A. A function that represents the attendance after t years can be written as y = 20,000(1 + 0.05t)
What does a math function mean?
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
This function represents the initial attendance of 20,000, multiplied by 1 + 5% increase each year (0.05) times the number of years (t).
B. To find out about how many people will attend the festival in the fifth year, we can substitute t = 5 into the function.
y = 20,000(1 + 0.05 * 5)
y = 20,000(1 + 0.25)
y = 20,000(1.25)
y = 25,000
So, approximately 25,000 people will attend the festival in the fifth year.
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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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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.
Check Understanding th
Math
Board
1 There are 46 swimmers and 7 lanes. The same number of
swimmers will go in each lane. Any remaining swimmers will
practice diving. How many swimmers will each lane have?
• Write a division equation to model the problem.
• Use the space at the right to show how you can use
repeated subtraction to solve.
Each lane will have ______
Module 6 Lesson 5
swimmers.
Answer: To model the problem with a division equation, we can write 46 ÷ 7 = x, where x represents the number of swimmers that each lane will have.
To solve the equation using repeated subtraction, we can subtract 7 from 46 several times until we reach a number that is less than 7. The number of times we subtract 7 will give us the number of swimmers each lane will have. Here's one way to do it:
46 - 7 = 39
39 - 7 = 32
32 - 7 = 25
25 - 7 = 18
18 - 7 = 11
11 - 7 = 4
As you can see, we are able to subtract 7 from 46 a total of 6 times before we get a number less than 7. This means that each lane will have 6 swimmers, and the remaining 4 swimmers will practice diving. So each lane will have 6 swimmers.
So the equation 46 ÷ 7 = 6, and also by repeated subtraction method it shows the same result of 6 swimmers each lane.
Step-by-step explanation:
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]
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:
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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Distribution of toys : Is this different or just the division with remainder
Answer:
Step-by-step explanation:
20)63(3
-60
-------
3
so every children gets 3 toys but 3 toys are left which can be distributed among 3 children.
so 3 children get 1 toy more.
Hence 3 children get 3+1=4 toys (each)
Find the missing numbers 46 62 87 123 ---- 236
Answer:
The missing numbers are 74, 105, and 178.
Graph the function n(x) = |x6|.
+Move Ray
-6
-4
-2
104
9
4
2
0
-2
Undo
2
4
Redo
6
x Reset
8
10
Answer:
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?
Devin purchased a container of sport drink that contains 300 calories. The label says that 80% of the calories are from carbohydrates. How many calories are from carbohydrates?
Answer: 240 Calories are from Carbohydrates
Step-by-step explanation:
First, we will convert 80% into the decimal 0.8, then we will multiply this by the amount of total calories in the drink to create the following equation:
300 * 0.8 = 240 Calories.
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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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.
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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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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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.
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.
A family buys a studio apartment for $140,000 They pay a down payment of $35,000
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $7,000 down payment be?
Answer:
a. Their down payment is 25% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$35,000 ÷ $140,000 = 0.25 = 25%
b. A $7,000 down payment would be 5% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$7,000 ÷ $140,000 = 0.05 = 5%
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.
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
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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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
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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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
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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7 - Select the equation that represents a true statement.
Mark all that apply.
A. 2+3 × 4 = 22 +12
B. z+zx9 = 9z O
C. -8y + 4.3y + 3.7 = 0
D. 12-1.8b+ 1.8b = 1.8b
E. m8+7(8) = m
So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
A. 2+3 × 4 = 22 +12 is not a true statement, because the order of operations is not followed, multiplication should be done before addition.
B. z+zx9 = 9z is not a true statement, because it is not clear what the operation is between z and x, and what the operation is between x and 9
C. -8y + 4.3y + 3.7 = 0 is a true statement because it is a linear equation with one variable y, it represents a straight line.
D. 12-1.8b+ 1.8b = 1.8b is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.
E. m8+7(8) = m is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.
So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0
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Tessa bought stock in a restaurant for $208.00. Her stock is now worth $284.96. What is the percentage increase of the value of Tessa's stock?
Answer:
37.04%
Step-by-step explanation:
To find the percentage increase in the value of Tessa's stock, we need to calculate the difference between the original price and the current price, and then divide that difference by the original price, and multiply by 100 to express the result as a percentage.
Here is the calculation:
percentage increase = ((284.96 - 208.00) / 208.00) * 100
= (76.96 / 208.00) * 100
= 37.04 * 100
= 37.04%
So Tessa's stock has increased in value by 37.04%.
Answer:
37 % increase
Step-by-step explanation:
To find the percentage increase, take the new amount and subtract the original amount
284.96 -208 =76.96
Divide this by the original amount
76.96/208=.37
Change the decimal form to a percent
.37 * 100% = 37 %
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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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 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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