Answer:
C. log(1/3)
Step-by-step explanation:
Remember the quotient/subtraction rule for logs:
log2 - log6 can be written as log(2/6)
Hence, it's equal to C. log(1/3)
Hope this helps!
Mark brainliest if you think I helped! Would really appreciate!
The expressions that are equivalent to [tex]\( \log 2 - \log 6 \)[/tex] are options A and C.
The correct option is (A&C).
To solve [tex]\( \log 2 - \log 6 \)[/tex], we can use the property of logarithms that states:
[tex]\[ \log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right) \][/tex]
Given [tex]\( \log 2 - \log 6 \)[/tex], applying the above property:
[tex]\[ \log 2 - \log 6 = \log\left(\frac{2}{6}\right) = \log\left(\frac{1}{3}\right) \][/tex]
So, the expression \[tex]( \log 2 - \log 6 \)[/tex] is equivalent to [tex]\( \log\left(\frac{1}{3}\right) \)[/tex], which matches option C.
Now, let's check the other options:
A. [tex]\( \log(2) + \log\left(\frac{1}{6}\right) \)[/tex]
This expression can be simplified using the properties of logarithms to [tex]\( \log\left(2 \times \frac{1}{6}\right) = \log(1/3) \),[/tex] which is equivalent to the original expression. So, option A is also correct.
B. [tex]\( \log 2 \)[/tex]
This option is not equivalent to the original expression. It only represents [tex]\( \log 2 \),[/tex] not the difference of [tex]\( \log 2 \) and \( \log 6 \).[/tex]
D. [tex]\( \log 3 \)[/tex]
This option is not equivalent to the original expression. It only represents [tex]\( \log 3 \)[/tex], which is unrelated to the expression [tex]\( \log 2 - \log 6 \).[/tex]
So, the expressions that are equivalent to [tex]\( \log 2 - \log 6 \)[/tex] are options A and C.
A drawer contains 60 coins consisting of dimes and quarters. If the total value of the coins is $12.30, how many dimes and how many quarters are in the drawer?
Answer:
my mistake sorry
Step-by-step explanation:
(8.) 12.5%
How do u write 12.5 percent as a fraction
Answer: 1/8
Step-by-step explanation: To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100.
So here, 12.5% can be written as the ratio 12.5 to 100 or 12.5/100.
To write 12.5/100 in lowest terms, first multiply the numerator and the denominator by 10 to get rid of the decimal. When we do this, we get the fraction 125/1000.
Now, we divide the numerator and the denominator of 125/1000 by the greatest common factor of 125 and 1,000 which is 125 and we end up with the equivalent fraction which is 1/8.
Therefore, 12.5% is equivalent to 1/8.
Find four consecutive numbers whose sum equals 218
Answer: 53, 54, 55, and 56
Step-by-step explanation: This problem states that the sum of 4 consecutive numbers is 218 and it asks us to find the numbers.
4 consecutive numbers can be represented as followed.
X ⇒ first number
X + 1 ⇒ second number
X + 2 ⇒ third number
X + 3 ⇒ fourth number
Since the sum of our 4 consecutive numbers is 218, we can set up an equation to represent this.
X + X + 1 + X + 2 + X + 3 = 218
On the left side of the equation, we can combine our x's and our numbers.
4x + 6 = 218
-6 -6 ← subtract 6 from both sides of the equation
4x = 212
÷4 ÷4 ← divide both sides of the equation by 4
X = 53
X ⇒ first number = 53
X + 1 ⇒ second number = 54
X + 2 ⇒ third number = 55
X + 3 ⇒ fourth number = 56
Therefore, our 4 consecutive numbers are 53, 54, 55, and 56.
Which of the following is 4.15 * 106 in standard notation?
A. 41.5000000
B. 415,000
C. 4,150,000
D. 4.15000000
At a sale this week, a sofa is being sold for $244.80. This is a 64% Discount from the original price. What is the original price?
Answer:
680$
Step-by-step explanation:
If this is a 64% discount, the price 244.80 is 36% of the original price
244.8 = 36% -Divide by 36 on both sides
6.8 = 1% - Times by a hundred
680 = 100%
The original price is 680$
To find the original price of the sofa given a 64% discount, divide the sale price by the discount percentage and subtract it from 100%.
Explanation:To find the original price, we need to determine what the discount percentage represents in terms of the original price. Since the sale price is 64% of the original price, the discount is 100% - 64% = 36%. Let's represent the original price as x:
36% of x = $ 244.80
To solve this equation, we can convert 36% to the decimal form by dividing it by 100: 36/100 = 0.36. Now we can solve for x:
0.36x = $ 244.80
Dividing both sides of the equation by 0.36, we get:
x = $ 244.80 / 0.36 = $ 680
Therefore, the original price of the sofa was $ 680.
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Find a slope that
goes through the points
(2,6) and (1,8)
Answer:
The slope is -2.
Step-by-step explanation:
m=(y2-y1)/(x2-x1)=(8-6)/(1-2)=2/-1=-2
For the last 5 years the origination has given out 278, 310, 320, 242, 303 backpacks. What is the average number given out the past five years?
An average of 291 backpacks were given out the past five years.
Step-by-step explanation:
Number of bags for last 5 years;
278, 310, 320, 242, 303
No. of terms = 5
Average = [tex]\frac{Sum\ of\ the\ terms}{No.\ of\ terms}[/tex]
[tex]Average=\frac{278+310+320+242+303}{5}\\Average=\frac{1453}{5}\\Average=290.6[/tex]
Rounding off to nearest whole number
Average = 291
An average of 291 backpacks were given out the past five years.
Keywords: average, addition
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Answer the question below. Type your response in the space provided.
Polygon ABCD is dilated by a scale factor of 2 with the center of dilation at the origin to create polygon A′B′C′D′. If the endpoints of AB are located at (0, -7) and (8, 8), what is the length of A'B? Use the distance formula to help you decide:
d= (x2 -x1)2 + (y2 - y1)2
Answer:
A'B'= 34 units long.
Step-by-step explanation:
The length A'B' will be 2 times the length of AB.
AD = sqrt( (8-0)^2 + (8- -7)^2 )
= sqrt 289
= 17
So A'B' = 34 .
Given that ABCD is a rhombus, what is the value of x?
(3x + 12
Answer:
19.5
is the correct answer
Answer:
The answer is 19.5
Step-by-step explanation
Have an amazing day :)
Megan has $50 and saves $5.50 each week. Conner has $18.50 and saves $7.75 each week. After how many weeks will Megan and conner have saved the same amount?
After 14 weeks, both Megan and Conner will have saved the same amount.
Step-by-step explanation:
Amount Megan have = $50
Amount saved each week = $5.50
Amount Conner have = $18.50
Amount saved each week = $7.75
Let,
x be the number of weeks.
According to given statement;
M(x) = 50+5.50x Eqn 1
C(x) = 18.50+7.75x Eqn 2
For amount to be same;
Eqn 1 = Eqn 2
[tex]50+5.50x=18.50+7.75x\\50-18.50=7.75x-5.50x\\31.50=2.25x\\2.25x=31.50\\[/tex]
Dividing both sides by 2.25
[tex]\frac{2.25x}{2.25}=\frac{31.50}{2.25}\\x=14[/tex]
After 14 weeks, both Megan and Conner will have saved the same amount.
Keywords: functions, division
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Find the value of 9y-9 given that 5y-2=3.
Answer:
0
Step-by-step explanation:
5y-2=3
5y=3+2
5y=5
y=5/5=1
9y-9=9(1)-9=9-9=0
3.78 divided by 0.9
The division of 3.78 by 0.9 equals 4.2 after rounding to the nearest tenth. The given problem is an arithmetic division question typically encountered in mathematics. The keyword 3.78 is the number being divided by 0.9.
Explanation:The division question posed: 3.78 divided by 0.9, is a simple arithmetic problem. To solve, we will perform the division calculation directly. First, we divide 3.78 (the dividend) by 0.9 (the divisor). This yields a quotient of approximately 4.2. Thus, 3.78 divided by 0.9 equals 4.2 when rounded to the nearest tenth. This division problem would be typically encountered in arithmetic, a branch of mathematics that deals with numbers and numerical computation.
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How do I find the slope, y-intercept, and coordinates of (-1,7) (0,5)?
Answer:
The slope for the given points is - 2 , and y- intercept is 5
Step-by-step explanation:
Given points as :
( - 1 , 7 ) and ( 0 , 5 )
Now slope of line in points form as
Slope = m = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
or, m = [tex]\dfrac{5 - 7}{0 + 1}[/tex]
or, m = - 2
so, Slope of line is - 2
Now equation of line is given as
y - [tex]y_1[/tex] = m × ( x - [tex]x_1[/tex] )
or, y - 7 = ( - 2 ) × ( x + 1)
or, y - 7 = - 2 x - 2
Or, equation of line is
y = - 2 x + 5
Now, for y - intercept , x = 0
So, from line equation
y = - 2 × 0 + 5
Or, y = 0 + 5
∴ y = 5
Hence The slope for the given points is - 2 , and y- intercept is 5 Answer
The height of Jake's window is 5x - 3 inches and the width is 3x + 2 inches. What is the perimeter of Jake's window ?
The perimeter of Jake window is 16x - 2 inches
Solution:Given that height of Jake window is 5x - 3 inches
Also given that width is 3x + 2 inches
To find: perimeter of Jake window
We know that, in general a window is of rectangular shape
The perimeter of rectangle is given as:
Perimeter of rectangle = 2(length + width)
Substituting the values we get,
Perimeter of rectangle = 2(5x - 3 + 3x + 2)
Perimeter of rectangle = 2(8x - 1) = 16x - 2
Hence, the perimeter of the window is 16x – 2 inches
The taxi ride costs 18.00 (mop). Now convert this to US Dollars. Here's the convertion fact: 1 US Dollar=7.98 MOP.
18.00 MOP equals to 2.26 US Dollars.
Step-by-step explanation:
Cost of taxi ride = 18.00 MOP
It is given that;
1 US Dollar = 7.98 MOP
It can also be written as,
7.98 MOP = 1 US Dollar
Therefore,
1 MOP = [tex]\frac{1}{7.98}\ US\ Dollars[/tex]
Now,
18.00 MOP = [tex]\frac{1}{7.98}*18.00\ US\ Dollars[/tex]
[tex]18.00\ MOP=\frac{18.00}{7.98}\ US\ Dollars\\18.00\ MOP= 2.26\ US\ Dollars[/tex]
18.00 MOP equals to 2.26 US Dollars.
Keywords: conversion, division
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simplify cos x csc x
Answer:
cot(x)
Step-by-step explanation:
csc(x) = 1/sin(x)
cos(x)*csc(x) = cos(x)*1/sin(x)
cos(x)*csc(x) = cos(x)/sin(x)
cos(x)*csc(x) = cot(x)
----
abbreviations
csc = cosecant
cos = cosine
sin = sine
cot = cotangent
To simplify cos x csc x, we can replace csc x with 1/sin x based on the trigonometric identity. This will give us cos x/sin x, which is the same as cot x based on the trig identities.
Explanation:The question is asking us to simplify the expression cos x csc x. To do this, we can use the trigonometric identity sin = 1/csc, which tells us what csc x is in terms of sin x.
So if that is the case, we can rewrite csc x as 1/sin x and replace csc x in the original expression giving us cos x * (1/sin x) or equivalently cos x/sin x.
And if we look at our trigonometric identities again, we can find that cos x/sin x is the same as cot x, our final simplified expression.
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What is a perimeter of a recangle that is 2 inches by 1 inch
Answer:
6 inches
Step-by-step explanation:
p=l+l+w+w
p=2+2+1+1
p=6
Answer:
6 in
Step-by-step explanation:
If 3 apples and 1 orange costs $5 and I apple and I
orange costs $3. how much does each apple and orange cost?
Equation 1:
Equation 2:
Solution:
Answer:
Step-by-step explanation:
Equation 1: 3a + 1o =5 3(1) + 1(2) = 5
Equation 2: 1a + 1o =3 2(1) + 1(2) = 3
Solution: apples are $1.00 each and oranges are $2.00 each
2(x-3)=/2(4x -12)
help me plzs!!!!.....
Assuming that the correct expression is 2(x - 3)= 2(4x -12)
(2 * x) + (2 * −3) = (2 * 4x) + (2 * −12)
2x - 6 = 8x − 24
2x − 6 − 8x = 8x − 24 − 8x
−6x − 6 = −24
−6x − 6 + 6 = −24 + 6
−6x = −18
-6x/-6 = -8/-6
x = 3 (Answer)
______
Best Regards,
Wolfyy :)
And exercise 17th pause grapes cost 2.35 per pound oranges cause 0.99 per pound and apples cost 1.65 per pound. Running to the nearest whole number about how much did Adrian pay for all the fruit
Answer:
Adrian needs to pay $5 for all the fruit.
Step-by-step explanation:
Consider the provided information.
Grapes cost $2.35 per pound, oranges cost $0.99 per pound, and apples cost $1.65 per pound.
In order to find how much Adrian needs to pay we need to add $2.35, $0.99 and $1.65.
[tex]\$2.35 + \$0.99 + \$1.65=\$4.99[/tex]
Now round $4.99 to the nearest whole number.
[tex]\$4.99\approx\$5[/tex]
Hence, Adrian needs to pay $5 for all the fruit.
16 is a factor of 24
True or false ?
Answer:
False
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
The multiples of 16: 16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,27
Factors of 24
The factors of 24.: 1,2,3,4,6,8,12,24,
The formula for converting Celsius temperatures to Fahrenheit temperatures is a linear equation. Water freezes at 0°C, or 32°F and it boils at 100°C, or 212°F. Find the slope and y-intercept for a graph that gives degrees Celsius on the horizontal axis and degrees Fahrenheit on the vertical axis. Then write an equation in slope-intercept form that converts degrees Celsius into degrees Fahrenheit
Answer:
1.8=100x+b
Step-by-step explanation:
The formula y = mx + b sometimes appears with
different symbols.
For example, instead of x, we could use the
letter C. Instead of y, we could use the letter F.
Then the equation becomes
F = mC + b.
All temperature scales are related by linear
equations. For example, the temperature in
degrees Fahrenheit is a linear function of degrees Celsius.
Water freezes at: 0°C, 32°F
Water Boils at: 100°C, 212°F
Find the linear approximation for f(x) = 12x3 + 3x2 + x + 2 at x= 1.
Answer:
y = 43x − 25
Step-by-step explanation:
Evaluate the function at x=1:
f(x) = 12x³ + 3x² + x + 2
f(1) = 12 + 3 + 1 + 2
f(1) = 18
Find the slope of the tangent line at x=1:
f'(x) = 36x² + 6x + 1
f'(1) = 36 + 6 + 1
f'(1) = 43
Point-slope form:
y − y₀ = m (x − x₀)
y − 18 = 43 (x − 1)
Convert to slope-intercept form:
y − 18 = 43x − 43
y = 43x − 25
Graph:
desmos.com/calculator/giumpkkphr
To find the linear approximation for the function f(x) = 12x^3 + 3x^2 + x + 2 at x = 1, we can use the equation for the linear approximation. First, we need to find the derivative of the function and then plug in the values into the formula. The linear approximation is f(1).
Explanation:To find the linear approximation for the function f(x) = 12x^3 + 3x^2 + x + 2 at x = 1, we can use the equation for the linear approximation:
() ≈ () + '()( − )
First, we need to find '(), which is the derivative of the function. Taking the derivative of f(x) gives us:
'() = 36^2 + 6 + 1
Next, we plug in x = 1 into the first equation:
(1) ≈ (1) + '(1)(1 − 1)
Simplifying, we have:
(1) ≈ (1)
So, the linear approximation for f(x) at x = 1 is f(1).
Find the y intersept of
y=logbase (b)(a-k) based on the constants b and k ?
Answer:
[tex](0, log_{b}(-k)), k < 0[/tex]
Step-by-step explanation:
[tex]y = \log_{b}(a - k)[/tex]
To find the y-intercept, set a = 0 and solve for y.
[tex]y = \log_{b}(0 - k)\\y = \log_{b}(-k)[/tex]
This equation is undefined for k ≥ 0.
There is a y-intercept only if k < 0. Only then can the argument of the log function be positive.
The y-intercept is at
[tex]\mathbf{(0, log_{b}(-k)), k < 0}[/tex]
For example, if b = 2 and k = -3, log₂(3) = 1.585
The intercept is at (0, 1.585).
please help me first thinks
Answer:
3 minutes
5 minutes.
Step-by-step explanation:
It is given that, Amelia can wash 8 plates in 24 minutes.
So, if this rate remains constant then 1 plate will be washed in [tex] \frac{24}{8} = 3[/tex] minutes.
Again, it is given that, Amelia bakes 12 cookies in 60 minutes.
So, if this rate also remains constant then she will bake 1 cookie in [tex] \frac{60}{12} = 5[/tex] minutes. ( Answer )
The equation S = -16t2 + 34t + 184 models the height of a ball that is thrown upward from the roof of a 184 foot building and falls to the street below. In this equation S is the height in feet of the ball above the ground and t is the time in seconds the ball has traveled. According to this model, how many seconds did it take the ball to reach a height of 91 feet? (round to 1 decimal place)
Answer:
t=1.6
Step-by-step explanation:
If the equation [tex]S=-16t^2+34t+184[/tex] models the height of a ball above the ground, where t is time the ball travelled.If the height of the ball above the ground is S=91 instead of 184, then the time the ball should take to get to the ground comes from the expression above: [tex]S=-16t^2+34t+91[/tex] (because now we want to know how much time does it takes to reach the ground if it is thrown from 91 foot, not 184). Then, to know when the ball reaches the floor, we must equal the equation to zero [tex]-16t^2+34t+91=0[/tex] (because when the equation is zero, the height of the ball is zero, which means it is in the ground).To obtain the value of t in the expression [tex]-16t^2+34t+91=0[/tex] , we can apply the well known formula [tex]t=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex], where a is the coefficient that accompanies the quadratic term (in this case a=16), b is the coefficient that accompanies the linear term (b=34 in this case), and c is the constant coefficient (c=91).Because time is always possitive, we only retain the possitive value for t that solves the equation:[tex]\frac{-34(+-)\sqrt{34^2-4\times(-16)\times93} }{2\times16}[/tex]. [tex]t=1.55\simeq1.6[/tex]1/9(-9x+18)-1/5(10+15x)
Answer:
-4x
Step-by-step explanation:
Write the equation of the line in slope intercept form that contains the point (-2,-1) and is perpendicular to the graph of y=-2x-3
Answer:
y = -0.5x -2
Step-by-step explanation:
We have to find a line perpendicular to the line y = -2x -3.
Let the required line will have slope m so ,
-2m = 1
m = -0.5.
So, the required line will have the slope -0.5.
Now, let the line be y = -0.5x + c.
This line is passing through (-2,-1), So putting this point in the line we will get
-1 = 1 + c
c = -2 .
So, the required line is
y = -0.5x -2.
Which of the following is equivalent to 18 + 36?
A 29+16)
6/3 + 12)
7(2+4)
2+36)
Answer:
None.
Step-by-step explanation:
18+36=54
A) 29+16=45
B) 6/3+12=2+12=14
C) 7(2+4)=7(6)=42
D) 2+36=38
Find the midpoint between A and C.
A. (1, 1)
B. (5, -7)
C. (-5, 7)
D. (0.5, 0.5)
Answer:
D. [tex]\displaystyle (0,5, 0,5)[/tex]
Step-by-step explanation:
C(3, −3) and A(−2, 4)
Just by looking at the graph, we can CLEARLY see that answer choice D is EXACTLY halfway in between the two given endpoints.
I am joyous to assist you anytime.