex]x \approx -113\ and\ x\approx88[/tex]
Demand must be greater than 0;
So: [tex]x=88[/tex]
So, we have: [tex]x=88[/tex]; [tex]p =10; \frac{dp}{dt} = 2[/tex]
The rate of change of demand is:
[tex]\frac{dx}{dt} = -\frac{5(88 + 20*10)}{4*88 + 5*10} * 2[/tex]
[tex]\frac{dx}{dt} = -\frac{5(288)}{402} * 2[/tex]
[tex]\frac{dx}{dt} = -\frac{2880}{402}[/tex]
[tex]\frac{dx}{dt} \approx -7.16[/tex]
This implies that the demand reduces by $7.12 per month
If 2^2x = 2^3, what is the value of x?
Answer:
x=2
Step-by-step explanation: