Answer: Choice D)
{(1, 4), (2, 3), (3, 2), (4, 1)}
========================================================
Explanation:
Let's go through the answer choices one at a time to see what is a function and what isn't.
A) This is not a function because x = 3 repeats itself. In other words, the input x = 3 leads to multiple outputs (y = 3 and y = 2 simultaneously). A function is only possible if any x input leads to exactly one y output. B) This isn't a function either for similar reasoning as choice A. This time x = 2 repeats itself.C) Same idea as the others. We don't have a function because x = 1 repeats itself.D) Each x input is only listed once, so we don't have any x repeats. Therefore, relation D is a function.In short, choices A,B,C are not functions because they have a repeated x coordinate; in contrast, choice D doesn't have any repeated x values so it is a function.
Side note: The y values are allowed to repeat themselves, but the function won't be one-to-one.
The quadratic function g(x)=ax^2+bx+c has the complex roots (10+i) and (10-i). You may assume that a=1.
What is the value of b?
What is the value of c?
The values are [tex]b=-20\text{ and }c=101[/tex]
The quadratic function, expressed in factored form is
[tex](x-(10+i))(x-(10-i))=g(x)[/tex]
Expanding and simplifying
[tex]g(x)=(x-(10+i))(x-(10-i))\\=x^2-x(10-i)-x(10+i)+(10+i)(10-i)\\=x^2-10x+xi-10x-xi+100-i^2\\=x^2-10x-10x+100+1\\=x^2-20x+101[/tex]
since
[tex]g(x)=ax^2+bx+c=x^2-20x+101[/tex]
we can equate coefficients of like-terms and conclude that
[tex]a=1,b=-20,c=101[/tex]
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Which equation is NOT a linear? function
Answer:
A
Step-by-step explanation:
Because the x-intercept is zero and if you want to show it on a graph it is a quadratic function.
Name two transformations that result in Figure ABCD being transformed back onto itself.
Answer:
(b) rotate 180°, then reflect across x and y axes
Step-by-step explanation:
A rotation of 180° cannot be "undone" by translation, or by reflection across the same line twice.
Reflection across the x- and y-axes, in either order, is equivalent to a rotation of 180° (or reflection across the origin). This pair of reflections will "undo" the rotation of 180°, putting the figure back in its original position
The transformation to map the figure to itself are ...
rotation 180°, reflection across the x-axis, reflection across the y-axis
a local factory has to add a liquid ingredient to make there product at a rate of 13 quarts every 5 minutes. how many gallons per hour of the ingredient do they need to add
Per hour, they would need to add 147 quarts of the liquid ingredient. When converting to gallons, every 4 quarts is one gallon, so we need to divide 147 by 4.
36.75 Gallons Per Hour
They need to add 39 gallons of ingredients to make the production they desire.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know 4 quarts are one gallon.
∴ They would be making (13/4) = 3.35 gallons every 5 minutes Or (3.25/5) = 0.65 gallons per minute.
∴ In an hour or 60 minutes, they would be making (0.65×6) = 39 gallons per hour.
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Two plus two equal four
Answer:
Two plus two equals sixxxxxxx
Dalia's family bought 5 adult tickets and 2 student tickets to the school play for $65. Shay's family bought
3 adult tickets and 6 student tickets for $69. How much does each type of ticket cost?
Answer:
Lets say a is adult tickets and s is student tickets. for dalias family its:
5a + 2s = 65
for shay
3a + 6s = 69
-15a -6s = -195
-15a = -195
Step-by-step explanation:
If 7 out of 25 students have a pet, what percent of the class has a pet?
Answer:
28%
Step-by-step explanation:
(25%-7%)×4
100%-28%
The distance between two cities is 180 km. The distance was
covered by a car at a rate of 50 km/h, by a bus at 45 km/h, by a
truck at 40 km/h, and a by a bicycle at 25 km/h. What is the constant of
variation?
Answer:
Step-by-step explanation:
he distance between two cities is 180 km.
Speed = distance/time
v = s/t from this we can calculate for time
Time = distance /speed
This distance was covered by a car at a rate of 50 km/h
Time taken by the car to cover this distance of 180km
= 180/50 = 3.6 hours
This distance was covered by a bus at 45 km/h
Time taken by the bus to cover this distance of 180km
= 180/45 = 4 hours
This distance was covered by a truck at 40 km/h
Time taken by the truck to cover this distance of 180km
= 180/40 = 4.5 hours
This distance was covered by a bicycle at 25 km/h
Time taken by the truck to cover this distance of 180km
= 180/25 = 7.2 hours
Therefore:
speed and time are directly proportional.
Speed, s is inversely proportional to time, t
xy = k (inverse variation) or y/x = k (direct variation), where k is the constant of variation
Introducing constant of variation, k
s = k/t
When s = 25, t = 7.2
25 = k/7.2
k = 7.2× 25 = 180
So
s = 180/k
Solve geometry perimeter
7.62
Step-by-step explanation:
Given that T is the centroid of △DEF and FT=12
The centroid of a triangle divides the median of the triangle into 1 : 2
The measure of FQ is 18, while the measure of TQ is 6
Because point T is the centroid, then we have the following ratio
[tex]\mathbf{TQ : FT =1 : 2}[/tex]
Where FT = 12.
Substitute 12 for FT in the above ratio
[tex]\mathbf{TQ : 12 =1 : 2}[/tex]
Express as fraction
[tex]\mathbf{\frac{TQ }{ 12} =\frac{1 }{ 2}}[/tex]
Multiply both sides by 12
[tex]\mathbf{TQ =\frac{1 }{ 2} \times 12}[/tex]
This gives
[tex]\mathbf{TQ =\frac{1 2}{ 2}}[/tex]
Divide 12 by 2
[tex]\mathbf{TQ =6}[/tex]
The measure of FQ is calculated using:
[tex]\mathbf{FQ = FT + TQ}[/tex]
Substitute 12 for FT, and 6 for TQ
[tex]\mathbf{FQ = 12 + 6}[/tex]
Add 12 and 6
[tex]\mathbf{FQ = 18}[/tex]
Hence, the measure of FQ is 18, while the measure of TQ is 6
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Owen is driving to a concert and needs to pay for parking. There is an automatic fee of $12 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $3 for every hour he had his car in the lot. How much total money would Owen have to pay for parking if he left his car in the lot for 5 hours? How much would Owen have to pay if he left his car in the lot for tt hours?
Answer:
27$
Step-by-step explanation:
I do not know what you mean by tt hours, but I can create an equation for the problem
Y=3x+12
Essentially, every X hours he spends in the lot you add 3$, but you start off with 12$. Please mark this brainliest or thank it.
Any help wit this ? Cause I’m kinda confused
Answer:
D. The hiker would climb up 46 meters
Step-by-step explanation:
It would make the negative cancel out and would make it 0. 0 is sea level
Answer:
D the hiker would climb up 46 meters.
Step-by-step explanation:
If the hiker is -46 meters from sea level, that means the hiker is 46 meters BELOW sea level. For them to return to sea level, they would have to increase their elevation 46 meters by going up 46 meters, to make it to sea level.
i have two Questions.
1. Find the unit rate of 90 miles/2 hours, in feet per second.
2.Find the unit rate of 120 miles in 8 hours, in feet per second.
(extra credit: Extra Credit: How many unique handshakes can be made between 5 people?)
Step-by-step explanation:
ww have that 90 miles /2 hours is given and we are asked to find it in feet per second.
[tex] \frac{90 \: mi}{2 \: hrs} \times \frac{5280 \: ft}{1 \: mi} \times \frac{1 \: hr}{60 \: min} \times \frac{1 \: min}{60 \: sec} = 66[/tex]
So we get
66 fps.
2.
[tex] \frac{120 \: miles}{8 \: hours} \times \frac{5280}{1 \: mile} \times \frac{1 \: hour}{60 \: min} \times \frac{1 \: min}{60 \: seconds} = 22[/tex]
So we get 22 fps.
Extra credit There is 5 people and 2 hands so we use the combinations formula.
n!/r!(n-r)!. where n is the number of objects (the number of people) and r is the things taken at the time( the hands)
Subsitue
[tex] \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 3 \times 2 \times 1} [/tex]
[tex] \frac{20}{2} = 10[/tex]
What two numbers multiplied together makes -15 then you add them together to make 2
Answer:
-3 and 5
Step-by-step explanation:
-3*5=-15
-3+5=2
Answer:
-3 and 5
Step-by-step explanation:
-3×5 I'd -15
also -3+5 is 2
Joe had some money. He spent $200 on clothes, 2/5 of his remaining money on a pair of boots and saved the rest. He saved $126. How much money did Joe have at first?
Answer:
im sorry i dont get it
Step-by-step explanation:
HELP PLEASE!! ;-; !! TWO PART QUESTION!! 1) Consider the image. Are the two triangles congruent if a is congruent to d and b is congruent to e?
A) Yes, by the ASA postulate.
B) Yes, by the SAS postulate.
Yes, by the SSS postulate.
D) No, they are not congruent.
2) suppose that three corresponding angles are congruent for two triangles (AAA), why can’t congruence be proved between the two triangles?
A) the triangles could have the same shape but not the same size.
B) The triangles could have the same size but not the same shape.
C) with three equal angles, only the shortest side of the triangles can be congruent.
D)With three equal angles, only the longest side of the triangles can be congruent.
Answer:
A
Step-by-step explanation:
A
Ahem please some help please
[tex]4 \div 0.5[/tex]
Which of the following would be a correct first step to solve the equation, 5(y+12) = 25?
Answer:
divide both sides by 5
Step-by-step explanation:
y + 12 = 5
y = -7
What is x, the distance between points A and A'? 2. 4 units 4. 8 units 13. 6 units 14. 4 units.
The distance between points A (3, -5) and A' (2, -3) is 2.4 units.
Given that,
The points A (3, -5) and A' (2, -3).
We have to determine,
The distance between point A and A'.
According to the question,
The distance between two points is determined by using the distance formula.
[tex]\rm Distance \ formula = \sqrt{(x_2-x_2) ^2+ (y_2-y_2)^2[/tex]
Then,
The distance between points A (3, -5) and A' (2, -3) is,
[tex]\rm Distance = \sqrt{(2-3) ^2+ ((-3)-(-5))^2}\\\\ Distance = \sqrt{(-1) ^2+ (2)^2}\\\\ Distance = \sqrt{1+4}\\\\Distance = \sqrt{5}\\\\Distance = 2.4 \ units[/tex]
Hence, The distance between points A (3, -5) and A' (2, -3) is 2.4 units.
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Answer:
13.6 units
Step-by-step explanation:
Edge
whats the exact length of BC?
-..........The answer is b-
--------------------------------------------------------
(15)²= (9)²+(BC)²
225=81+(BC)²
BC=√144
BC=12
Answer:
B:12
Step-by-step explanation:
The length of BC is 12 because we can use the Pythagorean theorem to solve this. First, we know what the hypotenuse is 15 and the one of the side lengths which is 9. he equation to solve this is h^2-a^2 when h is 15 and a=9. So, we we plug in the info, we get 15^2-9^2 which is 15*15-9*9 which is 225-81 and that is 144. We are not done yet because we need to find the square root of 144 since we squared 15 and 9 in the first place. The √144 is 12 because 12*12 is 144. Now, we have to check! The equation is a^2+b^2=h^2 when a=12, b=9, and h=15! So, it will be 12^2+9^2=15^2 which simplifies to 144+81=225 and that is true!! So thats why it is B. Hope this helps!!!!!!
Plz mark me as brainliest
Lisa is getting paid 96$ per hour, her salary per hour increases by 12%, how much is she getting paid now after in increases by 12% ?
Answer:
96$/12×100
=8 × 100
=800$
Answer:
After the raise, I believe she is now getting paid 107.52$ per hour,
Step-by-step explanation:
12% of 96$ is 11.52$
11.52$ + 96$ = 107.52$
I am not sure if all calculations are correct, but I hope this helps! :)
Building For safety, the angle a wheelchair ramp makes with the horizontal should
be no more than 3.5º. What is the maximum height of a ramp of length 30 ft? What
distance along the ground would this ramp cover? Round to the nearest tenth of
a foot.
Answer: 8.6
Step-by-step explanation:
8.57142857143 --> 8.6
What is the answer step by step explanation please.
w (3w + 2) + 5w
Answer:8w^2+2
w(3w+2)+5w
First distribute the w to the parentheses:
3w^2+w
Add on the 5w to the new equation:
3w^2+2w+5w
Combine like terms:
8w^2+2
Challenge Question Sally's bank account balance was $50 on Monday. On Tuesday, she bought a new pair of shoes for $45. On Thursday evening she earned $25 babysitting her neighbor's children. On Friday she spent $42 on pizza for her friends. She earned $20 dollars on Saturday raking leaves. What is her bank account balance on Sunday? ?
Answer:
$8
Step-by-step explanation:
After the shoe purchase, her balance was $50 -45 = $5.
After depositing her babysitting earnings, her balance was $5+25 = $30.
After buying pizza, her balance was $30 -42 = -$12.
Assuming no overdraft charge, her balance after depositing her earnings was ...
-$12 +20 = $8
Sally's balance on Sunday was $8.
I’m very smart. My hair is dark. I love to eat honey, insects, and bark.
I don't understand the question your asking
A. Express the following in scientific notation 1.0.948901 2.11,000,000 3.0.08907
Answer:
answer should be c good luck
Find 6889 + 3088 + 9062.
1903
pls mark brainliest
if u want
Answer:
19039
Step-by-step explanation:
hope that help mark me brinilylist
you need to explain more
it was easy
What is solution for 7y+9+6y=46
Answer:
combine like terms
7y + 6y
13y + 9
Step-by-step explanation:
here is the solution
13y + 9
A piece of metal with a length of 2. 83 cm was measured using four different devices. Which of the following measurements is the most accurate? 2. 837 cm 2. 829 cm 2. 812 cm 2. 805 cm.
Answer:
2.829 mm
Step-by-step explanation:
Correct: 2.83 mm
Measured(mm) Difference (mm)
2.837 0.007
2.829 -0.001 Smallest deviation from actual.
2.812 -0.018
2.805 -0.025
The measurement of the piece of metal that is the most accurate is 2.837 cm.
Given that,A piece of metal with a length of 2.83 cm was measured using four different devices.
We have to determine,Which of the following measurements is the most accurate?
According to the question,A piece of metal with a length of 2.83 cm was measured using four different devices.
Accuracy is the degree to which the measured value is close to the correct value.
The difference between the accepted value and the measured value of the quantity is called the error of measurement.
The measurement for the first device is,
[tex]=2.83 - 2.837\\\\=-0.007[/tex]
The measurement of the first device is -0.007.
The measurement for the second device is,
[tex]=2.83 - 2.829\\\\=-0.001[/tex]
The measurement of the second device is -0.001.
The measurement for the third device is,
[tex]=2.83 - 2.812\\\\=-0.018[/tex]
The measurement of the third device is -0.018.
The measurement for the fourth device is,
[tex]=2.83 - 2.805\\\\=-0.025[/tex]
The measurement of the fourth device is -0.02.
Hence, The measurement that is the most accurate is 2.837 cm.
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The function P(t)=25,000(1.1023)t2 can be used to model the population in the town of Madison t years from now. Interpret the function in terms of the context for this situation.
Answer:
A growth function has the following form.
where = Original amount,
r = annual rate of change,
n = number of periods,
t = time in years
Since the time is in years, we need to convert t into days. We know that 1 year = 365 days. So t years = 365t days.
So in this case, n = 365, r = 0.0095.
Then the function is rewritten as follows.
The daily growth rate would be
Step-by-step explanation:
Lets find year wise population for example
let years be 3t=3[tex]\\ \sf{:}\longrightarrow P(3)=25,000(1.1023)3^2[/tex]
[tex]\\ \sf{:}\longrightarrow P(3)=27557.5(9)[/tex]
[tex]\\ \sf{:}\longrightarrow P(3)=248017.5[/tex]