Answers
The values of a, b and c from the given exponential function are 7, 9 and 4 respectively
Laws of indicesAccording to the exponential law of indices
[tex]\sqrt[c]{a^b}[/tex]
This can be written as;
[tex]\sqrt[c]{a^b}=a^{\frac{b}{c} }[/tex]
Given the exponential expression
[tex]7^\frac{9}{4}[/tex]
Compare with the original expression
a = 7, b = 9 and c = 4
Hence the values of a, b and c from the given exponential function are 7, 9 and 4 respectively
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Related Questions
help please i need to turn this in
Answers
Answer:
Q3 = $5743.49117291326
Q4 = $10955.6157151671
Step-by-step explanation:
General formula for amount in Compound Interest
Amount [A] = [tex]P(1+r)^{t}[/tex]
Here, P = principal
r = rate of interest in decimal form
t = time in years
Q3
----
Substitute current values in question with formula to give you
$5743.49117291326
Q4
----
Substitute current values in question with formula to give you
$10955.6157151671
Hailey created her own cleaning service and uses the equation t = 20n + 15 to represent her total earnings, t, for each job. If she earned a total of $80, how many hours, n, did she work?
Answers
Step-by-step explanation:
t = 20n + 15
t = 80
80 = 20n + 15
65 = 20n
n = 65/20 = 13/4 = 3.25 hours
A culture of bacteria has an initial population of 9300 bacteria and doubles every 3
hours. Using the formula P = Po 25, where Pt is the population after thours, P
is the initial population, t is the time i hours and d is the doubling time, what is the
population of bacteria in the culture after 10 hours, to the nearest whole number
Answers
Answer:
The approximate population of bacteria in the culture after 10 hours is 93,738.
Step-by-step explanation:
General Concepts:Exponential Functions.Exponential Growth.Doubling Time Model.Logarithmic Form.BPEMDAS Order of Operations:
Brackets.Parenthesis.Exponents.Multiplication.Division.Addition.Subtraction.Definitions:We are given the following Exponential Growth Function (Doubling Time Model), [tex]\displaystyle\mathsf{P_{(t)}\:=\:P_0\cdot2^{(t/d)}}[/tex] where:
[tex]\displaystyle\sf{P_t\:\:\rightarrow}[/tex] The population of bacteria after “t ” number of hours. [tex]\displaystyle\sf{P_0 \:\:\rightarrow}[/tex] The initial population of bacteria. [tex]\displaystyle{t \:\:\rightarrow}[/tex] Time unit (in hours). [tex]\displaystyle{\textit d \:\:\rightarrow}[/tex] Doubling time, which represents the amount of time it takes for the population of bacteria to grow exponentially to become twice its initial quantity. Solution:Step 1: Identify the given values.
[tex]\displaystyle\sf{P_0\:=}[/tex] 9,300. t = 10 hours. d = 3.Step 2: Find value.
1. Substitute the values into the given exponential function.
[tex]\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow P_{(10)} = 9300\cdot2^{(10/3)}}[/tex]
2. Evaluate using the BPEMDAS order of operations.
[tex]\displaystyle\mathsf{P_{(10)} = 9300\cdot2^{(10/3)}\quad \Longrightarrow BPEMDAS:\:(Parenthesis\:\:and\:\:Division).}[/tex]
[tex]\displaystyle\sf P_{(10)} = 9300\cdot2^{(3.333333)}\quad\Longrightarrow BPEMDAS:\:(Exponent).}[/tex]
[tex]\displaystyle\sf P_{(10)} = 9300\cdot(10.079368399)\quad \Longrightarrow BPEMDAS:(Multiplication).}[/tex]
[tex]\boxed{\displaystyle\mathsf{P_{(10)} \approx 93,738.13\:\:\:or\:\:93,738}}[/tex]
Hence, the population of bacteria in the culture after 10 hours is approximately 93,738.
Double-check:We can solve for the amount of time (t ) it takes for the population of bacteria to increase to 93,738.
1. Identify given:
[tex]\displaystyle\mathsf{P_{(t)} = 93,738 }[/tex].[tex]\displaystyle\mathsf{P_0 = 9,300}[/tex].d = 3.2. Substitute the values into the given exponential function.
[tex]\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 93,378 = 9,300\cdot2^{(t/3)}}[/tex]
3. Divide both sides by 9,300:
[tex]\displaystyle\mathsf{\longrightarrow \frac{93,378}{9,300} = \frac{9,300\cdot2^{(t/3)}}{9,300}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 10.07936840 = 2^{(t/3)}}[/tex]
4. Transform the right-hand side of the equation into logarithmic form.
[tex]\boxed{\displaystyle\mathsf{\underbrace{ x = a^y}_{Exponential\:Form} \longrightarrow \underbrace{y = log_a x}_{Logarithmic\:Form}}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 10.07936840 = \bigg[\:\frac{t}{3}\:\bigg]log(2)}[/tex]
5. Take the log of both sides of the equation (without rounding off any digits).
[tex]\displaystyle\mathsf{log(10.07936840) = \bigg[\:\frac{t}{3}\:\bigg]log(2)}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 1.003433319 = \bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996)}[/tex]
6. Divide both sides by (0.301029996).
[tex]\displaystyle\mathsf{\frac{1.003433319}{0.301029996} = \frac{\bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996) }{0.301029996}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 3.3333333 = \frac{t}{3}}[/tex]
7. Multiply both sides of the equation by 3 to isolate "t."
[tex]\displaystyle\mathsf{(3)\cdot(3.3333333) = \bigg[\:\frac{t}{3}\:\bigg]\cdot(3)}[/tex]
[tex]\boxed{\displaystyle\mathsf{t\approx10}}[/tex]
Hence, it will take about 10 hours for the population of bacteria to increase to 93,378.
__________________________________
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What linear equation in slope intercept form does this graph represent?
Answers
Answer: Hope this helps
y = 3/5x + 100
Slope: 3/5
Y-int: 100
Step-by-step explanation:
y = mx + b
replace b with y-int
y = mx + 100
replace m with the slope which is 3/5
y = 3/5x + 100
How do you get slope?
Well I did rise/run with two points so I saw it ran 5 squares and rose only 3.
How do you get the y-int?
Well the y-int is the point where x is 0. So using the point (0,100), since x is 0, the y-int is 100.
Find the slope of the line.
Answers
Answer:
-1
Step-by-step explanation:
Rise/Run equates it to be -1/1 wich is -1
Question 5 ? Question What does the x-intercept of this relationship represent? O the initial amount of plant food the length of time it takes for Ryan to use all the plant food O the amount of plant food used each day O the length of time it takes for the height of the plant to reach 72 centimeters
Answers
Answer:
O the amount of plant food used each day
Step-by-step explanation:
O the initial amount of plant food the length of time it takes for Ryan to use all the plant food is the y-intercept therefore wrong.
O the length of time it takes for the height of the plant to reach 72 centimeters
$20.000 deposit earning 3.5% compounded monthly,after 10 years
Answers
Answer:
A = $28,338.18 after 10 yrs
Step-by-step explanation:
hope this helps
hope you can understand
Enter a range if values for x.
Answers
Answer:
See the attachment photo!
Please help I am so confused
The phone company Ringular has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 480 minutes, the monthly cost will be $277. If the customer uses 990 minutes, the monthly cost will be $532.
A) Find an equation in the form
y=mx+b, where x is the number of monthly minutes used and
y is the total monthly cost of the Ringular plan.
Answer:
y=
B) Use your equation to find the total monthly cost if 881 minutes are used.
Answer: If 881 minutes are used, the total cost will be
Answers
The total cost when 881 minutes is used is $477.50.
What are the equation that model the question?a + 480b = 277 equation 1
a + 990b = 532 equation 2
Where:
a = flat fee b = variable fee What is the flat fee and the variable fee?Subtract equation 1 from equation 2
510b = 255
b = 255 / 510
b = $0.50
In order to determine the flat fee, substitute for b in equation 1
a + 480(0.5) = 277
a + 240 = 277
a = 277 - 240
a = $37
What is the total cost when 881 minutes is used?
Total cost = flat fee + (variable cost x number of minutes spoken)
$37 + (881 x 0.5) = $477.50
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Collect info on minimum and maximum temperature if 7 consecutive days in creative manner
Answers
Write two numbers that multiply to the value on top and add to the value on bottom.
-84
17
Answers
Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
What is multiplication?Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.
The two given numbers are -84 and 17.
We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).
If we multiply 21 and -4, we get the product as -84.
That is, 21×(-4)=-84
If we add 21 and -4, we get the sum as -17.
That is, 21+(-4)=21-4=17
Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
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Help ASAP......
What are the dimensional formula of a and b in the relation F = at² + bx, whrer F is force, t is time and x is distance ?
Answers
Heya User !
Your Answer is in the attachment, do check out.
MᎥssAbhᎥ ☁
What’s 1938292+92268292
Answers
Step-by-step explanation:
the answer is 94206584 kk
Cara leaves her house at 10:03 and arrives at the library at 10:17.
Irena leaves her house at 11:55 and arrives at the library at 12:06.
Who takes longer to get to the library? How many minutes longer?
Choose...
takes longer. She takes
Choose...
minutes longer.
Answers
Answer: Cara takes longer
Step-by-step explanation:
cara takes 14 minutes
irena takes 11
Answer:
cara takes longer by 14 minutes than Irena who takes 11 minutes
How do I evaluate this double integral
Answers
Convert to polar coordinates with
[tex]x = r \cos(\theta)[/tex]
[tex]y = r \sin(\theta)[/tex]
so that [tex]x^2 + y^2 = r^2[/tex], and the Jacobian determinant for this change of variables is
[tex]dx\,dy = r \, dr \, d\theta[/tex]
D is the disk centered at the origin with radius 2; in polar coordinates, this is the set
[tex]D = \left\{(r, \theta) \mid 0\le\theta\le2\pi \text{ and } 0 \le r \le 2\right\}[/tex]
Then the integral is
[tex]\displaystyle \iint_D (x + y + 10) \, dx \, dy = \int_0^{2\pi} \int_0^2 (r \cos(\theta) + r \sin(\theta) + 10) r \, dr \, d\theta[/tex]
[tex]\displaystyle = \int_0^{2\pi} \int_0^2 (r^2 \cos(\theta) + r^2 \sin(\theta) + 10r) \, dr \, d\theta[/tex]
[tex]\displaystyle = \int_0^{2\pi} \left(\frac83 (\cos(\theta) + \sin(\theta)) + 20\right) \, d\theta[/tex]
[tex]\displaystyle = 20 \int_0^{2\pi} d\theta = \boxed{40\pi}[/tex]
(since cos and sin are 2π-periodic)
Given sine of x equals negative 5 over 13 and cos x > 0, what is the exact solution of cos 2x?
Answers
The value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have given:
sinx = -5/13
and cosx > 0
We know,
cos2x = 1 - 2sin²x
sinx = -5/13
Squaring on both sides:
sin²x = 25/169
Multiply by 2 on both the sides:
2sin²x = 2(25/169)
Add -1 on both sides:
-1 + 2sin²x = -1 + 2(25/169)
or
1 - 2sin²x = 1 - 2(25/169)
cos2x = 1 - 50/169
cos2x = 119/169 (as the cosx > 0)
Thus, the value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.
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Answer:
The guy above me is correct
Step-by-step explanation:
Look at the screen shot I got it correct
factoring using the distributive property
got really sick and missed a bunch of school, would really appreciate the help !
Answers
Answer:
Step-by-step explanation:
Factorizing using distributive property: Factorize the terms Find the Greatest Common factor. Take GCF from both the terms.1) 5a² - 15
5a² = 5 * a²
15 = 5 * 3
GCF = 5
5a² - 15 = 5*a² - 5*3
= 5a(a - 3)
5) 36x²y - 48xy²
36x²y = 2 * 2 * 3 * 3 * x² * y
48xy² = 2 * 2 * 2 * 2 * 3 * x * y²
GCF = 2 * 2 * 3*x*y = 12xy
36x²y - 48xy² = (12xy * 3x) - (12xy*4y)
= 12xy*(3x - 4y)
6)75b²c³ + 60bc⁶
75b²c³ = 3 * 5 * 5 * b² * c³
60bc⁶ = 2 * 2 * 3 * 5 * b * c⁶
GCF = 3*5*b*c³ = 15bc³
75b²c³ + 60bc⁶ = [15bc³* 5b] + [15bc³ * 4bc³]
= 15bc³ * (5b + 4bc³)
For each of the number lines, write an absolute value equation in the form |x - c |=d,
where c and d are some numbers, to satisfy the given solution set.
Answers
The absolute value equation that satisfy the solution set of -4 and -8 is |2 - x| = -6
How to determine the absolute value equation?The solution sets on the number line are given as:
x = {-8, -4}
Calculate the average of the solutions
Mean = (-8 - 4)/2
Mean = -6
Calculate the difference of the solutions divided by 2
Difference = (-4 + 8)/2
Difference = 2
The absolute value equation is the represented as:
|Difference - x | = Mean
Substitute known values
|2 - x| = -6
Hence, the absolute value equation is |2 - x| = -6
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Answer:
|b+6|=2
Step-by-step explanation:
which of the following rational functions is graphed below
Answers
Considering it's vertical asymptotes, the rational function graphed below is given by:
B. [tex]F(x) = \frac{1}{(x - 1)(x + 1)[/tex]
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
In this problem, the vertical asymptotes are at [tex]x = \pm 1[/tex], hence the function is given by:
B. [tex]F(x) = \frac{1}{(x - 1)(x + 1)[/tex]
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Which of the following is used only in non-Euclidean geometry?
A.
triangle
B.
circle
C.
great circle
D.
line
Answers
Answer:c
Step-by-step explanation:none of these are good answers as they can all exist in flat Euclidean space. The best answer is c because a great circle exists in spherical (non-flat) geometry . However it’s not really correct to say you could never describe a great circle in Euclidean space and whoever wrote this question (not you, the original author of the question) deserves to bite their tongue on their dinner tonight
Emily completed reading 24/3 books in 32/4 days. Find the number of books she would have completed in one day.
Answers
The number of books she would have completed in one day will be 2 books.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Emily completed reading 24/3 books in 32/4 days
Emily completed 8 books in 4 days. The number of the books will be calculated by using the expression below:-
4 days = 8 books
1 day = 8 / 4 = 2 books
Therefore the number of books she would have completed in one day will be 2 books.
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I need help solving this problem system of equations
Answers
Answer:
y= -6
Step-by-step explanation:
-4x and 4x are canceled out. -2y+8y= 6y. -12-24=-36
You are left with 6y=-36 . Divide from both sides and -36/6 is -6. So, y=-6.
Hope this helped.
PppppppppppppppppHELPppppppp
Answers
Step-by-step explanation:
please mark me as brainlest
THE ANSWER IS B I THINK IF ITS WRONG IM SORRY
The subtraction property of equality states that the two sides of an
equation remain unequal when you subtract the same number of each
side.
O True
O False
* 10 points
Answers
Answer:
False
Step-by-step explanation:
The answer is in its name. Its a property of equality meaning it makes sure that both sides are equal to each other
What are the coordinates of the point on the directed line segment from (−1,−6) to (8,-3) that partitions the segment into a ratio of 1 to 2?
Answers
The coordinates of the point on the directed line segment is (5,-4)
What is a line segment?A line segment is a line drawn to join two given points on the cartesian plane.
Analysis:
x coordinate = MX1 + NY1/M + N
y coordinate = MY1 + NY1/ M+N
where M and N are the ratio of division
x = 1(-1) + 2(8)/1+2 = 15/3 = 5
y = 1(-6) + 2(-3)/1+2 = -12/3 = -4
(5,-4)
In conclusion, the coordinates are (5,-4)
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Help will give brainly! :)
Answers
Answer:
4x²y² and 16x⁴y⁶
Step-by-step explanation:
A sector with an area of \goldE{54\pi\,\text{cm}^2}54πcm
2
start color #a75a05, 54, pi, start text, c, m, end text, squared, end color #a75a05 has a radius of \maroonD{9\,\text{cm}}9cmstart color #ca337c, 9, start text, c, m, end text, end color #ca337c.
What is the central angle measure of the sector in radians?
Answers
The central angle measure of the sector is 4.19 rad.
Area of a Sector
You need apply the formula: [tex]A= r^2*\frac{\alpha}{2}[/tex] for finding the area of the sector, in radians. In this formula, the variables are:
r= radius
[tex]\alpha[/tex]= central angle
The question gives:
A=54[tex]\pi[/tex] cm²
r= radius= 9cm
Thus, the central angle will be:
[tex]A= r^2*\frac{\alpha}{2}\\ \\ 54\pi =81*\frac{\alpha }{2} \\ \\ 1.33333\pi =\alpha[/tex]
For [tex]\pi[/tex]=3.14159..., you have :
[tex]\alpha=4.19\; rad[/tex]
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Answer:
4pi/3
Step-by-step explanation:
Is this rational or irrational?
Answers
Answer:
Irrational.
Step by step explanation:
[tex]\sqrt 6 + \dfrac{2}{3}\\\\\\=\dfrac{3\sqrt 6 +2}{3}\\\\\text{The sum of the these two numbers cannot be expressed as the the ratio of two integers,}\\\\\text{So the sum is not rational.}[/tex]
What is the slope of the line that passes through the points (1, 3) and (5, -2)?
Answers
Answer:
slope = -5/4
Step-by-step explanation:
Because you have been given two points, you can use point-slope formula to find the slope. In the equation, "m" is the slope.
1st Point: (1,3)
2nd Point: (5, -2)
y₁ - y₂ = m(x₁ - x₂) <----- Point-Slope Equation
3 - (-2) = m(1 - 5) <----- Plug "x" and "y" values into equation
5 = m(-4) <----- Combine like terms
-5/4 = m <----- Divide both sides by -4
Pleaseeee helppppp!!!!!!!!!
Answers
Answer:
107 degree
Step-by-step explanation:
interior angle sum of a hexagon is 720,
using S = (n - 2)*180
which is S =(4)*180
720-118-111-124-115-145=107