[tex]e^{3x}=12\\\\3x=\ln 12\\\\x=\dfrac{\ln 12}{3}\approx0.83\\\\\\[/tex]
Answer:
x=0.83
Step-by-step explanation:
Given: [tex]e^{3x}=12[/tex]
We are given an exponential equation and to solve for x.
[tex]e^{3x}=12[/tex]
Taking ln both sides
[tex]\ln e^{3x}=\ln 12[/tex]
[tex]3x\ln e=\ln 12[/tex] [tex]\because ln a^m=m\ln a[/tex]
[tex]3x=\ln 12[/tex] [tex]\because \ln e=1[/tex]
[tex]x=\dfrac{\ln 12}{3}[/tex] [tex]\text{divides both sides by 3}[/tex]
The exact value of x is [tex]\dfrac{\ln 12}{3}[/tex]
Using calculator to find ln 12
[tex]x=\dfrac{2.4849}{3}[/tex]
[tex]x=0.8283[/tex]
Hence, The value of x is 0.83
Could someone please help me on this? This is one question
The point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
We have a slope m = 2 and point (-8, 2)
Substitute:
[tex]y-2=2(x-(-8))\\\\y-2=2(x+8)[/tex]
The ages of the student in a dance class are 10 9 11 12 9 10 9 10 11 12 8 12 12. what is the mode for this set of data?
Unscramble all the words worth a lot of points please help!!!
1. rational number
2. percent
3. least common denominator
4. proportion
5. percent proportion
I am positive that these numbers are correct.
1 is rational number
2 is percent
3 is least common denominator
4 is proportion
5 is percent proportion
What is the solution set of the equation? x^2-14x=14
x^2 - 14x = 14
x^2 - 14x + 49 = 63
(x - 7)^2 = 63
x - 7 = √63
x = 7 ± √63 is the solution set to the provided equation.
Rewrite one of the two equations above in the form ax+by=c,where a,b,c are constants,so that the sum of the new equations and the unchanged equations from the original system results in an equation in one variable
To rewrite one equation like x = 4 - y into ax + by = c form, we adjusted it to x + y = 4. Then, we combined it with the unchanged equation y = 2x + 3 by substituting 'y' in the first equation with 'y' from the second, leading to 3x + 3 = 4, a one-variable equation.
Explanation:To rewrite one of the two equations into the form ax + by = c, it's essential to start by having an equation that resembles y = a + bx (which is the same as y = mx + b, the conventional form for a linear equation) and the other in any format initially. Let's assume these equations as the existing ones: y = 2x + 3 and x = 4 - y.
Step 1: Transform the equation x = 4 - y into the form ax + by = c.
Firstly, shift y to the left side of equation by adding 'y' to both sides:
x + y = 4,
That's it! We now have the equation in the required ax + by = c format, where a = 1, b = 1 and c = 4.
Step 2: Add this new equation to the unchanged equation.
x + y = 4 (New one after rearranging)
y = 2x + 3 (Unchanged equation)
By substituting y from the second equation into the first, it will result in an equation in one variable:
x + (2x + 3) = 4,
After simplifying the equation, we get
3x + 3 = 4,
That is the result as an equation in one variable.
Learn more about Linear Equations here:https://brainly.com/question/32634451
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8-x<5 solve the inequality and graph the solution
8 - x < 5 |-8
-x < -3 |change the signs
x > 3
Please help me!!!! This is due in 20 minutes!!!! Whoever finds the right answer will be marked brainliest!!!!
Answer:
[tex]x=28cos(z)\\y=28sin(z)[/tex]
Step-by-step explanation:
We have been given a right triangle, which the following dimensions:
Hypotenuse = 28
Angle = z
Adjacent = x
Opposite = y
Upon using trigonometric ratio for cosine, we can write:
[tex]cos(z)=\frac{\text{Adjacent}}{\text{Hypotenuse}} =\frac{x}{28}\\ x=28cos(z)[/tex]
Similarly, upon using trigonometric ratio for sine, we get write:
[tex]sin(z)=\frac{\text{Opposite}}{\text{Hypotenuse}} =\frac{y}{28}\\ y=28sin(z)[/tex]
At the end of one day, the value of a share of a certain stock was $12. Over the next three days, the change in the value of the share was -$1, then, -$1, and then $3.
a. Write an expression that describes the situation.
b. Evaluate the expression.
c. What does your answer to part b mean in context of the problem?
Given
end of one day, the value of a share of a certain stock was $12
next three days
the change in the value of the share was -$1, then, -$1, and then $3
ANSWER
proof of (a)
As given in the question
end of one day, the value of a share of a certain stock = $12
next three days
change in the value of the share was -$1, then, -$1, and then $3
The expression that describes the situation be
= $12 - $1 -$1 + $3
proof of (b)
The expression that describes the situation be
= $12 - $1 -$1 + $3
solving the above expression
we get
= $13
proof of c
The answer to part b mean in context of the problem is ,
The value of a share of a certain stock was $12 at one day end and after the next three days, the change in the value of the share was -$1, t, -$1, $3 than the value of share becomes $13.
Hence proved
Someone please help me with #28 and #30 I got myself super confused.
Question 28:
[tex]S-2\pi r^2=2\pi rh[/tex] Subtract [tex]2\pi r^2[/tex] on both sides
[tex]\frac{S-2\pi r^2}{2\pi r} =h[/tex] Divide [tex]2\pi r[/tex] on both sides
*(Answer)*= [tex]\frac{S-2\pi r^2}{2\pi r} =h[/tex]
Question 30:
[tex]a*t=v_{1}+v_{0}[/tex] Multiply [tex]t[/tex] on both sides
[tex]a*t+v_{0} =v_{1}[/tex] Subtract [tex]v_{0}[/tex] on both sides
*(Answer)*= [tex]a*t+v_{0} =v_{1}[/tex]
Hope This Helps
BangtanBoyScouts
3x+(2x+5)+(2x+10)+(2x-15)=360
[tex]\bf 3x+(2x+5)+(2x+10)+(2x-15)=360 \\\\\\\\3x+2x+2x+2x+10+5-15=360\implies 9x+0=360\\\\\\\\x=\cfrac{360}{9}\implies x=40\\[/tex]
How much more Ted saved
He saves $20 i did this and i got the right answer. hope this helps mark me as brainliest
Use properties to find the sum or product 21+25+39+5
the sum or product of 21+25+39+5 is 90
In a plane, if one line has an undefined slope and another line has a slope of zero, what can you conclude
Answer:
You can conclude that the lines are perpendicular, and will cross at exactly one point.
Step-by-step explanation: If one line has a zero slope, and the other's slope is undefined, that means one line is exactly vertical, and the other is exactly horizontal. This means that they will cross at exactly one point, and are perpendicular.
The slope of a line illustrates the direction of the line
The two lines are perpendicular lines
From the question, we understand that:
A line has an undefined slopeAnother line has a slope of 0As a general rule,
The line with an undefined line is a vertical lineThe line with a slope of 0 is a horizontal lineA vertical line and a horizontal line will meet at a right-angle
Hence, the conclusion about the two lines is that, the two lines are perpendicular lines
See attachment for illustration
Read more about slopes at:
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A corn vendor at a farmers market was selling a bag of 8 ears of corn for $2.56.Another vendor was selling a bag of 12 for $4.32.Which bag is the better deal?
To decide which one is the better deal, you need to compare them on price per ear. So, the the first vendor is $2.56/8ears= $0.32/ear
the second vendor: $4.32/12 = $0.36/ear
The first vendor with the bag of 8 ears is the better deal!
Answer:
The better deal is first vendor bag.
Step-by-step explanation:
Given : A corn vendor at a farmers market was selling a bag of 8 ears of corn for $2.56. Another vendor was selling a bag of 12 for $4.32.
To find : Which bag is the better deal?
Solution :
To compare which is better we find the unit rate of both vendor rate.
The selling price of first vendor of 8 ears of corn for $2.56.
The selling price of 1 bag is [tex]\frac{2.56}{8}[/tex]
The selling price of 1 bag is $0.32.
The selling price of second vendor of 12 ears of corn for $4.32.
The selling price of 1 bag is [tex]\frac{4.32}{12}[/tex]
The selling price of 1 bag is $0.36.
The unit price of first vendor bag is lower than second vendor.
So, the better deal is first vendor bag.
you ran 6 miles in 2 hours on friday. on saturday, you run 18 miles in 6 hours. your rate of change is 3 miles an hour true or false. Need it answered ASAP !!!
6/2 =3
18/3 = 3
(18-6)/((6-2)= 12/4 =3
True
6/2=3
18/6=3
The answer is True
In a survey, 125 people were asked to chose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number 1.
The experimental probability to choose card 1 (15/125) is 10 less than the theoretical probability which is 25/125.
Answer:
The theoretical probability of choosing a card with the number 1 is (20%). The experimental probability of choosing a card with the number 1 is (16%). The theoretical probability is (greater than ) the experimental probability.
Solve math problem 15xy-30y
Solve: x2 − x − 6 x2 = x − 6 2x + 2x + 12 x After multiplying each side of the equation by the LCD and simplifying, the resulting equation is
Answer:
C) 3x^2 + 20x + 12 = 0
Step-by-step explanation: Because it is the right answer
What are the solutions to the equation?
A. x = -6 and x = -2/3
Step-by-step explanation:
this was a second part to the question for me so i decided to give u guys it as well, incase u come across it
Divide 3/4 by 1/3 and reduce to lowest terms
How to get answer: [tex]\frac{3}{4}[/tex]÷[tex]\frac{1}{3}[/tex]
Apply the fraction rule: [tex]\frac{3}{4} * \frac{3}{1}[/tex]
= [tex]3 * \frac{3}{4}[/tex]
= [tex]\frac{3}{4} * \frac{3}{1}[/tex]
= [tex]\frac{3 * 3}{4 * 1}[/tex]
= [tex]\frac{9}{4 * 1}[/tex]
Answer in fraction form: = [tex]\frac{9}{4}[/tex]
Answer in decimal form: = 2.25
Final answer:
To divide 3/4 by 1/3, multiply 3/4 by the reciprocal of 1/3, which is 3/1, giving you 9/4. This fraction is already in its lowest terms.
Explanation:
To divide fractions, such as dividing 3/4 by 1/3, you need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 1/3 is 3/1. So, you should alter the division problem to a multiplication problem.
Here is the step-by-step process:
Write down the problem in multiplication form: (3/4) * (3/1).
Multiply the numerators together: 3 * 3 = 9.
Multiply the denominators together: 4 * 1 = 4.
You get the result of the multiplication as 9/4.
To reduce to the lowest terms, we see that 9/4 is already in its simplest form as both 9 and 4 are prime to each other.
Thus, when you divide 3/4 by 1/3, the answer in lowest terms is 9/4.
what is the mean of 33, 31, 36, 30, 35
27 issssssssssss the eeeeee mean
What is the value of X?
X=2.25
X=11.25
X=13
X=22
Answer: The correct option is (D) 22.
Step-by-step explanation: We are given to find the value of x from the given figure.
From the figure, we see that a triangle is shown where the measure of an external angle is (6x + 1)° and the measures of the two remote interior angles are 79° and (2x + 10)°.
Since the sum of the measures of two remote interior angles of a triangle is equal to the measure of the external angle, so we get
[tex]79^circ+(2x+10)^\circ=(6x+1)^\circ\\\\\Rightarrow 79+2x+10=6x+1\\\\\Rightarrow 6x-2x=88\\\\\Rightarrow 4x=88\\\\\Rightarrow x=\dfrac{88}{4}\\\\\Rightarrow x=22.[/tex]
Thus, the required value of x is 22.
Option (D) is CORRECT.
identify the range of the function shown in the graph
I think it is C
I hope this helps
Answer: The answer is (C). [tex]y\geq 0.[/tex]
Step-by-step explanation: We are given a graph in the figure and we are to identify the range of the graphed function from the given options.
We can see in the figure that the values of x are greater than or equal to 0 and the corresponding values of y are also greater then or equal to 0. Since we are talking about the range of the function, so we will consider the y-values.
Thus, the range of the function will be [tex]y\geq 0.[/tex]
Thus, (C) is the correct option.
Solve
6x−10(x+12)=−4x−24
Show your work.
6x - 10(x + 12) = -4x - 24
Distributive property.
6x - 10x - 120 = -4x - 24
Add 10x to both sides.
6x - 120 = 6x - 24
Cancel like terms.
Add 24 to both sides.
-96 ≠ 0.
This equation is incorrect, as -96 will never be equal to 0.
what is a fraction equation that equals 1
Any fraction in which the numerator's value is the same as the denominator's value will equal 1. For example:
7/7, 6/6, 500/500, etc.
~Rise Above the Ordinary
Here are some examples 3/3, 4/4, 5/5, 1/1, 2/2, 6/6. It's any number over it self.
Find the equation of the line that is parallel to y=-7x+2 and contains the point (-5,32).
The equation of the line parallel to the line y = -7x + 2 will be -
y = - 7x - 3.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the equation of line as y = -7x + 2.
The general equation of a straight line is given by -y = mx + c
Here - {m} is slope and {c} is y - intercept.The equation of line parallel to the given line will be of the form -
y = - 7x + c {parallel lines have same slope}
For the point (- 5, 32), we can write -
32 = - 7 x - 5 + c
c = 32 - 35
c = - 3 {y - intercept}
The equation of the line will be -
y = - 7x - 3
Therefore, the equation of the line parallel to the line y = - 7x + 2 will be -
y = - 7x - 3.
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simplify (x -3)(x + 7) using the table method, and identify the resulting
Answer:
The simplified form of given expression is [tex]x^2+4x-21[/tex].
Step-by-step explanation:
The given expression is
[tex](x-3)(x+7)[/tex]
Here, we have to factors (x-3) and (x+7).
Factor (x-3) has two terms x and -3. Write these terms in first row.
Factor (x+7) has two terms x and 7. Write these terms in first column.
Now, find the elements of the table by multiplying corresponding rows and columns.
The elements of the table are x², -3x, 7x, -21.
Now, add all these elements.
[tex]x^2-3x+7x-21=x^2+4x-21[/tex]
Therefore the simplified form of given expression is [tex]x^2+4x-21[/tex].
Convert 0.05 into a fraction
the answer is 5/100 because its in the hundreths place but it simplifies down to 1/20
thank you for your time and please mark brainliest
5(2x-3)+20=35
^^solve and justify each step with correct property. I'll mark branliest!! Please help.
Distrubute 5 through the (....)
10x-15+30=35
Calculate the Sum
10x+5=35
Move constant to the right side and change the sign
10x=35-5
Subtract the number
10x=30
Divide both sides by 10
x=3
There were 32 volunteers to donate blood. Unfortunately, n of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated 470 milliliters each.
How many milliliters of blood did the volunteers donate?
WRITE ANSWER AS AN EXPRESSION
Answer:
The volunteers donated [tex](15040-470n)[/tex] milliliters of blood.
Step-by-step explanation:
Total number of volunteers was 32 and the number of volunteers couldn't donate blood was [tex]n[/tex].
So, the number of remaining volunteers who donated blood will be: [tex](32-n)[/tex]
Each of these volunteers donated 470 milliliters blood.
So, the total amount of blood donated [tex]= 470(32-n) = (15040-470n)[/tex] milliliters.
Answer:
Answer: The answer to this problem would be (32-n)*470!
Step-by-step explanation:
Since there were 32 volunteers the beginning and some of them couldn't donate you would subtract (the variable you would use is 'n'). As you may know, each means that you multiply so if each volunteer is giving 470 mm of blood each you would multiply that by how many volunteers are remaining which is unknown.
Your final answer would be: (32-n)*470
Hope this helps and gets Brainiest Answer!!!
Step-by-step explanation:
For the last 4.5 hours, the temperature has decreased at a rate of 2.8 degrees per hour. Which best represents the overall change in temperature over this time period?
Answer:
The overall change in temperature over the time period ∆T = -12.6°F
Hope This Helps :DD
Step-by-step explanation: