In [tex]e^{2x} =10[/tex] , x = 1., by the properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
In [tex]e^{2x} =10[/tex] , taking natural logarithm on both side.
=> [tex]log_e(e^{2x})=log_e(10)[/tex]
By properties of logarithm, we know that: [tex]log_b(a)^m = m(log_b(a))[/tex]
=> [tex]2x(log_e(e))=ln(10)[/tex]
Also, as [tex]log_e(e)[/tex] = 1,
=> 2x (1) = ln(10)
=> 2x = 2.302 (approx)
=> x = 1.151
Hence, In [tex]e^{2x} =10[/tex] , x = 1.151, by the properties of logarithm.
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What is $210 to $35?
Answer:
210:35 = 6:1
Step-by-step explanation:
210:35
if divided by 35, then 6:1
Put the numbers in order from greatest to least. (photo down below)
Answer: 1 1/2> 5/4> 100%> 7/10> 0.25
Step-by-step explanation:
1 1/2= 1.50
5/4= 1.25
0.25
7/10= 0.70
100%= 1
1.50>1.25>1>0.70>0.25
please help me with this
Answer:
x=30
Step-by-step explanation:
on the left you have a ninety-degree angle.
5(x-12) = 90
5x-60=90
+60 +60
5x=150
/ /
5 5
x=30
Which graph represents a function?
Answer:
The 4th Option
Step-by-step explanation:
For a graph to be a function, it must not be broken up at any point (as in Option 3) and there can be no points that overlap each other vertically (as in Options 1 and 2). So, the only option that is continuous and with no overlapping points is Option 4.
What is the slope of the line on the graph?
Enter your answer in the box
Answer:
Step-by-step explanation: the answer is D. because all of the oher choices don't make sense obviously.
How do I graph y+4=5x?
To graph a linear equation, including the function y + 4 = 5 · x, we needed to rewrite the equation into its explicit form, mark two distinct points on a Cartesian plane and pass a line through them. The result is presented in the image attached below.
How to graph a linear equationHerein we find a linear equation in a non-canonical form and to which we are asked to graph. According to geometry, lines can be created by knowing the location of two distinct points on Cartesian plane. The detailed procedure is now shown.
First, clear the variable y to obtain the explicit form of the linear equation:
y = 5 · x + 4
Second, look up for two distinct points on Cartesian plane by evaluating the expression at distinct values of x:
x = 0
y = 5 · 0 + 4
y = 4
x = 1
y = 5 · 1 + 4
y = 9
The points (0, 4) and (1, 9) lie on the line.
Third, mark the coordinates of the two points and pass a line through them.
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A cooler contains eleven bottles of sports drinks: three lemon-lime flavored, five orange-flavored, and three fruit-punch flavored. You randomly grab a bottle. It is a lemon-lime or a fruit punch..
The probability of grabbing a lemon-limbed or a fruit punch bottle from the cooler is 6/11.
What is 'AND' and 'OR' statements in probability?'AND' represents multiplication and 'OR' represents addition.
The total number of bottles of sports drinks which is also our sample space
N(S) = 11.
The number of lemon-lime flavored bottles [tex]N(L_l)[/tex] = 3.
The Number of fruit punch flavored bottles [tex]N(F_p)[/tex] = 3.
So, the probability of grabbing a lemon-lime bottle [tex]P(L_l)[/tex] = [tex]\frac{N(L_l)}{N(S)}[/tex] = 3/11.
And, the probability of grabbing a fruit punch bottle [tex]P(F_p)[/tex] = [tex]\frac{N(F_p)}{N(S)}[/tex] = 3/11.
∴ The probability of grabbing a lemon-lime or a fruit punch bottle is the sum of the probability [tex]P(L_l) + P(F_p)[/tex].
= 3/11 + 3/11.
= 6/11.
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Sylvia has 6 1/2 boxes of chocolate to share at a family picnic. If she gives each person 1/3 of a box, how many people can receive chocolate?
The number of persons that would be able to receive the chocolates based on the question is 19
How to solve for the numberThe total number of chocolate = 6 1/2
This can be written to be 13 / 2 or 6.5
The number or amount that she has to give from what is contained in the box to each person is 1/3 = 0.33
Hence to get the number of people that would receive the chocolate we would have
6.5 / 0.33
= 19.5
This can be approximated to 19
Hence the total number that would receive the chocolate is 19
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Fill in the blanks
A=P e rt is known as the ______ formula.
A=P e rt is known as the continual" growth formula.
What is a PE RT formula?
A = PRT, where "A" is the ending amount, "P" is the beginning amount (principal, in the case of money), "r" is the growth or decay rate (represented as a decimal), and "t" is the time (in whatever unit was used on the growth/decay rate), is the equation for "continual" growth (or decay).
What is the purpose of a PE RT?
Often referred to as a PERT diagram, a PERT chart is a project management tool used to plan, schedule, and coordinate tasks within a project. Project managers can deconstruct each individual activity in the project for analysis since it provides a graphical depiction of the project's timeline.Learn more about continual" growth
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2. Twelve cans of sparkling water weigh 9 pounds.
a. How much would 4 cans of sparkling water weigh?
Answer:
Step-by-step explanation:
3 pounds
12 divided by 4= 3 pounds
what is the missing number 8X(_+7)=96
[tex]8(x + 7) = 96 \\ 8x + 56 = 96 \\ 8x = 96 - 56 \\ 8x = 40 \\ x = \frac{40}{8} \: \: \: \: \: so \: \: \: \: x = 5[/tex]
Answer:
5
Step-by-step explanation:
If im seeing this correctly, its 8(?+7) =96
if you put 5 instead of the ?
It will equal 12.
12×8 =96
-32x-2 pls help i know i should know this
Answer:
Step-by-step explanation:
64
Answer: -2 (16x + 1)
Step-by-step explanation:
chloe is 5 feet 4 inches tall. there are 2.54 centimeters in 1 inch. what is chloe's height in centimeters?
Answer:
162.56 centimeters
Step-by-step explanation:
60 inches + 4 inches = 64 inches
1 inch =
2.54 centimeters
64 inches = 162.56 centimeters
What will be the median of the following set of numbers? 126,132,128,124,134,142,134,146,134,132
Answer:
133
Step-by-step explanation:
for that we need to sort the numbers :
124,126,128,132,132,134,134,134,142,146
the median is the number, for which half of the other numbers are smaller, and the other half of the other numbers is larger.
as we have 10 numbers, there is no such single middle number.
instead, we take the 2 middle numbers and calculate their mean value. that is then the median.
the 2 middle numbers are based on our sorted list above
132, 134
the mean value is
(132 + 134)/2 = 133
and that is then the median.
A grocery store sells 6 oranges for $2. The cost of the oranges varies directly with the number of oranges.
The answer will be y =2
x and y graph also known as the x and y-axis are two important lines that make a graph. A graph consists of a horizontal axis and a vertical axis where data can be represented. A point can be described in a horizontal way or a vertical way, which can be easily understood using a graph. These horizontal and vertical lines or axis in a graph are the x-axis and y-axis respectively.
A x and y graph can be defined by the two axes i.e. x-axis and the y-axis that form a coordinate plane for a graph. The horizontal axis is represented by the x-axis and the vertical axis is represented by the y-axis. The point where the x and y-axis intersect is known as the origin and is used as the reference point for the plane.
y = 1/3x
when x =0
y = 0
when x =3
y = 1/3×3 = 1
when x=6
y=1/3×6= 2.
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a savings account recieves 12% simple interest p.a. how long would it take for £30000 to gain £7200 in interest
Answer:
2 years
Step-by-step explanation:
I= PRT/100
I=£30000 x 12 x 1 /100 =£3600
Since the interest for one year is £3600, the interest for two years is £3600x2 =£7200
Simplify m7m-4.
Please! ASAP!
Answer:
A. M^3
Step-by-step explanation:
Answer:
[tex]m^3[/tex]
Step-by-step explanation:
We can subtract the exponent 4 from the exponent 7.
Therefore,
[tex]m^{7-4}[/tex] is the answer
Then we simplify:
[tex]m^3[/tex] is our final answer.
Hope this helped!
Simplify 2.5p(2 - 0.5p) you please!!!
The simplified answer is 5p - 1.25p²
what is expression?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
2.5p(2 - 0.5p)
Now solving further
2.5p * 2 - 2.5p (0.5p)
5p - 1.25p²
Hence, the simplified answer is 5p - 1.25p².
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What is the EXPRESSION after applying the distributive property?
-0.4 (-2 + (-9))
30 points
abc is right angled triangle at a then cosine angle b sine angle c equals
abc is right angled triangle,
A triangle in which one of the interior angles is 90° is called a right angled triangle.
The longest side of a right triangle, which is also the side opposite the right angle, is the hypotenuse.The two arms of the right angle triangle are the height and the base.According to the diagram 'ab' is the height or perpendicular 'ac' is the base and 'bc' is the hypotenuse of the triangle.
Sin θ = [tex]\frac{perpendicular}{hypotenuse}[/tex]
Cos θ = [tex]\frac{base}{hypotenuse}[/tex]
Tan θ = [tex]\frac{perpendicular}{base}[/tex]
Cosine angle at b will be represented as Cos b = [tex]\frac{base}{hypotenuse}[/tex] = [tex]\frac{ab}{bc}[/tex]
the base considered for the angle at 'b' will be 'ab' since Cosine uses the base attached to the angle.
Sine angle at c will be represented as Sin c = [tex]\frac{perpendicular}{hypotenuse}[/tex] = [tex]\frac{ab}{bc}[/tex]
the perpendicular considered for the angle at 'c' will be 'ab' since Sine uses the perpendicular which lies opposite to the angle considered.
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Tavon have a gift card for $130 that loses three dollars for each 30 day It is not used he another gift card for $110 that loses 2.5 for each 30 day. It’s not used write and solve an equation for the number of 30 days periods Until the value of kid cards will be equal what will the value of each card Be when they have equal value
The equation for the number of 30 days periods until the value of both cards will be equal is 130 - 3x = 110 - 2.5x
Equationlet
Number of 30 days period = x
Gift card 1:
130 - 3x
Gift card 2:
110 - 2.5x
Equate both gift cards130 - 3x = 110 - 2.5x
130 - 110 = -2.5x + 3x
20 = 0.5x
divide both sides by 0.5x = 20/0.5
x = 40
So,
Gift card 1:
130 - 3x
= 130 - 3(40)
= 130 - 120
= $10
Gift card 2:
110 - 2.5x
= 110 - 2.5(40)
= 110 - 100
= $10
Therefore, the value of each card when they have equal value is $10
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The stingray population in a particular reef is decreasing at a rate of 1.4% per year. The population was 3800 in the year 2008.
What is the best prediction of the population in the year 2013? Round to the nearest whole number.
try do to division, 14÷3800
I'm not sure about the round though
The sum of two numbers is 56 and the difference is 24. What are the numbers?
Answer:
16 and 40Step-by-step explanation:
The sum of two numbers is 56 and the difference is 24. What are the numbers?
remove the difference from the sum and divide by two, you have the first number, add the difference to the first number and you will have the second number
(56 - 24) : 2 =
32 : 2 =
16 (1st number)
16 + 24 =
40 (2nd number)
HELP ITS DUE TOMORROW PLSS HELPP
2 is 4/6, 8/12
3 is 2/4, 4/8
4 is 8/10, 16/20
5 is =
6 is >
7 is >
8 is =
9 is =
10 is <
11 is =
12 is >
25x+5y=15
what would be the answer
Answer:
3-y/3
The slope is -2/5
Step-by-step explanation:
Factor each expression. x²-6 x+8
We will use factorization for the given equation. The factors of the expression x²-6 x+8 are x = 2, x = 4
What is factorization?Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics. For instance, the polynomial x2 - 4 and the number 15 may both be factored using the formula 3 × 5.
Given,
x²-6 x+8
Using factorization,
x² -4x - 2x + 8
⇒ x(x - 4) - 2(x - 4)
⇒ (x-2) (x-4)
⇒ x = 2, x = 4
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Two makes a necklace of Z wooden beads at $0.50 each and 6 glass beads at $1.25 each. The average cost of the beads in the necklace is $0.75. Choose an equation to model the situation
The equation model the situation is mathematically given as
(0.5x + 7.5) = 0.75(x + 6)
This is further explained below.
What is an equation to model the situation?Generally, the cost of the beads in a necklace is mathematically given as
0.50x + 6*1.25 = 0.5x + 7.5 dollars
Therefore
There are a total of x + 6 beads. Due to the fact that 0.75 is the typical cost of the beads,
[tex]\frac{0.5 x+7.5}{x+6}=0.75[/tex]
0.5 x+7.5=0.75(x+6)
In conclusion, The solution for x may be obtained as follows:
0.5x + 7.5 = 0.75x + 4.5
-0.25x = -3
x = -3/-0.25
x= 12
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NOTE; This is a complete question, with no given option, even on the internet.
Let g(x)=6-4 x
b. What is the inverse of g ?
Answer:
g-1(x)=-1/4x+3/2
Step-by-step explanation:
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $79. A season ski pass costs $350. The skier would have to rent skis with either pass for $30per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Answer:
Let s =cost of skiing per day. Here's what we know:
450 + 20s = 64s + 20s (the season pass plus ski rentals equates to daily skiing plus ski rentals)
We have 20s on both sides, so those cancel out easily:
450 = 64s
Divide both sides by 64:
7.03 ≈ s
You can't pay for a partial day, so the skier will have to ski for at least 8 days to make the season pass cheaper than getting daily passes.
Step-by-step explanation:
Hope this helps :D
4. Function f is defined by f(x) = 2x - 7 and g is defined by g(x) = 5*.
a. Find f(3), f(2), f(1), f(0), and f(-1).
1325104
b. Find g(3), g(2), g(1), g(0), and g(-1).
The values of the function f and g are -1, -3, -5, -7, -9 and 15,10,5,0,-5.
According to the statement
We have to find that the values of the function.
So, For this purpose, we know that the
The function is an expression that defines a relationship between one variable and another variable.
From the given information:
The functions are:
f(x) = 2x - 7 and g is defined by g(x) = 5x.
And Find f(3), f(2), f(1), f(0), and f(-1) and Find g(3), g(2), g(1), g(0), and g(-1).
Then
f(x) = 2x - 7
f(3) = 2(3) - 7 = 6 - 7 = -1.
f(2) = 2(2) - 7 = 4 - 7 = -3.
f(1) = 2(1) - 7 = 2 - 7 = -5.
f(0) = 2(0) - 7 = 0 - 7 = -7.
f(-1) = 2(-1) - 7 = -2 - 7 = -9.
And then
g(x) = 5x
g(3) = 5(3) = 15.
g(2) = 5(2) = 10.
g(1) = 5(1 ) = 5.
g(0) = 5(0) = 0.
g(-1) = 5(-1) = -5.
So, The values of the function f and g are -1, -3, -5, -7, -9 and 15,10,5,0,-5.
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