Explain what an exponential form is but leveled down for high schoolers
Answers
The required exponential function is given as y = aˣ where the value of a should be positive always.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
here,
Since from the above definition exponential function is given as y = aˣ,
This shows the exponential increase and decrease, by means of exponential increase and decrease, a sudden in increase and sudden decrease of function as the value of a varies, see in the graph after the answer. And the value of an always remains positive.
Thus, the required exponential function is given as y = aˣ where the value of a should be positive always.
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Related Questions
40% of an hour?
(I've tried 24 minutes...it's not the answer)
Answers
Given there are 60 minutes in an hour, we can multiply this by 0.4 to find that 24 minutes constitutes 40% of an hour. I assume the system is not working properly for you, but 40% of an hour is 24 minutes.
40% of an hour is 24 minutes = 2/5 hours.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Given that,
there are 60 minutes in an hour,
we can multiply this by 0.4 to find that 24 minutes constitutes 40% of an hour.
i.e. 60*40%= 24 minutes
Hence, 40% of an hour is 24 minutes = 2/5 hours.
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A savings account increased by $75 is now more than $500. What is the least amount of money that was originally put in the savings account?
Answers
The least amount of money that was originally put in the savings account is $426.
What is the least amount of money?The amount of money in the savings account is a function of the money that was originally in the account and the amount by which the account was increased by.
The inequality that represents the total amount of money in the savings account is:
amount originally in the account + amount deposited > 500
x + $75 > $500
x > $500 - $75
x > $425
The least amount would be $426 because this is the smallest number that is greater than $425 that would make the total amount more than $500.
To check:
$75 + $426 = $501
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5.7935 rounded to the nearest thousand
Answers
Answer:
5.794
Step-by-step explanation:
The seven after the decimal point is the tenth digit, the nine is the hundredth, and the 3 is the thousandth place. Therefore, we look at our neighbor (the number next to the thousandth place) and if its 5 or more we round up, but if its 4 or less we keep it the same.
I just need help with question A
Suppose your cousin missed class and asks you, “Why do we plug in 0 for x to find y-intercepts and 0 for y to find x-intercepts? That doesn’t make sense to me.” Explain to your cousin WHY this process works. Use the line
5x+4y=14 as an example.
A) A description in words why this works
Answers
The reason why the cousin's procedure for getting the x and y intercepts work is because they represent the definition of those points on a graph.
How to find the x and y intercepts?The x-intercept of a graph or function simply refers to the point at which the graph crosses the graph crosses the x-axis or the point at which y = 0. In a similar manner, the y-intercept simply refers to the point at which the graph crosses the y-axis or simply the point at which x = 0.
Now, we are given the equation of the line as;
5x + 4y = 14
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Rewriting the equation of the line in slope intercept form is;
y = -⁵/₄x + ⁷/₂
Now, the reason why we plug in 0 for x to get the y-intercept is because when x = 0, that is only where we can get the y-intercept as the corresponding value of x will be traced to 0.
Similarly, the reason why we plug in 0 for y to get the x-intercept is because when y = 0, that is only where we can get the x-intercept as the corresponding value of y will be traced to 0.
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A new homeowner is purchasing a living room set for $2,975 and must decide between two financing offers.
Offer 1: $250 down payment, 24.90% interest rate, compounded monthly, for 3 years, with no payments due for 6 months and then fixed payments of $139.05 for the remainder of the loan term
Offer 2: $400 down payment, 22.90% interest rate, compounded monthly, for 3 years, with no payments due for 12 months and then fixed payments of $165.76 for the remainder of the loan term
Part A: What is the total cost of offer 1? Explain which technology you used to solve and each step of your process. (3 points)
Part B: What is the total cost of offer 2? Explain which technology you used to solve and each step of your process. (3 points)
Part C: Which financing offer should the new homeowner choose? Explain your reasoning. (4 points)
Answers
Answer:
To compare the two financing offers, we need to calculate the total cost of each offer.
Part A: What is the total cost of offer 1?
To calculate the total cost of offer 1, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:
Total interest = (interest rate/12) * loan amount * number of payments
In this case, the loan amount is $2,975, the interest rate is 24.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:
Total interest = (0.2490/12) * $2,975 * 36
Calculating, we find that the total interest is approximately $1,534.89.
To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,534.89 = $4,509.89.
Therefore, the total cost of offer 1 is $4,509.89.
Part B: What is the total cost of offer 2?
To calculate the total cost of offer 2, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:
Total interest = (interest rate/12) * loan amount * number of payments
In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:
Total interest = (0.2290/12) * $2,
To continue the calculation of the total cost of offer 2, we need to calculate the total interest using the formula:
Total interest = (interest rate/12) * loan amount * number of payments
In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:
Total interest = (0.2290/12) * $2,975 * 36
Calculating, we find that the total interest is approximately $1,405.70.
To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,405.70 = $4,381.70.
Therefore, the total cost of offer 2 is $4,381.70.
Part C: Which financing offer should the new homeowner choose?
Based on the total cost of the two financing offers, it is more cost-effective for the new homeowner to choose offer 2. Offer 2 has a lower total cost ($4,381.70) compared to offer 1 ($4,509.89), so it would be the better choice for the new homeowner.
Step-by-step explanation:
PV = PMT * (1 - (1 + r)^-n) / r
Where PV is the present value (in this case, the total cost of the loan), PMT is the fixed payment amount, r is the monthly interest rate (in decimal form), and n is the number of payments.
Plugging in the values from Offer 1, we get:
PV = $139.05 * (1 - (1 + 0.2490)^-36) / 0.2490
Using a calculator or spreadsheet to compute the exponent and division, we find that the total cost of Offer 1 is $4,941.51.
To calculate the total cost of Offer 2, we can use the same formula:
PV = $165.76 * (1 - (1 + 0.2290)^-36) / 0.2290
Using a calculator or spreadsheet to compute the exponent and division, we find that the total cost of Offer 2 is $4,847.93.
Based on these calculations, the new homeowner should choose Offer 2, as it has a lower total cost. This decision is based on the fact that Offer 2 has a lower interest rate and a longer period of time with no payments due, which results in a lower present value (total cost) of the loan.
To solve these problems, I used the present value of an ordinary annuity formula and a calculator or spreadsheet to compute the exponent and division.
please help me with this thank you.
Answers
B) 1:55 PM
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.
Answers
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:
7. {MCC.7.G.2} *
Which set of numbers cannot
represent the lengths of the sides
of a triangle?
A) 7, 9, 12
B) 8, 6, 7
C) 8, 20, 12
D) 10, 13, 20
O A
B
O D
Answers
If
f
(
x
)
=
2
x
4
−
9999999kwwkqkkaosos
A new business borrows $320,000 at a yearly simple interest rate of 7%.
The total
amount the company repays for the loan and interest is $678,400. How long did it
take to pay off the loan? Pls help Mee!!
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{\frac{23}{25}}{0.07}=t\implies \boxed{16=t}[/tex]
(5x3)+(nx4)=5(3+4) write each missing number.
Answers
Answer:
5
Step-by-step explanation:
5 x 3 = 15
n x 4 = 4n
3 + 4 = 7
(5 x 3) + (n x 4) = 5(3 + 4)
15 + 4n = 5*7
15 + 4n = 35
4n = 35 - 15
4n = 20
n = 20/4
n = 5
Hence, the value of missing number (n) is 5.
The Science Club went on a two-day field trip. On the first day, the members paid $60 for transportation plus $15 per ticket to the planetarium. On the second day, they paid $95 for transportation plus $12 per ticket to the geology museum.
Write an expression to represent the total cost for two days for the ₙ members of the club.
Answers
Answer: Let n be the number of members in the Science Club.
On the first day, the total cost for transportation plus the cost of tickets is 60 + (15n) dollars.
On the second day, the total cost for transportation plus the cost of tickets is 95 + (12n) dollars.
So, the total cost for both days is (60 + 15n) + (95 + 12n) = 155 + 27n dollars.
The expression to represent the total cost for two days for the n members of the club is 155 + 27n dollars.
This equation represents the total cost for the transportation, planetarium and geology museum for 2 days for the n members in the club.
It should be noted that this is the monetary representation and it might vary depending on other factors, such as group discounts.
Step-by-step explanation:
Answer:
(n x 27)+155
Step-by-step explanation:
15 +12 = 27
Each member pays $27 for the tickets so we multiply it by the number of members.
95 + 60 = 155
The members pay $155 in total for transportation.
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?
Answers
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%
Identify and write down the keywords in the word problem. (1.) Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3. Evaluate the expression 2g + 3a when g = 4 and a = 8 to find the cost of buying 4 cartons of grape juice and 8 cartons of apple juice. What is the difference in price Missy and Jared paid? Show your work.
Answers
The cost of the 4 cartons of grape juice and 8 cartons of apple juice will be $32 and the difference is $12.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3.
The cost of 4 grapes and 8 apples will be,
Cost = 2g + 3a
Cost = ( 2 x 4 ) + ( 3 x 8 )
Cost = 8 + 24
Cost = $32
The difference in the price Missy and Jared paid is,
Difference = $32 - $ 20
Difference = $12
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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?
Answers
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.
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
Answers
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?
What is an equation of the line that passes through the points (4,7) and (-3,7)
Answers
Answer:y=
Step-by-step explanation:Firstly let's find the slope which is (7-7)/(4-(-3))=0. Using the point slope formula y-y1=m(x-x1) we plug in one of the points and simplify y-7=0(x-4). Simplifying and solving for y gives us y=
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
Answers
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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Which expression is equivalent to 3/2?
Answers
On solving the provided question we can say that expression which is equivalent form to 3/2 is (5/2-1).
What is Equivalent form ?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Equivalent systems refer to sets of equations with the same solution. We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.
When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.
The number is 3/2
The expression which is equivalent to 3/2 is (5/2-1)
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Solve: S=2(lw+lw+wh) for w
Answers
Answer:
[tex]w=\frac{s-2lh}{2(h+l)}[/tex]
Step-by-step explanation:
Given the equation, [tex]S=2(lw+lh+wh)[/tex], solve for w.
[tex]S=2(lw+lh+wh)[/tex], distribute the 2.
=> [tex]S=2lw+2lh+2wh[/tex], subtract [tex]2lh[/tex] from both sides.
=> [tex]S-2lh=2lw+2wh[/tex], factor out a [tex]w[/tex] from the right-hand-side.
=> [tex]S-2lh=w(2l+2h)[/tex], now divide [tex](2l+2h)[/tex] from each side.
=>[tex]\frac{S-2lh}{2l+2h}=w[/tex]
Final answer: [tex]w=\frac{s-2lh}{2(h+l)}[/tex]
Which of these systems of equations has infinitely many solutions? Explain your choice(s).
a. (1/2)x - 5y = 10
(-1/2)x + 5y = -10
b. 7x + 2y = -14
-7x + 2y = -14
c. x + 6y = -18
x - 6y = 18
d. (3/4)x - 9y = 12
(-3/4)x + 9y = 12
Answers
To see this, you can solve for x in one of the equations and substitute that expression for x in the other equation. For example, if you solve for x in the second equation, you get:
x = 18 + 6y
Substituting this expression for x in the first equation gives:
(18 + 6y) + 6y = -18
24y = -36
y = -1.5
Substituting this value for y back into the expression for x gives:
x = 18 + 6y = 18 + 6(-1.5) = 18 - 9 = 9
So, one solution to the system of equations is (x, y) = (9, -1.5). However, since there is a variable on both sides of the equation, there are infinitely many solutions to this system of equations.
All of the other systems of equations have either no solutions or exactly one solution.
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?
Answers
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 %
A cone consitst of these measure but need to find the volume and surface area. The diameter is 16m, height is 8m, and the slant height is 11.31m.
A.) V=769.17m³ SA=535.89m²
B.) V= 535.89m SA=769.17m
C.) V=535.89m³ SA= 769.17m²
D.) V=1607.68m³ SA=769.56m²
Answers
Volume = (1/3) * pi * radius^2 * height
Surface area = pi * radius * (radius + slant height)
In this case, the diameter is 16m, so the radius is 8m. The height is 8m and the slant height is 11.31m. Substituting these values into the formulas gives:
Volume = (1/3) * pi * 8m^2 * 8m = (1/3) * pi * 64m^3 = 21.333m^3 * 64m^3 = 1,365.33m^3
Surface area = pi * 8m * (8m + 11.31m) = pi * 8m * 19.31m = pi * 153.48m^2 = 483.04m^2
So, the volume of the cone is 1,365.33m^3 and the surface area is 483.04m^2. The correct answer is therefore C) V=535.89m³ SA= 769.17m².
The equation below represents the amount of work required to complete a project, where x represents the number of hours each group member must contribute to the project. How many hours does each group member work on the project? x+45/4=4x 2 hours 4 hours 16 hours 3 hours
Answers
The number of hours does each group member work on the project is 4 hours. Therefore, the correct answer is option B.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is x+45/4=4x.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
4x-x=45/4
3x=45/4
x=15/4
x=3.75
x≈4 hours
Therefore, option B is the correct answer.
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15 x 109 is how many times greater than 5 x 103?
Enter the answer using scientific notation
Answers
The number of times 5×10³ greater than 15×10⁹ is 3×10⁶.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
Given that, 15×10⁹ and 5×10³.
Number of times 5×10³ greater than 15×10⁹ is
Now, 15×10⁹/5×10³
= 3×10⁶
Therefore, 3×10⁶ times 5×10³ greater than 15×10⁹.
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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.
Answers
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.
Denise and Gabe met for dinner in downtown Belmont. Denise did flat-rate valet parking for $20. Gabe went to another valet and paid $4 up front and $4 for every hour, including the first hour. Ultimately, the friends ended up paying the same amount. How long did they stay? How much did each one pay?
Answers
y to the -3 power
pls help!!!!!!!!!
Answers
Answer:
any number goes down 3 places
Step-by-step explanation:
EX:10 to the power of -3 = 0.001
find angle D thank you so much need help. geomtry
Answers
The angle m∠D of the triangle is 78 degrees.
How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The ΔKDT and ΔKPQ are isosceles triangle.
Isosceles triangle is a triangle that has two sides and angles equal to each other.
Therefore,
∠D + ∠T + ∠k = 180
∠D = 6x + 6
∠T = 6x + 6
∠K = 2x
Therefore,
6x + 6 + 6x + 6 + 2x = 180
14x + 12 = 180
14x = 180 - 12
14x = 168
divide both side by 14
x = 168 / 14
x = 12
Therefore,
m∠D = 6x + 6 = 6(12) + 6 = 72 + 6 = 78 degrees.
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Distribution of toys : Is this different or just the division with remainder
Answers
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)
how to solve this equation for x x/3+7-5
Answers
the answer is right there