Find the domain and range of the relation and determine whether it is a function.
a. domain: all real numbers; range: all real numbers; Yes, it is a function.
b. domain: positive integers; range: positive integers; No, it is not a function.
c. domain: x ≥ 0; range: y > 3; No, it is not a function.
d. domain: x > 3; range: y > 0; Yes, it is a function.
Using function concepts, it is found that the correct option is:
d. domain: x > 3; range: y > 0; Yes, it is a function.
A relation is a function if for each value of the input, there is only one respective value of the output. In a graph, it means that for each value of x, there is only one respective value of y.
In this graph, there is only one value of y for each value of x, hence, it is a function.The domain of a function is the set that contains all possible input values. In a graph, it is the values assumed by x, the horizontal axis.
In this graph, x assumes values greater than 3, hence the domain is x > 3.The range of a function is the set that contains all possible output values. In a graph, it is the values assumed by y, the vertical axis.
In this graph, y assumes values greater than 0, hence the range is y > 0.A similar problem is given at https://brainly.com/question/10891721
One side of a triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate of 2 cm/s. if the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 21 cm long, the second side is 36 cm, and the angle is π/6? (round your answer to three decimal places.)
The rate at which the angle between the sides of the triangle is changing is 4/9 radians per second.
Explanation:In this problem, we are given that one side of the triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate of 2 cm/s. We need to find the rate at which the angle between the sides is changing.
To solve this, we can use the formula:
angle_rate = (-side2_rate/side1)*(cos(angle))/(sin(angle))
Substituting the given values:
angle_rate = (-(-2)/9)*(cos(π/6))/(sin(π/6))
Simplifying, we get:
angle_rate = 4/9
Therefore, the rate at which the angle between the sides is changing is 4/9 radians per second.
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Rebekah wants to read a certain number of pages each day during summer vacation. Today, she read 204 pages, which is 136% of her goal. How many pages does Rebekah want to read each day?
Answer:
Her goal is to read 150 pages each day.
Step-by-step explanation:
Let p represent the number of pages she wants to read each day.
Then 136% of that number is 204 pages, or, in an equation,
1.36p = 204
Solving for p, we get: p = 204/1.36 = 150 pages
Her goal is to read 150 pages each day.
Find the value of x to the nearest tenth.
10.0
6.0
9.3
4.0
Answer:
The value of x is 6
Step-by-step explanation:
Given the figure in which
DE=3x-8 and BC=20
we have to find the value of x.
By mid-point theorem which states that the line segment which is drawn to the mid-points of two sides of triangle is parallel to the third side and also half of the length of third side.
[tex]DE=\frac{1}{2}BC[/tex]
[tex](3x-8)=\frac{1}{2}\times 20[/tex]
[tex]3x-8=10[/tex]
[tex]3x=18[/tex]
[tex]x=\frac{18}{3}=6[/tex]
The value of x is 6
Option 2 is correct.
The distance from town A to town B is divided into 8 equal parts. So far, a bus has traveled 12 Miles. How far apart are town A and town B? Explain
Town A and Town B are 1.5 miles apart.
Explanation:The distance between town A and town B can be found by multiplying the distance traveled by the number of equal parts that make up the whole distance. In this case, the bus has traveled 12 miles out of 8 equal parts. To find the total distance, we can set up a proportion:
12 miles / 8 parts = x miles / 1 part
Cross-multiplying gives us:
8x = 12 miles
Dividing both sides by 8 gives us:
x = 1.5 miles
Therefore, town A and town B are 1.5 miles apart.
Factor
25m^100 − 121n^16
1. (5m^50 - 11n^8)^2
2. (5m^10 - 11n^4) (5m^10 + 11n^4)
3. (5m^50 - 11n^8) (5m^50 + 11n^8)
4. (5m^10 - 11n^4)^2
The correct answer is C) (5m^50 - 11n^8) (5m^50 + 11n^8)
We can tell this because of the rule regarding factoring the difference of two perfect squares. When we have two squares being multiplied, we can use the following rule.
a^2 - b^2 = (a - b)(a + b)
In this case, or first term is 25m^100. So we can solve that by setting it equal to a^2.
a^2 = 25m^100 -----> take the square root of both sides
a = 5m^50
Then we can do the same for the b term.
b^2 = 121n^16 ----->take the square root of both sides
b = 11n^8
Now we can use both in the equation already given
(a - b)(a + b)
(5m^50 - 11n^16)(5m^50 + 11n^16)
1.) A circle has a radius of 12 centimeters. Find the area of the sector of the circle formed by an angle of 25 degrees. is necessary, round the answer to two decimal places.
2.) Is the function f(theta) = sin theta + cos theta even, odd, or neither? show how
Consider a group of people who have received treatment for a disease such as cancer. let tt be the survival time, the number of years a person lives after receiving treatment. the density function giving the distribution of tt is p(t)=ce−ctp(t)=ce−ct for some positive constant cc, and the cumulative distribution function is p(t)=∫t0p(x)dxp(t)=∫0tp(x)dx. think carefully about what the practical meaning of p(t)p(t) is, being sure that you can put it into words.
Solution :- Let X be a group of people who have received treatment for cancer ,
and t be the survival time(The number of years a person lives after receiving treatment).
Now the density function giving the distribution of t =[tex]p(t)=ce^{-ct}[/tex]
for some positive constant c.
So to know the probability of a person of the given group live not more than d days, the cumulative distribution function is given by
[tex]P(X\leq\ d )=\int\limits^d_{t_0}{ce^{-ct}\ dt[/tex] where c be any constant.
The distribution function P(t), also called the cumulative distribution function (CDF) , which tells the probability that a variate T takes a value less than or equal to a number t. And P(t)is greater than 0 and less than1
In a circle with a radius of 27 2/5 in., an arc is intercepted by a central angle of 7π/4 radians. What is the arc length? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.
For future reference, Scapazzi was correct.
The arc length will be given as the circumference of the circle is 150.56 inches long.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
In a circle with a radius of 27 + 2/5 inches.
That can be written as 27.4.
An arc is intercepted by a central angle of 7π/4 radians.
The arc length will be given as the circumference of the circle
[tex]\rm Arc \ length = \dfrac{\theta}{2\pi} 2 \pi*r\\\\Arc \ length = \theta * r\\\\Arc \ length = \dfrac{7 \pi }{4} * 27.4 \\\\Arc \ length = 150.56[/tex]
Thus, the arc length will be given as the circumference of the circle is 150.56 inches.
More about the circle link is given below.
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Emily dropped a coin from rest, and the distance traveled by the coin is given by the formula below, where s is the distance the coin has fallen, g is a constant representing Earth's gravity, and t is the duration of time over which the coin falls. Emily measured the distance in feet, the time in seconds, and now wants to calculate the value of g. What must be the units of g?
To match the units of distance in feet and time in seconds, the units of the gravitational constant g must be feet per second squared (ft/s^2). On Earth, g is roughly 32.17 ft/s² in U.S. Customary units.
When Emily drops a coin from rest, the distance traveled by the coin (s) can be used to calculate the acceleration due to gravity (g) when the time (t) the coin took to fall is known. The formula provided suggests that distance is equal to 0.5 times gravity acceleration times the square of time (s = 0.5 * g * t²).
Given that Emily measured the distance in feet and the time in seconds, the units for g must be compatible with these measurements. Since distance is in feet and time is squared in seconds, the unit for g must be feet per second squared (ft/s²) to ensure that all units cancel out correctly, leaving us with the unit of distance in feet. On Earth's surface, the value of g using U.S. Customary units is approximately 32.17 ft/s².
Help please!!! Need to find the height!!
Lucy has been given a list of 5
bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?
If a sequence us defined recursively by f(0)= 3 and f (n+1)= -f (n) +5 for n>_ 0 then f (2) is equal to?
Sam's Discount Store offers a 2% discount for paying cash. How much would Joan pay if she pays cash for a set of skillets priced at $38.95?
a. 38.17
b.34.82
c.3695
Answer:
$ 38.17
Step-by-step explanation:
A thermometer is removed from a room where the temperature is 70° f and is taken outside, where the air temperature is 30° f. after one-half minute the thermometer reads 50° f. what is the reading of the thermometer at t = 1 min? (round your answer to two decimal places.)
Look at this cube and its net. Cube with one side labeled 8 centimeters. Net of the same cube also shown with one side labeled 8 centimeters. What is the surface area of this cube? cm²
Rocky's car moves to G then it moves to B.His ride is 360 degrees
Answer:
150
Step-by-step explanation:
30+30+30+30+30=150
Also 5*30=150
708,000 divided by 3,000 equals
Write 24 as a product of its prime factors.
Answer:
Prime factors of 24 is 2× 3×2×2
Step-by-step explanation:
Given : Number 24.
To find: Write 24 as a product of its prime factors.
Solution : We have given that number 24
Prime number : numbers which are divisible by 1 or itself only
Example = 2, 3, 5, 7,....etc
So we will find the factor of 24 by prime factorization
24 is divisible by 1
24 ÷ 3 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Hence we can write 24 as 2× 3×2×2
Therefore, Prime factors of 24 is 2× 3×2×2
select the location on the number line to plot the points 8/3 and 11/3
Answer:
8/3 is between 2 and 3 above 2.5
11.3 is between 3 and 4 above 3.5
Step-by-step explanation:
8/3 converts to the decimal 2.666666... which means its located on the number line between 2 and 3 above 2.5.
11/3 converts to 3.6666.... which means its located on the number line between 3 and 4 above 3.5.
Draw a horizontal number line. Mark the point 8/3 at approximately 2.67 and the point 11/3 at approximately 3.67 to visually represent these values.
To plot the points 8/3 and 11/3 on a number line.
Draw a Horizontal Number Line
Start by drawing a horizontal line on a piece of paper or a whiteboard. This line will serve as your number line.
Make sure it's long enough to accommodate the range of values working with.
Mark the Point for 8/3 (approximately 2.67)
To plot the point 8/3 on the number line, need to find its approximate location.
To do this, you can divide 8 by 3 to calculate its decimal value:
8 ÷ 3 ≈ 2.67 (rounded to two decimal places).
Now, locate the point approximately at 2.67 on the number line, and make a small mark or dot to represent this point.
Mark the Point for 11/3 (approximately 3.67)
To plot the point 11/3 on the number line, calculate its approximate location in a similar way:
11 ÷ 3 ≈ 3.67 (rounded to two decimal places).
Locate the point approximately at 3.67 on the number line and make a small mark or dot to represent this point.
Label the Points (Optional)
label these points to indicate what they represent.
label the point at 2.67 as "8/3" and the point at 3.67 as "11/3" to provide context for the values you've plotted.
Therefore, the plotting of the points 8/3 and 11/3 on the number line is on the right side of zero between 2 and 4.
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Write the equation of the parabola in vertex form.
vertex (0,4), point (1,-3)
f(x)=
The equation of the parabola in vertex form is f(x) = -7x^2 + 4
Explanation:To write the equation of a parabola in vertex form, we use the formula f(x) = a(x - h)^2 + k where (h, k) represents the vertex. In this case, the vertex is (0,4) so our equation becomes f(x) = a(x - 0)^2 + 4 which simplifies to f(x) = ax^2 + 4. To find the value of a, we substitute the coordinates of the point (1,-3) into the equation and solve for a. Plugging in these values, we get -3 = a(1)^2 + 4, which simplifies to -3 = a + 4. Solving for a, we find that a = -7. Therefore, the equation of the parabola in vertex form is f(x) = -7x^2 + 4.
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A computer and printer cost a total of 1136
. The cost of the computer is three times the cost of the printer. Find the cost of each item.
How to find the volume of a hemispherical bowl depth h?
NEED ANSWER IN LEAST THAN 3 Minutes
Anita owns a beauty supply store. Every two weeks she receives a supply of shampoo. Every four weeks she receives a carton of nail polishes. Every eight weeks she receives a box of combs, and every twelve weeks she receives a box of hair dyes. If Anita received a shipment of all these supplies today, when is the next time all four supplies will arrive on the same day?
Annie is planning a business meeting for her company. She has a budget of $1325 for renting a meeting room at a local hotel and providing lunch. She expects 26 people to attend the meeting. The cost of renting the meeting room is $270. Which inequality shows how to find the amount, x, Annie can spend lunch for each person? A. 26x + 270 ≥ 1,325 B. 26x + 270 ≤ 1,325 C. 270x + 26 ≥ 1,325 D.270x + 26 ≤ 1,325
Answer: B. [tex]26x+270\leq1,325[/tex]
Step-by-step explanation:
Let 'x' denote the amount of money Annie can spend lunch for each person.
Given: The cost of renting the meeting room = $270
The number of people attend the meeting = 26
Then, the expression for total amount spent on lunch will be :-
[tex]\text{Total amount on lunch}=26x[/tex]
The expression for total spent by Annie will be:-
[tex]26x+270[/tex]
Since, the budget for renting a meeting room at a local hotel and providing lunch= $1325
Thus, the inequality shows how to find the amount, x, Annie can spend lunch for each person will be :-
[tex]26x+270\leq1,325[/tex]
Roselyn wants to drive her car at a speed of 60 miles per hour for 1.251, point, 25 hours. Her car has a fuel efficiency of 15 miles per gallon. How many gallons of fuel does Roselyn need for her journey? Choose 1 answer: Choose 1 answer: A 2.52, point, 5 gallons B 3.1.25, point, 125 gallons C 0.20, point, 2 gallons D 5 gallons
The number of gallons of fuel Roselyn need for her journey is:
D. 5 gallons
Step-by-step explanation:It is given that:
Roselyn wants to drive her car at a speed of 60 miles per hour for 1.25 hours.
This means that the total distance she covers in 1.25 hours is:
[tex]60\times 1.25=75\ \text{miles}[/tex]
( Since, we know that speed is defined as the ratio of distance to time.
i.e.
[tex]Speed=\dfrac{Distance}{Time}\\\\i.e.\\\\Distance=Speed\times Time[/tex] )
Also, Her car has a fuel efficiency of 15 miles per gallon.
i.e.
She could cover 15 miles with 1 gallon of fuel.
Hence, in order to cover 75 miles.
i.e. to cover (15×5) miles she needs (1×5) gallons of fuel
i.e. she needs 5 gallons of fuel to cover 75 miles.
least common denominator for 1/49 1/21 1/3
CAN I GET SOME HELP?!?!?!?!
I have 11 hundreds 13 tens 2 ones and 15 tenths what number am I
if i have 2 c's 2 A's 3 b's and 1 d what is my gpa and would i be able to pass 8th grade