Answer:
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
The ratios are valid only in right triangles, or when one of the internal angles is 90°.
Take any of the acute angles as a reference, and the largest side as the hypotenuse, then:
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
[tex]\displaystyle csc\theta=\frac{\text{hypotenuse}}{\text{opposite leg}}[/tex]
[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
The missing side of the triangle x can be calculated by using Pythagora's Theorem:
[tex]10^2=9^2+x^2[/tex]
Solving:
[tex]x^2=10^2-9^2=100-81=19[/tex]
[tex]x=\sqrt{19}[/tex]
For the angle marked as θ:
[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan\theta=\frac{\text{9}}{\sqrt{19}}[/tex]
Rationalizing:
[tex]\displaystyle \tan\theta=\frac{9\sqrt{19}}{19}[/tex]
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
[tex]\displaystyle \cos\theta=\frac{\sqrt{19} }{10}[/tex]
[tex]\displaystyle \csc\theta=\frac{\text{hypotenuse}}{\text{opposite leg}}[/tex]
[tex]\displaystyle \csc\theta=\frac{10}{9}[/tex]
A circular oil spill in the ocean is increasing in diameter at a rate of 200 feet per hour. By how many square feet is the oil spill increasing per hour?
Increase in diameter: d(h) = 200h; h in hours
Increase in area: A(d) = π(0.5d)2; d in feet
Which composite function represents the total area of the oil spill as a function of hours?
Answer:
A(d(h)) = π(100h)2
Step-by-step explanation:
In edge it would be C
When solving these word problems it is helpful to remember that they ask us to use composition of functions to solve it so if it is the total area in regards to hours, what you would need to do look at the problem in this manner:
A( (d(h) )= A (Pi(0.5x200h)^2
and when you simplify like terms it would be:
Pi(100h)^2
Point A is located at (0, 7). After it is transformed, point A' is located at (0, -7). How was the point transformed?
it was reflected in the x-axis
it was rotated 270°
it was reflected in the y-axis
it was rotated 90° around the origin
Answer:
it was reflected over the x axis
Step-by-step explanation:
.......
A car can travel 135 miles with 5 gallons of gasoline. At this rate, how much gallons of gasoline the car needs to travel 675 miles?
Answer:
25 gallons
Step-by-step explanation:
Given
135 miles to 5 gallons
Required
Determine the number of gallons for 675 miles
From the question, number of miles is directly proportional to number of gallons:
So, we have:
[tex]135\ miles = 5\ gallons[/tex]
and
[tex]675\ miles = x[/tex]
Where x represents the number of gallons for 675 miles
Cross Multiply:
[tex]135 * x = 675 * 5[/tex]
[tex]135x = 3375[/tex]
Make x the subject
[tex]x = 3375/135[/tex]
[tex]x = 25[/tex]
Hence, the car needs 25 gallons
si el dominio de la función f(x)= 3x-2 es el conjunto {1,2,3} y su contradominio es el conjunto {1,4,7,10}. ¿Cuál es el rango de la función?
Answer:
I don't speak Spanish sorry
Write an expression for the area of the triangle below.
Simplify your expression as much as possible.
(2x - 4)
(3x + 5)
It should be A= 1/2bh but im not sure why you wrote those extra things. Are we supposed to use them?
The area of a trapezoid is 864cm². It has a height of 24 cm, and the length of one of its bases is 30 cm. What is the length of the other base?
The area A of a trapezoid with height h and bases b₁ and b₂ is equal to the average of the bases times the height:
A = (b₁ + b₂) h / 2
We're given A = 864, h = 24, and one of the bases has length 30, so
864 = (b₁ + 30) 24 / 2
864 = (b₁ + 30) 12
864 = (b₁ + 30) 12
72 = b₁ + 30
b₁ = 42
What is the formula for the area of a square?
Answer:
Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared. If a square has one side of 4 inches, the area would be 4 inches times 4 inches, or 16 square inches. (Square inches can also be written in2.)
Answer:
lxwxtor you can up it in the calculator
Amy's penny bank is 1/4 full. After she adds 240 pennies, it is 5/8 full. How many pennies can Amy's bank hold?
True or False 2 is a root of x^6-9x^4+24x^2-16=0 two times
Answer:
True
Step-by-step explanation:
No need for explanation
At the end of summer clearance sale Nathan sees a hat market at 65% off the original price was $12.98 after the discount what is the final price of the hat round your answer to the nearest cent
Answer:
$4.54
Step-by-step explanation:
Because if you take $12.98 and multiply that by 65% you will get 8.437 and when you subtract that by the original amount you will get $4.54.
The high temperature for the day is 28°F. The record low for the day was -12°F. What is the difference in temperature?
Answer:
40
Step-by-step explanation:
12 + 28
Answer:
40°
Step-by-step explanation:
So the highest is 28 and the lowest is -12. First, you get to zero so 28-28=0 then, to get to -12 you do 0-12= -12. Then I added 28+12 :D
A vitamin C tablet contains 1/4
of a gram of vitamin C. You take 1 1/2
tablets every day. In simplest form, how many grams of vitamin C do you take every day?
Answer:
3/8 gramsStep-by-step explanation:
1 tablet ⇒ 1/4 gramsMultiply the amount of tablets by 1/4 to find the answer
1 1/2 tablet ⇒ 1 1/2 *1/4 = 3/2 * 1/4 = 3/8 gramsThere are two numbers. The difference between them equals six, and one of the numbers is three times the other number. There are two pairs of numbers that satisfy these descriptions, What are they?
Answer:
Pair 1: 9 and 3 Pair 2: 3 and 9
Step-by-step explanation:
The difference is 6 and one three times more than the other. Draw a diagram below:
Figure out 1 unit: 6÷2=3
3 = one unit
3 is the first number
Figure out second number: 3+6=9
3 & 9, 9 & 3
So, Pair 1: 9 and 3 Pair 2: 3 and 9
Write the equation of the line that passes through the points (-9, -3) and (-7,7).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answer:
y - 7 = 5(x + 7).
Step-by-step explanation:
The slope m (7--3)/ (-7- -9)
= 10 / 2 = 5.
y - y1 = m(x - x1)
Using the point (-7, 7):
y - 7 = 5(x + 7).
Vedant received two quotes for new carpet for his home. The quote from Company A is $0.15 less per square foot than the quote from Company B. If Vedant plans to buy 1,200 square feet of carpet, how do his total costs from the two companies compare?
Company A is cheaper by $180.
Company B is cheaper by $180.
Company A is cheaper by $8,000.
Company B is cheaper by $8,000.
Don’t make any funny jokes about this and don’t say idk or something like that or I’ll report you.
Answer:
Company B is cheaper by $180.
Step-by-step explanation:
just do 1,200 square feet x 0.15 = 180
Answer:
b as in big cat
Step-by-step explanation:
Drag the missing statements and reasons to the correct spot to complete the proof
Answer:
See attached
Step-by-step explanation:
Answer is attached
PLEASE HELP ME ITS URGENT
Just the first one
Answer:
m=-1/3
Step-by-step explanation:
How would you describe this graph? Check all that apply.
continuous
discrete
increasing everywhere
decreasing everywhere
increasing then decreasing
decreasing then increasing
Answer:
A and E
Step-by-step explanation:
I took the test
Answer:
ae
Step-by-step explanation:
add (5y - 1)+ (-2y + 4)
Answer:
3y+3
Step-by-step explanation:
"Simplifying
(5y + -1) + (-2y + 4) = 0
Reorder the terms:
(-1 + 5y) + (-2y + 4) = 0
Remove parenthesis around (-1 + 5y)
-1 + 5y + (-2y + 4) = 0
Reorder the terms:
-1 + 5y + (4 + -2y) = 0
Remove parenthesis around (4 + -2y)
-1 + 5y + 4 + -2y = 0
Reorder the terms:
-1 + 4 + 5y + -2y = 0
Combine like terms: -1 + 4 = 3
3 + 5y + -2y = 0
Combine like terms: 5y + -2y = 3y
3 + 3y = 0
Solving
3 + 3y = 0
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + 3y = 0 + -3
Combine like terms: 3 + -3 = 0
0 + 3y = 0 + -3
3y = 0 + -3
Combine like terms: 0 + -3 = -3
3y = -3
Divide each side by '3'.
y = -1
Simplifying
y = -1 "
Answer:
3y + 3
Step-by-step explanation:
(5y - 1) + (-2y + 4) =
3y + 3
Chloe has 36/4 ounces of cocoa. She is making chocolate cakes for bake sale. If 9/2 ounces of cocoa are usef in each cake, how many cakes can Chloe make? Help please!
Answer:
2 cakes
Step-by-step explanation:
Lets divide these fractions (when dividing, remember keep, change and flip): 36/4 * 2/9 = 2
I hope this helps, please mark Brainliest, thank you !!
Answer:
B 2 cakes
Step-by-step explanation:
did the test
1936 —The electric guitar debuts.
1946 —Muddy Waters cuts the first records of Chicago's electric blues and Carl Hogan plays a powerful guitar riff on Louis Jordan's Ain't That Just Like a Woman.
1948—Columbia Records introduces the long playing (LP) vinyl record.
1949—Fats Domino cuts a new kind of boogie, The Fat Man.
1951—Cleveland disc jockey Alan Freed coins the term rock and roll.
1955—Elvis Presley’s Heartbreak Hotel makes him the first rock star.
1958—Billboard magazine begins their Hot 100 chart listing popular songs.
1959—The National Academy of Recording Arts and Sciences presents the first Grammy Award.
1959—Berry Gordy Jr. founds Motown Records. In the 1960s Motown stars include the Supremes, Stevie Wonder, and Marvin Gaye.
1961—Country Singer Patsy Cline becomes a mainstream pop music hit.
1964—The Beatles song I Want to Hold Your Hand is a sensation igniting the British invasion.
1969—The Woodstock Music and Art Fair, featuring such artists as Janis Joplin, Jimi Hendrix, the Who, and Joan Baez, is attended by hundreds of thousands of fans.
1975—CBGB (Country Bluegrass & Blues) club in New York showcases punk rock.
1977—The movie Saturday Night Fever popularizes disco music.
1978—Hip Hop, a blend of rock, jazz, and soul, is born in the South Bronx, characterized with African drumming.
1981—MTV music television debuts with nonstop music videos.
1983—Compact discs begin to replace vinyl records.
1984—Cyndi Lauper's Girls Just Wanna Have Fun moves up the charts. In his early teens, Ricky Martin begins his five-year stint with Menudo. Madonna releases her debut album; the single Holiday becomes a hit.
1985—Michael Jackson releases Thriller and the video becomes a classic.
1989—Britney Spears makes her musical television debut as an 8-year-old child on Star Search.
1990—Grunge rock rises in Seattle, featuring bands such as Nirvana and Pearl Jam.
Answer:
yes
Step-by-step explanation:
Determine which of the following angle measures are correct. Select all the apply
Answer:
The right answer is :
2 (108) and 3 (72)
Step-by-step explanation:
i did the test
The correst angle measures in the triangle ABC is that m∠BAC=72° and ∠BCD=108°.
What is isosceles triangle?An isosceles triangle is a triangle which is having two sides equal to each other.
How to determine angles?Firsty we have to find the value of x in the angles. We have been given that the triangle is isosceles because two sides are equal to each other and we know that angles opposite to two equal sides are also equal to each other.
So,
(4x+16)°+2(5x+7)°=180°
4x-16+10x+14=180
14x-2=180
14x=180+2
14x=182
x=182/14
x=13
Putting the value of x.
∠BCA=5x+7
=5*13+7
=65+7
=72
∠ABC=4x-16
=4*13-16
=52-16
=36
∠BAC=180-36-72
=180-108
=72
∠BCD=180-∠BCA
=180-72
=108°
Hence the correst angle measures in the triangle ABC is that m∠BAC=72° and ∠BCD=108°.
Learn more about isosceles triangle at https://brainly.com/question/1475130
#SPJ2
Will make you brainliest!!! If correct!!
Answer:
Step-by-step explanation:
y = - [tex]\frac{1}{4}[/tex] x + 3 ( equation of line t )
y - (- 2) = - [tex]\frac{1}{4}[/tex] [ x - (- 2)] ⇒ y = - [tex]\frac{1}{4}[/tex] x - [tex]\frac{5}{2}[/tex] ( equation of line u )
R - 27 / 6 = 7
SOLVE FOR R and thank you
Answer:
huh
Step-by-step explanation:
Someone help solve this pleAse and ty!!!
Answer:
1
Step-by-step explanation:
it has to be the same slope and only slope that is right is 1.
You and 5 friends are in a math club. A sponsor pays $75 to rent a bus to get to competition, a $100 entry fee for the team, and D dollars for each students t-shirt. Write an expression for the total amount the sponsor paid.
Answer:
Total amount paid by the sponsor = 175 + 6d
Step-by-step explanation:
You and 5 friends = 6 people
Cost of renting a bus = $75
Team entry fee = $100
Cost of each student t shirts = $d
Cost of 6 student t shirts = $d × 6
= $6d
Write an expression for the total amount the sponsor paid.
Total amount paid by the sponsor = Cost of renting a bus + Team entry fee + Cost of 6 student t shirts
= $75 + $100 + $6d
= $175 + $6d
Total amount paid by the sponsor = 175 + 6d
Where,
d = cost of each student t shirts
A company is packing cartons of candles. Each carton can hold 75 candles. So far, 50 cartons have been packed, but only 30 cartons have been loaded in the truck. How many more candles are left to load on the truck? Please help me
Answer:
34
Step-by-step explanation:
just guessing but u gotta really put a mind to it aha
a corn vendor at a farmers market was selling a bag of 8 ears of corn for $2.56 anithert vendor was selling a bad of 12 for 4.32. which bag is the better deal?
The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing at a rate of 3.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 10 centimeters and the area is 86 square centimeters? The base is changing at cm/min.
Answer:
-1.88cm/min
Step-by-step explanation:
Given
dh/dt = 1.5cm/min
dA/dt = 3.5cm²/min
Height h = 10cm
Area A = 86cm²
Required
db/dt
b is the base
h is the height.
Area of a triangle A = 1/2bh
dA/dt = dA/db•db/dt + dA/dh •dh/dt
dA/db = h/2 = 10/2 = 5cm
Get the base
86 = 1/2(10)b
5b = 86
b = 17.2cm
dA/ dh = 1/2b = 1/2(17.2)
dA/dh = 8.6cm
.substitute given values into the formula above;
dA/dt = dA/db•db/dt + dA/dh •dh/dt
3.5 = 5 db/dt + 8.6(1.5)
3.5 = 5 db/dt + 12.9
5 db/dt = 3.5-12.9
5 db/dt = -9.4
db/dt = -9.4/5
db/dt = -1.88cm/min
Hence the base is changing at -1.88cm/min
what is 328.618 round to the nearest hundredth
A. 300
B. 328.60
C. 330
D. 328.62
Answer:
D. 328.62
Step-by-step explanation:
328.618 round to the nearest hundredth
Rounding to the nearest hundredth means 2 numbers after the decimal point
Numbers that rounds to 1 are 5, 6, 7, 8, 9
Number that rounds to 0 are 0, 1, 2, 3, 4
When rounding up, to the nearest hundredth, you will consider the next number after the two figures after the decimal point
Here, the next number after the two figures after the decimal point is 8
8 is a number that rounds to 1
Therefore, add 1 to 1 to have
328.62