Answers
Exponential functions are typically organized in this format:
[tex]f(x) = a*c^x[/tex]
To find the equation given the graph of an exponential function:
Identify the horizontal asymptote⇒ asymptote - a line towards which a graph appears to travel but never meets
⇒ If the horizontal asymptote is not equal to 0, we add this at the end of the function equation. Identify the y-intercept
⇒ This is our a value.Identify a point on the graph and solve for c
Solving the Question
Identify the horizontal asymptote
In this question, it appears to be x = 0.
Identify the y-intercept
The y-intercept is the value of y at which the graph appears to cross the y-axis. In this graph, it appears to be 100. This is our a value. Plug this into [tex]f(x) = a*c^x[/tex]:
[tex]f(x) = 100*c^x[/tex]
Solve for c
We can use any point that falls on the graph for this step. For instance, (1,50) appears to be a valid point. Plug this into our equation and solve for c:
[tex]f(x) = 100*c^x\\50 = 100*c^1\\50 = 100*c\\\\c=\dfrac{1}{2}[/tex]
Plug c back into our original equation:
[tex]f(x) = 100*(\dfrac{1}{2})^x[/tex]
Answer[tex]f(x) = 100*(\dfrac{1}{2})^x[/tex]
Related Questions
I need this equation solved
Answers
Answer:
28
Step-by-step explanation:
similar triangles are proportional
and add all the sides of the bigger triangle
the photography club has 36 memebers, 16 girls and 20 boys. what is the ratio of girls to boys in the photography club?
A. 5:6
B. 4:5
C. 5:4
Answers
Answer:
4:5
girls:boys
16:20
divide both by 4
4:5
Step-by-Step Solution:
Total No. Of Members = 36
No. Of Girls = 16
No. Of Boys = 20
Ratio of Girls to Boys
= 16/20
= 8/10
= 4/5
=> 4:5
Correct Option is C) 4:5
When given
Slope=4
Point= (2,-4)
What is this written in slope-intercept form?
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = 4x - 12}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = 4, Point = (2, -4)}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: We need to plug in the values into point-slope form and after simplifying, distributing, and solving for y we will have our equation in slope-intercept form.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-4) = 4(x - 2)}[/tex]Distribute and simplify
[tex]\textsf{y + 4 = 4(x - 2)}[/tex][tex]\textsf{y + 4 = (4 * x) + (4 * -2)}[/tex][tex]\textsf{y + 4 = 4x + (-8)}[/tex][tex]\textsf{y + 4 = 4x - 8}[/tex]Subtract 4 from both sides
[tex]\textsf{y + 4 - 4 = 4x - 8 - 4}[/tex][tex]\textsf{y = 4x - 8 - 4}[/tex][tex]\textsf{y = 4x - 12}[/tex]Using the information that was provided in the problem statement we were able to determine that the equation in slope-intercept form was y = 4x - 12.
Answer:
y = 4x - 12
Step-by-step explanation:
Given:
slope of 4, and point (2, -4)
Here, we're being asked to write the equation in Slope-Intercept Form. As we have been given the slope and a point on the line, we can use the Point-Slope Form to be able to find that equation.
First, know the two forms:
⇒ Point-Slope Form: y - y₁ = m(x - x₁)
where: m is the slope, and (x₁, y₁) is the given point
⇒ Slope-Intercept Form: y = mx + b
where: m is the slope, and b is the y-intercept
Now, substitute the given values into the Point-Slope Form:
⇒ y - y₁ = m(x - x₁)
⇒ y - (-4) = 4(x - 2) [simplify]
⇒ y + 4 = 4x - 8
Change to the Slope-Intercept Form:
⇒ y + 4 = 4x - 8 [subtract 4 from both sides]
⇒ y + 4 - 4 = 4x - 8 - 4
⇒ y = 4x - 12
Therefore, the equation of the line in slope-intercept form is: y = 4x - 12
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Please help!!!!!!!!!!!asap
Answers
By solving y = 25 · x² - 100 through the square root method, we conclude that the two roots of the quadratic formula are y₁ = + 2 and y₂ = - 2.
How to obtain the roots of a second order polynomial
Herein we have a polynomials of the form y = a · x² - b. By algebra we find that two roots exists, which are described below according to the square root method:
[tex]y_{1} = +\sqrt{\frac{b}{a} }[/tex], [tex]y_{2} = -\sqrt{\frac{b}{a} }[/tex]
If we know that a = 25 and b = 100, then the two roots of the equation are:
y₁ = + 2, y₂ = - 2
By solving y = 25 · x² - 100 through the square root method, we conclude that the two roots of the quadratic formula are y₁ = + 2 and y₂ = - 2.
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If t = 0 in 1980, find the value for t in 1990
Answers
The value of t is 6.65
What is exponential function?An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is a variable, and a is a constant called the base of the function.
Given:
A= 210 million
P= A e^(kt)
225 = 210 * e ^ (0.0069t)
225/210= e ^ (0.0069t)
1.07 = e ^ (0.0069t)
Taking log on both side
log 1.047 = 0.0069 t log e
[tex]\frac{0.0069t\ln \left(e\right)}{0.0069\ln \left(e\right)}=\frac{\ln \left(1.047\right)}{0.0069\ln \left(e\right)}[/tex]
t= log ( 1.047) / 0.0069
t= 6.65
Hence, value of t is 6.65.
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Answer:
Step-by-step explanation:
most everyday purchases at the store are labeled with the piece of the item before sales tax. Which expression could be used to find the amount of tax
Answers
Amount of Tax = (Original Cost)(Tax %) , Option C is the right answer.
The complete question is
Most everyday purchases at the store are labeled with the price of the item before sales tax. Which expression could be used to find the amount of tax? Amount of Tax = Original Price + Total Cost Amount of Tax = (Total Cost)(Original Price) Amount of Tax = (Original Cost)(Tax %) Amount of Tax = (Total Cost)(Tax %)
What is Tax ?Tax is the % of the amount taken by the government on the sales or income of a person , There are many kinds of taxes imposed on various sectors.
The amount of tax is taken on the cost of the product ans thus can be represented by
Amount of Tax = (Original Cost)(Tax %) , Option C is the right answer.
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which statement is true about the function?
Answers
The correct answer is option D which is the function is even because of its symmetry about the y-axis.
What is even function?The function which remains unchanged when the negative value of the variable is filled in the function is called an even function and this function is symmetric about the y-axis.
Given function:-
f(x) = 3x⁴+2x²
Now put the value x = -x in the function
f(-x) = 3( -x⁴)+2(-x²)
f(-x) = 3x⁴ + 2x²
f(-x) = f(x)
here we can see that when we put the value of negative x the function remains unchanged.
Therefore the correct answer is option D which is the function is even because of its symmetry about the y-axis.
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6. Given that the term independent of x in the binomial expansion of (x²+p/x)^6 is 240,
(a) find the value of the positive constant p
Answers
By the binomial theorem,
[tex]\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}[/tex]
where
[tex]\dbinom kn = \dfrac{k!}{n!(k-n)!}[/tex]
is the so-called binomial coefficient.
The term that's independent of x is the constant term, which occurs when [tex]3n-6=0[/tex], or [tex]n=2[/tex]. Given that this constant 240, we have
[tex]p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2[/tex]
but [tex]p[/tex] must be positive, so [tex]\boxed{p=2}[/tex]
6x9(7-3)4+3x36+3
what is the answer
Answers
The given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].
The given expression is [tex]6x^{9} (7-3).4+3x^{36} +3[/tex].
We need to simplify the given expression.
What is an algebraic expression?In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.
First, multiply the numbers 6×4=24.
That is, [tex]24x^{9} (7-3)+3x^{36} +3[/tex].
Next, subtract the numbers 7-3=4.
[tex]24x^{9}.4+3x^{36} +3[/tex]
Finally, multiply the numbers 24×4=96.
[tex]96x^{9}+3x^{36} +3[/tex].
Hence, the given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].
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The perimeter of a rectangle is 34 cm. The length is 1 cm longer than the width. What is the length of the longest side of the rectangle?
Answers
Answer: 9 cm
Step-by-step explanation:
The formula for the perimeter of a rectangle is [tex]2l+2w=P[/tex]
Where
l is the length
w is the width
and P is the perimeter (34)
Because the length is 1 cm longer than the width instead of representing the length is l we can use w+1
Sub in the known values and solve
Step 1: Simplify both sides of the equation with the Distributive Property
[tex]2(w+1)+2w=34\\(2)(w)+(2)(1)+2w=34\\2w+2+2w=34\\(2w+2w)+(2)=34\\4w+2=34\\[/tex]
Step 2: Subtract 2 from both sides.
[tex]4w+2-2=34-2\\4w=32[/tex]
Step 3: Divide both sides by 4.
[tex]\frac{4w}{4}=\frac{32}{4} \\w=8[/tex]
Step 4: Add 1 to w to find the length of the longer side
[tex]w+1\\8+1\\9[/tex]
Step 3: Now multiply the values to get 14,918,904,000. That is almost
15 billion passwords.
That is a lot of passwords! How many passwords would the website
have if users were allowed to reuse the letters and numbers? (Enter
the number of successful outcomes in each of the blanks below.
2
Answers
The number of passwords that would be allowed if users were allowed to reuse the letters and numbers is 30891577600
How to determine the number of passwordsThe given parameters are:
Password length = 8
Letters = 6
Numbers = 2
There are 26 letters and 10 digits.
Since the letters and the numbers can be repeated, then the number of passwords is:
Count = 26^6 * 10^2
Evaluate
Count = 30891577600
Hence, the number of passwords is 30891577600
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mZACB = (6y-7)° and mZDCA = (8y - 1)°.
B
A
D
|
C
What is mZACB?
Answers
Answer: [tex]35^{\circ}[/tex]
Step-by-step explanation:
Angles ACB and DCA add to form angle ACB, which is a right angle, so:
6y - 7 + 8y - 1 = 90 [angles that add to form a right angle add to 90 degrees]14y - 8 = 90 [combine like terms]14y = 98 [add 8 to both sides]y = 7 [divide both sides by 14]So, [tex]m\angle ACB=6(7)-7=\boxed{35^{\circ}}[/tex]
\How could Brent use a rectangle to model the factors of x2 – 7x + 6?
He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
He could draw a diagram of a rectangle with dimensions x – 4 and x + 3 and then show the area is equivalent to the sum of x2, –4x, 3x, and half of –12.
Answers
Option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have a quadratic expression to model the area of the rectangle:
= x² – 7x + 6
[tex]\rm =\left(x^2-x\right)+\left(-6x+6\right)[/tex]
[tex]=\rm x\left(x-1\right)-6\left(x-1\right)[/tex]
= (x - 1)(x - 6)
Thus, option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.
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PLEASE HELP ASAP (timed)
Answers
Answer:
x = -19/7Step-by-step explanation:
-19 : 14 = x : 2
x = 19 * 2 : -14
x = 38 : -14
x = -19/7
Given right triangle QRS, what is the value of sin(30°)?
Answers
Answer:
1/2
Step-by-step explanation:
(Is this the question? In the pic above)
Sin of an angle os the side opposite over it divided by the hypotenuse.
Sin = opposite/hypotenuse
Sin = 5/10
Sin = 1/2
Find the area of the kite. ) 210m ^ 2 ) 140m ^ 2; 420m ^ 2; 224m ^ 2
Answers
Answer:
from the image above
Triangle ABE = Triangle ADE
AE = AE ( common).
angle AEB = angle AEO ( each 90°)
AB = AD ( given).
by side angle side criteria
so area of ABE = area of ADE
similarly,
BC = DC ( given)
BEC = DEC ( 90°)
EC = EC ( 9m each)
so area of BEC = Area of DEC
Area of Kite = 210 m²If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.
( x/6, y/4 )
( x - 4, y - 6)
(-6 x, -4 y)
( x - 6, y - 4)
Answers
T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)
A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.
Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)
and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)
So, the matrix of the transformation is
[tex]\left[\begin{array}{ccc}7&6\\4&5\end{array}\right][/tex]
The inverse of the matrix is
[tex]\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right][/tex]
So, the Inverse Transformation is given by
[tex]T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]
So, no option is correct. And the answer is
[tex]T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]
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pls help
B (20,25) (12,9)
C (150,125) (96,64)
D ( 25, 150) (16,96) (9,54)
E (5,125) (4,64)
Answers
Answer:
Side Length and Perimeter of One Face
Step-by-step explanation:
See attached image.
FACTOR THE EXPRESSION GIVEN BELOW. WRITE EACH FACTOR AS A POLYNOMIAL IN DESCENDING ORDER. ENTER EXPONENTS USING THE CARET (^). FOR EXAMPLE, YOU WOULD ENTER x TO THE POWER OF 2 AS x^2.
343x^3 + 216y^3
Answers
Each given factor written as a polynomial in descending order is; (7x + 6y)(49x² - 42xy + 36y²)
How to factorize Polynomials?We are given the polynomial;
343x³ + 216y³
343x³ + 216y³ is a sum of cubes and factors in general as;
a³ + b³ = (a + b)(a² - ab + b²)
Thus;
343x³ + 216y³ = (7x)³ + (6y)³
= (7x + 6y)((7x)² - 7x(6y) + (6y)² )
= (7x + 6y)(49x² - 42xy + 36y²)
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Find sin (ABC + 60) NEED QUICK 100 PPOINTS
Answers
Answer:
B
Step-by-step explanation:
using the addition identity for sine
sin(A + B) = sinAcosB + cosAsinB
using the sine and cosine ratios in the right triangle
sinABC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{4}{5}[/tex]
cosABC = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{3}{5}[/tex]
using the exact values
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos60° = [tex]\frac{1}{2}[/tex]
Then
sin(ABC + 60)
= sinABC cos60 + cosABC sin60
= ( [tex]\frac{4}{5}[/tex] × [tex]\frac{1}{2}[/tex] ) + ([tex]\frac{3}{5}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] )
= [tex]\frac{4}{10}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]
= [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]
sin<ABc
Perpendicular/Hypotenuse4/5cos<ABC
Base/Hypotenuse3/5Now
sin(<ABC+60)sin<ABC ×cos60+cos<ABC×sin604/5(1/2)+3/5(√3/2)2/5+3/10√3what is equivalent to 7/5y
Answers
Answer:
1.4y
Step-by-step explanation:
X. y
-6. -7
.1. 1
0. 9
3. -2
What is the domain of the given function?
(x|x = -6, -1, 0, 3}
(y|y) =-7.-2, 1, 9}
(x|x = -7, -6, -2.-1, 0, 1, 3, 9}
(y|y)= -7, -6, -2, -1, 0, 1, 3, 9}
Answers
Answer: Option (1)
Step-by-step explanation:
The domain is the set of input values, also known as the set of x-values.
Toby has five coins. Three of the coins add up to 30p. Three of the coins add up to 40p. All the coins add up to 50p. List Tony's coins in ascending order of value.
Answers
Tony's coins in ascending order of value will be 5p, 10p, and 15p.
How to depict the information?Based on the information given, the values of the coins will be 5p, 5p, 10p, 15p, and 15p.
In this case, 5p + 10p + 15p = 30p
10p + 15p + 15p = 40p
5p + 5p + 10p + 15p + 15p = 50p
Therefore, Tony's coins in ascending order of value will be 5p, 10p, and 15p.
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Answer:
5p, 5p, 10p, 10p, 20p
Step-by-step explanation:
5p, 5p, 10p, 10p, 20p,
If price of 12 eggs is Rs. 192, how many eggs can be bought for Rs. 160?
Answers
Answer:
10
Step-by-step explanation:
First, divide 192 by 12, you get a unit rate of Rs. 16 per egg, then divide Rs. 160 by 16 and you get 10
The number of eggs that can be purchased at Rs. 160 is 10.
What is a division operator?The division operator ( / ) has the quotient of its operands where the left operand exists the dividend and the right operand exists the divisor.
The cost of 12 eggs = Rs. 192
The cost of 1 egg = 192/12 = Rs. 16.
The number of eggs that can be purchased is Rs. 160 = 160/16 = 10.
Therefore, the number of eggs that can be purchased at Rs. 160 is 10.
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275 is divisible by ,2,3,4,5,6,8,9,10,11 yes or no
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
2: no
3: no
4: no
5: yes
6: no
8: no
9: no
10: no
11: yes
Step-by-step explanation:
there are some simple divisibility rules that we can utilize here:
a number is divisible by __ if...
2: ends in [last digit] 0, 2, 4, 6, 8
so 275 is not divisible by 2
3: sum of digits is 3
2 + 7 + 5 = 14 [14 is not divisible by 3]
so 275 is not divisible by 3
4: last two digits are divisible by 4
75 is not divisible by 4
so 275 is not divisible by 4
5: last digit is 0 or 5
so 275 is divisible by 5
6: number is divisible by both 2 and 3
we know that 175 is not divisible by 2 or 3, so 275 is not divisble by 6
8: last three digits are divisible by 8
>> we also know that any number that 8 goes into, 4 also goes into [not always the other way around], meaning that because 175 is not divisible by 4, it must not be divisible by 8
so, 275 is not divisible by 8
9: sum of digits is divisible by 9
>> we also know that 9 only can go into numbers that 3 can go into, so because 175 is not divisible by 3, it must not be divisible by 9
so, 275 is not divisible by 9
10: last digit is 0
so, 275 is not divisible by 10
11 is a bit complicated:
sum of digit in odd places and sum of digit in even places has a difference is divisible by 11 [or is 0]
2 7 5
odd places: 2, 5 (2 + 5 = 7)
even places: 7 (7 = 7)
difference between 7 and 7 is 0 (7-7 = 0),
so, 275 is divisible by 11
hope this helps!! :)
If f = {(-1, 0), (-2, 2), (-3, 4), (-4, 6), (-5, 8)}, what is the range?
Answers
Answer:
{0, 2, 4, 6, 8 }
Step-by-step explanation:
the range is the y- coordinates of the ordered pairs , then
range { 0, 2, 4, 6, 8 }
Does the chart below represent a proportional relationship? What is the rate of change?
x y
1 4
2 8
3 12
4 16
Answers
This chart represents a proportional relationship. The rate of change will be 4.
What is the constant of proportionality?Firstly, there is a proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called the constant of proportionality.
Given;
x y
1 4
2 8
3 12
4 16
Here, x = ky
put the first value
k = 1/4
This chart represents a proportional relationship.
So the rate of change will be
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\Rate = \dfrac{8 - 4}{2 - 1}\\\\Rate = 4[/tex]
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What is the value of y?
Answers
Answer:
y = 97°
Explanation:
Opposite angles in a quadrilateral inscribed in a circle sum ups to 180°
So following the rule:
A + C = 180°
y + 83° = 180°
y = 180° - 83°
y = 97°
a^½ха^2/3/a^3/5
I need help
P
Answers
Answer:
15 sqrt a ^4
Step-by-step explanation:
Determine if the lines through each set of ordered pairs are parallel, perpendicular, or neither. Explain your answer. Ordered pairs: (8, 3) (-2, 5) and (-2, -5) (-1, -10)
Answers
Considering the slope of the lines, it is found that the lines going through the points are neither parallel nor perpendicular.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.In this problem, the slopes are given as follows:
m1 = (5 - 3)/(-2 - 8) = -2/10 = -1/5 = -0.2.m2 = (-10 - (-5))/(-1 -(-2)) = -5/1 = -5.The multiplication is of 1, not -1, hence they are neither parallel nor perpendicular.
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