Given: Parallelogram PORS, QT is perpendicular to PS, SU is perpendicular to QR
Prove: PT congruent to RU
Answers
Since RQ is congruent to PS and RS is congruent to QP, QT = SU, therefore QT and SU are congruent which means PT and RU are also congruent
What is a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.
One the property of a parallelogram is that the opposite lines are parallel and congruent.
Therefore RQ = PS ( they are both congruent)
PS = RS ( they are both congruent )
Therefore the measure of line PT = line SU = QT.
This means that the value of PT = R U , we can therefore say that PT and RU are congruent.
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Related Questions
A sports center offers party packages. They advertise a flat rate of $325 for the first 10 guests. They charge $15 per person for each additional guest. A formula for the cost of the party is:
C = 325 + 15p
where p is the number of guests more than 10. (For example, if 12 people come to the party, p = 2.) Suppose you want to have a huge birthday celebration this year. However, you have budgeted $600 for your party. How many guests can you invite if you decide to have your party at this sports center?
Answers
Using the given linear equation, we conclude that you can invite a maximum number of 21 guests.
How many guests can you invite if you decide to have your party at this sports center?Here the function is:
C(p) = 325 + 15*p
Where p is the number of guests minus 10, now we know that your budget is $600, then the maximum value of guests allowed is such that:
C(p) = 600 = 325 + 15*p
Now we can solve this equation for p:
600 - 325 = 15*p
275 = 15*p
175/15 = p = 11.67
Then the maximum whole number that p can take is p = 11
This means that the maximum number of guest that you can have is:
Guests = 10 + p = 10 + 11 = 21.
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39 kg Rice of taken out of a bag of rice. If 8/22 of the rice is left in the beg then find the quantity of rice the bag contained in the beginning
Answers
Answer:
429/7 kg or 61 2/7 kg
Step-by-step explanation:
I'll answer according to how I understand this problem, but I'm not sure this is correct.
"39 kg of rice is taken out of bag of rice. If 8/22 of the rice is left, what was the original weight of the rice in the bag?"
8/22 is a strange number to work with because it could have been given as 4/11. This is another reason I'm not too sure about this problem.
8/22 = 4/11
If 4/11 is left, then since 11/11 - 4/11 = 7/11, 7/11 of the rice remains.
7/11 x = 39
x = 39 × 11/7
x = 429/7
x = 61 2/7
find the lcm of 48,64,72,96,108
Please help me fast i will give you50 pts
Answers
2|48,64,72,96,108
2|24,32,36,48,54
2|12,16,18,24,27
2|6,8,9,12,27
2|3,4,9,6,27
2|3,2,9,3,27
3|3,1,9,3,27
3|1,1,3,1,9
3|1,1,1,1,3
LCM
2⁶×3⁴64×815184We are given a Student's t distribution with d.f. = 11 and t = 1.910. We wish to find an interval containing the corresponding P-value for a two-tailed test. To do this, we will use the Critical values for Student's t Distribution. Below is an excerpt from this table.
one-tail area 0.250 0.125 0.100 0.075 0.050 0.025 0.010 0.005 0.0005
two-tail area 0.500 0.250 0.200 0.150 0.100 0.050 0.020 0.010 0.0010
d.f. \ c 0.500 0.750 0.800 0.850 0.900 0.950 0.980 0.990 0.999
⋮
9 0.703 1.230 1.383 1.574 1.833 2.262 2.821 3.250 4.781
10 0.700 1.221 1.372 1.559 1.812 2.228 2.764 3.169 4.587
11 0.697 1.214 1.363 1.548 1.796 2.201 2.718 3.106 4.437
To determine where the given t-value would fall, we look for the row with heading d.f. =
. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t =
Answers
To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201
How to determine the t values?The given parameters are:
Degree of freedom, df = 11Sample statistic, t = 1.910This means that
df = 11 and t = 1.910
To calculate the t value,
We check the row where the heading of the degree of freedom is 11
i.e. df = 11
On this row, the t value 1.910 would be between 1.796 and 2.201
This is because 1.910 is greater than 1.796 and it is less than 2.201
Hence, the complete statement is
To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201
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What is the equation of the directrix?
Answers
The equation of the directrix is y = -5
How to determine the directrix equation?The equation is given as:
(x -1)^2 = 12(y + 2)
Express 12 as a product of 4 and 3
(x -1)^2 = 4 * 3(y + 2)
The parabola is represented as:
(x -h)^2 = 4p(y - k)
Where the directrix is
y = k - p
By comparison, we have:
k = -2 and p = 3
So, we have:
y = -2 - 3
Evaluate
y = -5
Hence, the equation of the directrix is y = -5
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Solve the inequality for x.
5x-39-3(6-4x)
Simplify your answer as much as possible.
Answers
Answer:
= 5x-39-18-12x
=5x-12x-39-18
=-7x-57
What is the equivalent expression of 3x^2-4x-3
Answers
Answer:
C. 3(x+1)(x-1)-4x
Step-by-step explanation:
3(x+1)(x-1)-4x
(x+1)(x-1)=x^2-1
3(x^2-1)-4x
3x^2-4x-3
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number.
Answers
The number whose sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed is 32
Equationx = tens digit y = ones digitthe number can be expressed as 10x + y
x + y = 5
nine is subtracted from the number(10x+y) - 9
= 10y+x
x + y = 5
9x - 9y = 9
x + y = 5
x - y = 1
Add the equations
2x = 6
x = 6/2
x = 3
substitute into
x + y = 5
3 + y = 5
y = 5 - 3
y = 2
Therefore, the unknown number is 32.
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the sum of two numbers is 48.
the second number is seven times the first number
Answers
Answer:
[tex]\huge\boxed{\sf x =6,\ y = 42}[/tex]
Step-by-step explanation:
Let the numbers be x and y
Given condition:x + y = 48 --------(1)
y = 7x -------------(2)
Put Eq. (2) in (1)
x + 7x = 48
8x = 48
Divide 8 to both sides
x = 48/8
x = 6Put x = 6 in Eq. (2)
y = 7 (6)
y = 42[tex]\rule[225]{225}{2}[/tex]
Assume a is the 1st number and b is the 2nd number, a + b = 48
b = 7a (the second number is seven times the first number)
a = a
So, equation: a + 7a = 48
a + 7a = 48
8a = 48
a = 6
To find b = 7 (6) = 42
Hope it helps!
en una fiesta hay 16 personas de las cuales el 25% son mujeres, luego llegan mas mujeres a la fiesta, de tal manera que ahora los hombres son el 60% ¿cuantas mujeres llegan a la fiesta?
Answers
Answer:
English (Ingles):
10 Women come to the party.
Spanish (Espanol):
10 Las mujeres vienen a la fiesta.
Step-by-step explanation:
English (Ingles):
We know that there are 16 people there at the start. 25% of those people are women. We can work out by subtracting 100 by 25 that 75% of the p-eople there are men. We need to do 25% of 16 so we can work out how many men and women there are there.
So we find 10% of 16 which is 1.6 then we take off 5% of 1.6 which is 0.08. We then double 1.6 to get 20% which gives us 3.2. We now add on the 5% to make it 25% which gives us 4.
This means 25% of 16 is 4.
This tells us that there are 4 women at the party and 12 men as 16 - 4 = 12.
It now says that more women arrive which makes the percentage for men go down to 60%. We now need to add 5% on to the 25% of women there are which will tell us how many more women there are now and it will let us work out how many women and men there are in total now.
As we can't do this without it giving us 4.8, we know that 25% of people is 4 women which means 50% of people would be 8 women and we make an estimate of how many women have joined which gives us 6 people which means the total amount of women at the party is 10.
Spanish (Espanol):
Sabemos que hay 16 personas allí al principio. El 25% de esas personas son mujeres. Podemos calcular restando 100 por 25 que el 75% de las personas son hombres. Necesitamos hacer el 25% de 16 para poder calcular cuántos hombres y mujeres hay allí.
Así que encontramos el 10 % de 16, que es 1,6, luego quitamos el 5 % de 1,6, que es 0,08. Luego duplicamos 1,6 para obtener el 20%, lo que nos da 3,2. Ahora sumamos el 5% para convertirlo en 25%, lo que nos da 4.
Esto significa que el 25% de 16 es 4.
Esto nos dice que hay 4 mujeres en la fiesta y 12 hombres como 16 - 4 = 12.
Ahora dice que llegan más mujeres lo que hace que el porcentaje de hombres baje al 60%. Ahora necesitamos agregar un 5% al 25% de mujeres que hay, lo que nos dirá cuántas mujeres más hay ahora y nos permitirá calcular cuántas mujeres y hombres hay en total ahora.
Como no podemos hacer esto sin que nos dé 4.8, sabemos que el 25% de las personas son 4 mujeres, lo que significa que el 50% de las personas serían 8 mujeres y hacemos una estimación de cuántas mujeres se han unido, lo que nos da 6 personas que significa que la cantidad total de mujeres en la fiesta es 10.
The marital status distribution of the U.S. male population, ages 15 and older, is as follows: 35.4% never married, 53.6% married, 2.7% widowed, and 8.3% divorced/separated. A random sample of 300 U.S. young adult males, 18 to 24 years old, found 141 never married, 132 married, 3 widowed, and 24 divorced/separated. Using α = 0.10, is this evidence that males in this age group follow a different distribution than all males in the U.S.? Write the hypotheses, calculate the expected counts, check the condition, calculate the test statistic, and use either the critical value approach or the p-value approach to make a conclusion about the question being asked.
Answers
The hypothesis illustrates that the males in the group don't follow a same distribution as all the males that are in the United States.
How to illustrate the information?Based on the information given, it should be noted that the degree of freedom given in this case will be:
= 4 - 1
= 3
By using the Excel function, the p-value is given as 0.0002. In this case, we've to reject the null hypothesis if the p value is less than 0.1.
Therefore, we will reject the null hypothesis in this case. In inferential statistics, the null hypothesis is that two possibilities are the same. It is observed difference is due to chance alone. Using statistical tests, it is possible to calculate the likelihood that the null hypothesis is true
Therefore, the hypothesis illustrates that the males in the group don't follow the same distribution as all the males that are in the United States.
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?? what’s these answers? part A,B and C
Answers
Answer:
you need to upload a pic so we can see what you're talking about
Represent each expression as a power of a, a cannot be equal to 0
Answers
Answer:
a^-27
Step-by-step explanation:
(a^3)^-3)^3)
(a^-9)^3)
a^-27
When we represent the expression ((a³)⁻³)³ as a power of a, the result obtained is a⁻²⁷
How to represent the expression as a power of a?The following data were obtained from the question:
Expression: ((a³)⁻³)³Representation as power of a =?We can represent the expression ((a³)⁻³)³ as a power of a by using the power law of indices as illustrated below:
((a³)⁻³)³
Recall
(Bᵐ)ⁿ = Bᵐⁿ (i.e multiply the power)
Thus,
((a³)⁻³)³ = (a⁻⁹)³
= a⁻²⁷
Thus, we can conclude from the above calculation that the representation of the expression ((a³)⁻³)³ as a power of a is a⁻²⁷
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what percent of 74.39 is 8 %
Answers
Answer:
5.9512
Step-by-step explanation:
1. Convert the percentage to decimal
8% = 8/100 = 0.08
2. Multiply the decimal by the quantity to be extracted
(0.08)(74.39) = 5.9512
Hope this helps
you can correct your mistake.
Oliver flipped a coin 10 times. The
outcomes are shown in the table below.
a) Work out the experimental probability of
the outcome being heads. Give your
answer as a decimal.
b) Using one of the options below, copy
and complete the sentence to explain how
Oliver could improve his experiment to get
a better estimate for the probability.
a)
Outcome Frequency
Heads
7
Tails
3
b) He could improve his experiment by
using a different coin
wearing a hat
flipping the coin outside
doing more coin flips
doing fewer coin flips
Answers
a) The probability of a head exists at 0.7.
b) He could improve his experiment by doing more coin flips.
What is probability?Probability signifies possibility. It exists a branch of mathematics that values the event of a random event. The value exists represented from zero to one.
Given: Coin flipped 10 times.
The Head comes T times and the tail comes 7 times.
To estimate the probability of head in the outcome.
The total number of outcomes is 10 and the head comes 7 times.
a) Probability(head) = 7/10 = 0.7
The probability of a head exists at 0.7.
b) He could improve his experiment by doing more coin flips
Therefore, the correct answer is option c) doing more coin flips.
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1. A boat drifted 15 m out into the water off Ocean Beach, where the shore drops off
at 4°. Can Brooke walk out to bring the boat back without getting water over the
tops of her hip boots which are 1 m tall? Explain your reasoning.
2. are the engineer who designed a new branch for the Mountain Railroad
Company. You sent your plans calling for 100 km of track up Bixby Mountain
taking trains 99 km east of the city of Bixby, to the City Council for approval.
But before the Council got around to looking at your plans, they passed a
regulation that no railroad tracks could go up their mountain at an angle of more
than 8°. Will your plans be approved? Why or why not?
3. The residents of Quietville, a little town 9 km from the San Francisco Airport,
insist that any plane flying over their town disturbs them if it is lower than 3 km.
Will a plane that took off at a 21° angle disturb them? Why?
4. You are an air pollution inspector, checking that factories in your city have
chimneys at least 65 m tall. Standing 50 m from the Ore Smelting Company’s
chimney, you find the angle from the ground to the chimney top is 51°. Can the
company use that chimney legally? Explain.
6. River City is offering a $3 million contract to build a bridge between points A and
C on opposite sides of City River. Along the side of the river that makes a right
angle with the line of the bridge at point C, a surveyor walked 72 m to point B
where she measured the 55° angle form B to A. Long Company will build the
bridge for $3 million if it is not more than 103 m from point A to point C. Short
Company agrees to build it if it is no more the 100 m. Which contracting firm
will be awarded the contract? Why?
7. An elderly woman is trapped 17 m up in her burning home. Can a fireman reach
her on his 26 m ladder if it has to make a 43° angle in order to clear the woman’s
greenhouse under her window? Explain your reasoning.
8. A ski lift 1000 m long goes at a 29° angle up Mt. Gentleslope. Does the lift take
skiers all of the way up to the top of the mountain where there is a snack bar at
the 500 m elevation? Explain your reasoning.
9. Mr. Johnson is a jet pilot who just moved with his family to Suburbia, 26 km
from Toledo Airport. His seven-year-old son, Eric, would like to see his father’s
plane as it flies over their new home for the first time today, but there is a layer of
clouds 5 km above the house. Will Eric be able to see his Dad’s plane if it takes
off at a 9° angle? Explain.
10.You are the cost control expert for an engineering firm designing a giant
television tower having several metal braces, each built in 21 m from the base at a
73° angle with the ground. Part of your job is to decide which standard length of
metal brace wastes less metal: the brace that comes 71 m long, or the one that is
73 m long. What is your decision?
Answers
The correct responses found using trigonometric ratios are as follows;
Brooke's cannot bring the boat back without getting water over her boots.The plan will not be approvedThe plane will not disturbThe company can not use the chimney legallyThe Long company will build the bridgeThe fireman can reach her.The lift does not take the skiers up to the bar.Eric will be able to see his Dad's plane.The 73 m. braceHow can trigonometric ratios be used to find the right responses?1. The depth of the water = 15 × tan(4°) = 1.049 m
The height of Brooke's boot = 1 m
Therefore;
Brooke's cannot bring the boat back without getting water over her boots.2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°
Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;
The plan will not be approved.3. Height reached by the plane = 9 × tan(21°) = 3.455
Therefore;
The plane will not disturb.4. Height of the chimney at the factory = 50 × tan(51°) = 61.745
The minimum chimney height = 65 m.
Therefore;
The company can not use the chimney legally.6. Length of the bridge = 72 × tan(55°) ≈ 102.83
Therefore;
The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7
Therefore;
The fireman can reach her.8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8
Therefore;
The lift does not take the skiers up to the bar.9. Height reached by plane = 26 × tan(9°) ≈ 4.12
The plane flies under the cloud therefore;
Eric will be able to see his Dad's plane.10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83
Therefore;
The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.Learn more about trigonometric ratios here:
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simplify (4a) × (3b)
Answers
Answer:
Step-by-step explanation:
hello :
(4a) × (3b) =12ab
Graph the parabola.
y=x^2
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex.
Then click on the graph-a-function
button.
Answers
Answer:
Vertex: (0,0)
Left 2 points: (-1,1) , (-2,4)
Right 2 points: (1,1) , (2,4)
Step-by-step explanation:
PLEASE HELP 100 POINTS!! Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate and show ur work.
Answers
Answer: 100
Step-by-step explanation:
A small company has 6 employees with associate degrees, 2 employees with bachelor's degrees, and 8 employees with master's degrees. If a single employee is picked at random, what is the probability that he or she has a bachelor's or a master's degree
Answers
Using it's concept, there is a 0.625 = 62.5% probability that he or she has a bachelor's or a master's degree.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The company has 6 + 2 + 8 = 16 employees, out of which 2 + 8 = 10 have a bachelor's or a master's degree, hence the probability is:
p = 10/16 = 0.625.
0.625 = 62.5% probability that he or she has a bachelor's or a master's degree.
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Combine like terms to simplify the following polynomial.
5a²b+7ab² +9c+ 11a²b-3ab² - 9c
Answers
Answer:
5a²b + 7ab² + 9c + 11a²b - 3ab² - 9c
= (5a²b + 11a²b) + (7ab² - 3ab²) + (9c - 9c)
= 16a²b + 4ab²
Primer numbers list maths
Answers
Answer:
1 - 100 primes numbers
Step-by-step explanation:
2,3,5,7,11,13,17,19,23,29,31,37,41,47,57,59,61,67,71,79,83,8797
The accompanying table shows the number of bacteria present in a certain culture over a 6 hour period, where x is the time, in hours, and y is the number of bacteria. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth. Using this equation, determine the number of bacteria present after 15 hours, to the nearest whole number.
Answers
The number of bacteria present after 15 hours is 18928
How to determine the exponential equation?An exponential equation is represented as;
y = ab^x
Where
a = y, when x = 0
From the table, we have:
y = 1796 when x = 0
So, we have:
y = 1796b^x
Also, we have the point (1, 2097)
This gives
2097 = 1796b^1
Divide by 1796
b = 1.17
Substitute b = 1.17 in y = 1796b^x
y = 1796(1.17)^x
This means that the exponential equation is y = 1796(1.17)^x
After 15 hours, we have:
y = 1796(1.17)^15
Evaluate
y = 18928
Hence, the number of bacteria present after 15 hours is 18928
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Henry wants to laminate the tabletop in his study room. The tabletop is the shape of an isosceles trapezoid shown here. If laminating costs $4 per square foot, what is the total cost to laminate the tabletop?
A trapezoid with a height of 3 feet and bases of 6 feet and 10 feet is shown.
Answers
The total cost to laminate the tabletop is $96.
What is the total cost to laminate the tabletop?The first step is to determine the area of the trapezoid.
Area of the trapezoid = 0.5 (sum of parallel sides) x height
0.5 x (6 + 10) x 3 = 24 feet²
The total cost of laminating = cost per square feet x area
$4 x 24 = $96
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Which ordered pair below is a solution to the following system of equations? x + 2y = 7 2x − y = -1
Answers
Answer: (1,3)
Step-by-step explanation:
Let's solve this system of equations by elimination. We will multiply one or both equations such that when we combine the equations, one of the variables will completely cancel out.
Let's multiply the whole first equation by -2 to achieve this:
[tex]-2(x+2y=7)[/tex] now becomes [tex]-2x-4y=-14[/tex]
Now let's add both equations
[tex]-2x-4y=-14[/tex]
[tex]2x-y=-1[/tex]
[tex]-5y= -15[/tex]
Since we got y into a form we can solve it for, lets divide both sides by -5 to isolate it.
[tex]\frac{-5y}{-5} = \frac{-15}{-5}[/tex]
[tex]y=3[/tex]
Now that we have the value of y, we can substitute it into any equation to solve for x. Only if we have both x and y can we make an ordered pair. Let's use the second equation and substitute 3 for y.
[tex]2x-3=-1[/tex]
We can now solve for x.
[tex]2x=2[/tex] [Adding 3 to both sides]
[tex]x=1[/tex] [Dividing by 2 on both sides]
We now have both x and y, so we can put it in an ordered pair to answer the question.
[tex](1,3)[/tex]
In general, in y=asjn[k(x-d)]+c the equation of the axis of the curve is determined by
the value of
a) d
b) k
c) c
d) a
Answers
The equation of the axis of the curve is determined by (c) c
How to determine the equation of the axis?The equation is given as:
y= a sin[k(x - d)] + c
In the above equation, the midline is
y = c
This represents the equation of the curve axis
Hence, the equation of the axis of the curve is determined by (c) c
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the equation of a line is 1.5x2 what are its slope a y intercept
Answers
Answer:
1.5 is the slope and 2 is the intercept
Step-by-step explanation:
I am assuming that the equation is y = 1.5x + 2.
27. Which is wrongly spelt? A. reliable B. sociable C. viable D. avialable
Answers
Answer:
D. Avialable
Step-by-step explanation:
the correct spelling is available :)
The answer is D.
The correct spelling of the word in the given option is : Available
Instead, here the places of a and i have been interchanged, causing it to be misspelt.
If the side length of of rectangle is 3x-3 and the top length is 6, how do I write a linear equation the represents the area and a linear equation that represents the perimeter, all measurements are in cm if that is useful.
Answers
Perimeter of the rectangle is: 6x + 6 cm
Area of the rectangle is: 18x - 18 cm²
What is the Area and Perimeter of a Rectangle?Area = (length)(width)
Perimeter = 2(length + width).
Given the following:
Length of rectangle = 3x - 3
Width = 6
Area = (3x - 3)(6)
Area = 18x - 18 cm²
Perimeter = 2(3x - 3 + 6) = 2(3x + 3)
Perimeter = 6x + 6 cm
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the function f(x)=-x^2-x+15 is shown on the graph. what are donain and range of the function? t
Answers
Answer:
Domain: All real numbersRange: [tex]y \leq 61/4[/tex]Step-by-step explanation:
The domain is the set of x values.
The range is the set of y values.