Answers
[tex]~~~~~2^{x+1} = 3^x\\\\\implies \ln \left(2^{x+1}\right) = \ln\left(3^x \right)\\\\\\\implies (x+1) \ln 2 = x \ln 3\\\\\\\implies \dfrac{x+1}x = \dfrac{\ln 3}{\ln 2}\\\\\\\implies 1+ \dfrac 1x = \dfrac{\ln 3}{\ln 2}\\\\\\\implies \dfrac 1x = \dfrac{\ln 3 }{ \ln 2}-1\\\\\\\implies \dfrac 1x = \dfrac{ \ln 3 - \ln 2}{\ln 2}\\\\\\\implies x = \dfrac{\ln 2}{\ln 3 - \ln 2}\\\\\\\implies x \approx 1.7095\\\\\\[/tex]
Related Questions
Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 5. If the volume of rectangular prism B is 5125 km°, find the volume of rectangular prism A, the preimage
Answers
The volume of the rectangular prism A, the preimage is 41km^3
How to determine the volume?The given parameters are:
Volume B = 5125km^3
Scale factor, k = 5
The volume of B is calculated using:
B = A * k^3
So, we have:
5125 = A * 5^3
Divide both sides by 5^3
A = 41
Hence, the volume of rectangular prism A, the preimage is 41km^3
Read more about dilation at:
https://brainly.com/question/3457976
#SPJ1
Can anybody help me with this please!!
Answers
Answer:
C. Complementary angles
Step-by-step explanation:
Since it's mentioned that <DAB is 90 degrees then that means that <BAE is also 90 degrees and since angles A and B are the only angles in <BAE, it means that Angle A and B are complimentary
Find the area of the complex figure.
Answers
Answer:
1863M
Step-by-step explanation:
split into smaller rectangles
(31 * 23) * 2 = 713 *2 = 1426
31-12 = 19
19 * 23 = 437
1426 + 437
• A bag contains 5 orange, 3 yellow, and 5 black marbles. What are the odds of picking an orange marble?
Answers
Answer:
The odds will be 5/13.
Step-by-step explanation:
There are 13 marbles total in this situation. 5 orange, 3 yellow and 5 black (5+3+5) will give us 13 as our overall total. Now, because we have 5 orange marbles available, we'll write this as a 5/13 odds/ chance of picking an orange marbles because it is how many orange marbles are present over how many marbles there are total.
Also! You can't simplify this any further, thus you'd have 5/13 odds.
pls help 50 points for reward.
Answers
Answer:
-2
Using the slope formula (y1-y2)/(x1-x2), the slope of the line is (-10-8)/(9-0), which is equal to (-18)/9= -2.
Slope
m=y2-y1/x2-x1m=8+10/0-9m=18/-9m=-2Tanisha owns a small business selling bagels. She knows that in the last week 61 customers paid cash, 5 customers used a debit card, and 45 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash as a decimal to the nearest hundredth.
Answers
Answer:
The probability as a decimal to the nearest hundredth is 0.550.55.
Step-by-step explanation:
61 cash, 5 debit card, and 45 credit card.
\color{steelblue}{61}+5+45=
61+5+45=
\,\,\color{indianred}{111}
111
There were a toal of 111 customers. 61 paid with cash.
Probability the next customer will pay with cash:
\frac{\color{steelblue}{61}}{\color{indianred}{111}}=
111
61
=
\,\,0.549549...
0.549549...
\approx
≈
\,\,0.55
0.55
Round to the nearest hundreth
The probability that the next customer will pay with cash is 0.55.
What is the formula for probability?Probability is the ratio of the number of favorable events divided by the total outcome.
We have, given that, Tanisha owns a small business selling bagels. She knows that in the last week 61 customers paid cash, 5 customers used a debit card, and 45 customers used a credit card.
The total number of payments is,
61+45+5=111.
We have to find the probability that the next customer will pay with cash as a decimal to the nearest hundredth.
The number of the favorable outcome for the customer will pay with cash is 61, and the total number of outcomes is 111.
Therefore, the probability is,
P(A)=61/111
P(A)=0.5495.
Therefore, the probability of the nearest hundredth is 0.55.
To learn more about the probability, visit:
https://brainly.com/question/24756209
#SPJ1
Will mark branlyest (Polynomial Functions)
1. Find the zeros: 2x^2 + 12x + 18 = 0
A . {-3}
B .{3}
C .{-9}
D.{-3,3}
2. Find the x-intercepts: 2r^2 = 5r + 3
A. {-1/2,3}
B.{-1/2,-3
C.{1/2,3}
D.{1/2,-3}
Answers
Answer:
1. A
2. A
Step-by-step explanation:
Question 1
1 Factor out the common term 2.
2(x^2+6x+9)=0
2 Rewrite x^2+6x+9 in the form a^2+2ab+b^2a, where a=x and b=3.
2(x^2+2(x)(3)+3^2)=0
3 Use Square of Sum: (a+b)^2=a^2+2ab+b^2(a+b).
2(x+3)^2=0
4 Divide both sides by 2.
(x+3)^2=0
5 Take the square root of both sides.
x+3=0
6 Subtract 3 from both sides.
x=-3
Question 2
1 Move all terms to one side.
2r^2-5r-3=0
2 Split the second term in 2r^2-5r-3 into two terms.
2r^2+r-6r-3=0
3 Factor out common terms in the first two terms, then in the last two terms.
r(2r+1)-3(2r+1)=0
4 Factor out the common term 2r+1.
(2r+1)(r-3)=0
5 Solve for r.
r=-1/2,3
in order to make a specific shade of green paint a panter mixes 1 1/2 quarts of blue paint 2 cups of green paint and 1/2 gallion of white paint how much of each collor is needed to make 100 cups of this shade of green paint
Answers
Answer:
37.5 cups of blue
12.5 cups of green
50 cups of white
Find the area of the blue shaded region
Answers
Step-by-step explanation:
Area of shaded region= area of rectangle- area of semi-circle
Area of rectangle= l×b
=6×4
=24 in²
Area of semi-circle=[tex]\frac{\pi r^{2} }{2}[/tex]
= [tex]\frac{\pi (2)^{2} }{2}[/tex]
= 6.28 in²
Area of shaded region= area of rectangle- area of semi-circle
= 24-6.28
=17.72 in²
The product of two consecutive integers is 72. the equation x(x 1) = 72 represents the situation, where x represents the smaller integer. which equation can be factored and solved for the smaller integer? x2 x – 72 = 0 x2 x 72 = 0 x2 2x – 72 = 0 x2 2x 72 = 0
Answers
The equation that can be factored and solved for the samller integer is x² + x - 72 = 0
How to form an equation?The product of two consecutive integers is 72. The equation that represents the situation is as follows:
x(x + 1) = 72
where
x = smaller numberTherefore,
x(x + 1) = 72
x² + x = 72
x² + x - 72 = 0
Therefore, the equation that can be factored and solved for the samller integer is x² + x - 72 = 0
learn more on equation here: https://brainly.com/question/10440486
#SPJ4
Billy has 10 bouncy balls. His brother has 30 bouncy balls. He washed 10 of his and 10 of his brother. How many bouncy balls do they have left?
Answers
Answer:
20
Step-by-step explanation:
10 + 30 = 40
40 - 10 = 30
30 - 10 = 20
answer is 20
Answer:
20 bouncy Balls!
Step-by-step explanation:
10+30 - 20 = 20
A large rectangular prism is 5 feet long, 3 feet wide, and 4 feet tall. A small rectangular prism is 2.5 feet long, 1.5 feet wide, and 2 feet tall.
How many small prisms would it take to fill the large prism?
Write your answer as a whole number or decimal. Do not round.
Answers
Answer:
2 small prism could fit.
Step-by-step explanation:
the large prism is 4 feet tall, 5 feet long, And 3 feet wide. So it would take to small prism to fit because the small prism is 2 feet tall, 2.5 feet long, And 1.5 feet long. Do you see it the small prism is exactly half the size of the large prism there the large prism could fit two small prism with in its self.
please help! this is due soon and im a bit confused
Answers
Two would be 70-y and so on
If h(x) = 5 x and k (x) = startfraction 1 over x endfraction, which expression is equivalent to (k circle h) (x)? startfraction (5 x) over x endfraction startfraction 1 over (5 x) endfraction 5 (startfraction 1 over x endfraction) 5 (5 x)
Answers
The composition of the two given functions is:
(k°h)(x) = 1/5x
How to get the composition of the functions?
Here we have the functions h(x) = 5x and k(x) = 1/x.
We want to get (k°h)(x), which is equal to:
k(h(x))
Then we have:
k(h(x)) = 1/h(x)
Replacing h(x) we get:
k(h(x)) = 1/h(x) = 1/(5x)
So the composition is just one over 5x.
If you want to learn more about compositions:
https://brainly.com/question/10687170
#SPJ4
The half-life of a certain radioactive material is 36 days. An initial amount of the material has a mass of 487kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.
Answers
Answer:
442.302 kg
Step-by-step explanation:
amount = 487 (1/2)^(t/36) where t is the number of days.
if t = 5
amount = 487(.5)^(5/36)
= 442.302 kg
3Your new mobile phone costs £360.
The probability you leave it on the bus is 0.1.
The probability someone will hand it in to lost property and you will recover it
is 0.4.
The cost of insurance to cover the loss of the phone is £30.
Should you pay for this control measure?
List any assumptions that you make
Answers
Assuming you have to pay 30 pounds for somebody handing it in to lost property, you'll have a 0.5 probability that you'll have to pay the 30 pounds if you lose the phone.
Also assuming there are no other ways to lose your phone, you have a 0.5 probability (50% chance?) to lose your phone.
Also assuming the "control measure" is the insurance and you won't have to pay a larger amount, you'll probably be better off paying the 30 pounds instead of the larger amount because you have such a high chance of losing your phone.
I apologize if I misunderstood the question.
In a right-angled triangle, the sum of the squares of the three sides is 72. What is the length of the hypotenuse?
Answers
Answer:
The hypotenuse has a length of 6
Step-by-step explanation:
Remark
The first step is to create the 2 equations needed to solve this problem.
Then substitute one into the other.
Equations
c^2 + a^2 + b^2 = 72
c^2 = a^2 + b^2
Solution
c^2 + a^2 + b^2 = 72 The sum of the sides each squared of a right triangle = 72
c^2 = a^2 + b^2 The pythagorean theorem says the hypotenuse of the right triangle = the sum of the squares of two smaller sides. You can substitute the hypotenuse squared into the top equation for a^2 + b^2
c^2 + c^2 = 72
2c^2 = 72
c^2 = 36
c = 6. minus 6 is meaningless
100 points. bee fast
Jalen says that the height, radius, and diameter of a cone lie entirely on the base of the cone. What is Jalen’s error? The height does not lie on the base because it is perpendicular to the base. The radius does not lie on the base because it contains the center of the base. The diameter does not lie on the base because it contains a radius of the circle. The base does not contain the height, the radius, or the diameter because it is a circle.
Answers
Answer:
The height does not lie on the base because it is perpendicular to the base.
What’s the area formula, of 48m
Answers
Answer:
The area formula of a circle is [tex]A=\pi* r^2[/tex] where r is the radius and in this case our r is 48 m. So we would just plug in 48 m into r which would get squared and then multiplied by pi to give us [tex]7,238.23\ m[/tex].
Hope this helps! Let me know if you have any questions
Answer:
[tex]\pi[/tex]r²
Step-by-step explanation: Youre welcome :)What is the value of x innthe equation 1.5(x+4)-3=4.5(x-2)
Answers
[tex]~~~~~~1.5(x+4)-3 = 4.5(x-2)\\\\\implies 15(x+4) -30 =45(x-2)~~~~~~~~;[\text{Multiply both sides by 10]}\\\\\implies 3(x+4)-6=9(x-2)~~~~~~~~~~;[\text{Divide both sides by 5]}\\\\\implies 3x+12-6=9x-18\\\\\implies 3x+6=9x-18\\\\\implies 9x-3x = 18+6\\\\\implies 6x = 24\\\\\implies x = \dfrac{24}6\\\\\implies x =4[/tex]
If point a is at (-1,2) and point b is at (11,-7), what is length of line ab?
Answers
Answer:
15
Step-by-step explanation:
Distance formula: [tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
Plug in (-1,2) and (11, -7):
[tex]d=\sqrt{(11-(-1)^{2}+(-7-2)^{2} } = d=\sqrt{(12)^{2}+(-9)^{2} }=\sqrt{144+81} = \sqrt{225} = 15[/tex]
Evaluate each expression.
6! =
3! - 2!=
61/
3!
=
Answers
Answer:
6! = 720
3! - 2! = 4
6! ÷ 3! = 120
Step-by-step explanation:
I used a calculator. ^v^
Roberta grows pea plants, some in shade and some in sun. she picks 8 plants of each type at random and
records the heights.
shade plant heights (in.) 7 12 7 10 8 12 8 8
sun plant heights (in.) 19 24 21 22 23 19 20 20
express the difference in the means as a multiple of their ranges.
the difference in the means is times the ranges.
Answers
Carl makes $10.25 per hour, h, plus a daily bonus of $25. Which equation represents his total earnings, t, each day?
Answers
Answer:
10.25 × h + 25= t
Step-by-step explanation:
he gets 10.25 for every hour, so you do 10.25 × h, than for his extra bonus of 25 dollars a day, you add 25. than t shows the final earnings
the history of pi and it’s importance to geometry!!!!!!
Answers
Answer:
Famous mathematician Archimedes of Syracuse did the first calculation of pi around 250 BC. Without pi, we cannot calculate the ratio of the circumference of a circle to its diameter. Pi is made up of 31.4 trillion digits. Within pi, you can find your birthday, social security number, and every word ever if put into alphabetic values (1=a, 2=b, etc). You can get your entire life story from beginning to end just from pi!
hope this helps:)
Of the last 15 people at a carnival booth, 6 won a prize. what is the experimental probability that the next person at the booth will win a prize?
Answers
Answer:
40% or 2/5
Step-by-step explanation:
won = 6
total no. of people = 15
probability of winning = 6/15 = 2/5
2/5*100
=40%
Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1? f(x) = 3(x 4)(x – i)(x – 2) f(x) = (x – 3)(x 4)(x – i)(x – 2) f(x) = (x – 3)(x 4)(x – i)(x i)(x – 2) f(x) = 3(x 4)(x – i)(x i)(x – 2)
Answers
The polynomial function with leading coefficient of 3 and root -4, i, and 2 all with multiplicity of 1 is f(x) = 3(x+4)(x-i)(x+2)
Polynomial function
The Leading coefficients are the numbers written in front of the variable with the largest exponent.
Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero.
The multiplicity is the number of times a given factor appears in the factored form of the equation of a polynomial.
Therefore, the polynomial f(x) = 3(x+4)(x-i)(x+2) has a root -4 , 1 and -2.
The leading coefficient is 3. The multiplicity is all one.
learn more on polynomial here: https://brainly.com/question/13309002
#SPJ4
Answer:
d
Step-by-step explanation:
what is the initial value of the linear relationship of -2, 3
Answers
A coordinate plane is shown. A line passes through the x axis at negative 3 and the y axis at 5.
−4
−3
five over three
5
help will give brainliest
Answers
Answer:
0.7°
Step-by-step explanation:
From the figure:
CF = 4000.2 miles, CE = 4000.01 miles
so FT = √CF² - CT², TE = √CE² - CT²
so FT = 40 miles, TE = 8.94 miles
so ½ × 4000.2 × 4000.01
xsin angle FCE = ½ × 4000 × 140 + 8.94
so sin angle FCE = 0.0122
so angle FCE = 0.7°
so m SB = 0.7°
HOPE THIS HELPS AND HAVE A NICE DAY <3
8 3/4 - 5 2/3 what is the answer
Answers
Answer:
3 1/12
Step-by-step explanation: