Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a Not-equals 1 and b Not-equals 1? log Subscript x Baseline x StartFraction log Subscript b Baseline x Over log Subscript b Baseline a EndFraction StartFraction log Subscript b Baseline a Over log Subscript b Baseline x EndFraction StartFraction log Subscript a Baseline b Over log Subscript x Baseline b EndFraction StartFraction log Subscript a Baseline x Over log Subscript b Baseline x EndFraction.
Answers
The expression that can be used to approximate the expression below is[tex]log_a x = \frac{log_{b}a}{log_{b}x}[/tex]
Given the logarithmic function expressed as [tex]log_a x[/tex], we need the log expression that is equivalent to the given expression.To do this, we will write the logarithm as a quotient to the same base. Using the base of 10, the expression can be written as;[tex]log_a x = \frac{log_{10}a}{log_{10}x}[/tex]
This is similar to the option c where the base of "b" was used as [tex]log_a x = \frac{log_{b}a}{log_{b}x}[/tex]
Learn more on law of logarithms here: https://brainly.com/question/11587706
Answer: C
Step-by-step explanation:
If you don't want to read it all
Related Questions
a trader is given 15% discount on goods bought from a factory. If the original price of an item in the factory is 45000. Calculate the amount the trader paid for them
Answers
Answer:
38,250
Step-by-step explanation:
Its a 15% discount so youre only paying 85% of the original 45,000. You then multiply 45,000 by .85 to find what youre paying because the decimal version of 85% is .85. You can find the decimal version of a percentage by dividing the percentage by 100; 85/100=.85. Once you multiply 45,000 by .85 you get 38,250.
Solve the following, where 0° < θ < 360°.
If cos θ=2/3 and tan θ<0
Find θ.
Answers
Answer:
The angle θ = 312°.
Step-by-step explanation:
0° < θ < 360°
If cos θ = 2/3 and tan θ < 0
As cos θ is positive and tan θ is negative so the angle is in fourth quadrant.
cos θ = 2/3
θ = 312°
I need help to find the value of x. Round to the nearest tenth
Answers
Answer:
17.1
Step-by-step explanation:
tan(35)=12/x, x=17.1
Answer:
x ≈ 17.1
Step-by-step explanation:
The angle is 35 degrees, so we do tan(35)
Which equals the side divided by x.
tan(35) = 12 / x
So x ≈ 17.1
When solving the system of equations, which expression could be substituted for r in the first equation?
3r + 2t = 15
r = 4 – t
Answers
Answer:
4-t
Step-by-step explanation:
We use the second equation and r = 4-t
every time we see r in the first equation replace it with 4-t
Find the product using suitable property: a.46*102 b.55*1004
Answers
Answer:
please
Step-by-step explanation:
follow me
please
please
please
Someone can help me with this ? I don’t understand
Answers
Answer:
-3
Step-by-step explanation:
Factor completely, show work.
x² - 49
Answers
You want to pull out the square roots of each term since they are both perfect squares.
Factor using the difference of squares formula: a2-b2=(a+b)(a-b)
This formula allows the middle term to cancel out.
=x2 - 49
=(x + 7)(x - 7)
ANSWER: (x + 7)(x - 7)
Hope this helps! :)
what is the total cost
Answers
Answer:
Step-by-step explanation:
We need to first find the perimeter of this oddly-shaped rink. We have a rectangle for which we are enclosing 3 of its sides, and the fourth "side" is a half-circle. Let's find the perimeter (or circumference) of the circle, divide it in half because we have half a circle, then add in the remaining 3 sides from the rectangle, shall we?
C = πd. The diameter of the circle is the same as the shorter length in the rectangle, 26. Therefore,
C = (3.14)(26) so
C = 81.64 m for a whole circle, and for half of that circle, the circumference is
C = 40.82 m
Now we can find the perimeter of the rink:
40.82 + 61 + 26 + 61 = p so
p = 188.82 m
If the fencing costs $6.20 per meter and we have 188.82 m, then the total cost is
[tex]cost=\frac{6.20dollars}{meter}*188.82meters[/tex]. The label "meter" cancels out, leaving us with
cost = $1170.82
i need alot of help in this
Answers
Not the best way to do it, but it should look something like this.
Nigel makes the claim that x=6 is the solution to the equation 4(5x−12)−7x=5x. His work to support his claim follows. Given: 4(5x−12)−7x=5x Step 1: 20x−48−7x=5x Step 2: 20x−7x−48=5x Step 3: 13x−48=5x Step 4: 13x−13x−48=5x−13x Step 5: 0−48=−8x Step 6: 6=x Which of the following justifications can be used to justify and support Nigel's work? Select all justifications that are correct.
Step 1 is justified by the Distributive Property. , Step 1 is justified by the Distributive Property. , ,
Step 4 is justified by the Symmetric Property. , Step 4 is justified by the Symmetric Property. , ,
Step 5 is justified by the Property of Additive Inverses. , Step 5 is justified by the Property of Additive Inverses. , ,
Step 2 is justified by the Commutative Property. , Step 2 is justified by the Commutative Property. , ,
Step 6 is justified by the Associative Property.
Answers
Answer:
Step 1 is justified by the Distributive Property.
Step 4 is justified by the Symmetric Property
Step-by-step explanation:
Given the equation solved by Nigel expressed as
4(5x−12)−7x=5x.
First, we need to expand the bracket using the distributive property
4(5x−12)−7x=5x.
4(5x)-4(12) -7x = 5x
20x - 48 - 7x = 5x
Hence Step 1 is justified by the Distributive Property.
Next is to collect the like terms;
20x - 7x - 48 = 5x
Take the difference
13x - 48 = 5x
Next is to subtract 13x from both sides according to the symmetric property
13x - 48 - 13x = 5x - 13x
Hence Step 4 is justified by the Symmetric Property
The resulting equation will be
0-48 = -8x
Divide both sides by -8
-48/-8 = -8x/-8
6 = x
Hence the correct justifications are Step 1 is justified by the Distributive Property AND Step 4 is justified by the Symmetric Property
which is the total length of both sides of the roof 4x
Answers
Answer:
b. 40m
Step-by-step explanation:
[tex]length \: of \: x \\ {x}^{2} = {8}^{2} + {6}^{2} \\ {x}^{2} = 64 + 36 \\ {x}^{2} = 100 \\ \sqrt{ {x}^{2} } = \sqrt{100} \\ x = 10m[/tex]
[tex]x = 10m \\ 4x = 4 \times 10 \\ 4x = 40m[/tex]
Find Tan(ß) in the triangle
Answers
Answer:
the answer is
tan (B)=p/b
=5/12
Answer: C)5/12
Step-by-step explanation:
The tangent is equal to the ratio of the opposite cathet to the adjacent one.Then [tex]\bf tg \beta = \dfrac{5}{12}[/tex]find the shaded area ..
Answers
Answer:
39°
Step-by-step explanation:
The angle adjacent to 115° in the lower triangle = 180° - 115° = 65°
angle on circle in lower triangle
= 180° - (65 + 76)° ← angle sum in triangle
= 180° - 141° = 39°
Angles on the circle subtended from the same arc are congruent, then
shaded angle = 39°
Find the values of x and y that make these triangles congruent by the HL Theorem.
Answers
Select the correct answer from each drop-down menu.
CD is perpendicular to AB and passes through point 95, 12).
If the coordinates of A and B are (-10, -3) and (7,14), respectively, the x-intercept of CĐ is (blank). The point
(Blank) lies on CD.
Answers
Answer:
Hello! the answer is CD is 17,0 (-2,19)
I need help with this one pls!
Answers
Hi there!
[tex]\large\boxed{b = \frac{a}{ac - 1}}[/tex]
We can begin by making each fraction have a common denominator:
If we make each have a common denominator of ab, we get:
[tex]\frac{b}{ab} + \frac{a}{ab} = c[/tex]
Simplify:
[tex]\frac{a + b}{ab} = c[/tex]
Multiply both sides by ab:
[tex]a + b = cab[/tex]
Move b to the opposite side:
[tex]a = cab - b[/tex]
Factor out b:
[tex]a = b(ac - 1)[/tex]
Divide by (ac - 1):
[tex]\frac{a}{ac - 1} = b[/tex]
Doubling x and adding 3 is the same as tripling x and adding 1
Answers
Answer:
2x + 3 = 3x + 1
x = 2
hope that helps ✌
What’s the rate of change please help
Answers
Answer:
Rate of change, is also another word for slope.
Slope --> y2 - y1 / (x2-x1)
Assuming the table is already in xy, the cords are in xy form too.
1) (8,8)
2) (11,10)
Plug points into slope eq
--> 10 - 8 = 2
----> 11 - 8 = 3
2/3 Is the slope/rate of change.
Find all solution(s) of the quadratic equation x2 – 100 = 0. Question 9 options: A) x = 10, –10 B) x = –10 C) x = 10 D) x = 100, –100
Answers
Answer:
x = - 10, x = 10
Step-by-step explanation:
Given
x² - 100 = 0 ( add 100 to both sides )
x² = 100 ( take the square root of both sides )
x = ± [tex]\sqrt{100}[/tex] = ± 10
solutions are x = - 10, x = 10
Likes s and t are perpendicular if the slope of line s is 5 what is the slope of line t?
Answers
Answer:
Gradient of line t is -1/5
Step-by-step explanation:
[tex]{ \sf{m _{s} \times m _{t} = - 1}} \\ { \sf{5 \times m _{t} = - 1 }} \\ { \sf{m _{t} = - \frac{1}{5} }}[/tex]
Because they are perpendicular one will be (+) while the other is (-).
The formula to get the answer is: y=mx+b
Fill in the slope (m)
Fill in the y intercept (b)
REfer and answer
Pls its urgent
Pls fast
Answers
A stationary shop markdown their writing boards by 40%. The markdown is $32. What is the original selling price and selling price after markdown of the writing boards?
A.$50, $25
B.$60, $24
C.$80, $48
D.$70, $28
Answers
Answer:
The original price is 80
The new price is 48
Step-by-step explanation:
Let x be the original price
x - .4x = new price
.6x = new price
.4x = markdown
.4x= 32
.4x/.4 = 32/.4
x =80
The original price is 80
.6x = new price
.6(80) = 48
Find the area of the regular polygon. Round your answer to the nearest hundredth
Answers
Answer:
Step-by-step explanation:
Use the Pythagorean theorem to find the length of the missing side that is 1/2 the side of the missing heptagon. You have to assume that the figure is a regular heptagon, something you should point out to your teacher. Math really requires well qualified diagrams.
c^2 = a^2 + b^2
c = 2.77
a = 2.5
b = 1/2 the side of the heptagon.
2.77^2 = 2.5^2 + b^2
7.6729 =6.25 + b^2
7.5629 - 6.25 = b^2
b^2 = 1.4229
b = sqrt(1.4229)
b = 1.1928
But the side is twice that long
s = 2.3857
Now draw another line from the side you just found. It will be the same length as 2.77. It's a radius of the circumcircle.
Area of the triangle so formed is
Area = 1/2 * b * h
b = 2.3857
h = 2.5
Area = 1/2 * 2.5 * 2.3857
Area = 2.982
There are 7 such triangles.
Answer: 7 * 2.982
Answer: 20.87
Which linear inequality represents the graph below?
(-2,3)
(0-2)
A. y<-{x-2
O B. y<-x-2
O C. ysx-2
O D. ys-x-2
Answers
Answer:
B.
Step-by-step explanation:
1. We can clearly see that the "rise" is 5 and the "run" is 2, which cancels out both A. and D.
2. The line is dashed, which therefore cancels out both C. and D.
3. Just by canceling out those two can help you see that B fits what is seen in this figure because option A. has the wrong amount of "rise" over "run".
The linear inequality can be obtained from the given graph (the nature
of the line and the feasible (shaded) region).
Response:
[tex]B. \ y < -\dfrac{5}{2} \cdot x - 2[/tex]
How can the graph of the inequality be determined?The given points in the graph are;
(-2, 3), and (0, -2)
The slope of the line is therefore;
[tex]Slope = \dfrac{-2 - 3}{0 - (-2)} = \mathbf{-\dfrac{5}{2}}[/tex]
The equation of the line is therefore;
[tex]y - 3 = \mathbf{ -\dfrac{5}{2} \cdot (x - (-2))}[/tex]
[tex]y = -\dfrac{5}{2} \cdot x - 5 + 3 = -\dfrac{5}{2} \cdot x - 2[/tex]
[tex]y = \mathbf{-\dfrac{5}{2} \cdot x - 2}[/tex]
Given that the left side (below the line of the equation of the graph) is
shaded and the line of the graph is a broken line, the correct option is
therefore;
[tex]B. \ y < -\dfrac{5}{2} \cdot x - 2[/tex]
Learn more about the graph of inequalities here:
https://brainly.com/question/19251897
PLEASEEE HELP What is the solution to the equation represented by the model below?
XX
Х
X
X
X
O x=-14
O x=-2
X= 2
OX= 14
Answers
Answer:
C) x=2
[tex]3x+8=4x+6[/tex]
[tex]8-6=4x-3x[/tex]
[tex]x=2[/tex]
~OAmalOHopeO
3x + 8 = 4x + 6
3x - 4x = 6 - 8
-x = -2
x = 2
Translate the sentence into an equation.
Three more than the quotient of a number and 6 is equal to 5.
Use the variable b for the unknown number.
Answers
Answer:
3 + b/6 = 5
solve it too?
b/6 = 2
b = 12
Answer:
is it like
3x+6=5
to solve this
3x+6=5
collect like terms
3x= -6+5
3x= -1
divide both side by 3
3x/3=-1/3
x= -0.3
Can someone help me out
Answers
Answer: V=9.4 cm^3
Step-by-step explanation:
[tex]V=\pi r^2h\\V=\pi (1)^2(3)\\V=9.4cm^3[/tex]
Instructions: Find the measure of the indicated angle to the nearest
degree.
50
?
17
Answers
Answer:
x = 19
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan ? = 17/50
Taking the inverse tan of each side
tan ^-1 (tan ?)) = tan^-1 (17/50)
? =18.77803
To the nearest degree
x = 19
Find the value of x in the triangle shown below.
Answers
Answer:
50
Step-by-step explanation:
A payday loan store charges $25 for a one-month loan of $600. What annual interest rate is this equivalent to?
Answers
Answer:
50%
Step-by-step explanation:
1. determine the monthly interest rate
monthly interest rate = interest / loan amount
monthly interest = 25 / 600 = 4.17%
2, multiply the monthly interest rate by 12 to determine the annual interest rate
Annual interest = 4.17 x 12 = 0.5 = 50%
