Answer:
It is in its simplest form
Step-by-step explanation:
What is the greatest common factor of 20 and 65
Answer:
5
Step-by-step explanation:
Answer:I believe it would be 5
Step-by-step explanation:
because if you do it on a table chart you reach five first as the same number
Prove that for any natural n: a the number 7^(n+4) −7^n is divisible by 30.
For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.
What is mathematical induction?An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.
Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.
Let, n = 0.
Therefore,
7⁴ - 7⁰.
= 2401 - 1.
= 2400.
= 30×80, Divisible by 30.
Similarly for n = 1 we have,
7⁵ - 7¹.
= 16807 - 7.
= 16800.
= 30×560.
Hence by induction, the cycle will continue.
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d. Describe the relationship between the 9s in Ithaca's average annual rainfall?
Precipitation (inches), 2.08, 1.98, 2.64, 3.29; Snowfall (inches), 17.6, 14.2, 11.7, 3.4; The Ithaca Climate Page.
What is the relationship between the patterns in rainfall and temperature?Increased evaporation as a result of rising average temperatures at the Earth's surface leads to more precipitation overall. As a result, many places might expect more precipitation as a result of a hotter environment.Moving from the equator toward the poles results in less precipitation. Because temperature impacts how much moisture air can contain, precipitation often decreases with increasing latitude, with higher precipitation typically occurring at lower latitudes.There is a larger than 28% chance of rain on any given day during the wetter season, which lasts for 6.4 months from April 2 to October 14.June is the month in Ithaca with the most rainy days, with an average of 11.3 days with at least 0.04 inches of precipitation. From October 14 to April 2, the dry season lasts 5.6 months.Tho learn more about Ithaca climate refer to :
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carmela translates f (x) = x2 to create p (x). If p 9 (x) = f (x+3) -10 sketch the graph
The function p(x) = (x + 3)² is transformed 3 units left along the x-axis.
What are some rules of function transformations?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over the x-axis, (x, -y).
Given, A function f(x) = x².
Now, p(x) = f(x + 3).
p(x) = (x + 3)² and it is a transformed function to the parent function f(x).
Now, The function p(x) = (x + 3)² is transformed 3 units to the left along the x-axis.
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This system of equations has been placed in a matrix
y 650x+175
y=25,080-120x
Column 1 Col 2 Col 3
Row 1 : ___ -1 ___
Row 2 : 75 ___ ___
Answer: This system of equations can be represented in matrix form as
| -1 | 650 | 175 |
| 75 | -120 | -25080 |
This matrix is called the augmented matrix of the system of equations. The first and second column of this matrix represent the coefficients of the variables x and y, respectively, in the system of equations. The third column represents the constant terms of the equations.
You can use a method such as Gaussian elimination or Gauss-Jordan elimination to solve the system of equations.
The Gaussian elimination method, you would use elementary row operations to transform the matrix into an echelon form or reduced row echelon form. Then you can back-substitute the variables with their values.
Also, the Gaussian-Jordan elimination is similar to Gaussian elimination, but it keeps continuing the elimination process until the matrix becomes an Identity matrix(A matrix with 1 on diagonal and 0 everywhere else) The values on the diagonal of the matrix will give you the solution of the variables.
Step-by-step explanation:
The relative frequency table below displays the proportion of colors of cars for sale at a dealership.
What proportion of cars are yellow?
0.04
0.1
0.15
0.4
Proportion of cars which are yellow -
= 1 - (0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10)
= 1 - 0.96
= 0.04
Answer:
A) 0.04
Step-by-step explanation:
edge 2023
Rachel has 13 books and some empty boxes. She can put 4 books in each box. How many boxes can she fill completely?
How many books will be left over?
Answer:
she can fill 3 boxes completely and one book will be left over
Step-by-step explanation:
if a box can be filled with 4 book then we do 4 multiply 3 and then 12 books will can fill 3 box and there is 13 books so 1 book will be left over
find x
y=\frac{1}{4} x+3
Work Shown:
[tex]\text{y} = \frac{1}{4}\text{x}+3\\\\\text{y}-3 = \frac{1}{4}\text{x}\\\\\frac{1}{4}\text{x}=\text{y}-3\\\\\text{x}=4(\text{y}-3)\\\\\text{x}=4\text{y}-12\\\\[/tex]
A new car loan has a term of loan from 2 - 6 years and the interest rate is between 4% and 8%. what is the longest amount of time you could take to pay off the loan? what is the best interest rate you could get?
a) The longest time a borrower can take to pay off the new car loan of 2 - 6 years is 6 years.
b) Based on the above, the best interest rate the borrower could get is 8%.
How is the interest rate determined?Many factors are considered in determining the interest rate for a loan.
Some of the factors include:
Loan TermLoan TypeCredit ScoreLoan AmountDown PaymentInterest rate type.We know that the longer the term of a loan, the higher the interest rate charged. This higher rate is meant to compensate the lender for the time value of money, made variable by inflation and credit risks.
Thus, if a loan term varies between two and six years, the longest time to pay off the loan is 6 years while the best interest rate the borrower can be granted is 8%.
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An architect is designing a circular window to be installed in the
gable of a house. The metal window frame will be 1 foot wide and will be bordered by
the roof above and a wood beam below. The distance from the center of the window to the roof is 3 feet. What will be the circumference of the circular glass pane that will be
needed?
Answer:
12.57 ft
Step-by-step explanation:
First thing we need to find is the radius of the circular glass pane. We are given the information that the center of the glass plane is directly in the center of the triangle and that the closest distance from the center to the roof is 3 ft, including a metal border with a width of 1 ft.
Since the metal frame is the same width all the way around the window, we can safely conclude that the radius of the circular glass pane is 2 ft, as the 3ft measurement included the radius and the metal frame.
Now that we have our radius we can use the formula:
[tex]C=2\pi r[/tex] (Circumference = 2 x pi x radius)
Using 3.14 for pi we get:
[tex]C=2(3.14)(2)[/tex]
[tex]C=4 \pi[/tex] or 12.57 ft (2.d.p)
Given right triangle JKM, which correctly describes the locations of the sides in relation to ∠J?
Answer:
It is the first answer,
Step-by-step explanation:
The hypotenuse is always the longest side and opposite of the right angel. Side b is the adjacent side to J and c is the opposite side of J.
What is the value of x? Show your work in arriving at your answer.
The value of x is 18.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
First, both angles shown are equal to each other.
5x + 5 = 95
Next, the opposite side of the equation to isolate x value (5x).
5x + 5 (-5) = 95 (-5)
5x = 90
Finally, we need to divide both sides of the equation by 5.
5x / 5 = 90 / 5
x = 18
The final answer: x = 18
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What is the difference between 28%and 18%of 4900
Answer:
Step-by-step explanation:
Find, rounded to the nearest hundredth, the diagonal of a rectangle whose sides are 6 and 11.
WHAT IS THE ANSWER. I NEED IT ASAP
Answer:
The length of the diagonal is 12.53
Step-by-step explanation:
Since we have a rectangle, the diagonal is the hypotenuse of a right triangle. So we can use Pythagorean Theorem.
a^2 + b^2 = c^2
We know the two legs are 6 and 11, so we can find the hypotenuse (which is the diagonal) see image.
See image.
38) Your bank account has$82in it when you write checks for$54,$35, and$15. You then deposit $35and $42. How much is in the account? Are you overdrawn
the answer is 55 can you show me how to get that answer.
If you have $82 in your bank account and you write checks for $54, $35, and $15, then the total amount you have written in checks is $54 + $35 + $15 = $104.
So the remaining balance is $82 - $104 = -$22, which means you are now overdrawn.
After you deposit $35 and $42, the new balance will be $82 - $22 + $35 + $42 = $155
So after the deposit, the account balance is $155
It is important to keep track of your bank account balance, if you do not have enough funds in the account and the check you wrote is cashed the bank will bounce the check and incur additional fees.
mila was baking cookies this weekend. she took 3 over 20 of the cookies to school on monday. and she gave 7 over 20 of the cookies to her neigbor. how much of the cookies did she gave away?
A
G
O
N
S
A
Answer:
Step-by-step explanation:
As she is baking cookies = 3/20
she egave it to her neigbour = 7/20
Remaining = ?
R = 3/20 -7/20 = -1/5
1.2/4=x/28 what is the value of x
Answer:
8.4
Step-by-step explanation:
You want to know the value of x that satisfies 1.2/4 = x/28.
One-step equationThe equation ...
x/28 = 1.2/4
can be solved in one step by multiplying by 28.
x = 28(1.2/4) = 8.4
The value of x is 8.4.
__
Additional comment
The fraction involving x can be cleared by multiplying by its denominator, effectively the inverse of the coefficient of x. This is the same way you solve any similar one-step equation.
Often, you are told to "cross-multiply" a proportion. Doing that gives you ...
4·x = 28·1.2
Then you have to divide by 4 (multiply by the inverse of the coefficient of x) to find the value of x:
x = 28·1.2/4 . . . . same as above.
That is, there is no need to multiply by 4, and then divide by 4. You can simply multiply by 28 and be done.
Answer:
8.4
Step-by-step explanation:
[tex]\frac{1.2}{4}[/tex] = [tex]\frac{x}{28}[/tex]
cross multiply to solve for x:
(1.2)(28) = 4x
4x = 33.6
x = 33.6/4 = 8.4
A business gained 50 new customers in April, 100 new customers in May, and 150 new customers in June. During that time, they were running a campaign with a budget of $3000. What was their Customer Acquisition cost?
Their Customer Acquisition cost was $10
What is customer acquisition cost?Customer Acquisition Cost is the cost of winning a customer to purchase a product or service. As an important unit economic, customer acquisition costs are often related to customer lifetime value. Customer acquisition cost can also be referred as the fee associated with convincing a customer to buy your product or service.
To calculate customer acquisition cost
Customer Acquisition Cost (CAC) = Customer Acquisition Cost/total marketing cost
From the question,
The business gained 50+100+150= 300 new customers
Campaign budget = $30000
Customer Acquisition Cost (CAC) = $3000/300
=$10
Hence, it cost the business $10 to acquire a new customer
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Use the figure shown to answer the question that follows.
What is the order of rotation of this figure?
2
4
6
8
On solving the provided question we can say that - The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.
What is the order of rotation?The order of rotational symmetry is the maximum number of rotations that a geometry may fit in. 360°A°, where A° is the smallest angle by which a figure may be rotated from its rotated shape to match its original shape, represents the degree of rotational symmetry. (180 degrees) A shape's degree of rotational symmetry is determined by how many times a perfect circle may be turned while maintaining its appearance. Only when a triangle is back in its original beginning position will a full 360° revolution appear the same.
If a geometric figure maps onto itself when rotated around an angle at its center, it possesses rotational symmetry.The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.
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Find the missing numbers 46 62 87 123 ---- 236
Answer:
The missing numbers are 74, 105, and 178.
fatima flies her drone 5 feet above the ground diamond she rotates the drone to the right so far the drone has flown a total of 12 feet how far is the drone from the start point
Therefore , the solution of the given problem of triangle comes out to be the distance of the drone from the start point is 13feet.
What is the triangle?Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.
Here,
Given : Height of drone = 5 feet
and distance of drone covered is 12 feet
Thus ,
to calculate the distance of the drone from the start point
distance can be represented as H
Since it forms right triangle.
By using pythagoras theorem,
=> 5² + 12² = H²
=> H² = 169
=> H = √169
=> H = 13
Therefore , the solution of the given problem comes out to be the distance of the drone from the start point is 13feet.
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if x=1−sin a and y= 1+cos a, Express y in terms of x and a only
Answer:
Step-by-step explanation:
Given
[tex]x=1-sin(a)\\y=1+cos(a)[/tex]
Solve for [tex]a[/tex] in the second equation.
[tex]y=1+cos(a)[/tex]
[tex]y-1=cos(a)[/tex]
[tex]a=cos^{-1}( y-1)[/tex]
Insert our answer for [tex]a[/tex] into the first equation.
[tex]x=1-sin(a)[/tex]
[tex]x=1-sin(cos^{-1}( y-1))[/tex]
[tex]cos^{-1}=arccos[/tex]
[tex]x=1-sin(arccos( y-1))[/tex]
Lets simplify [tex]1-sin(arccos( y-1))[/tex]
A piece of graph paper would be helpful in my opinion.
Here is how I would go about doing so
Draw a triangle in the plane with vertices [tex](y-1,\sqrt{1^2-(y-1)^2}),(y-1,0)[/tex] and the origin.
[tex]arccos(y-1)[/tex] is is the angle between the positive x-axis and the ray beginning at the origin and passing through [tex](y-1,\sqrt{1^2-(y-1)^2})[/tex]. Therefore [tex]sin(arccos(y-1))[/tex] is [tex]\sqrt{1-(y-1)^2}[/tex]
Now we have
[tex]x-1-\sqrt{1-(y-1)^2}\\a=arccos(y-1)[/tex]
We can write [tex]1[/tex] as [tex]1^2[/tex]. Since both terms are now perfect squares, we can factor using the difference of squares formula.
[tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=1[/tex] and [tex]b=y-1[/tex]
[tex]x=1-\sqrt{(1+y-1)(1-(y-1))}[/tex]
After simplifying we get
[tex]x=-\sqrt{y(-y+2)}+1[/tex]
[tex]x=-\sqrt{y(-y+2)}+1[/tex]
[tex]a=arccos(y-1)[/tex]
I think this is what your question was. If not let me know.
Using the following conversions between the metric and U.S. systems, convert the measurement.
Round your answer to 6 decimal places as needed.
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
26.794 yd = _________km.
By sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
What is the value of 1meter in terms of centimeter ?
1 meter can be equal to 100 centimeters and suppose for x meters , then it could be around 100x centimeters .
Given,
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
we know that ,
1yard = 0.0009144 km
so ,
26.794 yard = 26.794*0.0009144 km
= 0.024500
Hence by sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
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Solve the system of equations -x-y=-2 and 5x + 7y= 28 by combining the
equations.
Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.
What is equation?The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.
Here,
Given :
=> -x-y=-2
=> 5x + 7y= 28
So ,
=>x = 2-y
thus,
=> 5(2-y) + 7y =28
=> 10 -5y + 7y =28
=> 10 -2y = 28
=> -2y = 18
=> y =-9
and
=> x = 2 - (-9)
=> x = 11
Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.
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Find the volume of a cube that has a taotal surface area of 96 squares feet.
A.) 84.0ft³
B.) 84.06ft
C.) 84.06ft³
D.) 84.06ft^2
f(x)=Sin2x ,x0=pi:3
f(x)=3x-x^2 ,x0=-1
Please help and if someone has discord server to help solve math problema please give me invite
Answer:
For the first function, F(pi:3) = sin(2 * pi:3) = sin(6 * pi / 3) = sin(2 * pi) = 0.
For the second function, f(-1) = 3 * -1 - (-1)^2 = -3 + 1 = -2.
Step-by-step explanation:
It looks like you are trying to find the value of two different functions at specific points.
For the first function, F(x) = sin(2x) and x0 = pi:3, we want to find the value of F(x) when x = pi:3. Plugging this value into the function gives us F(pi:3) = sin(2 * pi:3) = sin(6 * pi / 3) = sin(2 * pi) = 0.
For the second function, f(x) = 3x - x^2 and x0 = -1, we want to find the value of f(x) when x = -1. Plugging this value into the function gives us f(-1) = 3 * -1 - (-1)^2 = -3 + 1 = -2.
Helppp asp !! A system of equations is shown x+y=7. 2x-y=-1. What is the solution to the system of equations
Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.
what is equations ?Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either contingent equations or identities are categories for equations. An identity holds true for whatever value of the variables.
given
x+y=7
2x-y=-1
8x=20
x= 5/2
-4y = -8
y = 2
Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.
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The ratio of the measure of an exterior angle of a triangle to the measure of the adjacent interior angle is 1:4. Is the
triangle acute or obtuse?
Justify your answer.
A.) Acute; the measure of the interior angle must be 144º.
B.)Acute; the measure of the interior angle must be 36°.
C.)Obtuse; the measure of the interior angle must be 144º
D.)The triangle could be acute or obtuse, depending on the measures of the other two angles.
Solve for x. 6x−24=x−2
OPTIONS:
Enter answer in the box!
X = [?]
Answer:
point A
Step-by-step explanation:
Simplify x+2+3x++5+x+3+2x
Answer: 7x+10
Step-by-step explanation:
combine like terms
x+3x+x+2x+2+5+3
7x+10
Answer:
Step-by-step explanation:
Simplification of : x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10
First: find the (x) and collect them, put them in the bracket (to ensure the + or -)
(x + 3x + x + 2x) + 2 + 5 + 3
= 7x + 2 + 5 + 3
Then we add up the numbers
= 7x + 10
This is the end result.
x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10
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