Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a. 1 and b.
1?
log,
logo
logna
logna
logo
log,
log,b
logo
logo
Save and
Next
Submit
Answers
Step-by-step explanation:
We have,
[tex]\log _{a}x[/tex]
To find, the value of [tex]\log _{a}x[/tex] = ?
∴ [tex]\log _{a}x[/tex] , where a, b and x are positive
a ≠ 1 and b ≠ 1
We know that,
The logarithm identity,
[tex]\log_{p}m=\dfrac{\log_{y}m}{\log_{y}p}[/tex]
∴ [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]
Where, b is the common base of logarithm
∴ The value of [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]
Thus, the required option A) [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex] is correct.
Related Questions
Which expression is equivalent to 6y - 12
Answers
Answer:-12+6y
Step-by-step explanation:
Since the 12 is a negative and the 6y is a positive you can switch it around.
The expression 6y - 12 is equivalent to 6(y - 2). This can be verified by expanding the factored form, which results in the original expression.
This expression can be factored to find an equivalent expression. Factoring out the greatest common factor (GCF) from both terms, we get:
6y and 12. The GCF is 6.Factor out the GCF: 6(y - 2).Thus, the expression 6y - 12 is equivalent to 6(y - 2).
The average rate of hair growth is 2.5 centimeters every 2 months. At that rate, how many months will it take to grow 22.5 centimeters of hair?
Answers
Answer: 18 months or a year and a half
Step-by-step explanation:
2.5 centimeters every 2 months, so...
1.25 centimeters every month.
22.5 ÷ 1.25 = 18
So it will take 18 months to grow 22.5 centimeters of hair
find the exact value of the eighth term of the geometric sequence: 648,216,72,24
Answers
8th term is 0.30
Step-by-step explanation:
Step 1: nth term of a GP = a × r^n-1Step 2: Find r.⇒ r = a2/a1 = 216/648 = 1/3
Step 3: Calculate 8th term. a = 648, r = 1/3 and n = 8⇒ 8th term = 648 × (1/3)^8-1 = 648 × (1/3)^7 = 648/2187 = 0.30
Find the value of y for the given value of x.
y=1−2x;x=9
Answers
Answer:
y = - 17
Step-by-step explanation:
[tex]y = 1 - 2x[/tex]
When x = 9
[tex]y = 1 - 2(9)[/tex]
[tex]y = 1 - 18[/tex]
[tex]y = - 17[/tex]
Therefore, given equation y = 1 - 2x; when x = 9, y = - 17
The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x + 1 On a coordinate plane, a parabola opens up. It goes through (negative 4, 5), has a vertex at (negative 1.75, 6.75), and goes through (1, 5).
f(x) = x2 – 3x – 3 On a coordinate plane, a parabola opens up. It goes through (negative 2, 7), has a vertex at (1.75, 5), and goes through (5, 7).
f(x) = x2 + 6x + 3 On a coordinate plane, a parabola opens up. It goes through (negative 6, 3), has a vertex at (negative 3, negative 6), and goes through (0, 3).
f(x) = x2 – 6x – 1 On a coordinate plane, a parabola opens up. It goes through (0, negative 1), has a vertex at (3, negative 10), and goes through (6, 0).
Answers
Answer:
The function in the fourth option will have an axis of symmetry at x = 3.
Step-by-step explanation:
We have to choose the function from options, the graph of which has an axis of symmetry at x = 3.
The function in the fourth option will have an axis of symmetry at x = 3.
It is f(x) = x2 – 6x – 1 On a coordinate plane, a parabola opens up. It goes through (0, negative 1), has a vertex at (3, negative 10), and goes through (6, 0). (Answer)
Answer:
D
Step-by-step explanation:
The function S(D) =(7/2) √2D can be used to approximate the speed S, in miles per hour, of a car that has left skid marks of length D, in feet. How fast would would a car have been traveling if it left a skid mark that is 102.04 feet long?
Answers
Answer: The other answer is wrong. The answer would be about 50 miles per hour or 49.99 mph.
Step-by-step explanation:
The required approximate speed of the car when the skid mark is 10204 feet long is 49.99 miles per hour.
Given that,
The function S(D) =(7/2) √2D can be used to approximate the speed S, in miles per hour, of a car that has left skid marks of length D, in feet, how fast would a car have been traveling if it left a skid mark that is 102.04 feet long is to be determined.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given the function of speed,
S(D) =(7/2) √(2D)
Substitute the value of D = 102.04
S(102.04) = (7/2)√(2*102.04)
S(102.04) = 49.99
Thus, the required approximate speed of the car when the skid mark is 10204 feet long is 49.99 miles per hour.
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What is the slope of the line passing through the points (2, 5) and (0, -4)?
9/2
2/9
-9/2
-2/9
Answers
Answer:
9/2
Step-by-step explanation:
Slope of line=rise/run=
y2-y1/x2-x1
Where
x1=2
x2=0
y1=5
y2= -4
Slope =(-4-5)/(0-2)
Slope=-9/-2
Slope=9/2
Answer:
look at the picture shown
ASAP PLS !! WILL MARK BRAINLIST
Answers
Answer:
it is D. $9.50
Step-by-step explanation:
Answer: The answer is (D) $9.50/9.50 dollars
Giving brainliest What is the value of x? A right angle is shown divided into two parts. The measure of one part of the right angle is 30 degrees. The measure of the other part is 2x 10 15 30 45
Answers
Answer:
30
Step-by-step explanation:
a right angle is 90 degrees so if it split into two parts and one is 30 degrees and the other is x (an unknown) you could do 90-30 to get 60 but since it is 2x but has to equal 60 it is going to be 30 because 30 times 2 is 60
Answer:
The answer is 30
Step-by-step explanation:
hope this helps!
simplify 3(4x+7)−4(12x−15)
Answers
The expression 3(4x+7)−4(12x−15) simplifies to -36x + 81. First distribute the constants to the terms inside the parentheses, then combine like terms.
Explanation:In mathematics, to simplify an algebraic expression like 3(4x+7)−4(12x−15), you need to perform the operations in a certain order, respecting the laws of arithmetic. This is often referred to as simplifying the expression using the distributive property.
First, distribute the 3 to both of the terms in the first set of parentheses: 3 * 4x + 3 * 7 equals 12x + 21.Next, distribute the -4 to both of the terms in the second set of parentheses: -4 * 12x -4 * -15 equals -48x + 60.Combine like terms: 12x - 48x equals -36x. Similarly, 21 + 60 equals 81.So the original expression, 3(4x+7)−4(12x−15), simplifies to -36x + 81.Learn more about Simplifying Algebraic Expressions here:
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PLEASE HURRY ILL DO ANYTHING
A group of seventh graders and a group of teachers at a local middle school were asked how many siblings they each have. The dot plots below show the results.
When comparing the shape of the two sets of data, what conclusion can someone draw?
The students tend to have fewer siblings than the teachers.
The teachers tend to have fewer siblings than the students.
Both the students and the teachers have a wide range of siblings.
Both sets of data have the same shape.
Answers
First, we need to find out how many siblings the students have in total and how many siblings the teachers have in total.
The students: (1 x 4) = 4 + (2 x 7) = 18 + (3 x 5) = 33 + (4 x 2) = 41. The students have a total of 41 siblings.
The teachers: (1 x 3) = 3 + (2 x 2) = 7 + (3 x 4) = 19 + (4 x 5) = 39 + (5 x 3) = 54 + (6 x 1) = 60 + (8 x 1) = 68. The teachers have a total of 68 siblings.
Now that we have this information, we know that the answer is option 1, the students tend to have fewer siblings than the teachers. This is because the students had a total of 41 siblings and the teachers had a total of 68 siblings, and 41 is less than 68 so the students have fewer siblings than the teachers.
I really hope I could help! I put a lot of work into this answer! :D
What is the area of the following circle?
Either enter an exact answer in terms of # or use 3.14 for
i and enter your answer as a decimal.
d=8
Answers
Answer:
The answer is 28.27
Which option gives f(x) = x² - 4x - 12 rewritten in vertex form as well as the function's correct axis of symmetry ?
f(x) = (x - 2)² - 16, x = - 16
f?(x) = (x + 2)(x - 6), x = 6
f(x) = (x + 2)(x - 6), x = -2
f(x) = (x - 2)² - 16, x = 2
Answers
y
=
−
(
x
−
2
)
2
+
16
is the vertex form
Explanation:
The vertex form of a quadratic function is given by
y
=
a
(
x
−
h
)
2
+
k
where (h, k) is the vertex of the parabola.
when written in vertex form
(h, k) is the vertex of the parabola and x = h is the axis of symmetry
the h represents a horizontal shift (how far left, or right the graph has shifted from x = 0)
the k represents a vertical shift (how far up, or down the graph has shifted from y = 0)
Now let convert this
y
=
−
x
2
+
4
x
+
12
into vertex form
y
=
−
x
2
+
4
x
+
12
y
−
12
=
−
x
2
+
4
x
y
−
12
=
−
(
x
2
−
4
x
)
y
−
12
=
−
(
x
2
−
4
x
+
4
−
4
)
y
−
12
=
−
(
x
2
−
4
x
+
4
)
+
4
y
−
16
=
−
(
x
2
−
4
x
+
4
)
y
−
16
=
−
(
x
−
2
)
2
y
=
−
(
x
−
2
)
2
+
16
is the vertex form
show the vertex in the figure below
graph{-x^2+4x+12 [-10.06, 15.25, 6.58, 19.25]} Hope iam right
The function f(x) = x² - 4x - 12 in vertex form is f(x) = (x - 2)² - 16, and the axis of symmetry is x = 2.
To rewrite the function f(x) = x² - 4x - 12 in vertex form and find the axis of symmetry, we need to complete the square. The general vertex form of a quadratic is f(x) = a(x - h)² + k, where (h, k) is the vertex, and the line x = h is the axis of symmetry.
The first step is to factor the coefficient of x², which is 1 in this case, so we can leave it as is. The next step is to rearrange the equation as x² - 4x and then add and subtract the square of half the coefficient of x, which is (4/2)² = 4. Adding and subtracting 4 inside the parentheses gives us:
f(x) = (x² - 4x + 4) - 4 - 12
Now we can rewrite this as:
f(x) = (x - 2)² - 16
This equation is in vertex form, with the vertex at (2, -16), and the axis of symmetry is the line x = 2.
Therefore, the correct option is f(x) = (x - 2)² - 16, with the axis of symmetry being x = 2.
In a survey at a shoe store, 200 customers were asked whether they have
running shoes or basketball shoes. The results are in the relative frequency
table.
A. 58%
B. 60%
C. 42%
D. 40%
Answers
Answer: 42%
Step-by-step explanation:
Add 0.16 and 0.26, you get 0.42. Covert 0.42 into percentage and you get 42%
4 - 2b = 2
What is the value of b
Answers
Answer:
Step-by-step explanation:
4 - 2b = 2
collect terms
4 - 2 = 2b
2 = 2b
divide both side by 2
2/2 = 2b/2
b = 1
If the measure is 3= 122, then the m6= ?
122 degrees
58 degrees
68 degrees
28 degrees
Answers
Yo sup??
m3 and m6 for a supplementary pair therefore
m3+m6=180
122+m6=180
m6=58
Hope this helps
The required measure of the angle m∠6 is given as 58 degrees. Option B is correct.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
For the bisection of parallel line by transversal line,
Corresponding angles always have an equal measure,
So, ∠2 = ∠6
Now,
∠2 + ∠3 = 180
∠6 + 122 = 180
∠6 = 58°
Thus, the required measure of the angle m∠6 is given as 58 degrees. Option B is correct.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Hana wants to buy a charm bracelet. Dayton Fine Jewelry charges $17 per charm, plus $62 for the bracelet. Cain Jewelers, in contrast, charges $18 per charm and $60 for the bracelet. If Hana wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. What would the total cost of the bracelet be? How many charms would that be?
Answers
Final answer:
To determine the number of charms for the bracelet to cost the same at both jewelry shops, we set up a system of equations and solved it using substitution. We found that Hana will need to add 2 charms, resulting in a total cost of $96 for the bracelet at either shop.
Explanation:
To determine the number of charms Hana can add to her bracelet such that the cost is the same at Dayton Fine Jewelry and Cain Jewelers, we need to set up a system of equations and solve using the substitution method.
System of Equations:
Let x represent the number of charms and y represent the total cost of the bracelet with charms.
Equation for Dayton Fine Jewelry: y = 17x + 62
Equation for Cain Jewelers: y = 18x + 60
Solution Using Substitution:
Set the two equations equal to each other since the cost is the same:17x + 62 = 18x + 60Subtract 17x from both sides:
62 = x + 60Subtract 60 from both sides to solve for x:
x = 2Substitute x = 2 into either of the original equations to find y:
y = 17(2) + 62
y = 34 + 62
y = 96
Hana will need to add 2 charms to her bracelet, and the total cost of the bracelet will be $96 at either jewelry shop.
Find the area of the triangle below. Show as much work as possible.
Answers
The area of the triangle is (5/12)x²
Step-by-step explanation:
Area of a triangle = 1/2 bhb is the base of the triangle.h is the height of the triangle.Substitute b=(5/6)x and h=x
Area = 1/2[tex]\times[/tex](5/6)x(x)
Area of triangle = (5/12)x²
PLS HELP ASAP I WILL MARK BRAINLIEST FOR WHOEVER ANSWERS FIRST AND CORRECTLY!!
Consider the function represented by the table.
What is f(0)?
4
5
6
7
Table:
x | f(x)
0 | 6
2 | 7
4 | 0
7 | 5
Answers
Answer:
We are given the table as:
x f(x)
0 6
2 7
4 0
7 5
i.e. corresponding to different values of x we are given the values of f(x)
we have to find the value of f(0)
i.e. we have to find the value of f(x) when x=0
As we can see from the table the value of f(x) at x=0 is 6
Hence, Correct option is:
C) 6
Have a Great day!
Answer:
c
Step-by-step explanation:
a sign says that the price marked on all music equipment is 30% off the original price you buy an electric guitar for sale price of $315 what is the original price
Answers
The original price is $450.
Step-by-step explanation:
Step 1:
Given details, Discount%, D% = 30 and Selling Price, SP = $315
Step 2:
Write down formula for calculating the Original Price
Selling Price (SP) = Original Price (OP) - Discount (D)
Discount (D) = Original Price (OP) * (D%/100)
Step 3:
Substitute given values in the formula
315 = OP - D
D = [tex]OP \times30/100[/tex]
D = 0.3 OP
Step 4:
Substitute value of D in the first formula
315 = OP - 0.3 OP
315 = OP (1 - 0.3) = 0.7 OP
Original Price, OP = 315/0.7 = $450
Janey wants to add 2 more equal sections to the garden. She tells Mika to buy11 tomato plants if she wants to use 3/4 of the garden for tomatoes. Is Janey correct?
Answers
What is the half of 14.5
Answers
Answer:
7.25
Explanation:
14.5×½=7.25
What is the coefficient of the c-term of the algebraic expression 14 a minus 72 r minus c minus 34 d?
Answers
When there's no number in front of a variable, that means it has a coefficient of 1.
So the coefficient is 1. Hope that makes sense.
The coefficient of the c-term of the algebraic expression 14a - 72r - c - 34d is -1.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an algebraic expression:
= 14a - 72r - c - 34d
From the above equation, the coefficient of the c term is:
= -1
Thus, the coefficient of the c-term of the algebraic expression 14a - 72r - c - 34d is -1.
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at its highest setting, jeds shower head releases 6.2 gallons of water per minute. Jed took a shower lasting 5 minutes and 12 seconds. What is the maximum amount of water Jed could have used?
Answers
Answer:
32.24 gallons
Step-by-step explanation:
From the question,Jed’s shower head releases
6.2 gallons = 1 minute
x gallon = 5 mins 12 secs
First convert 12 secs to minutes and add it to 5 mins .
1 minute = 60secs
x minute = 12 secs
x = 12/60
= 0.2 mins + 5 mins
= 5.2 mins
Therefore,
6.2 gallons = 1 minute
x gallons = 5.2 mins
Cross multiply
x = 6.2 x 5.2 /1
= 32.24/1
= 32.24 gallons
Solve and explain please
Answers
Therefore the inequality is x≤11
and maximum I can withdraw 11 bills.
Step-by-step explanation:
Given ,
Current balance $320
Minimum balance $100
I could spent =$(320-100) = $220
Let the number of bills be x.
Total amount of x bills = $20x
According to the problem,
20x≤ 220
⇔x ≤ [tex]\frac{220}{20}[/tex]
⇔x≤11
Therefore the inequality is x≤11
and maximum I can withdraw 11 bills.
Lauren's bedroom measures 18 feet by 12 feet, with a closet that measures 2 feet by 4 feet. If carpet costs $4.15 per square foot, how much will it cost to carpet Lauren's room and closet?
Answers
Answer:
$929.60
Step-by-step explanation:
step 1
Find the area of Lauren's bedroom
Remember that the area of a rectangle is equal to
[tex]A=LW[/tex]
so
[tex]A=(18)(12)=216\ ft^2[/tex]
step 2
Find the area of closet
Remember that the area of a rectangle is equal to
[tex]A=LW[/tex]
so
[tex]A=(2)(4)=8\ ft^2[/tex]
step 3
Find the total area
Adds the areas
[tex]216+8=224\ ft^2[/tex]
step 4
Find the cost
Multiply the total area by the cost per square feet
so
[tex]224(4.15)=\$929.60[/tex]
Final answer:
The cost to carpet Lauren's bedroom including her closet is found by calculating the total area and then multiplying by the carpet's cost per square foot. The total area is 224 square feet and with a carpet cost of $4.15 per square foot, the total cost is $930.40.
Explanation:
To calculate the cost to carpet Lauren's room and closet, we must first determine the total area that needs to be carpeted. We already know that the room measures 18 feet by 12 feet. Taking the square footage of the room, we perform a multiplication: 18 ft imes 12 ft = 216 square feet.
Next, we calculate the area of the closet separately, which measures 2 feet by 4 feet. The calculation would be 2 ft imes 4 ft = 8 square feet. Now, we add the area of the room and the closet to get the combined area: 216 sq ft + 8 sq ft = 224 square feet.
Lastly, we find the cost to carpet this combined area. The carpet costs $4.15 per square foot, therefore, we multiply the total area by the cost per square foot: 224 sq ft imes $4.15/sq ft = $930.40. So, the total cost to carpet Lauren's room and closet will be $930.40.
What is 5 1/2 in a whole number
Answers
Answer:
6
Step-by-step explanation:
5 1/2
(5×2+1)/2
11/2
5.5
6 ( nearest whole number)
2x - y = -13
2x + y = 1
Answers
Answer:
x = -3
y = 7
Step-by-step explanation:
Is 23 a compatible number?
Answers
Answer:
In mathematics, compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally...For instance, if we have to add 493 and 549, we can make the numbers compatible by rounding them up to the nearest tens or hundreds.
SO YES! :)
Fred spent half of his allowance going to the movies. He washed the family car and earned 9 dollars. What is his weekly allowance if he ended with 11 dollars?
Answers
Answer:
Weekly allowance $4
Step-by-step explanation:
Fred ended with $11. So, subtract $9 from washing the car.
$11 - $9 = $2
$2 Is the amount of weekly allowance Fred hasn't spent yet. However, at the beginning of the week, Fred used half his allowance. This means $2 was what was left. So,
$2 × 2 = $4
meaning Fred had $4 in allowance at the beginning of the week.