Answer:
t(r) = log(r)/log(5) = log₅(r)
Step-by-step explanation:
You want the inverse of r(t)=5^t.
Solve for tAn exponential function is solved using logarithms.
[tex]r = 5^t\qquad\text{given}\\\\\log(r)=t\cdot\log(5)\qquad\text{take logarithms}\\\\\boxed{t(r)=\dfrac{\log(r)}{\log(5)}}\qquad\text{divide by the coefficient of t}[/tex]
The change of base formula can be used to simplify this a bit.
[tex]\boxed{t(r)=\log_5(r)}[/tex]
__
Additional comment
The latter form of the inverse function can be found directly at the first step by taking logarithms base 5.
The notation here is slightly different from the usual "inverse function" notation, where we designate the inverse of f(x) using f⁻¹(x). The notation we have used recognizes that the function r(t) generates ordered pairs (t, r), and the inverse function t(r) generates ordered pairs (r, t).
You are welcome to make use of whatever inverse function notation will satisfy your grader.
A quantity x varies directly with the square of y and
inversely with the cube root of z. if x = 6 when y = 2
and z = 8, find the x when y = 1 and z = 27.
Answer:
x = 1-----------------------------
Given relationx = ky²/∛z, where k- constantGiven valuesx = 6, y = 2, z = 8Find the value of k6 = k×2²/∛86 = k×4/23 = kThe equation is nowx = 3y²/∛zFind the x when y = 1 and z = 27x = 3 × 1/∛27 = 3/3 = 1Answer:
x = 1
Step-by-step explanation:
k is the constant of proportionality
This question I need help with asap
The image vertices for a dilation with center (0,0) and a scale factor of 4 are A'(-12,4), B'(16,-12), C'(8,12), and D'(-4,16).
What are dilation and scale factors?
A figure or point that has undergone a change in size and location is known as dilation.
The amount by which the figure is stretched or contracted in a dilation is known as the scale factor.
The coordinates of the points in the pre-image can be multiplied by the scale factor to get the points in the picture if we are dilating a figure that is centered at the origin.
Given, vertex A = (-3,1), vertex B = (4,-3)
vertex C = (2,3), vertex D = (-1,4)
scale factor = 4 and center = (0,0)
Now, we need to find the image of the given vertices for dilation with center (0,0) and scale factor 4, then we have to multiply the given vertices with scale factor 4
A' = (-3*4,1*4) = (-12,4)
B' = (4*4,-3*4) = (16,-12)
C' = (2*4,3*4) = (8,12)
D' = (-1*4,4*4) = (-4,16)
Hence, the image of the given vertices are A'(-12,4), B'(16,-12), C'(8,12) and D'(-4,16).
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IXL Help Fast ! Please And Thank You For Helping Me :)
Answer:
52 degrees
Step-by-step explanation:
first solve for x
9x-20=2x+36
9x=2x+56
7x=56
x=8
Now we find angle PTU
9(8)-20
72-20
52
Hopes this helps please mark brainliest
I am a multiple of 2 , 5 and 7. The sum of my three digits is 10 . I am not 280.
The multiple of 2, 5, and 7, such that the sum of the 3 digits is 10 is:
630
How to find the number?We want to find a number that is a multiple of 2, 5 and 7, such that the sum of the 3 digits is 10. (such that the number is not 280)
So our number N is of the form:
N = a*(2*5*7)
Where a is an integer.
N = a*70
Here we just need to find the value of a such that the sum of the 3 digits of the outcome is equal to 10.
For example, if a = 2 then:
N = 2*70 = 140
The sum gives 1 + 4 + 0 = 5
Now we jut need to keep trying values of a.
Eventually, we will get to:
if a = 9 then:
N = 9*70 = 630
The sum gives: 6 + 3 + 0 = 10
So this is our number.
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Michael's mom loves Bright Scents candles. A 4-inch candle will burn for 8 hours. Michael bought his mom a 10-inch candle for Mother's Day.
If Bright Scents candles all burn at the same rate, how many hours will the 10-inch candle burn?
Answer:
Step-by-step explanation:
OAN, OMB, APB and MPN are straight lines and AN = 20A.
M is the midpoint of OB.
OA = a
OB = b
AP = KAB where k is a scalar quantity.
Express AB and MN in terms of a and b.
Express MP in terms of a, b and k.
Finally, find the value of k.
The length of AB = b - a, MN = 3a - b/2 and MP = b/2 + (k + 1)(b - a).
What is triangle?A triangle is defined as a two-dimensional shape with three sides, three interior angles, and three vertices.
Given that OB = b and OA = a
From ΔAOB we have
OB + BA + AO = 0
b + (- AB) -a = 0
AB = b - a
Now from ΔMNO we get
MN + NO + OM = 0
MN + (-ON) + OB/ 2 = 0
MN - (OA + AN) + b/2 = 0
MN - (a + 2a) + b/2 = 0
MN = 3a - b/2
Now from ΔMBP, we have
MB + BP + PM = 0
OB/2 + (BA - PA) + PM = 0
b/2 + (- AP/k + AP) + PM = 0
b/2 + (-kAB /k + kAB) + PM = 0
b/2 + (k AB + AB) + PM = 0
PM = -b/2 - (k + 1) (b - a)
MP = b/2 + (k+1) (b - a)
Hence, The length of AB = b - a, MN = 3a - b/2 and MP = b/2 + (k + 1)(b - a).
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State all integer values of a in the interval [0, 7] that satisfy the following inequality:
−5x+3>-4
All integer values of x in the interval [0, 7] are 0,1
What is an integer?
A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
−5x+3>-4
-5x > -4-3
-5x > -7
Divide by -5 on both sides
x< -7/-5
x< 7/5
x< 1.4
So, all integer values of x in the interval [0, 7] are 0,1
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x/3 + 2 = 16 What is X
Answer:
[tex]\sf x=42[/tex]Step-by-step explanation:
[tex]\sf \cfrac{x}{3}+2=16[/tex]
First, subtract 2 from both sides:-
[tex]\sf \cfrac{x}{3}+2-2=16-2[/tex]
Simplify:-
[tex]\sf \cfrac{x}{3}=14[/tex]
Now, let's multiply both sides by 3:-
[tex]\sf \cfrac{3x}{3}=14\times\:3[/tex]
Simplify:-
[tex]\sf x=42[/tex]
____________________Hope this helps!
Have a great day! :)
f(x) = 5x - 6 , g(x) = x - 2
(fog)(x)
Answer:
(f∘g)(x) = 5x -16
Step-by-step explanation:
You want the simplified form of the composition (f∘g)(x) when f(x)=5x-6 and g(x)=x-2.
CompositionThe notation (f∘g)(x) is a shorthand way to write f(g(x)). The composition operator (ring operator) works right to left, meaning that g(x) is evaluated first, then the result is used as an argument to the function f.
EvaluationFunctions are evaluated in the usual way.
f(g(x)) = f(x-2) = 5(x-2) -6 = 5x -10 -6 = 5x -16
(f∘g)(x) = 5x -16
x²+5x-9=0 , solve by completing the square.
Answer:
x=1/2
Step-by-step explanation:
x^2+5x-9=0
Plus 9: x^2+5x=9
square root: x+5x=3
6x=3 so x=1/2
steps for graphing y= x^2 - 4x
The graph using the direction, vertex, focus, and axis of symmetry is shown below.
The given equation is y=x²-4x.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Put x=0, 1, 2, 3, 4,....in the given equation, we get
When x=0
y=0
When x=1
y=-3
When x=2
y= -4
When x=3
y= -3
When x=4
y=0
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (2, -4)
Focus: (2, -15/4)
Axis of Symmetry: x=2
Directrix: y= -17/4
Hence, the graph using the direction, vertex, focus, and axis of symmetry is shown below.
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How much would $300 invested at 4% interest compounded monthly be worth after 2 years? Round your answer to the nearest cent.
Equation: A(t)=P(1+r/n)^nt
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$300\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &2 \end{cases}[/tex]
[tex]A=300\left(1+\frac{0.04}{12}\right)^{12\cdot 2} \implies A=300\left( \frac{301}{300} \right)^{24}\implies A \approx 324.94[/tex]
Write the equivalent fraction for 9/3
Answer: Let 5/9=□/54
Clearly shows 54=(9×6)
Now multiply the numerator by 6 also
∴5 / 9 = (5 \times 6) / (9 \times 6) = 30 /54$$
Hence, 30/54 is the equivalent fraction of 5/9 having denominator 54
(ii) Let 5/9=35/□
Clearly shows 35=(5×7)
Now multiply the denominator by 7 also
∴5/9=(5×7)/(9×8)=35/63
Hence, 35/63 is the equivalent fraction of 5/9 having numerator 35
Step-by-step explanation:
If two lines cross at the point (2, 3), then the system has two solutions.
False
True
Answer:
Step-by-step explanation:
False. They have one point in common meaning there is only 1 solution.
A number x minus 1 is no less than 3. write in algebric equation form
Answer:
[tex]x - 1 \geqslant 3[/tex]
marbles are sold in boxes in bags or single marbles each has 10 bags or marbles in it each bad has 10 in it
Answer:
The first blank is 13, the second blank is 19.Step-by-step explanation:
GivenEach bag has 10 marbles and each box has 10 bags.Each box has10*10 = 100 marblesNow, to complete the sentences assume the missing value is x.
1) 1 box, x bags and 9 single marbles:
1*100 + 10x + 9 = 239109 + 10x = 23910x = 239 - 10910x = 130x = 132) 2 boxes, 2 bags and x single marbles:
2*100 + 2*10 + x = 239200 + 20 + x = 239220 + x = 239x = 239 - 220x = 19[tex]2\sqrt{4} * \sqrt{9}[/tex]
According to the given square root value, the resulting value of the expression 2√4 × √9 is 12
Square root:
Square root refers any number that is equal to a number, which when squared gives the original number.
Given,
Here we have the expression 2√4 × √9.
Now, we have to find the value of the expression.
While we looking the given expression we have identified that the value of the square roots are
√4 = √(2 x 2) = 2
Similarly, the value of
√9 = √(3 x 3) = 3
So, now we have to replace the root with these values, then we get,
=> (2 x 2) x 3
=> 4 x 3
=> 12
Therefore, the resulting value is 12.
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If the sum of two rational numbers is-5/16
and if one of the number is -9/20, then
find other national number?
The other rational number is -23/60.
What are rational numbers?The ratio or fraction of two numbers, p/q, where p and q are the numerator and denominator, respectively, can be used to express a rational number in mathematics. For example, 3/7 and any integer are rational numbers. Examples from the rational number range include 1/3, 2/4, 1/5, 9/3, and so on.So, the other rational number is:
We know that,
The Sum of 2 rational numbers is -5/16.One of the numbers is -9/20.Now, get the other number as follows:
x -9/20 = -5/6x = -5/6 + 9/20x = 10(-5) + 3(9)/60x = -50 + 27/60x = -23/60Therefore, the other rational number is -23/60.
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Denise subtracted -9
8 and came up with an answer of -17 feet. Is
Denise correct? Why or why not?
Answer:she is correct i dont really get the formula but if -9 - 8 = -17
Step-by-step explanation:
Minutes : 0 3 6 9 12
Words typed: 0 120 ? 360 480
Kenny is practicing for a typing test to obtain a job as paralegal. The number of words he can type is proportional to the number of minutes he types. If the test is 18 mins long how many word will Kenny be able to type
2.what is the missing number in the table above
As per the proportionally concept, the missing value in the table is 240
and in 18 minute Kenny type 720 words.
Proportionality:
If two objects are proportional to each other, then it means that as one object increases the other will also increase and the ratio of the quantities is the same for all values.
Given,
Kenny is practicing for a typing test to obtain a job as paralegal. The number of words he can type is proportional to the number of minutes he types.
Here we need to find if the test is 18 mins long how many word will Kenny be able to type and the missing value in the table.
Here we have assume that if number of words typed is proportional to number of minutes
So, it can be written as Word typed α number of minutes
As in the equation form of the relation is,
Word typed = k * number of minutes
where k refers constant of proportionality
So, first we have to find the value of k, in order to solve this,
For, that we have to take the following,
=> 120 = k * 3
=> k = 120/3
Therefore, k = 40
So, if test is 18 minutes long, then the number of words is calculated as,
=> Word typed = k * 18
=> Word typed = 40 * 18
=> Word typed = 720
And the missing value of the table is,
=> words = 40 * 6
=> words = 240
Therefore, the number of words in 6 minutes is 240.
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A bacteria culture initially contains 2000 bacteria and doubles every half hour.
Find the size of the baterial population after 80 minutes.
Find the size of the baterial population after 8 hours.
I need BOTH questions answered pls!
Answer:
32000 bacteria
Step-by-step explanation:
because it doubles every half hour and it has 200 then it would be 32000 bacteria
CAN SOMEONE HELP ME WITH THIS BASIC GEOMETRY??
Answer:
147 degrees
Step-by-step explanation:
a straight line is always 180 degrees so the sum of these 2 angles equal 180 degrees so we pop it into an equation to solve for a
33+a=180
-33. -33
a=147
Hopes this helps please mark brainliest
Answer:
a = 147°
Step-by-step explanation:
33° + a form a straight line which is 180 °
33 + a = 180
a = 147°
-5x² + 6x -1 =7-7x²
it’s the zero product rule
Simplifying
-7x2 + 5x + -18 = 0
Reorder the terms:
-18 + 5x + -7x2 = 0
Solving
-18 + 5x + -7x2 = 0
Solving for variable 'x'.
Begin completing the square. Divide all terms by
-7 the coefficient of the squared term:
Divide each side by '-7'.
2.571428571 + -0.7142857143x + x2 = 0
Move the constant term to the right:
Add '-2.571428571' to each side of the equation.
2.571428571 + -0.7142857143x + -2.571428571 + x2 = 0 + -2.571428571
Reorder the terms:
2.571428571 + -2.571428571 + -0.7142857143x + x2 = 0 + -2.571428571
Combine like terms: 2.571428571 + -2.571428571 = 0.000000000
0.000000000 + -0.7142857143x + x2 = 0 + -2.571428571
-0.7142857143x + x2 = 0 + -2.571428571
Combine like terms: 0 + -2.571428571 = -2.571428571
-0.7142857143x + x2 = -2.571428571
The x term is -0.7142857143x. Take half its coefficient (-0.3571428572).
Square it (0.1275510204) and add it to both sides.
Add '0.1275510204' to each side of the equation.
-0.7142857143x + 0.1275510204 + x2 = -2.571428571 + 0.1275510204
Reorder the terms:
0.1275510204 + -0.7142857143x + x2 = -2.571428571 + 0.1275510204
Combine like terms: -2.571428571 + 0.1275510204 = -2.4438775506
0.1275510204 + -0.7142857143x + x2 = -2.4438775506
Factor a perfect square on the left side:
(x + -0.3571428572)(x + -0.3571428572) = -2.4438775506
Please help l need in it
Solve the following percent problems using the appropriate percent equation. Describe
the steps used to calculate each answer.
1) What distance is 24% of 710 miles?
2) 62 hours is what percent of 3 days?
3) 16% of what number is 8
The distance 170.4 is 24% of 710 miles, 86.1% is the percent of 62 hours of 3 days and 50 is the 16% of the 8.
What is percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
1) given, 24% and 710 miles,
24/100×710= 170.4
2) first convert 3 days into hours.
=(3)(24) = 72 hours.
62/72×100=86.1%
3) let x be that number,
16%of x = 8
16/100×x = 8
x = 800/16
x =15
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Please help me. I really need help
Answer:
10
Step-by-step explanation:
line LF divides the triangle into two equal parts
since LH is 5
therefore, GH is 5*2=10
Sherman has 3 cats and 2 dogs. He wants to buy a toy for each of his pets. Sherman has $27 to spend on pet toys. How much can he spend on each pet? Enter the answer as a fraction and then as an amount in dollars and cents. I'm so confused could you guys help me?
Answer:
delete
Step-by-step explanation:
ok this is wrong pls delete
I don’t know how to solve this one
(x+2)(x+5)(x-3) These are the factor of x³+4x²-11x-30
Hence x+3 is not the factor of this equation
What in mathematics is a binomial equation?
A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.
factor the equation
x³+(2x²+2x²)-(-4x+15x)-30
x³+2x²+2x²+4x-15x-30
x²(x+2)+2x(x+2)-15(x+2)
(x+2)(x²+2x-15)
(x+2)(x+5)(x+3)
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Jan needs 1000 signatures on a petition. If 230 people sign the petition each day, how many days will it take 1000 people to sign the petition
The number of days which it would take 1000 people to sign the petition as required in the task content is; 4.35 days.
What is the number of days required for 1000 people to sign the petition?It follows from the task content that the number of days which it would take Jan to get 1000 signatures on the petition be determined.
Since it is given in the task content that 230 people sign the petition each day.
It therefore follows from proportion that the number of days needed for 1000 people to sign the petition is;
= 1000/230
= 4.3478 days.
Hence, the number of days which it would take 1000 people to sign the petition is approximately; 4.35 days.
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10
When can you use proportional reasoning to solve a problem?
Proportional reasoning can be used to solve a problem in which one quantity is a constant multiple of the other.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
Proportional reasoning is the reasoning based on the cognition that a relationship exists between the multiples of the variables in the problem, such that the magnitude of a variable can implied from the changes made to the relationships connecting the variables.
An example of proportional reasoning is the distance travelled, d, after a given time, t, at a constant velocity, v;
d = v·t
To judge the distance travelled, a constant, v, multiplies the time, t, such that, at a longer time, it can be reasoned that the distance travelled is much further.
Therefore, proportional reasoning can be used to solve a problem in which one quantity is a constant multiple of the other.
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Every month, Theresa sets aside $410.60 of her paycheck to use as spending money. This month, she plans to use of her spending money for groceries.How much money would Theresa have this month to 2/5 spend on items other than groceries?
The amount spent for other than groceries is $246.36.
Given that the money to spend this month = $410.60
Theresa uses 2/5 of the money to groceries.
So she spent on groceries = 410.60*(2/5) = 164.24
We have to subtract the spending on groceries from the total spending in order to find the required.
Then the amount spend other than groceries = 410.60-164.24 = 246.36
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