The function Formula is, f(t) = 6t + 8.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The collection of values that could result in a function's outputs is known as the co-domain.
Given:
Carolina charges an initial fee plus $6 for each hour of work
Her total fee for a 4-hour job = $32
So, if she work for 't' hours then linear equation will be of the form
f(t) = mt + b
Here m is the constant rate = 6
Now we plug in the values and find out b, m=6
f(t) = mt + b
32 = 6(4) + b
32= 24 + b
8 = b
So, the function is f(t) = 6 t+8.
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How do you match a logarithmic function with its graph?
Matching a logarithmic function with its graph can be done by understanding the key characteristics of logarithmic functions and how they are represented on a graph.
A logarithmic function is of the form y = log base b (x), where b is the base of the logarithm (usually 10 or e).
The graph of a logarithmic function is a reflection of the exponential function of the same base b, across the line y=x.
Here are some key characteristics of logarithmic functions and their corresponding graphs:
1) Asymptote: The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.
2) Domain: The domain of a logarithmic function is x>0, since the logarithm of a negative number is undefined.
3)Range: The range of a logarithmic function is all real numbers
4) Increasing or decreasing: A logarithmic function is increasing over its domain
5) Shape: The graph of a logarithmic function is concave down.
6) x-intercept: The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.
By keeping these characteristics in mind, you can match a logarithmic function with its graph by observing the shape, asymptote, domain and range of the graph.
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Ella stacks two boards under a table to make it level. One board is inch thick. The
other board is inch thick. Which equation most closely estimates the thickness of
the two boards?
"Thickness of two boards = Thickness of first board + Thickness of second board" would be the closely estimated equation.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, separated by the 'equal' sign.
Define quadratic equation.x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
The thickness of the two boards together can be represented by the sum of the thickness of each individual board. Therefore, the equation that most closely estimates the thickness of the two boards stacked together is:
Thickness of two boards = Thickness of first board + Thickness of second board
So in this case, the equation would be:
Thickness of two boards = inch + inch
This equation gives the total thickness of two boards stacked together and it's the closest estimation.
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What’s is
2^x=1/32•x=
Answer:
I believe it would be x=-5
Step-by-step explanation:
..
Willl mark you brainlieestttt
Answer:
7/12
Step-by-step explanation:
y = 12
x = 7
y = Kx
K = y/x
K = 7/12
The large sphere has a diameter of 12 feet.
What is the volume of the shaded figure? Express the answer in terms of Pie.
A. 252Pie ft³
B. 261Pie ft³
C. 288Pie ft³
D. 324Pie ft³
Answer:
C. 288π ft³
Step-by-step explanation:
V(Sphere) = 4/3πr³
V(Sphere) = 4/3π(6)³
V(Sphere) = 4/3π(216)
V(Sphere) = 288π ft³
y=1/4x+3 in standard form
Answer:
Step-by-step explanation:
2
You need to study the satisfaction of customers of a specific restaurant. You decide to order food and talk to those customers sitting next to you. This would most closely describe which type of sampling technique
This is how the Cluster of sampling technique is best described.
Describe cluster sampling.Cluster sampling divides a population into clusters, which are more compact groupings. From these clusters, they next randomly select a sample. Cluster sampling is a probability sampling approach that is frequently used to explore large populations, especially those that are widely geographically dispersed.Large, dispersed populations should be investigated using cluster sampling. This is because interviewing each individual is expensive, time-consuming, and in some cases impossible. Building more compact, comparable representations of the population under study is made possible by cluster sampling.For instance, if you wanted to investigate the consumption of soda in a certain city, you could use area sampling to divide the city into several regions, or clusters, and then choose out specific clusters to study.Learn more about cluster sampling refer to :
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If 8 times a number is decreased by 2, the result is less than 15. What is the number?
Answer:
2
Step-by-step explanation:
1
8x1 = 8
8-2=6
2
8x2=16
16-2=14
Find the output (y) of the function y= -7+5 if the input is (x) is 15
Y=
Answer: -100
Step-by-step explanation: -7(15)+5
It said x=15 so put 15 in and solve from there and that would be -100
HOPE THIS HELPS ANY I JUST completed FUNCTIONS AND MAN IT WAS FUN
When merida divides her age by 3 and adds 5, the result is 9 which equation represents this situation where m is meridas age?
a/ 9= (m ~ 3) x 5
b/ m= (9 - 3 ) + 5
c/ m = (9~3) +5
d/ 9= (m~ 3) +5
Answer:
d which implies m/3 + 5 = 9
Select the correct answer from each drop-down menu. the function has been transformed, resulting in function h. to create function h, function f was translated 2 units , translated 4 units , and reflected across the _______.
Across the y-axis, translated 2 units to the right and four units to the left, the new function is now h(x) = -(x + 2)3 - 4
Step (i): The type of transformation change of the function
a) The translated left "c" units are x - c;
b) The translated right "c" units are x + c
Step (ii) The given function is translated "2" units right side, then the new function is
h(x) = (x + 2 )3followed by the translated "4" units left sides and reflected across the y-axis.
Now the new function is h(x).
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Obtain the length of a ladder leaning against a wall 4.33 m high and forming an angle of 60 ° with respect to the floor of the
PLEASE HELP
The numbers to choose from are 27, 333, 117, 207, 297, and 153.
BARINLIST ANSWER ;))))
Answer:
This might not be right but...
Step-by-step explanation:
jk: 27
nj: 153
jl: 117
knm: 333
mjl: 207
jlk: 297
Im Sorry if its wrong
A boy wants a game which cost $180, but he only has 1/3 of the money, how much more money does he need to buy the game?
Answer: $120
Step-by-step explanation:
So you find 1/3 of 180, basically, you multiply them which is 60.
So if he has a third of the money, he has $60, but he needs 180. So we subtract $180 (how much money he needs) from $60 (the money he has). Which is 120 dollars, so the boy needs $120.
Or 2/3 more.
Analyze and Persevere
Javi is building
a birdhouse. Each of the four walls of the
birdhouse needs to be 5.5 inches long.
Javi has a piece of board that is 24.5 inches
long. Is the board long enough to be
cut into the four walls of the birdhouse?
Estimate using compatible numbers.
Answer:
yes, the board is long enough
Step-by-step explanation:
5.5 in x 4 walls = 22 inches
The board is 24.5 in, so there is enough.
24.5 > 22, there is an extra 2.5 in left over.
PLZ HELP I NEED THIS DONE TO PASS
Answer:
F, T, T, F
Step-by-step explanation:
1) F because the die is labeled 1 through 8. Because 1 through 3 are included within the die, it is possible to roll a number less than 4.
2) T because the die is from 1 to 8, meaning 5 through 8 - number 4 and greater - are able to be rolled. Rolling a 4, 5, 6, 7, or 8, has a probability of 5/8 chance of being rolled, making it a likely roll (as 5/8 is over a 50% chance).
3) T as numbers are always either even or odd, meaning it is impossible not to roll an even or odd number. In other words, it is certain to roll an even or odd number.
4) F as it is extremely likely to roll a number less than 7 with a whopping 6/8 chance of being rolled. What would be unlikely is rolling a number greater than 7.
It took Xander 31 minutes to run a 5-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many minutes did it take Xander to run 1 mile during the race
So it took Xander approximately 9.96 minutes to run 1 mile during the race.
To convert the distance of the race from kilometers to miles, you can use the conversion factor 1 kilometer = 0.621 miles.
To find the time it took Xander to run 1 mile, you can divide the total time it took him to run the entire race by the number of miles he ran.
First, convert the distance of the race from 5 kilometers to miles:
5 kilometers * 0.621 miles/kilometer = 3.105 miles
Then, divide the total time it took Xander to run the race by the number of miles he ran:
31 minutes / 3.105 miles = 9.96 minutes/mile
So it took Xander approximately 9.96 minutes to run 1 mile during the race.
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What is the degree measure of ∠M?
Answer:
<M=32 degrees
Step-by-step explanation:
triangle equals 180 degrees total
76+72=148
180-148= 32
<M= 32
0.39+0.11= adding decimals
To get to the different parts of the race course you need to use local transport. One bus company offers a 10 trip ticket, with each trip costing £6.74. How much will the 10 trip ticket cost?
Answer: 10 trip ticket will cost £67. 4.
Step-by-step explanation:
Each (1)trip of One bus company costs= £6.74.
10 trip ticket will cost = £6.74 x 10 = £67. 4.
help. pls.
-photo attached !
Find the measures of the numbered angles.
(the angles i need to find)
<1 _?
<2 _?
<3 _?
<4 _?
<5 _?
<6 _?
<7 _?
<8 _?
Answer:
<1=75°[corresponding angles are equal]
<2=180-<1=(180-75)°=105°[sum of st.angles is supplementary]
<3=<2=105°[Vertically opposite angles are equal]
<4=75°[Alternate angles are equal]
<6=<2=105°[Corresponding angles are equal]
<7=<6=105°[Vertically opposite angles are equal]
<8=75°[Vertically opposite angles are equal]
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what part of 3$ is the sum of 7 dimes, 1 nickel and 3 pennies?
Answer:
7/60
Step-by-step explanation:
First, we would need to add up all of the coins and know their values.
1 dime (d) = 10¢
1 nickel (n) = 5¢
1 penny (p) = 1¢
An equation we can use will look something like this:
(d × 7) + (n × 1) + (p × 3) =?
Now just add the numbers and solve.
(10 × 7) + (5 × 1) + (1 × 3) = 78
Therefore, the total amount is 78¢.
Now to figure out how much 78¢ is out of $3, we can use an equation that looks something like this:
3 ÷ 0.78 = 3.84615385 or 7/60
So, this means that with 7 dimes, 1 nickel and 3 pennies it is 7/60 of $3.
So I was doing a math problem and they gave me the perimeter and told me to find the radius from that, how do I do that?
At 10:00 a.m. two planes leave an airport. if the northbound plane flies at 280 mph and the southbound at 320 mph, at what time will they be 1,000 miles apart? which equation can be used to solve for t, the time it takes the planes to be 1,000 miles apart?
280t + 320t = 1,000 is distance equation can be used to solve for t, the time it takes the planes to be 1,000 miles apart.
What does distance mean in a nutshell?
Distance is the overall movement of an object without consideration of direction.
Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.
At 10:00 a.m. two planes leave an airport. If the northbound plane flies at 280 mph and the southbound at 320 mph
Let 't' be the time taken when they are 1000 miles apart
the northbound plane flies at 280 mph
Distance = speed * time
distance covered by northbound plane D1= 280 * t= 280t
the southbound at 320 mph
distance covered by southbound plane D2=320 t
Distance is 1000 miles apart
D1 + D2= 1000
280t + 320t = 1,000
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What is the coefficient of 5x² in 5x² 5x?
The coefficient of expression 5x^2 in 5x^2 5x is 5.
The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. In this expression, the number multiplied with 5x^2 is 5, so the coefficient of 5x^2 is 5.
The expanded expression is 5x^2 5x = 5x^3 + 5x^2. The coefficient of 5x^2 in this expression is still 5.
The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. When we expand the expression 5x^2 5x, it becomes 5x^3 + 5x^2. The number that is multiplied with 5x^2 in this expression is still 5, so the coefficient of 5x^2 is 5.
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In AJLP. m/JMP = (3x −6)°, JK = 3y-2, and LK = 5y-8. Find LK if PK is a median.
LK=
On solving the provided question, we can say that - the value ox in the following angle = 3x = 84 => x = 28
what are angles?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.
here
angle JMP = 3x-6 - 90
3x = 84
x = 28
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A hotel is offering two weekend specials. The first special is 3 nights and 4 meals for $233. The second
special is 3 nights and 3 meals for $226.50.
Part A: Write a system of equations to represent cost per night x and cost per meal y.
Part B: What is the cost per night and the cost per meal?
Answer: Part A:
To represent the cost per night x and cost per meal y in a system of equations, we can use the information provided in the question:
First Special:
3x + 4y = 233
Second Special:
3x + 3y = 226.50
Where x is the cost per night and y is the cost per meal.
Part B:
To find the cost per night and the cost per meal, we can use the information provided in the question and system of equations.
We can solve this system of equations using several methods: substitution or elimination method.
One common method to find the solution is by substitution method, where we find the value of x in terms of y from one of the equations and then substitute it into the other equation to solve for y.
x = (233 - 4y)/3
then substitute it into the other equation:
3(233 - 4y) + 3y = 226.50
now solve for y:
699 - 12y + 3y = 226.50
-9y = -472.50
y = 52.50
and we can substitute it back into the first equation:
3x + 4(52.50) = 233
3x = 80.50
x = 26.83
So the cost per night is $26.83 and the cost per meal is $52.50
Step-by-step explanation:
The figure was created by repeatedly reflecting triangle NMP.
A figure is created by continuously reflecting triangle N M P. The length of side N M is 6 inches, the length of side M P is 4 inches, and the length of side N P is 8 inches.
The scale factor of the dilation of segment HG is One-sixth.
Point P is the center of dilation. Line segment H G is dilated to form shorter line segment H prime G prime. The length of P G prime is 0.5
If PG' equals 0.5 units, what is PG?
2.5 units
3 units
4.5 units
6 units
The length of PG if PG' is 0.5 units is; 3 units.
What is dilation?The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)
Here, given that,
Dilation is simply defined as the shrinking or enlarging of an object by a scale factor.
Now, we are told that Line HG is dilated to form a shorter line H'G'.
We are told that the scale factor is 1/6.
Point P is the center of dilation and if PG' is 0.5 units, then we can write the relation as follows;
Length of PG'/Length of PG = 1/6
Thus;
0.5/length of PG = 1/6
Length of PG = 0.5/(1/6)
Length of PG = 4 units
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Which quantity is proportional to 12/4?
Check all that are true.
48/18
36/12
35/15
2416
3/1
The quantities which are proportional to 12/4 are 36/12 and 3/1 .
What is proportional ?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.
12/4 ⇒ 3/1
48/18= 24/9
= 8/3
The quantity 12/4 is not proportional to 48/18
36/12= 18/6
= 3/1
The quantity 12/4 is proportional to 36/12
35/15= 7/3
The quantity 12/4 is not proportional to 35/15
24/16= 12/8
= 6/4
= 3/2
The quantity 12/4 is not proportional to 24/16
3/1The quantity 12/4 is proportional to 3/1
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