Suppose logbx = logcx, where b ≠ c. Then the value of x can be
A) 0 only
B) 1 only
C) b^c or c^b only
D) any positive real number
Not A: We can't have [tex]x=0[/tex] because [tex]\log0[/tex] is undefined for a logarithm of any base.
B is true: [tex]\log1=0[/tex] for any base.
Not C: If [tex]x=b^c[/tex], then [tex]\log_bb^c=c[/tex], but [tex]\log_cb^c=c\log_bc[/tex] which only reduces to [tex]c[/tex] if [tex]\log_bc=1[/tex]. This can only happen if [tex]b=c[/tex], however, but we've assumed otherwise.
Not D: The reasoning for C not being correct is enough to rule out this possibility.
A pair of jeans was in a 15% off sale but, when Bill came to buy them a month later, the sale was over and he had to pay the regular price of $70. How much money did Bill lose?
Answer:
10.5
Step-by-step explanation: if he got the pants on sale the price would be 59.5 becuase 70*15%=10.5 and u would subtract 70-10.5=59.5
70-59.5=10.5
Answer:
$10.5
Step-by-step explanation:
Brad puts an equal amount of money in his savings account once a month. He started with $27. The next month, he had $44 in his account. Two months after that, he had $78 in his account. How much money will Brad have in his account after 6 months?
Brad deposits $17 per month. Hence, after 6 months, Brad will have $115 in his account.
Explanation:The subject of the question is a simple arithmetic problem involving Brad's savings account. The first month, he started with $27. The next month, he had $44 in his savings account, so he adds ($44-$27) = $17 to his account each month. In the third and fourth months, he added the same amount twice, so he had $78 ($44 + $17*2). Hence, after 6 months, he will have $115 in his savings account because for the fifth and sixth months he will add ($17*2 = $34) to his account of $78 from the fourth month.
In simpler terms, we can break down these steps into the following:
Determine the monthly deposit amount ($44-$27)= $17.Add the monthly deposit to the current amount for each subsequent month.Calculate for the 6th month: $27 + $17 * 5 = $115.Learn more about Arithmetic progression here:
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Given the fact that Brad saves an equal amount of $17 each month, after 6 months, his total saved amount will be $129.
Explanation:The question is about calculating the amount of money Brad will have saved in 6 months, given that he saves an equal amount each month. From the information provided, we can determine that Brad saves $17 each month ($44 - $27 = $17). After two months, we can see that $78 - $44 = $34, which confirms that Brad is indeed saving $17 each month, since $34 / 2 = $17. Now, to find how much Brad will have saved after 6 months, we need to multiply the monthly saving amount by 6 and add that to the initial amount. This gives us: $27 + ($17 * 6) = $27 + $102 = $129.
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I need help with this right away. Please.
IF=2x+2, IZ=2x+12 solve for x
A particle moves along the x-axis with position function s(t) = ecos(x). How many times in the interval [0, 2π] is the velocity equal to 0?
Answer:
It goes to zero three times
Step-by-step explanation:
s(t) = e^ cos(x)
To find the velocity, we have to take the derivative of the position
ds/dt = -sin x e^ cos x dx/dt
Now we need to find when this is equal to 0
0 = -sin x e^ cos x
Using the zero product property
-sin x=0 e^cos x= 0
sin x = 0
Taking the arcsin of each side
arcsin sinx= arcsin 0
x = 0 ,pi, 2 pi
e^cos x= 0
Never goes to zero
Answer:
The velocity is equal to 0 for 3 times.
Step-by-step explanation:
Given position function s = ecos(x)
Its velocity function, s' = ds/dt = e(-sinx)dx/dt
Between [0,2π], s'=0, -e(sinx)dx/dt=0
sinx=0
x=0, π, 2π
The velocity is equal to 0 for 3 times.
How much less than 3x^2−7x+9 is 2x^2+4x−8? What is the value of the result when x=2?
^=power
Answer:
1
Step-by-step explanation:
well 3x2^2-7x2+9 = 7
well 2x2^2+4x2−8 = 8
8-7 =1
The difference is x² - 11x + 17 and the value is -1.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Difference = ( 3x²−7x+9 ) - ( 2x²+4x−8 )
Difference = x² - 11x + 17
The value of expression at x= 2 will be calculated as,
E = x² - 11x + 17
E = (2)² - ( 11 x 2 ) + 17
E = 4 - 22 + 17
E = -1
Therefore, the difference is x² - 11x + 17 and the value is -1.
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lim
x->infinity (1+1/n)
Answer:
Can not be determined.
Step-by-step explanation:
We can easily notice that the limit is x tends to infinity, whereas x is not present in the given function, we are given (1 + 1/n). So we can not evaluate the given limit for x as parameter, we must have some function of x to solve this problem.
Hence, option C is correct i.e. the limit can not be determined.
Please help me with this!!!!
Answer: the no. is doubled every time we get an answer. therefore the next two no.s n the sequence are 48, 96
Answer:
3, 6, 12, 24 , 48, 96
A recipe for 9 banana dash nut muffins calls for 1 cup of flour. The number of muffins that can be made varies directly with the amount of flour used. There are 1 1/3 cups of flour available. How many muffins can be? made?
Answer:
12 muffins can be made.
Step-by-step explanation:
12 muffins because if one cup makes 9 muffins, and 1/3 of 9 is 3. Than 9+3=12 so you can make 12.
Which is an x-intercept of the graph of the function y=cot(3x)
The x-intercept of the graph of the function y = cot(3x) is [tex]x = \frac{\pi}6[/tex]
The graph of the function is given as:
y = cot(3x)
To determine the x-intercept of the graph, we set the graph to 0.
So, we have:
cot(3x) = 0
Take the arccot of both sides
3x = arccot(0)
Evaluate the arccot of 0
[tex]3x = \frac{\pi}2[/tex]
Divide both sides by 3
[tex]x = \frac{\pi}6[/tex]
Hence, the x-intercept of the graph of the function y = cot(3x) is [tex]x = \frac{\pi}6[/tex]
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The x-intercepts of the graph of the function [tex]\( y = \cot(3x) \)[/tex] occur at points where y = 0 , which happens when [tex]\( \cot(3x) = 0 \).[/tex]
1. Set [tex]\( y = \cot(3x) \)[/tex] and solve for x : [tex]\( \cot(3x) = 0 \).[/tex]
2. Since [tex]\( \cot(x) = \frac{1}{\tan(x)} \)[/tex], this equation becomes [tex]\( \frac{1}{\tan(3x)} = 0 \)[/tex].
3. Tangent is zero at multiples of [tex]\( \frac{\pi}{2} \)[/tex], so [tex]\( \tan(3x) \)[/tex] is zero at [tex]\( 3x = \frac{\pi}{2} \)[/tex], [tex]\( 3x = \frac{3\pi}{2} \)[/tex], [tex]\( 3x = \frac{5\pi}{2} \)[/tex], and so on.
4. Solve for [tex]\( x \)[/tex]: [tex]\( x = \frac{\pi}{6} \)[/tex], [tex]\( x = \frac{\pi}{2} \)[/tex], [tex]\( x = \frac{5\pi}{6} \)[/tex], and so on.
5. Each of these values represents an x-intercept on the graph of [tex]\( y = \cot(3x) \)[/tex].
The width of a painting is 4 inches less than the length , and the surface area is 320 square inches. Find the length.
PLEASE HELP!!!!!
WILL MARK BRAINLIEST!!!!
Answer:
D
Step-by-step explanation:
Rational functions are functions whose main operation on the variable is a ratio or fraction. This means we find x or the input value in the denominator of the function. Since fractions involve division and division has special circumstances, this reflects on the graph. Because when we divide we cannot divide by 0, any x value which makes the denominator 0 is an asymptote. On the graph, asymptotes are represented by dashed lines where the function doesn't follow.
To find the asymptotes, we set the factors in the denominator to 0 and solve for x. Let's do the each for each options:
a. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.
b. x=0 and x+5=0 so x=-5. This does not match the graph.
c. x=0. This does not match the graph.
d. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.
This means only a and d are options. We will substitute a value to see the behavior of the graph. We pick x=-2. In D, this would give us a positive y. This matches the graph. In A, this would give us a negative y which does not match the graph.
Two angles are complementary . The first angle measures 35 Percent . What's the measurement of the second angle ?
Answer:
55 degrees
Step-by-step explanation:
Find the value of x to the nearest tenth.I will mark the brainlest
Answer:
The value of x nearest to tenth is, 1.5 units
Step-by-step explanation:
In right angle triangle as shown in figure
by definition of tangent ratio i,e [tex]\tan \theta = \frac{opposite side}{Adjacent side}[/tex]
[tex]\tan 37^{\circ} = \frac{x}{2.1}[/tex]
[tex]0.7535540501= \frac{x}{2.1}[/tex]
or
[tex]x = 0.7535540501 \times 2.1 = 1.58246351[/tex] units
Therefore, the value of x nearest to tenth is, 1.5 units
Arnolds workout consisted of 10 minutes of warm up exercises 25 minutes of lifting weights and 15 minutes on the treadmill. What was the ratio of the number of minutres he lifted weights to the total number of minitues of his entire workout
The perimeter of a rectangle is 84m. The length is two and a half times the width. Find the dimensions of the rectangle. Question 5 options: Length = 30m; Width = 12m Length = 28m; Width = 70m Length = 12m; Width = 30m Length = 70m; Width = 28m
w - width
2.5w - length
84m - perimeter
w + w + 2.5w + 2.5w = 7w - perimeter
The equation:
7w = 84 divide both sides by 7
w = 12 m
length = 2.5w → 2.5w = 2.5(12) = 30 m
Answer: length = 30m; width = 12mSolve this system of linear equations. Separate the x- and y- values with a coma. 3x=36-15y. 11x =-78+15y
Answer:
(-3,3)
Step-by-step explanation:
3x=36-15y and 11x =-78+15y
We move all x and y terms to the left hand side of the equation , so that we can apply elimination method
3x=36-15y , Add 15 y on both sides , 3x + 15y = 36
11x =-78+15y, subtract 15y on both sides, 11x -15y = -78
Now we add both equations
3x + 15y = 36
11x -15y = -78
------------------------
14x = -42
divide both sides by 14
x= -3
Now Plug in -3 for x in any one of the given equation
3x=36-15y
3(-3) = 36 - 15y
-9 = 36 - 15y
Subtract 36 on both sides
-45 = -15y
Divide both sides by -15
So y= 3
Answer is (-3,3)
A coin is flipped 20 times. 13 times the coin lands on heads. What is the theoretical probability that the coin lands on tails?
Answer:
[tex]\frac{7}{20}[/tex]
EXPLANATION:
The coin is flipped 20 times. 13 times it lands on tails. 20-13 = 7
A student who didn't study for the upcoming quiz decides to 'wing it' and just guess on the 10 question quiz. Every question is a True/False question. What is the pobability that he will pass the quiz with a grade of at least 70%? Please express your answer as a percent rounded to the hundredths decimal place. Include the '%' symbol.
Answer:
There is around a 40% chance if I have done my calculations correctly
Answer: 17.19%
Step-by-step explanation:
[tex]P=\dfrac{_{10}C_7 + _{10}C_8 + _{10}C_9 + _{10}C_{10}}{2^{10}}[/tex]
[tex]= \dfrac{120+45+10+1}{1024}[/tex]
[tex]= \dfrac{176}{1024}[/tex]
= 0.171875
= 17.1875%
The length of a rectangular room is 5 feet more than its width. The perimeter of the room is 66 feet. Let L represent the length of the room and let W represent the width in feet. What are the room's dimensions?
Angel Grant takes out a $150,000 mortgage this is a 30 year at $725 per month what is the total amount of interest that angel will pay on this mortgage
The lowest temperature ever recorded at Oymyakon in Russia was 96.2°F below 0°F. The lowest temperature ever recorded at Prospect Creek in Alaska was 80°F below 0°F. The thermometer reading of the lowest recorded temperature at Oymyakon was °F. The thermometer reading of the lowest recorded temperature at Prospect Creek was °F.
Answer:
Thermometer reading of the lowest recorded temperature at Oymyakon was -96.2° F
Thermometer reading of the lowest recorded temperature at Prospect Creek was -80° F
Step-by-step explanation:
If the temperature is x° F below 0° F then the thermometer reading is -x° F
It is given that the Lowest temperature recorded at Oymyakon in Russai was 96.2°F below 0°F
So the thermometer reading of the lowest recorded temperature at Oymyakon was -96.2° F
Also it is given that the Lowest temperature recorded at Prospect Creek in Alaska was 80°F below 0° F
So the thermometer reading of the lowest recorded temperature at Prospect Creek was -80° F
Answer:
-96.2 first, -80
Step-by-step explanation:
I took le test it was le correct
Burj l Arab Hotel,one of the world's tallest buildings,was finished in 1999.Located in Dubai,it is 1,053 feet high with 60 stories.If each floor is the same height,how much taller or shorter is each floor than the height of the floors in the Aon Center?
Each floor is 3.35 feet taller than each floor of the Aon Center
Each floor of Burj I Arab Hotel is 3.815 feet taller than the height of Aon Center.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
As per the given,
Height of Burj l Arab Hotel = 1053 feet
Number of floors = 60
Per floor height = 1053/60 = 17.55 feet
Height of Aon center = 1140 feet
Number of floors = 83
Per floor height = 1140/83 = 13.73 feet
17.55 - 13.73 = 3.815 feet bigger than the Aon center.
Hence "Each floor of Burj I Arab Hotel is 3.815 feet taller than the height of Aon Center".
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For what value of α is (α, 9) a solution of the equation y=2x+1?
The student is seeking the solution for a linear equation in the form 'y = mx + b'. From the problem, the equation is 'y = 2x +1' and we have to find the x value (α) for y = 9. The answer is α = 4 when (α, 9) is a solution to our equation.
Explanation:The subject of this problem is Mathematics, and it specifically deals with linear equations, in the form of y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The equation given in the problem is y = 2x + 1. The student wants to find the value of α such that (α, 9) is a solution to the equation.
To solve this, we substitute 9 for y in the equation and solve for x:
9 = 2x + 1
Subtract 1 from both sides:
8 = 2x
Finally, divide both sides by 2 to solve for x:
x = 4
Thus, the value of α that makes (α, 9) a solution to the equation y = 2x + 1 is α = 4.
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Determine the domain and range for the inverse of f(x) = 1/4x + 2
The required domain of the inverse function is {2}, and the range is (-∞, 0) U (0, +∞).
To determine the domain and range of the inverse of the function f(x) = 1/(4x) + 2, we need to find the domain and range of the original function.
The domain of f(x) is the set of all possible values for x that make the function defined. In this case, the only restriction is that the denominator (4x) should not be zero since division by zero is undefined. So, we need to find the values of x that make 4x ≠ 0. Dividing both sides of the inequality by 4, we get x ≠ 0. Therefore, the domain of f(x) is all real numbers except 0, or (-∞, 0) U (0, +∞).
To find the range of f(x), we consider the behavior of the function as x approaches positive infinity and negative infinity. As x approaches negative infinity, the term 1/(4x) approaches zero, and adding 2 to zero gives us 2. As x approaches positive infinity, the term 1/(4x) approaches zero as well, and again adding 2 gives us 2. Therefore, the range of f(x) is the single value 2, or {2}.
Now, to find the domain and range of the inverse function, we interchange the domain and range of the original function. So, the domain of the inverse function is {2}, and the range is (-∞, 0) U (0, +∞).
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help!! at least take a look
What is the recursive rule for this geometric sequence?
27, 9, 3, 1, ...
Enter your answers in the boxes.
an= ⋅an−1
a1=
A recursive rule for a geometric sequence:
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
---------------------------------------------------
[tex]a_1=27;\ a_2=9;\ a_3=3;\ a_4=1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\r=\dfrac{9}{27}=\dfrac{1}{3}\\\\\boxed{a_1=27;\qquad a_n=\dfrac{1}{3}\cdot a_{n-1}}[/tex]
Emily is making a meal for her family. She uses coconut milk for the dessert she is making. The coconut milk is in a can but she doesn't know how much the can holds. The can is 12cm high and 8cm in diameter. Using the formula V=pie r squared h. Work out how much coconut milk is in the can
Geometric or arithmetic or neither ?
Answer:
Sequence 1 is an 'Arithmetic but not Geometric Sequence'
Sequence 2 is 'Geometric but not Arithmetic Sequence'
Step-by-step explanation:
We know that,
1. Arithmetic Sequence is a sequence in which the difference of one term and the next term is a same constant for all terms.
2. Geometric Sequence is a sequence in which the division of two terms gives the same value for all terms.
Now, we check the above properties in the given options,
In Sequence 1 i.e. [tex]\frac{1}{2} , \frac{7}{6} ,\frac{11}{6} ,\frac{5}{2}[/tex] , . . . .
We see that the difference between the terms comes out to be [tex]\frac{2}{3}[/tex],
for eg. [tex]\frac{7}{6} - \frac{1}{2}[/tex] = [tex]\frac{4}{6} = \frac{2}{3}[/tex]
But, the division of two terms gives different values,
for eg. [tex]\frac{\frac{7}{6} }{\frac{1}{2} } = \frac{7}{3}[/tex] and [tex]\frac{\frac{11}{6} }{\frac{7}{6} } = \frac{11}{7}[/tex]
Hence, this sequence is not a Geometric Sequence but an Arithmetic Sequence.
In Sequence 2 i.e. [tex]\frac{1}{2} , \frac{1}{3} ,\frac{2}{9} ,\frac{4}{27}[/tex] , . . . .
We see that the difference of terms is not same constant but are different values,
for eg. [tex]\frac{1}{3} - \frac{1}{2}[/tex] = [tex]\frac{-1}{6}[/tex] and [tex]\frac{1}{3} - \frac{2}{9}[/tex] = [tex]\frac{1}{9}[/tex]
But, the division of different terms gives same constant i.e. [tex]\frac{2}{3}[/tex],
for eg. [tex]\frac{\frac{1}{3} }{\frac{1}{2} } = \frac{2}{3}[/tex].
Hence, this sequence is not a Arithmetic Sequence but a Geometric Sequence.
Nathan has just bought a new car. He models the value, V, in dollars, of the car after t years as V(t) = 21,000(0.861)t. Based on this model, by what percent does the value of Nathan's car decrease each year?
Answer:
13.9%
Step-by-step explanation:
The value of car is modeled as:
[tex]V(t)=21,000(0.861)t[/tex]
Here we can see that, each year Nathan has considered 0.861 of the previous year value or we can say that Nathan has considered 86.1% of the previous year value. So,
[tex]100-86.1=13.9[/tex]
We subtract the percentage value considered from 100 to find out the percentage decrease in the value of the car.
The value of new car is decreasing by 13.9% each year.
Final answer:
Nathan's car decreases in value by 13.9% each year according to the depreciation model [tex]V(t) = 21,000(0.861)^t.[/tex]
Explanation:
The value of Nathan's car decreases by a certain percentage each year, which can be determined from the depreciation model [tex]V(t) = 21,000(0.861)^t.[/tex]The model shows that each year, the value is multiplied by 0.861. To find the percent decrease, we subtract this number from 1 and then convert the result into a percentage:
1 - 0.861 = 0.139
0.139 imes 100% = 13.9%
Therefore, the value of Nathan's car decreases by 13.9% each year based on this model.