Mathematics College
Answers
Answer 1
Given:
a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰.
To find:
The GCF of given terms.
Solution:
Greatest common factor (GCF): To find the GCF of two or more numbers, we need to find the product of their prime factor with their maximum powers.
The given terms are
[tex]a^{12}b^{4},a^{4}b^8, a^{24}b^{16}, a^{12}b^{20}[/tex]
Here, each term has two prime factors a and b. The highest power of a is 24 and the highest power of b is 20. So, the GCF of given terms is
[tex]GCF=a^{24}\times b^{20}[/tex]
[tex]GCF=a^{24}b^{20}[/tex]
Therefore, the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰ is a²⁴b²⁰.
Related Questions
Can some please help 17-19 please
Answers
Answer:
Step-by-step explanation:
17. 2(x+6) common factor is 2
18. 8(3+y-2w) common factor is 8
19. 2(7-4m)
Help pleaseee I need some assistance right now
Answers
Answer:
69°
Step-by-step explanation:
if CA and AT are congruentsides, this means that the angle of C and T must also be the same.
In order for a triangle to be a triangle, they must meet the angle of 180 degrees.
We know CAT is = to 42
So we subtract 42 from 180 = 138 degrees
we then divide 138 by 2 and we get 69
angles c + t are both 69 degrees
Answer:
69°
Step-by-step explanation:
The measure of angle A is given as 42 and the sum of interior angles in a triangle is equal to 180° we subtract 42 from 180 and divide the result with 2 because this is an Isosceles triangle since |AC| = |AT| m<C = m<T
(180 - 42) ÷ 2 = 69°
Please help for number 8 I don't understand.
Answers
Answer:
8a. x = 16√3
8b. y = 8√3
Step-by-step explanation:
8a. Determination of the value of x
Adjacent = 24
Hypothenus = x
Angle θ = 30°
The value of x can be obtained by using cosine ratio as illustrated below:
Cos θ = Adjacent /Hypothenus
Cos 30 = 24 / x
√3/2 = 24/x
Cross multiply
x × √3 = 2× 24
x × √3 = 48
Divide both side by √3
x = 48/√3
Rationalise
x = 48/√3 × √3/√3
x = 48√3 / √3 × √3
x = 48√3 / 3
x = 16√3
8b. Determination of the value of y
Opposite = y
Adjacent = 24
Angle θ = 30°
The value of y can be obtained by using Tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 30 = y / 24
1 / √3 = y /24
Cross multiply
y × √3 = 1 × 24
y × √3 = 24
Divide both side by √3
y = 24 /√3
Rationalise
y = 24 /√3 × √3/√3
y = 24 ×√3 / √3 × √3
y = 24√3 / 3
y = 8√3
A major corporation is building a 4,325-acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Cove's population (in thousands) t years from now will be given by
(25t2 + 150t + 100)/(t2 + 6t + 24)
A) Find the rate at which Glen Cove's population is changing with respect to time.
B) What will be the population after 10 years?
C) At what rate will the population be increasing when t = 10?
Answers
Answer:
See explanation
Step-by-step explanation:
We have that;
P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)
a) rate at which Glen Cove's population is changing with respect to time.
dP/dt = (t^2 + 5t + 40) (50t + 125) - (25t^2 + 125t + 200) (2t + 5)/(t^2 + 5t + 40)^2
dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2
b) population after 10 years
P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)
P(t) =(25(10)^2 + 150(10) + 100)/((10^2 + 6(10) + 24)
P(t) = 4100/184
P(t) = 22283
c) when t = 10
dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2
dP/dt = 1000(10) + 3000/(10^2 + 6(10) + 24)^2
dP/dt = 13000/33856
dP/dt = 0.384
Y really help in this problem !
I will give you 40 points
Answers
Answer:
160
Step-by-step explanation:
The point
P
is on the unit circle. If the y-coordinate of
P
is
−
3
5
, and
P
is in quadrant IV , then
Answers
If the y-coordinate of P is −3/5, and P is in quadrant IV, then x = 4/5
How to find the coordinate of a unit circle?
In Trigonometry, the unit circle is a special circle that is centered on the origin of a coordinate grid, with a radius equal to 1 unit.
Now, we are told that the point P is on the unit circle and also we know that the length of the line from P to the origin is exactly 1 unit.
We're also given a y-coordinate as, y = -3/5.
The y-coordinate denotes the length of a perpendicular line from point P to the x-axis.
If x is the x-coordinate, y is the y-coordinate, and h is the hypotenuse length, we can set up the equation vis Pythagoras theorem as:
x² + y² = h²
Making x the subject gives;
x = √(h² – y²)
Plug in the relevant values h = 1 and y = -3/5 to get;
x = √(1)² – (-3/5)²
x = √1 – 9/25
x = √16/25
x = 4/5
We are told that P is in quadrant IV, which has negative values for both y and positive values for x and as such x is positive.
Thus, x = 4/5
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Solve the equation. Leave your answer as an improper fraction. Check your solution: -1/2=-5/18=h
Answers
Answer:
cant answer with two equal signs
Step-by-step explanation:
but if u mean
-1/2=-5/18+h that equals h=-2/9
and if u mean
-1/2+-5/8=h it equals h= -7/9
2 points
4. In 2016, a school started its own aquarium with x fish. In 2019, there
were x^2 fish in the same aquarium. There were 144 fish in 2019. How
many fish were there in 2016? Show your work *
Answers
Answer:
171 fish
Step-by-step explanation:
512/3=170.667 (keeps going on but I just rounded it to add 1 to the total of 170) so that is why 171 is the answer.
The amount Cami raised during last year’s charity walk, $45.50, is StartFraction 7 over 10 EndFraction of the amount she raised this year. Which equation represents n, the number of dollars she raised this year?
45.50 (StartFraction 7 over 10 EndFraction) = n
45.50 = 0.7 n
45.50 + n = StartFraction 7 over 10 EndFraction
45.50 = 0.7 + n
Answers
Answer:
45.50 (StartFraction 7 over 10 EndFraction) = n
Answer:
the correct answer on edge is B. 45.50=0.7n
Step-by-step explanation:
a gumball machine gives you no gum if you insert 5c, 5 gumballs if you insert 10c , 10 gumballs if you insert 15c and 15 gumballs if you insert 20c. how many gumballs could you expect to receive if you insert 35c?
Answers
Answer:
30
Step-by-step explanation:
create a function where x is the money you insert in cents and y is the amount of gumballs you get.
y = x - 5 (meaning you get five less gumballs than the amount of cents you insert)
Therefore, when x = 35:
y = 35 - 5 = 30.
You will get 30 gumballs.
Can anyone help explain this my daughter is 7 does not understand it
Answers
it’s basically addition. in the first square , you put the number that adds with 426 to make 726. the second square you add 10 to the 726 and put the answer there. third square you put the number that adds with the answer in the second square to equal 741.
PLS HELP I WILL BRAINLIEST 15 PTS
An ice cream truck sells ice cream between 2 p.m. and 10 p.m. each night in the summer. At the end of the night, the driver calculates his profits and makes a graph to analyze the data. What is the average rate of change for the data from the 2nd hour to the 6th hour? Be sure to include the correct units of measurement.
a scatter plot with x axis labeled Hour and y axis labeled Money Earned in Dollars per Hour with points at 1 comma 54 and 2 comma 58 and 3 comma 64 and 4 comma 78 and 5 comma 96 and 6 comma 126 and 7 comma 99 and 8 comma 75
17 hours
68 dollars
17 dollars per hour per hour
68 dollars per hour per hour
Answers
Answer:
17
Step-by-step explanation:
A slope is also known as the gradient of a line. The correct option is C, 17 dollars per hour.
What is Slope?
A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
The average rate of change for the data from the 2nd hour to the 6th hour is,
Average rate = ($126 - $58)/(6 hour - 2 hour)
= 68/4 dollar per hour
= 17 dollars per hour
Hence, The average rate of change for the data from the 2nd hour to the 6th hour is 17 dollars per hour.
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How many liters of an 18% alcohol solution must be added to a 10% alcohol solution to get 20L of a 15% alcohol solution
Answers
Answer:
Let x= liters of 18% solution to be added to a 10% solution.
20-x= liters of 10% solution to be mixed with 18% solution.
..
18%(x)+10%(20-x)=15%(20)
.18x+2-.1x=3
..08x=1
x=1/.08=12.5
ans:
12.5 liters of an 18% alcohol solution must be added to a 10% alcohol solution to get 20 L of a 15% acohol solution.
I hope it's helpful!
William receives a weekly allowance according to the following formula: For each day that he remembers to do his chores, he eams 51.50, and for each day that he doesn't remember to do his chores, he loses
50.25. What amount of allowance would William receive for a week in which he remembers to do his chores on five days and forgets to do them on two days?
Answers
answer = 150.75
50.25 * 5 = 251.25
50.25 * 2= 100.5
251.25-100.5= 150.75
On average, Haley is able to read 4 5/6 Chapters in the her book each week . How many weeks will it take Haley to read 9 2/3 Chapters
Answers
Answer:
2 weeks
Step-by-step explanation:
y = mx + b
y = total number of chapters read = [tex]9\frac{2}{3}[/tex]
m = number of chapters read per week = [tex]4\frac{5}{6}[/tex]
x = number of weeks = what we're solving for
b is not needed to find this solution
[tex]9\frac{2}{3}[/tex] = [tex]4\frac{5}{6}[/tex] x divide [tex]4\frac{5}{6}[/tex] from both sides
x = 2 weeks
Find the degree measure of the indicated angle.
?
40°
80°
Answers
Answer:
60
because you need to add the number to get 180 so I would be 80+20 = 120+60=180 I hope it helps!
The graph below represents a recent 10 meter race between two remote control cars.
A graph titled Remote Control Car Race has seconds after race start on the x-axis and distance from start line (meters) on the y-axis. A line labeled red car goes through (3, 2) and (6, 4). A line labeled blue car goes through (3, 0) and (5, 2).
Which statements about the race are true? Check all that apply.
The red car won the race because it started above the blue car.
The cars crashed at 9 seconds into the race because that is the point of intersection, and neither car continued on after that point in time.
The blue car passed the red car at 6 m into the race because that is the point of intersection, and the blue car has a greater distance than the red car after that time.
The blue car is faster because the slope of its line is steeper than the slope of the line representiong the red car.
The blue car started 3 seconds late because it has an x-intercept of (3, 0) and x represents the time and y represents the distance from the starting line.
Answers
Answer:
options c d e
Step-by-step explanation:
Answer:
C D E
Step-by-step explanation:
Need it ASAP no rocky
Answers
Answer:
Value of x = 19.42 unit (Approx)
Step-by-step explanation:
Given:
Base = 6 unit
Angle θ = 72°
Find:
Value of x
Computation:
Cos θ = base / Hypotenuse
Cos 72° = 6 / x
0.3090 = 6 / x
x = 19.4174
Value of x = 19.42 unit (Approx)
show the working pls :))
Answers
Answer:
$ 78.68
Step-by-step explanation:
The following data were obtained from the question:
Pay >>>>>>>>>> Frequency
40 – 59 >>>>>> 15
60 – 79 >>>>>> 58
80 – 99 >>>>>> 27
100 – 119 >>>>> 22
Mean pay =?
Next, we shall determine the class pay. This can be obtained by adding the pay together and dividing by 2 as shown below:
L => is the lower pay interval
U => is the upper pay interval
Pay >>>>>>>>>> Class pay [(L+U)/2)]
40 – 59 >>>>>> 49.5
60 – 79 >>>>>> 69.5
80 – 99 >>>>>> 89.5
100 – 119 >>>>> 109.5
Thus, the table becomes
Pay >>>>>> Class pay >> Frequency
40 – 59 >> 49.5 >>>>>>> 15
60 – 79 >> 69.5 >>>>>>> 58
80 – 99 >> 89.5 >>>>>>> 27
100 – 119 > 109.5 >>>>>> 22
The mean pay can be obtained as follow:
Summation of class pay and frequency (ΣCF) = (49.5×15) + (69.5×58) + (89.5×27) + (109.5×22)
= 742.5 + 4031 + 2416.5 + 2409
= 9599
Summation of frequency (ΣF) = 15 + 58 + 27 + 22
= 122
Mean pay = ΣCF / ΣF
ΣCF = 9599
ΣF = 122
Mean pay = 9599 / 122
Mean pay = $ 78.68
Therefore, the mean pay is $ 78.68
Solve 3 - x=-9
a. x=16
b.x=12
c.x=-6
d.x=12
Answers
Answer:
3 - x =-9
3+ 9 =x
x = 12
so, correct answer
x =12
Oh gosh lol lol did it say hi
is 1.150 and 1.15 the same? (ANSWER QUICKLY)
Answers
Yes because the 0 at the end is just a place holder basically so 1.150 and 1.15 are the same
Explain how you can tell whether a group of ratios represents a proportional relationship
Answers
Answer:
Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional
Step-by-step explanation:
thx for the free points gl
A large discount store wants to determine the average yearly income of its shoppers. A researcher chooses 100 shoppers at random between 1:00 p.m. and 5:00 p.m. on a Saturday to survey. Identify the population.
A. All shoppers at the discount store between 1:00 p.m. and 5:00 p.m. on this particular Saturday.
B. The 100 surveyed shoppers at the discount store between 1:00 p.m. and 5:00 p.m. on this particular Saturday.
C. All shoppers at the discount store on this particular Saturday.
D. All shoppers at the discount store during a year's time.
E. None of the above.
Answers
Answer:
The population is:
D. All shoppers at the discount store during a year's time.
Step-by-step explanation:
Since the discount store wants to determine the average yearly income of its shoppers, the population of interest here is all the shoppers that visit the discount store during a year's time. The population includes all the individual shoppers. However, this number may be too difficult to obtain and work on their data. This is the researcher can choose a sample, calculating its statistics to approximate the population parameters.
Subtract. −5−(−9)−3
−17
−7
1
I don't know.
Answers
Answer:
-87
Step-by-step explanation:
Answer:
-87
Step-by-step explanation:
Because of the commutative property of multiplication, it is true that
3/4
×
4
=
4
×
3/4
. However, these expressions can be calculated in different ways even though the solutions will be the same.
Below, show two different ways of solving this problem.
First, show how
3/4*4
can be solved using repeated addition.
Answers
¾ + ¾ + ¾ + ¾ = (3+3+3+3)/4 = 12/4 = 3
¾ × 4 = (3 × 4)/4 = 12/4 = 3
In the equation -3x - 9.6 = 20, what is the coefficient?
A. 20
B. -9.6
C. -3
D. -3x
Answers
Answer:
x=-3
Step-by-step explanation:
I need help with this ion understand it
Answers
Answer:
c. 30
Step-by-step explanation:
Reference angle = [tex] /theta [/tex] = ?
Hypotenuse = 23
Adjacent side = 20
Thus, applying CAH:
[tex] Cos(/theta) = \frac{adj}{hyp} [/tex]
[tex] Cos(/theta) = \frac{20}{23} [/tex]
[tex] /theta = cos^{-1}(\frac{20}{23}) [/tex]
[tex] /theta = 29.5918458 [/tex] ≈ 30° (nearest degree)
Suppose that f (x) = 1.5x2 for -1 < x < 1 and f (x) = 0 otherwise. Determine the following probabilities.
a. P(0 < X)
b. P(0.5 < X)
c. P(-0.5 = X = 0.5)
d. P(X<-2)
e. P(X < 0 or X>-0.5)
f. Determine x such that P(x < X) = 0.05.
Answers
Answer:
a) P(0 < X) = 0.5
b) P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5) = 0.125
d) P(X< -2) = 0
e) P(X < 0 or X>-0.5) = 1
f) value of x is -0.9654
Step-by-step explanation:
Given that;
f(x) = 1.5x²
Now. the probabilities would be the integral of the given function from (-1 to 1)
a) P(0 < X)
P(X > 0)
⇒ Integral from 0 to 1 of f(x)
= (1/2)x³
= 1/2 - 0
= 0.5
Therefore; P(0 < X) = 0.5
b) P(0.5 < X)
P(X > 0.5)
this will also be done in the same way except that, the limits changes to { 0.5 to 1]
= (1)³/2 - (0.5)³ /2
= 0.4375
Therefore; P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5)
The limits become [-0.5 , 0.5]
= (0.5)³/2 - (-0.5)³/2
= 0.125
Therefore; P(-0.5 = X = 0.5) = 0.125
d) P(X<-2)
since value of f(x) = 0 in that region
Therefore P(X< -2) = 0
e) P(X < 0 or X>-0.5)
= P(X < 0) + P(X > -0.5) - P( -0.5 < X < 0 )
= 0.5 + 0.5625 - 0.0625
= 1
Therefore; P(X < 0 or X>-0.5) = 1
f) Determine x such that P(x < X) = 0.05.
Let the value be 'a'
Then, integral from -1 to a will = 0.05
a³ - (-1)³ = 0.05 × 2
a³ + 1 = 0.10
a³ = 0.10 - 1
a³ = -0.9
a = ∛-0.9
a = -0.9654
Therefore, value of x is -0.9654
a) P(0 < X) = 0.5
b) P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5) = 0.125
d) P(X< -2) = 0
e) P(X < 0 or X>-0.5) = 1
f) value of x is -0.9654
Determine the following probabilities:
a) P(0 < X)
P(X > 0)
⇒ Integral from 0 to 1 of f(x)
[tex]= (1\div 2)x^3\\\\= 1\div2 - 0[/tex]
= 0.5
So; P(0 < X) = 0.5
b) P(0.5 < X)
P(X > 0.5)
Now
[tex]= (1)^3\div 2 - (0.5)^3 \div2[/tex]
= 0.4375
Therefore; P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5)
The limits become [-0.5 , 0.5]
[tex]= (0.5)^3\div 2 - (-0.5)^3\div 2[/tex]
= 0.125
Therefore; P(-0.5 = X = 0.5) = 0.125
d) P(X<-2)
since value of f(x) = 0 in that region
Therefore P(X< -2) = 0
e) P(X < 0 or X>-0.5)
= P(X < 0) + P(X > -0.5) - P( -0.5 < X < 0 )
= 0.5 + 0.5625 - 0.0625
= 1
Therefore; P(X < 0 or X>-0.5) = 1
f) Determine x such that P(x < X) = 0.05.
Let us assume the value be 'a'
So, integral from -1 to a will = 0.05
[tex]a^3 - (-1)^3 = 0.05 \times 2\\\\a^3 + 1 = 0.10\\\\a^3 = 0.10 - 1\\\\a^3 = -0.9\\\\a = \sqrt[3]{-0.9}[/tex]
a = -0.9654
Therefore, the value of x is -0.9654
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A scientist changes the temperature of a solution at a rate of
-6°C per minute. How many minutes will it take for the solution's
temperature to change from 0°C to -54°C?
A 9 min
B 324 min
C 60 min
D 48 min
Answers
Answer: A 9 min
Step-by-step explanation: 54/6=9
(9)
-6-6-6-6-6-6-6-6-6=-54
Lorrie bought 3 1/2 yards of ribbon. She had 2 feet 6 inches of ribbon left after trimming a banner. How many inches of ribbon did Lorrie use for the banner?
Answers
Answer:
7 ft 11 inches
Step-by-step explanation:
Convert 3 1/2 yards into 10 ft 5 inches.
Subtract 2 ft 6 inches from 10 ft 5 inches.
Lorrie used 88 inches of ribbon for the banner.
What are Arithmetic operations?
Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operation is called the arithmetic operator.
We have been given that Lorrie bought 3 1/2 yards of ribbon. She had 2 feet 6 inches of ribbon left after trimming a banner.
We have to determine the number of inches of ribbon did Lorrie use for the banner.
Here the quantity of ribbon bought by Lorrie = 3 1/2 yard = 3.5 yard
The quantity of ribbon she has left.
⇒ 2 ft 6 inches
⇒ 2×12 + 6
∵ 1 feet = 12 inches
⇒ 30 inches
Since we know that 1 yard = 36 inch
So 3.5 yard = 36×3.5 inches = 126 inches
The quantity of ribbon which is trimmed :
⇒ 126 - 30 = 88 inches
Therefore, Lorrie used 88 inches of ribbon for the banner.
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