Answer:
No real solutions.
Step-by-step explanation:
We want to solve the equation:
[tex]\ln(x-2)+\ln (x+2)=4[/tex]
Recall that:
[tex]\displaystyle \ln a-\ln b=\ln\left(\frac{a}{b}\right)[/tex]
Therefore:
[tex]\displaystyle \ln\left(\frac{x-2}{x+2}\right)=4[/tex]
By Definition:
[tex]\displaystyle e^4=\frac{x-2}{x+2}[/tex]
Cross-multiply:
[tex]e^4(x+2)=x-2[/tex]
Distribute:
[tex]xe^4+2e^4=x-2[/tex]
Isolate the x:
[tex]xe^4-x=-2-2e^4[/tex]
Factor:
[tex]\displaystyle x(e^4-1)=-2-2e^4[/tex]
Divide. Therefore:
[tex]\displaystyle x=\frac{-2-2e^4}{e^4-1}=\frac{2+2e^4}{1-e^4}\approx-2.07[/tex]
However, note that logs cannot be negative and must be nonzero. According to the first logarithm, x > 2 and according to the second, x > -2. Since the answer is not greater than two, there are no real solutions.
The lengths of nails produced in a factory are normally distributed with a mean of 5.16 centimeters and a standard deviation of 0.04 centimeters. Find the two lengths that separate the top 8% and the bottom 8%.
Answer:
The length that separates the top 8% is of 5.2162 centimeters, and the length that separates the bottom 8% is of 5.1038 centimeters.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 5.16 centimeters and a standard deviation of 0.04 centimeters.
This means that [tex]\mu = 5.16, \sigma = 0.04[/tex]
Length that separates the top 8%
The 100 - 8 = 92th percentile, which is X when Z has a p-value of 0.92, so X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 5.16}{0.04}[/tex]
[tex]X - 5.16 = 1.405*0.04[/tex]
[tex]X = 5.2162[/tex]
Length that separates the bottom 8%
This is the 8th percentile, which is X when Z has a p-value of 0.08, so X when Z = -1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.405 = \frac{X - 5.16}{0.04}[/tex]
[tex]X - 5.16 = -1.405*0.04[/tex]
[tex]X = 5.1038[/tex]
The length that separates the top 8% is of 5.2162 centimeters, and the length that separates the bottom 8% is of 5.1038 centimeters.
Having trouble with these questions, please help.
Answer:
(a)=50%(b)=2.1and(c)=16.1
Step-by-step explanation:
Hope this helps
Please help so urgent
Answer:
Option E. None of the above.
Step-by-step explanation:
From the question given above, the following data were obtained:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
Recall:
When a function f(x) is multiplied by it's inverse f¯¹(x), the result is equal to 1 i.e
f(x) × f¯¹(x) = 1
With the above information, we can determine the inverse of function given above as follow:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
f(x) × f¯¹(x) = 1
(x – 5)/(2x + 3) × f¯¹(x) = 1
f¯¹(x)(x – 5) / (2x + 3) = 1
Cross multiply
f¯¹(x)(x – 5) = (2x + 3)
Divide both side by (x – 5)
f¯¹(x) = (2x + 3) / (x – 5)
Thus, the inverse of the function is (2x + 3) / (x – 5).
Option E gives the correct answer to the question.
Simplify 3 · 2x. What is the coefficient?
• 2
• 3
• 6
Answer:
6x coefficient is 6. the number next to the letter
Step-by-step explanation:
What are the solutions to x2 -8x =13
Answer:
See image below for answer:)
Step-by-step explanation:
Answer fast please and thanks!
Answer:
tan 30 = x / 15
General Formulas and Concepts:
Trigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 30°
Opposite Leg = x
Adjacent Leg = 15
Step 2: Solve for x
Substitute in variables [tangent]: tan 30 = x / 15Answer:
3rd one
Step-by-step explanation:
Recall that
Sin = opposite over hypotenuse
Cos = adjacent over hypotenuse
Tan = opposite over adjacent
For the angle with a measure of 30 degrees we are given it's adjacent side length and need to find it's opposite side length
When dealing with opposite and adjacent we use tangent
If tan = opposite over adjacent
Then tan30 = x / 15 and the correct answer choice is the third one
Assuming p: she is beautiful,q :she is clever,the verbal form of ~p^ (~q) is she is beautiful but not clever. she is beautiful and clever she is not beautiful and not clever.she is beautiful or not clever.
Answer:
C. she is not beautiful and not clever.
Step-by-step explanation:
A. she is beautiful but not clever. B. she is beautiful and clever
C. she is not beautiful and not clever.
D. she is beautiful or not clever.
p: she is beautiful
q :she is clever
~p^ (~q) in verbal form
~p = she is not beautiful
~q = she is not clever
~p^ (~q) = she is not beautiful and not clever.
C. she is not beautiful and not clever.
What the cubic inches…
Step-by-step explanation:
The radius r is 5 in (r = D/2). so the volume V of the beach ball is
[tex]V= \dfrac{4 \pi}{3}r^3 = \dfrac{4 \pi}{3}(5\:\text{in})^3[/tex]
[tex]\:\:\:\:\:= 523.6\:\text{in}^3[/tex]
Taking 0.5 cm as 1 unit, plot the following points on the graph paper: A(1,3), B (-3,-1), C (1,- 4), D (- 2,3), E (0-8), F (1.0)
Answer:
It's letter c
Step-by-step explanation:
you have to × the 0.5 and 1
Which expression is equivalent to a^7
Answer:
here is your answer
Step-by-step explanation:
here is your answer
Using the diagram below, which of the following parts of the triangles are
congruent?
9514 1404 393
Answer:
B. ∠A ≅ ∠E
Step-by-step explanation:
The similarity statement tells you the corresponding angles are ...
ΔCAB ~ ΔCED
∠C ≅ ∠C . . . . listed first in the similarity statement
∠A ≅ ∠E . . . . listed second in the similarity statement
∠B ≅ ∠D . . . . listed third in the similarity statement
The relationship between angles A and E is properly shown in answer choice B.
The police measured the skid marks made by a car that crashed into a tree. The formula used to approximate the distance in feet that it takes to stop a car after the brakes are applied for a car traveling at a rate of r miles per hour is d= 0.045 r^2 + 1.1 r . If the measurement gave a braking distance of 250 ft, was the driver exceeding the legal speed limit of 55 mi/h? Find the speed of the car before the brakes were applied.
Replace r in the equation with 55 mph and solve for d.
D = 0.045(55)^r + 1.1(55)
Simplify:
D = 0.045(3025) + 60.5
D = 136.125 + 60.5
D = 196.625
At the speed limit of 55 mph the skid mark would be 196.625 feet long.
Because the skid mark was greater than that it was going faster than 55 mph.
To find the speed the car was going replace d with 250 and solve for r:
250 = 0.045r^2 + 1.1r
Multiply both sides by 1000 to remove decimals:
250000 + 45r^2 + 1100r
Subtract 250000 from both sides
45r^2 + 1100 -250000 = 0
Use the quadratic formula to solve:
R = -1100 + sqrt(1100^2 14x45(-250000) /(2 x45)
R = 63.308 miles per hour
The speed of the car was 63.3 miles per hour
Suppose that y varies inversely with x. Write a function that models the inverse function x=7 when y=3
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Answer:
y = 21/x
Step-by-step explanation:
The inverse variation relation means ...
y = k/x
For the given values, we can determine the constant k:
3 = k/7
3×7 = k = 21
Then the function is ...
y = 21/x
Here is a table of values for y = f(x).
Х
-2 -1 0 1 2 3
4.
5
6
f(x) 5
6 7 8 9 10 11 12 13
Mark the statements that are true.
Step-by-step explanation:
the true answers are:
A. f(-1)=6
D. the domain for f(x) is the set
{-2,-1,0,1,2,3,4,5,6}
tiệm cận ngang của đồ thị y= 2-x/x+3
tiệm cận ngang của đồ thị 3/x+3
There are 25 black cars, 15 blue cars, 21 red cars and 30 white cars what is the probability of getting a red car
A cylindrical water tower has a volume of
10007 ft.
If the tower is 10 ft tall, what is the radius of the tower?
Answer:
r≈17.85
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
Answer:
r=17.85
Step-by-step explanation:
i just got it and did the math
which geometric figures are shown in the diagram
Answer:
A circle to start off, encompassing almost the entire figure, then a triangle, with D, A and C as its vertices, then a fan (a sector of a circle), with C, E and B as its vertices. Next, a chord (DA) which serves as a line segment at the same time, and finally three rays, starting from C and ending in A, B and E respectively. In total, six geometric figures.
Step-by-step explanation:
Hope this helped!
Any help? Algebra I
9514 1404 393
Answer:
2p +3d = 18.25; 4p +2d = 27.50popcorn: $5.75; drink: $2.25Step-by-step explanation:
a) Let p and d represent the prices of a bag of popcorn and a drink, respectively.
Mohamed's purchase is ...
2p +3d = 18.25
Miguel's purchase is ...
4p +2d = 27.50
__
b) We can subtract half the second equation from the first to get an equation for the cost of a drink.
(2p +3d) -1/2(4p +2d) = (18.25) -1/2(27.50)
2d = 4.50 . . . . . . simplify
d = 2.25 . . . . . . divide by 2
4p +2(2.25) = 27.50 . . . . substitute for d in the second equation
4p = 23.00 . . . . . . . . . subtract 4.50
p = 5.75 . . . . . . . . . divide by 4
The cost of a bag of popcorn is $5.75; the cost of a drink is $2.25.
-5(-3x+1)= 45 solve for x
Answer:
x=[tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Hi there!
We are given the equation -5(-3x+1)=45 and we need to solve for x
we do this by isolating x by itself on one side of the equation; the numbers (the value of x) is on the other side
First, do the distributive property and distribute -5 on -3x and 1 on the left side (multiply both -3x and 1 by -5)
15x-5=45
add 5 to both sides (-5+5=0)
15-5=45
+5 +5
_________
15x=50
divide both sides by 15 (15÷15=1)
15x=50
÷15 ÷15
________
x=[tex]\frac{50}{15}[/tex]
we can simplify this fraction by factoring five out of 50 and 15
x=[tex]\frac{10*5}{3*5}[/tex]
cancel 5 out of the numerator and denominator
x=[tex]\frac{10}{3}[/tex]
The answer can be left as an improper fraction
Hope this helps! :)
If someone can pls give the answer with steps that would be greatly appreciated :)
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The measures of [tex]x[/tex] and [tex]y[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\: 210°\:and\:\:y\:=\: -30°}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
An exterior angle of a triangle is equal to sum of two opposite interior angles.
And so we have,
[tex] 40° = 70° + y[/tex]
[tex]➪ \: y= 40° - 70°[/tex]
[tex]➪ \: y = - 30°[/tex]
Also,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
[tex]y[/tex] + [tex]x[/tex] = [tex]180°[/tex]
[tex]➪ \: -30° + x= 180°[/tex]
[tex]➪ \:x = 180° + 30°[/tex]
[tex]➪ \:x = 210°[/tex]
[tex]\sf\purple{Therefore,\:the\:measures \:of\:the\:unknown\:angles\:are\:"x=210°"\:and\:"y=-30°.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
What equation is always true?
Answer: 4)
Step-by-step explanation: angles 2 and 3 equal 7 because they are both missing angle 4 to make it either 180 degrees or 360 degrees respectively.
Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.
Given right triangle GYK, what is the value of tan(G)?
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction
StartRoot 3 EndRoot
Answer:
The answer is A
Step-by-step explanation:
just took it on egde
si franco comió 8/3 de pizza y Fabián comió 5/6 de la misma pizza. ¿quien comió más ? si quedó 4/9 de pizza.
Answer:
Franco comió 8/3 de pizza.
Fabián comió 5/6 de pizza.
Queremos saber quien comió más.
Entonces básicamente queremos ver cuál número es más grande, 8/3 o 5/6,
Podemos reescribir el primero como:
8/3 = (2 + 3 + 3)/3 = 2/3 + 3/3 + 3/3 = 2/3 + 1 + 1
= 2 + 2/3
En cambio, para el número 5/6, el numerador es menor que el denominador, entonces sabemos que:
5/6 < 1
Claramente podemos ver que 8/3 > 5/6
Entonces podemos concluir que Franco comió más.
In the figure below net of cube is show
Find the surface area of cube.
3 in
Answer:
Surface Area = 54 in^2
Step-by-step explanation:
SA = [tex]6a^{2}[/tex]
SA = [tex]6(3)^2[/tex] Solve for the exponents first
SA = 6(9) Then multiply
SA = 54 square inches
if the ratio of the volume of two cubes is 1 : 8 , then find the ratio of the total surface area of the two cubes
Answer:
V = L^3 where v is volume and L the length of one side
A = 6 * L^2 total area of cube with side L
A = 6 * V^2/3 area of cube expressed in V
A2 / A1 = (V2 / V1)^2/3 6 cancels
A2 / A1 = 8^2/3 = 4 ratio of areas
Use the exact values of the ratios and find the value of tan 45° + sin 30°
Answer:
1.5
tan45=1
sin30=1/2
so 1+1/2=1.5 or 3/2
Select the correct answer. Using synthetic division, find (2x4 + 4x3 + 2x2 + 8x + 8) ÷ (x + 2). A. B. C. D.
Step-by-step explanation:
If you use synthetic division, you get,
[tex]2x {}^{3} + 2x + 4 + \frac{0}{x + 2} [/tex]
Which is,
[tex]2x {}^{3} + 2x + 4[/tex]
Answered by GAUTHMATH
Answer:
The correct answer is:
2x^3+2x+4
Step-by-step explanation:
I got it right on the Plato test.
simplification please
Answer:
5
Step-by-step explanation:
WHen we raise a power to a power, we multiply them, in this case 5 is the base so we can just ignore it for now and replace it with x.
(X^1/3)^3
Multiply 1/3 by 3 and we get 1
So:
X^1
Which does nothing, so we can simplify to just:\
X
Remember x is 5 so the answer is:
5
No step by step answers or links
Answer:
1. k = 15
2. d = 20
3. n = 3