Answers
Given:
[tex]\log_34\approx 1.262[/tex]
[tex]\log_37\approx 1.771[/tex]
To find:
The value of [tex]\log_3\left(\dfrac{4}{49}\right)[/tex].
Solution:
We have,
[tex]\log_34\approx 1.262[/tex]
[tex]\log_37\approx 1.771[/tex]
Using properties of log, we get
[tex]\log_3\left(\dfrac{4}{49}\right)=\log_34-\log_349[/tex] [tex]\left[\because \log_a\dfrac{m}{n}=\log_am-\log_an\right][/tex]
[tex]\log_3\left(\dfrac{4}{49}\right)=\log_34-\log_37^2[/tex]
[tex]\log_3\left(\dfrac{4}{49}\right)=\log_34-2\log_37[/tex] [tex][\log x^n=n\log x][/tex]
Substitute [tex]\log_34\approx 1.262[/tex] and [tex]\log_37\approx 1.771[/tex].
[tex]\log_3\left(\dfrac{4}{49}\right)=1.262-2(1.771)[/tex]
[tex]\log_3\left(\dfrac{4}{49}\right)=1.262-3.542[/tex]
[tex]\log_3\left(\dfrac{4}{49}\right)=-2.28[/tex]
Therefore, the value of [tex]\log_3\left(\dfrac{4}{49}\right)[/tex] is [tex]-2.28[/tex].
Related Questions
i will give u brain list! :)
Answers
Solve the problem:
Kiram has 5 ziploc bags. He puts an equal number of marbles (X). Then he realized that he
needed to add 2 more marbles for each bag. If the total number of marbles is 30 how many
marbles in each bag?
Answers
Answer:
Step-by-step explanation:
ohfpifpijpijsfpjspijpsijfpsjfpsjfpisjfpijsfpsijf
Laptop computers are measured according to the diagonals of their screens. A 16-inch laptop has a screen that is 7 inches tall. How wide is the screen?
Answers
can someone help me on this. i dont understand it at ALL. please du~mb it down beacuase i am not smart at all.
Answers
Answer:
So basically you have to create a set of coordinates like (3,2) to create a linear function. Make sure to make a linear equation and represent it through a graph or table. Then take its coordinates.
An example is the table I attached. It is a linear function.
y = 4x is the linear equation.
(2,8) is the coordinate.
Hope I helped in time!
:)
Enter numbers in figures to complete the passage below.
Give all values in pounds and pence, e.g. £3.50 not £3.5
SALE
Taal buys a jacket in the sale.
It has 15% off and he pays £42.50.
The original price of the jacket was £
He saved £
Answers
Answer:
£50 ; £7.50
Step-by-step explanation:
Given that:
Discount on sale, d = 15%
Amount paid = £42.50
Hence the relation to obtain the amount paid goes thus ;
Amount paid = (1 - d) * original amount
Let original amount = x
42.50 = (1 - 0.15)x
42.50 = 0.85x
x = 42.50 / 0.85
x = £50
Amount saved :
£(50 - 42.50) = £7.50
RADICALS
NEED HELP ASAP PLEASE!!!
Answers
Answer:
[tex]\sqrt[3]{64} = 4[/tex] [tex]\sqrt{64} = 8[/tex]
Step-by-step explanation:
Given
mZAOC = 104°
mZAOB = 7x + 30°
mZBOC = 9x + 42°
Find mZBOC:
Answers
Answer:
The answer is 60°
Step-by-step explanation:
From looking at the problem we know that mZAOB and mZBOC make up angle mZAOC.
We also know that mZAOC is 104°
This means that the two other angles have to make up 104°
To figure out mZBOC,
First, you can subtract 30 and 42 from 104.
We do this because it allows us to focus on the variables.
104-30-42=32
Next, we can look at the variables and the coefficients and see that in order for 7x and 9x to make 32, x has to equal 2.
7(2)+9(2)=32
Now that we know what x equals we can substitute it into the equation for mZBOC.
9x + 42°
9(2) + 42°
60°
Thus, mZBOC equals 60°
please help me 80% of what number is 16
What is the part?
What is the total?
What is the percent?
What is the answer?
Answers
Answer:
80 percent of 16 is 12.8 I'm sorry but that's all I know
I need help asap !!! please show how you did the work please please
Answers
Mrs. Hicks can grade 25 quick checks in 20 minutes. Ms. Place can grade 36 quick checks in 30 minutes. Which teacher is working at a faster rate? How do you know?
Answers
Answer:
Ms place is working at a faster rate because Mr.Hicks is doing 0.8 per minute while Ms.Place is doing 0.83 per minute.
I need help pls. I'm not sure how to solve it
Answers
Answer:
0 is an integer and a whole number
Can someone please help and explain? Will give brainliest to most helpful
Answers
Answer:
x = 44
y = 22
Step-by-step explanation:
✔️Find x:
Reference angle = 60°
Hypotenuse = x
Opposite side length = 22√3
Applying the trigonometric FUNCTION, SOH, we have:
Sin 60 = opp/hyp
Sin 60 = (22√3)/x
x × Sin 60 = 22√3
x = (22√3)/Sin 60
x = (22√3)/(√3/2) (sin 60 = √3/2)
x = 22√3 × 2/√3
x = (22√3 × 2) / √3
x = (44√3) / √3
x = 44
✔️Find y:
Reference angle = 60°
Hypotenuse = x = 44
Adjacent length = y
Applying CAH, we have:
Cos 60 = adj/hyp
Cos 60 = y/44
44 × Cos 60 = y
44 × ½ = y (cos 60 = ½)
22 = y
y = 22
Answer:
x=44,y=22
Step-by-step explanation:
sin 60=22√3/x
x=22√3/sin60=44
sin30=y/x
y=sin30×44=22
What is the solution to the system of equations?
3x – 9y = -13
x – 3y = -7
(a) Use the substitution method to justify that the given system of equations has no solution.
(b) What do you know about the two lines in this system of equations?
PLEASE PLEASE PLEASE HELPPP
Answers
Answer:
a. it has no solution
b. you can only substitute by making either the 'x' or 'y' the subject of either of the two equations.
Step-by-step explanation:
3x - 9y = -13.............. eqn 1
x - 3y = -7................... eqn 2
from eqn 2
x - 3y = -7, substitute by making 'x' the subject
x = -7 + 3y.................. eqn 3
put eqn 3 into eqn 1
3x - 9y = -13
3( -7 + 3y) - 9y = -13
-21 + 9y - 9y = -13
9y - 9y = -13 + 21
0 = 8, which is not possible.
Solve for the unknowns.
a, b , c ,d
Answers
Answer:
can u plz make a good picture to solve I can't see good
Step-by-step explanation:
and thanks
i know an isosceles triangle has 2 congruent (equal) sides but does it have any equal angles?
Answers
Answer:
Step-by-step explanation:
To have two equal sides there must also be two equal angles.
Can you please solve these systems of equations using elimination for x and y?
1. 8x+2y=46
7x+3y=47
2. 4x+6y=62
7x+3y=47
3. 4x+6y=62
2x+6y=76
4. 8x+1y=43
2x+4y=98
Answers
Answer:
(4.4, 5.4), (3.2, 8.3), (-7, 15), (23 4/15, 2 7/15)Step-by-step explanation:
1.
Multiply the first equation by 3/2:
3/2×8x + 3/2×2y = 3/2×46 12x + 3y = 69Subtract the second equation:
12x - 7x = 69 - 475x = 22x = 4.4Find y:
4*4.4 + y = 23y = 23 - 17.6y = 5.42.
Double the second equation and subtract the first one:
14x - 4x = 94 - 6210x = 32x = 3.2Find y:
4*3.2 + 6y = 626y = 62 - 12.86y = 49.8y = 8.33.
Subtract the second equation from the first one:
4x - 2x = 62 - 762x = -14x = -7Find y:
4(-7) + 6y = 626y = 62 + 286y = 90y = 154.
Multiply the second equation by 4 and subtract the first one:
16y - y = 4(98) - 4315y = 349y = 349/15y = 23 4/15Find x:
8x + 23 4/15 = 438x = 19 11/15x = 2 7/15Answer:
1. [tex]x\x=\frac{22}{5}=4.5, y=\frac{27}{5}=5.5[/tex]
2. [tex]x=\frac{16}{5}=3.2,y=\frac{41}{5}=8.3[/tex]
3. x=−7,y=15.
4. [tex]x=\frac{37}{15}=2\frac{7}{15},y=\frac{349}{15}=23\frac{4}{15}[/tex]
Step-by-step explanation:
I hope this helps.
ASAP pls help
A chef has 5 blocks of butter. Each block weighs 1 pound. She cuts each block into fourths. How many 1/4 -pound pieces of butter does the chef have?
Answers
Answer:
20, 1/4 pound pieces of butter
Step-by-step explanation:
1/4*4= 1 pound
so,
4*5=20
:)
Find the value of each variable in the parallelogram
Answers
9514 1404 393
Answer:
k = 7
m = 8
Step-by-step explanation:
The diagonals bisect each other, so each half is equal to the opposite half.
k +4 = 11 . . . . down-sloping diagonal
k = 7
__
m = 8 . . . . up-sloping diagonal
Determine the multiplier in each situation below.
a. A 44% increase
b. A 93% decrease
Answers
Answer:
Step-by-step explanation:
%s can drive a person crazy.
44% increase
Cost = 100% * x + 44%x
Cost = x ( 100 / 100 + 44/100)
Cost = x (1 + 0.44)
Cost = 1.44 x
93% decrease
Cost = 100%x - 93%x
Cost = x * (100/100 - 93/100)
Cost = x * (1 - 0.93
Cost = 0.07 x
Answer:
1.44 and 0.07
Step-by-step explanation:
(a)
A 44% increase of the original amount (100%) is
100 + 44 = 144% = [tex]\frac{144}{100}[/tex] = 1.44 ← multiplier
(b)
A 93% decrease of the original amount (100%) is
100 - 93 = 7% = [tex]\frac{7}{100}[/tex] = 0.07 ← multiplier
Find LR, given kite FLRD with diagonals intersecting at A and FA = 4, AR = 12, LA = 5
Answers
Answer:
LR = 13
Step-by-step explanation:
LAR is a right triangle and if two sides are known you can you use the pythagorean theorem to find the missing side
LA = 5
AR = 12
5² + 12² = LR²
LR² = 25 + 144
LR² = 169
LR = √169 = 13
URGENT PLZ HELP
for what values of X and Y is quadrilateral ABCD a parallelogram
Answers
Answer:
x = 9
y = 3
Step-by-step explanation:
Since this is a quadrilateral the opposite side lengths must be equal
5x - 20 = 7x - 38
38 - 20 = 7x - 5x
18 = 2x divide both sides by 2
9 = x same goes for y
6x - 31 = 4y + 11 we already know x = 9 so
6×9 - 31 = 4y + 11
54 - 31 - 11 = 4y
12 = 4y divide both sides by 4
3 = y
Cassie hit a golf ball. The function f models the height of the ball above the ground (in meters) as a
function of time (in seconds) after Cassie hit it.
MARK BRAINLIEST
Answers
Answer:
your answer will be (0,25)
Step-by-step explanation:
have a nice day and good luck with your test ^_^
The point that corresponds to the ball's maximum height on the graph is (4, 80).
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
Cassie hit a golf ball.
The function f models the height of the ball above the ground (in meters) as a function of time (in seconds) after Cassie hit it.
We can see from the graph that the highest point the ball could reach is 80 units.
Therefore, The point that corresponds to the ball's maximum height is (4, 80).
Learn more about points lying on the graph of a function here:
brainly.com/question/1979522
#SPJ2
Which represents the value of c?
Oc=
(3) sin(409)
sin (45)
C =
(3) sin(45)
sin (409)
C =
sin(409)
(3) sin(45°)
sin(45)
(3) sin(409)
Answers
Answer:
c = 3.3 cm
Step-by-step explanation:
A = 180 - (95 + 45) = 40° (sum of triangle)
a = 3.0 cm
C = 45°
c = ?
Applying the Law of Sines, we have:
[tex] \frac{Sin(40)}{3} = \frac{Sin(45)}{c} [/tex]
Cross multiply
[tex] Sin(40)*c = Sin(45)*3 [/tex]
Divide both sides by sin(40)
[tex] c = \frac{Sin(45)*3}{sin(40)} [/tex]
c = 3.3001886 ≈ 3.3 cm (nearest tenth)
Hiromi spends 100 minutes on a research project. Al spends 1/2 of the time Hiromi spent on his research project. How many hours did Hiromi and Al spend on their research projects altogether?
(Mixed number and fraction)
Answers
Answer:
Step-by-step explanation:
Use the estimates from (c) and (d) to calculate the relative change in the average household
income from 2002 to 2012. Round to the nearest one percent. Indicate if the change is an
increase or decrease.
Answers
Answer:
it decreased by 5.55% change of 6%
The relative change is -6% Rounding to the nearest percent.
What are average?The average can be calculated by dividing the sum of observations by the number of observations.
Average = Sum of observations/the number of observations
The relative change can be calculated by dividing the absolute change (the subtraction of the values) by the initial value.
The absolute change is the final value minus the initial value;
Absolute change = 51000 - 54000 = -3000
Now, calculating the relative change;
Relative = -3000/54000
Relative = - 0.0555
Since the relative change is negative, this change indicates a decrease.
Therefore, the relative change is -6% Rounding to the nearest percent.
Learn more about average here;
https://brainly.com/question/27851466
#SPJ2
which equation is equivalent to 2/3 x -5 / 6 equals -5 / 12 x + 1 / 4
Answers
Answer:
13x=13
Step-by-step explanation:
...............
Wilbur landed his plane.
The plane's elevation relative to the ground (in meters) as a function of time (in seconds) is graphed.
8000+
7000
6000
5000 -
Elevation (meters)
4000
3000
2000
1000
200
400
1600
an 00 1009 1200 1400
Time seconds)
Will mark brainiest
Answers
DEFG maps out Carrie’s dog walking route. If she does one complete loop, how far does she walk with her dogs?
Answers
Answer:
Step-by-step explanation:
Actually it’s 4 square root 17
What is the BEST estimate for the measure of angle c?
A) 77
B) 88
C) 99
D) 111
Answers
Answer:
88
Step-by-step explanation:
Looks close to a right angle so 88 degrees most likely.
Answer:
b 88
Step-by-step explanation:
Need helppp with this
Answers
Answer:
fhted ghtf. hyrdvhurf gjyev vr htrevhuwf ngttgnm