The greatest common factor of the monomials 25x^5 and 20x^6 is 5x^5.
To find the greatest common factor (GCF) of the monomials 25x^5 and 20x^6, we first break down each monomial into its prime factors and include the variables.
25x^5 = 5 × 5 × x × x × x × x × x
20x^6 = 2 × 2 × 5 × x × x × x × x × x × x
Next, we find the common factors between the two:
The common prime number is 5.
The common variable factor is x raised to the minimum power between the two terms, which is x^5 (since x^5 is the lower power compared to x^6).
Therefore, the greatest common factor is 5x^5.
Which of these terms does not describe polygon A'B'C'D ?
A) rotation
B) image
C) preimage
D) transformation
Answer:
Hence, Option: C is correct.
The term that does not describe polygon A'B'C'D' is:
Pre-image.
Step-by-step explanation:
Clearly we could observe that the polygon A'B'C'D' is the image that is obtained by the applying some transformation to the polygon ABCD.
The transformation that is applied to ABCD to obtain A'B'C'D' is:
Rotating the figure anticlockwise 90° and then translating it 7 units to the left and 1 unit downward.
Hence, Polygon A'B'C'D' is not a pre-image.
Since it is an image which is formed or obtained by applying required transformation to the pre-image ABCD.
The correct option is C) preimage. Polygon [tex]\(A'B'C'D'\)[/tex] is the image of the transformation, not the preimage.
To determine which term does not describe polygon [tex]\(A'B'C'D'\)[/tex], we need to understand the definitions of each term in the context of transformations in geometry:
Rotation : This is a type of transformation that turns a figure around a fixed point at a certain angle. Polygon [tex]\(A'B'C'D'\)[/tex] could be a result of rotating polygon [tex]\(ABCD\)[/tex]
Image : The image is the result of applying a transformation to a figure. [tex]A'B'C'D'\)[/tex] is the image of [tex]\(ABCD\)[/tex] after some transformation.
Preimage : The preimage is the original figure before a transformation is applied. In this context, [tex]\(ABCD\)[/tex] is the preimage, not [tex]\(A'B'C'D'\)[/tex]
Transformation : This is a general term that refers to any operation that moves or changes a figure in some way to produce a new figure. The process that produced [tex]\(A'B'C'D'\)[/tex] from [tex]\(ABCD\)[/tex] is a transformation.
From these definitions, the term that does not describe polygon [tex]\(A'B'C'D'\)[/tex] is preimage.
5 1/3 * (-3 9/18) Simplify and Show your work
The scale factor of the blueprint of a gymnasium to the actual gymnasium is 1in/15ft. The area of the flow on the blueprint is 114in2.
What is the area of the actual gymnasium?
B) 25, 650 ft^2
If the ratio is 1:15, then the measurements of each side of the actual gym are 15 times greater than the scale's. So the areas would have a ratio of 1:225. 114 times 225 is equal to 25, 650
Dakota has $5.38 in her savings a count. Each week she adds $2.93. How much money does Dakota have after 5 weeks? After N weeks?
What is 7.5 as a fraction ?
Trent is 25 years old and works for a company that matches his 401(k) contribution up to 5%. The interest rate for his 401(k) is 7.3%. If he puts away 10% of his $32,000 salary every year, how much would he have saved in 10 years? Round your answer to the nearest cent.
Answer:
The answer is : $67,266.16
Step-by-step explanation:
This question is a future value question.
As given, Trent puts away 10% of his $32,000 every year and the company will put half amount of $1,600. So, total amount becomes =[tex]3200+1600=4800[/tex] each year.
Formula for future value or FV is Fv = Pmt (1 + r/n)^(nt) – 1 / (r/n)
Where, Fv = Future Value , Pmt = repeated payments , R = interest rate ,N = total number of payment periods
Putting the values in the formula,
Fv = 4800 (1 + 0.073/1)^(1x10) – 1 (0.073/1)
Fv = $67266.16
Hence, the answer is $67266.16
The amount saved in 10 years is [tex]\boxed{\$ 67266.20}.[/tex]
Further Explanation:
Annuity is a series of payment that is made after equal interval of time.
Future value of annuity of payment P for n year if the return is i can be expressed as,
[tex]\boxed{{\text{Future Value}} = {\text{P}} \times \frac{{{{\left( {1 + \frac{i}{n}} \right)}^{nt}}}}{{\frac{i}{n}}}}[/tex]
Given:
Total salary is [tex]\$ 32000.[/tex]
The interest rate is [tex]7.3\%.[/tex]
Trent save [tex]10\%[/tex] of his salary every year.
Company puts [tex]5\%[/tex] of salary every year.
Calculation:
The [tex]10\%[/tex] of [tex]\$32000[/tex] can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}}&= \frac{{10}}{{100}} \times 32000\\&= \$ 3200\\\end{aligned}[/tex]
The amount that company put can be obtained as follows,
[tex]\begin{aligned}{\text{Company Amount}} &= \frac{5}{{100}} \times 32000\\&= \$ 1600\\\end{aligned}[/tex]
The total amount can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}} &= 3200 + 1600\\&= \$ 4800\\\end{aligned}[/tex]
The future value can be obtained as follows,
[tex]\begin{aligned}{\text{FV}} &= 4800 \times \frac{{{{\left( {1 + 0.073} \right)}^{10}} - 1}}{{0.073}} \\ &= 4800 \times 14.014\\&= \$ 67266.20\\\end{aligned}[/tex]
Hence, the amount saved in 10 years is [tex]\boxed{\$ 67266.20}.[/tex]
Learn more:
Learn more about inverse of the function https://brainly.com/question/1632445 Learn more about range and domain of the function https://brainly.com/question/3412497 Learn more about profit and loss https://brainly.com/question/2479097
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Investment and return
Keywords: Trent, 25 years old, works, company, matches, 401(k), 7.3%, 10%. $32000, salary, every year, 10 years, amount, 5%, nearest cent.
What is 1.2 divided by 9?
Use trigonometric substitution to write the algebraic expression as a trigonometric function of θ, where 0 < θ <π/2.
√(100) - 4x^(2), x = 5cos(θ)
Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 212212 h. Train B reaches station B after 4 h. Station A and B are 585 mi apart.
What is the rate of the trains?
Answer:
90 mph
Step-by-step explanation:
Let speed of both train=x mph
Time taken by train A to reach station A=[tex]2\frac{1}{2}[/tex] hr=\frac{5]{2} h[/tex]
Time taken by train B to reach station B=4 h
Distance between two trains=585 miles
We know that
Distance=[tex] speed\times time[/tex]
Distance covered by train A=[tex]\frac{5}{2} x[/tex]
Distance covered by train B=[tex]4x[/tex]
When two trains travel in opposite direction then total distance
[tex]\frac{5}{2}x+4x=585[/tex]
[tex]\frac{5x+8x}{2}=585[/tex]
[tex]\frac{13}{2}x=585[/tex]
[tex]x=585\times \frac{2}{13}=90 mph[/tex]
Hence, the rate of both trains=90 mph
For the following pair of lines, identify the system by type.
A) consistent
B) equivalent
C) inconsistent
Answer:
Option (c) is correct.
The system is Inconsistent.
Step-by-step explanation:
Given : A pair of lines.
We have to identify the system by type.
Consider the given system of pairs of lines.
Since, the graph shows two parallel lines.
1) Consistent : A system of linear equation is said to be consistent if the graph of equation either intersect at a single point or two lines overlap each other.
that is a unique solution or infinite many solution.
2) equivalent : When two system of equations have same solution then the two system are said to be equivalent.
3) Inconsistent : A system of linear equation is said to be inconsistent if the graph of equation are parallel to each other.
Thus, the given graph shows parallel lines,
Hence, The system is Inconsistent
How many feet are in 30 yards?
__ ft
Write the point-slope form of the equation of the line that passes through the point (1, 3) and has a slope of 2. Include your work in your final answer
Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle? The triangle is acute because 22 + 52 > 42. The triangle is acute because 2 + 4 > 5. The triangle is not acute because 22 + 42 < 52. The triangle is not acute because 22 < 42 + 52.
Let
[tex]a=2\ in\\b=4\ in\\c=5\ in[/tex]
we know that
If [tex]c^{2} =a^{2}+b^{2}[/tex] -----> is a right triangle
If [tex]c^{2} > a^{2}+b^{2}[/tex] -----> is an obtuse triangle
If [tex]c^{2} < a^{2}+b^{2}[/tex] -----> is an acute triangle
so
substitute the values
[tex]5^{2} > 2^{2}+4^{2}[/tex] ------> is an obtuse triangle
therefore
the answer is
The triangle is not acute because [tex] 2^{2}+4^{2}< 5^{2}[/tex]
Answer: The correct option is
(C) The triangle is not acute because 2² + 4² < 5².
Step-by-step explanation: We are to select the statement that best explains the type of the triangle having lengths of three sides as 2 inch, 5 inch and 4 inch.
We know that a triangle with side lengths a, b and c (c > a, b)is
(i) an acute-angled if a² + b² > c², and
(ii) an obtuse-angled if a² + b² < c².
For the given triangle,
a = 2 inch, b = 4 inch and c = 5 inch.
So, we have
[tex]a^2+b^2=2^2+4^2=4+16=20,\\\\c^2=5^2=25.[/tex]
Since,
[tex]20<25\\\\\Rightarrow a^2+b^2<c^2,[/tex]
so the given triangle is not acute, but obtuse.
Thus, the triangle is not acute because 2² + 4² < 5².
Option (C) is correct.
Find the missing coefficient in the equation of the line that passes through the given point. ...?
The sum of nine times a number and fifteen is less than or equal to the sum of twenty-four and ten times the number
On a map the length of a river is 4.75 in. The actual length is 247mi. What's the scale of the map?
Polar coordinates of a point are given. Find the rectangular coordinates of the point. (2.1 ; 2pi/9)
A. (-1.6, -1.3)
B. (1.6, 1.3)
C. (1.3, 1.6)
D. (-1.3, -1.6)
What is the length of a picture frame whose width is 3 inches and whose proportions are the same as a 9-inch wide by 15-inch long picture frame?
A = a+b+c / 3
Solve for b.
A.) 3A - a - c = b
B.) -c / 3 = b
C.) A - c / 3 = b
C.) -3 - c = b ...?
To solve for b in the equation A = (a + b + c) / 3, multiply both sides by 3 and then subtract a and c from both sides. The correct answer is A) 3A - a - c = b.
Explanation:To solve for b in the equation A = (a + b + c) / 3, you need to isolate the variable b.
First, multiply both sides of the equation by 3 to eliminate the denominator:
3A = a + b + c
Then, subtract a and c from both sides to get b by itself:
3A - a - c = b
So, the correct answer is:
A) 3A - a - c = b
The table below shows the distance d(t) in feet that an object travels in t seconds.
t d(t)
(second) (feet)
1 15
2 60
3 135
4 240
What is the average rate of change of d(t) between 2 seconds and 4 seconds and what does it represent?
A) 50 m/s; it represents the average speed of the object between 2 seconds and 4 seconds
B) 90 m/s; it represents the average speed of the object between 2 seconds and 4 seconds
C) 90 m/s; it represents the average distance traveled by the object between 2 seconds and 4 seconds
D) 50 m/s; it represents the average distance traveled by the object between 2 seconds
Answer:
Option B is correct
The average rate of change of d(t) between 2 second and 4 second is; 90 ft/s
and it represents the average speed of the object between 2 seconds and 4 seconds.
Step-by-step explanation:
Average rate of change of function is defined as the ratio of the difference in the function f(x) as it changes from a to b to the difference between a and b. Then, the average rate of change is denoted as A(x).
[tex]A(x) =\frac{f(b)-f(a)}{b-a}[/tex]
As per the given statement, the distance d(t) is in feet and t is the time in second.
To find the average rate of change of d(t) between 2 seconds and 4 seconds.
From the table we have;
at t = 2 , d(2) = 60
and
at t =4 , d(4) = 240.
Then, by the definition of average rate of change ;
[tex]A(t) = \frac{d(4)-d(2)}{4-2}[/tex] = [tex]\frac{240-60}{4-2} =\frac{180}{2}[/tex]
Simplify:
[tex]A(t) = 90 ft/s[/tex]
therefore, the average rate of change of d(t) between 2 second and 4 second is; 90 ft/s and it represents the average speed of the object between 2 seconds and 4 seconds.
Carlon plans to evaporate a number of gallons of water from 90 gallons of a 15% salt solution to make a 25% salt solution. Which equation can he use to find x, the number of gallons that should be evaporated?
the options are
1. 13.5/90-x = 25/100
2. 13.5/x =25/100
3. 13.5(90-x) = 0.25
4. 13.5(90-x) = 25
A
first option is correct
Patrick hit his neighbor's car while backing his vehicle out and caused $700 worth of damage. The insurance company paid for $300 of the damage while Patrick had to pay the remaining $400. The amount Patrick paid was his _____.
The distance between two cities is one hundred miles, and a woman drives from one city to the other at a rate of fifty mph. At what rate must she return if the total travel time is three hours and forty minutes?
well in her first travel (when she goes to the anther city)
v1= 50mph
d1=100 m
t1=?
t=d/v=100/50=2h
that's meat that she will take 2hours during the first travel
and total travel time = 3h
she wants to take only 1 h in her second travel
v2=?
d2=100 m
t2= 1h
v2= d2 *t2 =100mph
total travel time is 3 hours and 40 minutes so i belive the correct answer is 60mph
____ two points are collinear.
A. Any
B. Sometimes
C. No
Isabel earned 350 points wile she was playingblastibg robot.isaabels mom earned 3 times as many then isabel. how many points did isabels mom earn
At the bank, brent exchanges $50 in bills for 50 one-dollar coins. the total mass of the coins is 405 grams. estimate the mass of 1 one- dollar coins
What is the total interest on a 10 year 6.1% loan with a principle of 32,000
F = 32,000 (1+ 0.061*10)
F = 51,520
That makes the total interest equal 51,520 -32,000 = 19, 520.
What are the x-intercept and y-intercept of the graph of
y=1/3 x−6
x:
Y:
if a rubik's cube has a volume of 384 cubic centimeters, how long is one side of the cube? (recall that the volume of a cube is calculated by L3, where L is the length of one side.
To determine the side length of a Rubik's cube with a volume of 384 cubic centimeters, take the cube root of 384 to find that each side is approximately 7.24 centimeters long.
To find the length of one side of a cube when given the volume, you can use the formula for the volume of a cube, which is V = L³, where V is the volume and L is the length of a side of the cube.
In this case, the volume is 384 cubic centimeters, so we need to find the cube root of 384 to find the length of one side.
The calculation is as follows:
L³ = 384 cm³L = ∛384 cm³L ≈ 7.24 cmTherefore, each side of the Rubik's cube is approximately 7.24 centimeters long.
What is 20% of 300 EXPLAIN ...?