Final answer:
Given an angle θ in Quadrant IV with cotθ = -2/17, a right triangle is formed. Using the Pythagorean theorem, the hypotenuse is calculated, and the five additional trigonometric functions of θ are determined with appropriate signs for Quadrant IV.
Explanation:
If θ is an angle in the standard position whose terminal side is in Quadrant IV and cotθ = -2/17, we can find the five remaining trigonometric functions.
The cotangent of an angle θ, which is the reciprocal of the tangent, tells us that the tangent of θ is -17/2. Since the angle is in Quadrant IV, where cosine and secant are positive but sine and cosecant are negative, we can form a right triangle within the coordinate plane to represent this scenario. In this triangle, the adjacent side (x) to the angle θ will be positive, and the opposite side (y) will be negative.
Using the Pythagorean theorem, if we assume the adjacent side to be 17 (because cotθ = adjacent/opposite), and the opposite side to be -2 (to make cotθ = 17/(-2) = -2/17), the hypotenuse (r) can be calculated as:
√(17² + (-2)²) = √(289 + 4) = √293
Now we can find the other five trigonometric functions:
Sinθ = opposite/hypotenuse = -2/√293Cosθ = adjacent/hypotenuse = 17/√293Tanθ = opposite/adjacent = -2/17 (which was given)Cscθ = hypotenuse/opposite = -√293/2Secθ = hypotenuse/adjacent = √293/17The signs of these values are consistent with the properties of trigonometric functions in the fourth quadrant.
Which expression is equivalent to 6y - 12
Answer:-12+6y
Step-by-step explanation:
Since the 12 is a negative and the 6y is a positive you can switch it around.
The expression 6y - 12 is equivalent to 6(y - 2). This can be verified by expanding the factored form, which results in the original expression.
This expression can be factored to find an equivalent expression. Factoring out the greatest common factor (GCF) from both terms, we get:
6y and 12. The GCF is 6.Factor out the GCF: 6(y - 2).Thus, the expression 6y - 12 is equivalent to 6(y - 2).
The function S(D) =(7/2) √2D can be used to approximate the speed S, in miles per hour, of a car that has left skid marks of length D, in feet. How fast would would a car have been traveling if it left a skid mark that is 102.04 feet long?
Answer: The other answer is wrong. The answer would be about 50 miles per hour or 49.99 mph.
Step-by-step explanation:
The required approximate speed of the car when the skid mark is 10204 feet long is 49.99 miles per hour.
Given that,
The function S(D) =(7/2) √2D can be used to approximate the speed S, in miles per hour, of a car that has left skid marks of length D, in feet, how fast would a car have been traveling if it left a skid mark that is 102.04 feet long is to be determined.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given the function of speed,
S(D) =(7/2) √(2D)
Substitute the value of D = 102.04
S(102.04) = (7/2)√(2*102.04)
S(102.04) = 49.99
Thus, the required approximate speed of the car when the skid mark is 10204 feet long is 49.99 miles per hour.
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How do you solve 6x+18=2(3x+9)
Answer:
infinite solutions
Step-by-step explanation:
6x + 18 = 2(3x + 9)
1. 6x + 18 = 6x + 18 Distribute the 2
2. X can be any number since they are the same.
The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x + 1 On a coordinate plane, a parabola opens up. It goes through (negative 4, 5), has a vertex at (negative 1.75, 6.75), and goes through (1, 5).
f(x) = x2 – 3x – 3 On a coordinate plane, a parabola opens up. It goes through (negative 2, 7), has a vertex at (1.75, 5), and goes through (5, 7).
f(x) = x2 + 6x + 3 On a coordinate plane, a parabola opens up. It goes through (negative 6, 3), has a vertex at (negative 3, negative 6), and goes through (0, 3).
f(x) = x2 – 6x – 1 On a coordinate plane, a parabola opens up. It goes through (0, negative 1), has a vertex at (3, negative 10), and goes through (6, 0).
Answer:
The function in the fourth option will have an axis of symmetry at x = 3.
Step-by-step explanation:
We have to choose the function from options, the graph of which has an axis of symmetry at x = 3.
The function in the fourth option will have an axis of symmetry at x = 3.
It is f(x) = x2 – 6x – 1 On a coordinate plane, a parabola opens up. It goes through (0, negative 1), has a vertex at (3, negative 10), and goes through (6, 0). (Answer)
Answer:
D
Step-by-step explanation:
PLS HELP ASAP I WILL MARK BRAINLIEST FOR WHOEVER ANSWERS FIRST AND CORRECTLY!!
Consider the function represented by the table.
What is f(0)?
4
5
6
7
Table:
x | f(x)
0 | 6
2 | 7
4 | 0
7 | 5
Answer:
We are given the table as:
x f(x)
0 6
2 7
4 0
7 5
i.e. corresponding to different values of x we are given the values of f(x)
we have to find the value of f(0)
i.e. we have to find the value of f(x) when x=0
As we can see from the table the value of f(x) at x=0 is 6
Hence, Correct option is:
C) 6
Have a Great day!
Answer:
c
Step-by-step explanation:
Find the area of the circle if it has a circumference of 40
Answer:
127.39 square units
Step-by-step explanation:
We are given;
Circumference of the circle as 40 unitsWe are supposed to determine its area;
The circumference of a circle is given by;Circumference = πD or 2πr , where D is the diameter and r is the radius
Thus;
40 = 2πr
πr = 20
r = 20/π
Area of a circle is given by;
A = πr²
but, r = 20/π
Hence;
Area = π × (20/π)²
= π × 400/π²
= 400/π
Taking π to be 3.14
Area = 400 ÷ 3.14
= 127.39 square units
Thus, the area of the circle is 127.39 square units
Determine whether a figure with the given vertices is a parallelogram. A(4,5), B(-7,-10), C(-4,-9), D(7,6) distance and slope formula
Answer:
C i think..
Step-by-step explanation:
Simplify: -(-6x + 3)
What is 5 1/2 in a whole number
Answer:
6
Step-by-step explanation:
5 1/2
(5×2+1)/2
11/2
5.5
6 ( nearest whole number)
If AC = 4x – 60 and BD = 30 – x, find BD.
Answer:
Since AC is perfectly equal to BD, 4x-60=30-x. If you solve for x, x=18. Then plug 18 into BD=30-x. Therefore, BD=12.
Fred spent half of his allowance going to the movies. He washed the family car and earned 9 dollars. What is his weekly allowance if he ended with 11 dollars?
Answer:
Weekly allowance $4
Step-by-step explanation:
Fred ended with $11. So, subtract $9 from washing the car.
$11 - $9 = $2
$2 Is the amount of weekly allowance Fred hasn't spent yet. However, at the beginning of the week, Fred used half his allowance. This means $2 was what was left. So,
$2 × 2 = $4
meaning Fred had $4 in allowance at the beginning of the week.
John and his best friend found some money and is in an envelope they split the money equally getting 14 how much money did they find
Answer:
$28
Step-by-step explanation:
Since each person got $14 and we know that there are 2 people receiving money, the total amount of money is equal to the amount of money John received, added to the amount of money his best friend got. Since both received $14, we can use the following equation:
Money found = $14 + $14 = $28
To make a soup, 2 cups of chicken broth are needed for each 1/4 cup of dried lentils. How many cups of chicken broth are needed if 2 1/4 cups of dried lentils are used?
Answer:
You'll need 18 cups of chicken broth!
Step-by-step explanation:
You are using a ratio of 1/4 cup (lentils) to 2 cup (broth). Therefore, you need to find the relationship between lentil and broth.
In order to get from 1/4 to 2, you multiply by 8. (1/4 * 8 = 2)Therefore, the common relationship is multiplying the lentil amount by 8So, 2 1/4 * 8 = 18Therefore, 18 cups are needed :D
To make a soup with 2 1/4 cups of dried lentils, you would need 9 cups of chicken broth.
Explanation:To find the number of cups of chicken broth needed, we need to multiply the given number of cups of dried lentils (2 1/4 cups) by the ratio of chicken broth to dried lentils. The ratio is 2 cups of chicken broth per 1/4 cup of dried lentils. So, for 2 1/4 cups of dried lentils, we would need:
2 1/4 cups × (2 cups/1/4 cup) = 9 cups of chicken broth
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a sign says that the price marked on all music equipment is 30% off the original price you buy an electric guitar for sale price of $315 what is the original price
The original price is $450.
Step-by-step explanation:
Step 1:
Given details, Discount%, D% = 30 and Selling Price, SP = $315
Step 2:
Write down formula for calculating the Original Price
Selling Price (SP) = Original Price (OP) - Discount (D)
Discount (D) = Original Price (OP) * (D%/100)
Step 3:
Substitute given values in the formula
315 = OP - D
D = [tex]OP \times30/100[/tex]
D = 0.3 OP
Step 4:
Substitute value of D in the first formula
315 = OP - 0.3 OP
315 = OP (1 - 0.3) = 0.7 OP
Original Price, OP = 315/0.7 = $450
What scale factor was used in the dilation shown below?
Answer:
-3
Step-by-step explanation:
to find the scale factor dividex^1 by x (so old shape to new shape)
Wat does it mean to estimate a math problem
Answer: Estimate means a close guess.
For example, when estimating with decimals, we would round them to the nearest whole number to estimate the answer.
Example: 3.6 + 1.2
1.2 is closest to 1
3.6 is closes to 4
4 + 1 = 5
A good estimate is 5
3.6 + 1.2 = 4.8
4.8 is very close to 5, so 5 is a very good estimate.
Final answer:
Estimating a math problem involves making an educated approximation of a quantity using prior knowledge and reasoning. It applies to various fields and helps to rule out unrealistic numbers, as well as develop important problem-solving skills.
Explanation:
To estimate a math problem means to find a rough approximation or a ballpark figure of the quantity in question, rather than calculating the exact number. Estimations are based on sound reasoning, prior experience, and a strong grasp of the relevant variables and physical principles. The process is not a wild guess but a calculated approximation that can be derived from formulas where the input quantities are known to a limited precision.
For example, to estimate the mean rent for a two-bedroom apartment in a town, you might calculate the average of several listed rents. Or, in physics, to estimate how large a current will be in a circuit when it is turned on, you would apply the relevant principles and any known quantities to arrive at an approximate value. The goal of estimation is to get within a reasonable range of accuracy without needing a precise computation.
The skills of estimation are vital in many fields, including physics, and they help in ruling out unrealistic results. Practicing these skills, getting familiar with units, and understanding relationships between variables all contribute to making better estimates. Moreover, after arriving at an estimate, it's important to do a sanity check to make sure the result seems reasonable within the context of what is known.
Suppose 4/5 of a different box of oranges weighs 8 pounds how many pounds of oranges are in the full box
Answer:
10
Step-by-step explanation:
if you take 8 and divide it by 4 you get 2 meaning that each fifth is 2 pounds. if there are 5/5 that means there are 10 pounds
What is the half of 14.5
Answer:
7.25
Explanation:
14.5×½=7.25
In a survey at a shoe store, 200 customers were asked whether they have
running shoes or basketball shoes. The results are in the relative frequency
table.
A. 58%
B. 60%
C. 42%
D. 40%
Answer: 42%
Step-by-step explanation:
Add 0.16 and 0.26, you get 0.42. Covert 0.42 into percentage and you get 42%
Calculate the distance
Benjamin rides
his scooter if he rides 3/5mile
each day
for 10 days.
Answer:
Step-by-step explanation:
30/5=6
Final answer:
Benjamin rides his scooter for a total of 6 miles over a period of 10 days, by multiplying the daily distance of 3/5 mile by 10 days.
Explanation:
To calculate the distance Benjamin rides his scooter over 10 days, we multiply the daily distance by the number of days. Benjamin rides 3/5 of a mile each day.
Distance per day = 3/5 mile
Number of days = 10 days
The total distance is:
3/5 mile/day × 10 days = 6 miles
Therefore, the correct answer is Benjamin will have traveled a total of 6 miles over the course of 10 days.
Combine the like to simplify the expression: -5y + 12 + 8y − 6 − 2 =
First, let's move combine like terms:
-5y + 8y = 6 + 2 -12.
3y = -4.
y = -4/3
Answer:
x = -3 + 2y
Step-by-step explanation:
I'm not sure if that's correct, sorry, dear~!
15. A band expects to have 16 songs on their next
album. The band writes and records 62.5% more
songs than they expect to have in the album.
During the editing process, 50% of the songs are
removed. How many songs will there be in the
final album?
Answer:
There will be 13 songs in the final album.
Step-by-step explanation:
i) number of songs expected = 16 songs
ii) the band wrrites 62.5% more
therefore the band writes [tex]16 \times ( 1 + 0.625) = 16 \times 1.625 = 26[/tex] songs
iii) During the editing process 50% of the songs are removed.
Therefore there will be in the final album = [tex]( 1 - 0.5) \times 26 = 0.5 \times 26 = 13[/tex] songs.
Add: (8x – 2y) +(4x + 4y – 6)
+ 2y - 6
12x – 6y - 6
12x – 2y - 6
14xy – 6
Tell how you could use a proportion to find 125% of 500. Why is the solution greater than the original number?
11-5 6th grade work
Answer:
625
Step-by-step explanation:
We have to find 125% of 500
= [tex]\frac{125}{100} * 500 = 1 .25 * 500[/tex] = 625 .
Here the solution (625) is greater than the original (500) because the percentage value is more than 100% . so the answer will come more than its original value.
What is the coefficient of the c-term of the algebraic expression 14 a minus 72 r minus c minus 34 d?
When there's no number in front of a variable, that means it has a coefficient of 1.
So the coefficient is 1. Hope that makes sense.
The coefficient of the c-term of the algebraic expression 14a - 72r - c - 34d is -1.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an algebraic expression:
= 14a - 72r - c - 34d
From the above equation, the coefficient of the c term is:
= -1
Thus, the coefficient of the c-term of the algebraic expression 14a - 72r - c - 34d is -1.
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Rita works at a gym where she gets paid $450 each week plus $15.50 for any new gym membership she sells. If y represents the total pay per week and x represents the number of new memberships sold, which of the following equations represents a higher rate per membership sold?
Answer:
D
Step-by-step explanation:
Lauren's bedroom measures 18 feet by 12 feet, with a closet that measures 2 feet by 4 feet. If carpet costs $4.15 per square foot, how much will it cost to carpet Lauren's room and closet?
Answer:
$929.60
Step-by-step explanation:
step 1
Find the area of Lauren's bedroom
Remember that the area of a rectangle is equal to
[tex]A=LW[/tex]
so
[tex]A=(18)(12)=216\ ft^2[/tex]
step 2
Find the area of closet
Remember that the area of a rectangle is equal to
[tex]A=LW[/tex]
so
[tex]A=(2)(4)=8\ ft^2[/tex]
step 3
Find the total area
Adds the areas
[tex]216+8=224\ ft^2[/tex]
step 4
Find the cost
Multiply the total area by the cost per square feet
so
[tex]224(4.15)=\$929.60[/tex]
Final answer:
The cost to carpet Lauren's bedroom including her closet is found by calculating the total area and then multiplying by the carpet's cost per square foot. The total area is 224 square feet and with a carpet cost of $4.15 per square foot, the total cost is $930.40.
Explanation:
To calculate the cost to carpet Lauren's room and closet, we must first determine the total area that needs to be carpeted. We already know that the room measures 18 feet by 12 feet. Taking the square footage of the room, we perform a multiplication: 18 ft imes 12 ft = 216 square feet.
Next, we calculate the area of the closet separately, which measures 2 feet by 4 feet. The calculation would be 2 ft imes 4 ft = 8 square feet. Now, we add the area of the room and the closet to get the combined area: 216 sq ft + 8 sq ft = 224 square feet.
Lastly, we find the cost to carpet this combined area. The carpet costs $4.15 per square foot, therefore, we multiply the total area by the cost per square foot: 224 sq ft imes $4.15/sq ft = $930.40. So, the total cost to carpet Lauren's room and closet will be $930.40.
2x - y = -13
2x + y = 1
Answer:
x = -3
y = 7
Step-by-step explanation:
During one waiter's shift, he delivered 13 appetizers, 17 entrees, and 10 desserts. what percentage of the dishes he delivered were
Question
During one waiters shift he delivered 13 appetizers, 17 entrées, and 10 desserts what percentage of the dishes he delivered were: A. Desserts B. Appetizers C. entrees
Answer:
A)Desserts = 25 %
B)Appetizers = 32.5 %
C)Entrées = 32.5 %
Step-by-step explanation:
Given:
Number of appetisers = 13
Number of entrees = 17
Number of desserts = 10
Solution:
Total number of dishes = 13 + 17 + 10 = 40
percentage of the dishes he delivered were Desserts is = [tex]\frac{10}{40} \times 100 = 0.25 \times 100 = 25%[/tex]
percentage of the dishes he delivered were Appetizers is =[tex]\frac{13}{40}\times 100 = 0.325 \times 100[/tex] = 32.5%
percentage of the dishes he delivered were Entrées is = [tex]\frac{17}{40} \times 100 = 0.425 \times 100[/tex]= 42.5 %
To find the percentage of each type of dish a waiter has delivered, add up the total number of dishes, then divide the number of each type of dish by this total and multiply by 100.
Explanation:The subject question requires us to determine what the percentage is of the various types of dishes a waiter delivers during his shift. We're given that the waiter delivered 13 appetizers, 17 entrees, and 10 desserts. We can solve this by doing some basic calculations:
First, we need to figure out the total number of dishes the waiter delivered. We do this by adding together the appetizers, entrees, and desserts he delivered: 13 appetizers + 17 entrees + 10 desserts = 40 dishes in total.
Next, to find the percentage of each type of dish, we divide the number of that type of dish by the total number of dishes, and then multiply the result by 100. For example, for appetizers: (13 appetizers / 40 total dishes) * 100 = 32.5%.
You can do the same calculations for entrees and desserts to find their percentages. These basic calculations are useful not only in a restaurant setting, but also in allocation of tasks in modern businesses and in many other real-world scenarios.
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What is the area of the following circle?
Either enter an exact answer in terms of # or use 3.14 for
i and enter your answer as a decimal.
d=8
Answer:
The answer is 28.27