An exponential function in the form y=abˣ is y = 7×4ˣ .
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Write the equation of the function:
y = abˣ
For point (0 , 7)
7 = ab⁰
for point (2 , 112)
x = 2
y = 112
Substitute:
112 = ab²
Swap the sides:
ab⁰ = 7
ab² = 112
Find the quotient of the equations:
ab²/ ab⁰ = 112/7
Simplify the equations:
b² = 16
b = ±√16
Split into two equations: b = +√16 or b = -√16
Simplify the radical expression:
b = 4
b = -4
Combine the results: b = 4 or b = -4
Any fraction with a denominator of 1 is equal to its numerator:
a = 7
7 = a (±4)°
Substitute into one of the equations:
a = 7
b = ± 4
y = 7×4ˣ
Hence , y =7×4ˣ is an exponential function with the formula y=abˣ.
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Hi guys.I was sick on Friday and I don’t understand the work.I watched all my teachers videos and still don’t understand.I’ll be giving out 10 points to whoever helps.
An ice cream shop owner's business assets and liabilities are listed below. Owned Inventory $32,500 Cash $75,420 Building Mortgage $154,265 Savings Account $25,000 Owned Equipment $15,670 Small Business Loan $15,652 Other Debt $1,235 Accounts Receivable $12,540 Property Value $125,768 What is the total value of the ice cream shop owner's business assets? $125,768 $171,152 $274,358 $286,898
The total value of the ice cream shop owner's business assets is D. $286,898.
What are business assets?Business assets are the value of the assets of the Ice Cream Shop.
Business assets are distinct from the owner's assets.
The business assets consist of liabilities (amounts owed outsiders) and equity (the difference between assets and liabilities).
Business Assets:Owned Inventory $32,500
Cash $75,420
Savings Account $25,000
Owned Equipment $15,670
Accounts Receivable $12,540
Property Value $125,768
Total assets = $286,898
Business Liabilities:Small Business Loan $15,652
Other Debt $1,235
Building Mortgage $154,265
Total liabilities = $171,152
Equity = $115,746 ($286,898 - $171,152)
Thus, the business assets for this ice cream shop are worth Option D.
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Rewrite 0 = 1-2y+14x. As a linear equation
Answer:
y = 7x + 1/2
Step-by-step explanation:
0 = 1 - 2y + 14x
+2y +2y
2y = 1 + 14x
/2 /2 /2
y = 1/2 + 7x
y = 7x + 1/2
Marsha buys 3 pounds of cheddar cheese and some Swiss cheese Both cheeses cost $450 per pound. The total cost is $24.75. How many pounds of Swiss cheese did Marsha buy?
Let x represent the number of pounds of Swiss cheese that Marsha bought.
We were told that Marsha buys 3 pounds of cheddar cheese and some Swiss cheese Both cheeses cost $450 per pound. This means that the cost of 3 pounds of cheddar cheese is 3 * 4.50 = 13.5
Also, the cost of x pounds of Swiss cheese is 4.5 * x = 4.5x
If the total cost is $24.75, it means that
4.5x + 13.5 = 24.75
The equation is
4.5x + 13.5 = 24.75
We would solve for x. Thus,
4.5x = 24.75 - 13.5
4.5x = 11.25
x = 11.25/4.5
x = 2.5
Thus, she bought 2.5 pounds of Swiss cheese
For a particular nature trail, the amounts of time that hikers take to walk the trail are normally distributed.The mean of the times is 30.1 minutes,and the standard deviation is 3.6 minutes.For a sample of 4 hikers,what is the probability that the mean time for the sample is less than 28 minutes?
Let X be the normally distributed random variable representing the time hiker takes to walk the trail.
Given that mean and standard deviation are 30.1 and 3.6 minutes, respectively,
[tex]\begin{gathered} \mu=30.1 \\ \sigma=3.6 \end{gathered}[/tex]The sample size is 4,
[tex]n=4[/tex]The z-score corresponding to any value of 'x' is given by,
[tex]z=\frac{x-\mu}{\sigma}[/tex]So the probability that the mean time for the sample is less than 28 minutes is calculated as,
[tex]\begin{gathered} P(X<28)=P(z<\frac{28-30.1}{3.6}) \\ P(X<28)=P(z<-0.58) \\ P(X<28)=P(z>0.58) \\ P(X<28)=P(z>0)-P(0From the Standard Normal Distribution Table,[tex]\varnothing(0.58)=0.2190[/tex]Substitute the value,
[tex]\begin{gathered} P(X<28)=0.5-0.2190 \\ P(X<28)=0.281 \\ P(X<28)=28.1\text{ percent} \end{gathered}[/tex]Thus, there is approximately 28.1% probability that the mean time for the sample is less than 28 minutes.
A college student completed some courses worth 6 credits and some courses worth 4 credits. The student earned a total of 104 credits after completing 21 courses.How many courses worth 4 credits did the student complete?A. 11B. 26C. 13 D. 10
Let x be the number of four credit courses and let y be the number of six credit courses.
We know that the student have completed 21 courses, this means that:
[tex]x+y=21[/tex]We also know that he has 104 credits in total. This means that:
[tex]4x+6y=104[/tex]Then we have the system of equations:
[tex]\begin{gathered} x+y=21 \\ 4x+6y=104 \end{gathered}[/tex]To solve the system we solve the first equation for y and plug the value in the second one. That is:
[tex]y=21-x[/tex][tex]\begin{gathered} 4x+6(21-x)=104 \\ 4x+126-6x=104 \\ -2x=104-126 \\ -2x=-22 \\ x=\frac{-22}{-2} \\ x=11 \end{gathered}[/tex]Therefore, the student has taken 11 four credit courses.
What is the degree of a polynomial?
Answer:
A polynomial's degree is the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients)
Step-by-step explanation:
The degree of a polynomial is the exponent of the leading term. For example, (x + 1) is a first-degree polynomial because x has an exponent of 1. (x^5 + 2y^4 - 3y^3 + y^2 - x + 3) is a fifth-degree polynomial because x has an exponent of 5.
The function h is defined as follows.
h(x)=3x²+2
Since functions are frequently composed of two smaller functions to create new functions, this definition of function is sometimes used.
What is the domain and range of f/x )= 3x 2?The graph of the function will be a straight line with no discontinuities when the equation f(x) = 3x - 2 is used.
The domain of this expression is all real integers.
The expression f(x) = 3x - 2 has as its domain "x | x is a real number," which can be written as (-,","") for any x > R.
F (x) = 3 x f (x) = 3 x f (x) = 3 x is the given function.
The domain of f f f is R mathbbR R since 3 x 3x 3x is defined for any x R x in mathbbR xR (where R mathbbR R is the set of all real numbers).
Consider the function y = f(x),
which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
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Right triangle GEO has right angle E.The length of segment EO is 10 and the length of segment OG is 15.Find the measure of angle G.
Solution
- The sketch of the triangle is given below:
- To solve for the angle [tex]\begin{gathered} \sin\angle G=\frac{Opposite}{Hypotenuse}=\frac{10}{15} \\ \\ \angle G=\sin^{-1}(\frac{10}{15}) \\ \\ \\ \angle G=41.81031489...\approx41.81\degree \end{gathered}[/tex]
Final Answer
The answer is 41.81
The length of a rectangle is 4ft less than 3 times width. Perimeter is 54 ft. What equation can be used to find the width of the rectangle
(3w-4)+2w=54
2(3w-4)+2w=54
w(3w-4)=54
2(4w-3)+2w=54
Answer:
b
Step-by-step explanation:
Here,
The length of a rectangle is 4ft less than 3 times the width
Then,
length=3w-4ft
Now,
2(l+w)=P
2(3w-4+w)=54
6w-8+2w=54
2(3w-4)+2w=54
Equation b can be used to find the width of the rectangle
I need help putting these from greatest to least 20.22.00220.0220
EXPLANATION:
The correct order is as follows:
2.002
20.2
20.02
20
The previous order is due precisely to the location it would have on the number line, in the case of whole numbers with decimals, the decimals that immediately follow the whole number must be compared to know which is the greater of the two.
Helps ASAP just 6 and 7 please and thank you
Using a calculator, we calculate the following
[tex]\begin{gathered} 1.41^2=1.9881 \\ 1.42^2=2.0164 \end{gathered}[/tex]Based on these calculations, the square root of 2 is between 1 and 2.
2. Solve each problem in two different ways as modeled in the example,Example; } x 6 = ?---&*6=zmedena. x 164x 16Kb. x12fx 12
Let's begin by listing out the given information:
[tex]\begin{gathered} \frac{2}{3}\cdot6=\frac{2\cdot6}{3}=\frac{12}{3}=4 \\ \frac{2}{3}\cdot6=2\cdot\frac{6}{3}=2\cdot2=4 \\ \\ \frac{3}{4}\cdot16=\frac{3\cdot16}{4}=\frac{48}{4}=12 \\ \frac{3}{4}\cdot16=3\cdot\frac{16}{4}=3\cdot4=12 \\ \\ \frac{4}{3}\cdot12=\frac{4\cdot12}{3}=\frac{48}{3}=16 \\ \frac{4}{3}\cdot12=4\cdot\frac{12}{3}=4\cdot4=16 \end{gathered}[/tex]What is 24 divided by 1200 in long division
Answer:
50
Step-by-step explanation:
First you'll want to start off with the 3 main numbers "120" so divide that by 24 and you'll get 5 after bringing that up you want to multiply 5 by 25 and you'll get 120 then you want to minus the original 120 by it and you'll get 0 which after that you'll want to bring the other 0 down that you did nothing to and divide it by 24 which will get you 0 and bring that up and then you got your answer
I'll be there tomorrow thank you so very sweet for the reminder of my day
we are told to complete the tables using the same ratio. To do that we need to multiply each number in the upper row by the same number to get the number in the lower row. Or divide the same number in the lower row to get the number in the upper row. In the case of table 4 we have that in the first column the numbers:
[tex]\begin{gathered} 1 \\ 9 \end{gathered}[/tex]Therefore, we need to multiply the number in the first row by 9, to get the number in the lower row. Therefore, for the second column we have:
[tex]\begin{gathered} 3 \\ 27 \end{gathered}[/tex]Since 9x3 = 27. In the third column:
[tex]\begin{gathered} 5 \\ 45 \end{gathered}[/tex]Since 9x5 = 45. In the fourth row:
[tex]\begin{gathered} 7 \\ 63 \end{gathered}[/tex]Since 9x7=63. In the final row:
[tex]\begin{gathered} 9 \\ 81 \end{gathered}[/tex]Since 9x9 = 81. And thus we complete the table.
The complete table would be:
[tex]\begin{bmatrix}{1} & 3 & {5} \\ {9} & {27} & {45} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{7} & {9} & {} \\ {63} & {81} & {} \\ {} & {} & {}\end{bmatrix}[/tex]
Rearrange x = 3g + 2 to make g the subject.
g = 1/3 x - 2/3 is a function of g .
In the simplest terms, what is a function?
A relationship between a group of inputs and one output each is referred to as a function. A function, expressed simply, is an association between inputs where each input is connected to one and only one output. A domain, codomain, or range exists for every function.x =3g + 2
Switch sides:
3g + 2 = x
Take away 2 from both sides:
3g = x - 2
Divide both sides by 3:
g = 1/3 x - 2/3
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Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the button on your calculator to solve. 8 mi. 5 mi. Volume of the cylinder = mi3
Write out the volume of a cylinder shown below
Formula
[tex]\begin{gathered} \text{Volume of a cylinder = }\Pi r^2\text{ h} \\ where\text{ radius = 5mi , height = 8mi , }\Pi\text{ = 3.142} \\ \text{Volume of a cylinder = }3.142x(5)^2x8 \\ V=628.4mi^3 \\ ThereforeVolumeofthecylinder=628.4mi^3\text{ (nearest tenth)} \end{gathered}[/tex]Hence the volume of the figure = 628.4mi³
I need help with my scale project is there anyway you could make me two similar figures with this and it also has the proportions.
To make a similar figure, we measure the lengths of each component of the figure - for example, the leg of the figure is 2 units - and then multiply each measured length by a number. This number could be any number - could be 2, 3, 4 ... but we will choose a small enough number that will give us a figure that can fit inside the graph.
Now here are the measurements of the figure.
The legs = 1 units
bottom = 2 units
top = 2 units
sides = 2 units
nose = 0 units (it is a point)
eyes - 0.5 units
Now let's multiply the measurements above by 3, which gives
The legs = 3 units
bottom = 6 units
top = 6 units
sides = 6 units
nose = 0 units (it is a point)
eyes - 1.5 units.
Finally, we draw a figure with these measurements.
your grade must be at least 64 to pass this class g least 64 g least or equal to 64 g greater 64 g greater equal 64
The given statement is your grade must be at least 64 to pass this class.
The inequality that represents this situation is
[tex]g\ge64[/tex]What function translates the function f(x) = to the right 2 units and up 10 units?
g(x)= |
Answer:
g(x) = | x - 2 | + 10
Step-by-step explanation:
given g(x) then g(x± h ) is a horizontal translation of g(x)
• if h > 0 then a move to the left of h units
• if h < 0 then a move to the right of h units
here the move is 2 units to the right, then
g(x) = | x - 2 |
given g(x) then g(x) + c is a vertical translation of g(x)
• if c > 0 then a move up
• if c < 0 then a move down
here the move is 10 units up , then
g(x) = | x - 2 | + 10
What is the image point of (-2,-3) after a translation right 2 units and up 4 units?
Does someone mind helping me please?
The proportion used to find the missing side is RS/QS = RO/PQ, the value of y = 12ft
First we need to see whether triangle RQS is similar with triangle RPO
Angle QRS = Angle PRQ (common angle)
Angle RSQ = ROP (Given, that they are right angles)
So, triangle RQS is similar with triangle RPO
Now the sides of one triangle is in proportion with the other
RS/RO = RQ/RP = QS/PQ
RS/RO = QS/PQ
RS/QS = RO/PQ
9/12 = y/16
3/4 = y/16
3/y = 4/16
3/y = 1/4
y = 4 x 3
y = 12
To find the missing side the proportion used is RS/QS = RO/PQ, the value of y = 12ft
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Solve for z-p(d + z) = -2+59
Answer
[tex]z=-(\frac{57}{p}+d)[/tex]Explanation
The question ask us to solve for z in the equation
-p (d + z) = -2 + 59
-p (d + z) = 57
Divide both sides by -p
[tex]\begin{gathered} \frac{-p(d+z)}{-p}=\frac{57}{-p} \\ d+z=\frac{-57}{p} \\ \text{Subtract d from both sides} \\ d+z-d=\frac{-57}{p}-d \\ z=\frac{-57}{p}-d \\ z=-(\frac{57}{p}+d) \end{gathered}[/tex]Hope this Helps!!!
Which number line
represents the solution to 5+8x < 3(2x+4)
Answer:
x < 3 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
I cannot see a number line, but the solution can be found by:
5 + 8x < 3(2x+4) Distribute the 3
5 + 8x < 6x + 12 Subtract 6x from both sides
5 + 2x < 12 Subtract 5 from both sides
2x < 7 Divide both sides by 2
x < [tex]\frac{7}{2}[/tex]
or
x < 3[tex]\frac{1}{2}[/tex] This means that all of the numbers less than 3 1/2 are answers.
help;aaefefdsfsd fnujyhvbnmhgf rfdgtrbtg get it?
The value of the expression [tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex] is - 98.
The abbreviation BODMAS rule is used to assist kids to recall the proper order of operations when performing mathematics. Operations are essentially the various mathematic operations we can do on numbers. "Brackets, Order, Division, Multiplication, Addition, Subtraction" is what it stands for.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Consider the expression,
[tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex]
Using the BODMAS rule,
We will first solve the parenthesis.
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-4[35-65-19]}{-2}[/tex]
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140+260+76}{-2}[/tex]
Now, the next step is to divide the expression.
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140}{-2}+\frac{260}{-2}+\frac{76}{-2}[/tex]
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=70-130-38[/tex]
Subtracting the expression,
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=-98[/tex]
Hence, the value of the expression is - 98.
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Instruction: State whether the data are symmetrical, skewed to the left, or skewed to the right:a.1; 1; 1; 2; 2; 2; 2; 3; 3; 3; 3; 3; 3; 3; 3; 4; 4; 4; 5; 5b.16; 17; 19; 22; 22; 22; 22; 22; 23c.87; 87; 87; 87; 87; 88; 89; 89; 90; 91
Based on the data in question a, the graph for the data is skewed to the left. This can be graphed and seen visually but also by calculating the mean and the median of the data set. The mean of the data is 2.85 and the median is 3. Since the mean is less than the median, we can see that the data is negatively skewed, or skewed to the left.
What is the slope of the following equation? -3y-x=0
Given the equation
[tex]-3y-x=0[/tex]To determine the slope, first write the equation in slope-intercept form (y=mx+b)
[tex]\begin{gathered} -3y-x=0 \\ -3y=x \\ y=-\frac{1}{3}x \end{gathered}[/tex]The slope corresponds to the coefficient multiplying x.
For this equation the slope is equal to -1/3.
help me pleasee!!
thank you
Answer:
f(x) = -9 * (x - 2) + 7
f(x) = -9x + 18 + 7
f(x) = -9x + 25
Help me out please please
The statement that the graph y = 2x² - 4x - 2 has a y-intercept of (0, 2) is false.
How to find y-intercept of a graph?The y-intercept is the point where a graph crosses the y-axis.
In simple terms, it is the value of y when x = 0.
Therefore, the graph is express as follows:
y = 2x² - 4x - 2
Let's check when x = 0
Therefore,
y = 2x² - 4x - 2
y = 2(0)² - 4(0) - 2
y = 2(0) - 4(0) - 2
Therefore,
y = 0 - 2
y = -2
The statement is false that the y-intercept of the graph is (0, 2)
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For which intervals is the function negative?Select each correct answer. (4,∞)(−1.5,4.2)(1,4)(−2.5,2.5)(−3,1)(−∞,−3)
Answer:
(−∞,−3)
(1,4)
Explanation:
To find the interval where the function is negative, we would look at the regions on the graph where the values of y are negative. The required intervals are the values of x in those regions. Looking at the graph,
On the left, the values of y are negative between x = - infinity and x = - 3
On the right, the values of y are negative between x = 1 and x = 4
Thus, the correct options are
(−∞,−3)
(1,4)
Answer:
(−3, 1) and (4, ∞)
Step-by-step explanation:
