The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b.
How to analyze and solve logarithmic expressionsLogarithms are trascendental functions, that is, functions that cannot be described algebraically.
In this question we must apply logarithm and algebraic properties to determine firstly the value of [tex]x[/tex] and later to find value of the latter logarithm. Now we proceed to find the value of [tex]x[/tex]:
[tex]\log_{b} x^{2} = 10[/tex]
[tex]2\cdot \log_{b} x = 10[/tex]
[tex]\log_{b} x = 5[/tex]
x = b⁵
Then, the value of the latter logarithm is:
log₃ (x⁻¹)[tex]^{1/b}[/tex]
- b⁻¹ · log₃ x
- b⁻¹ · log₃ b⁵
- 5 · b⁻¹ · log₃ b
The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b. [tex]\blacksquare[/tex]
RemarkThe statement is poorly formated, correct form is described below:
Let [tex]x[/tex] and [tex]b[/tex] be positive real numbers so that [tex]\log_{b} x^{2} = 10[/tex]. Find [tex]\log_{3} \sqrt [b]{\frac{1}{x} }[/tex].
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PLEASE HELP ME MATH IS HARD
Use the rectangle shown in the coordinate plane to answer each question.
1. Rotate rectangle KLMN 90º counter-clockwise about the origin. List the ordered pairs for each vertex of K'L'M'N'.
2. What do you notice about the ordered pairs of the original figure and the ordered pairs of the rotation about the origin?
Answer:
See below ↓
Step-by-step explanation:
1)
On rotating KLMN by 90° counterclockwise,the new coordinates are :K' = (-3, -6)L' = (-5, -4)M' = (-2, -1)N' = (0, -3)2)
What do we notice here?We notice that on rotating from Quadrant II to Quadrant III, we find that all the x and y values become negative (other than N' which changes intercepts from x to y)Answer:
Step-by-step explanation:
Rotate counter-clockwise = from right towards left
Rotate 90° about the origin = We can think that our rectangle is a flag and that we added a pole to it. The pole is rotated counter-clockwise about the origin until we have the 90°. Where is the flag now positioned?
(Draw a line from origin to one of the rectangle's points; draw another line from origin that is ⊥ to the previous one. You rotate that point 90° from right to left and will lend on the new line.)
1. K (-6, 3) L (-4, 5) M (-1, 2) N (-3, 0) → K' (-3,-6) L'(-5, -4) M'(-2, -1) N'(0, -3)
2. We notice that the rule for rotating 90° about the origin is (x, y)→(-y, x)
train covers 20 km in one hour then how much distance will it cover in 1 min?
[tex]\sf\large\underline{Given:-}[/tex]
Speed of the train = 20km / 1hr.
[tex]\rightarrow[/tex] 1 hour = 60 minutes.
So, speed of the train = 20km/60min.
[tex]\sf\large\underline{To\: Find:-}[/tex]
[tex]\rightarrow[/tex]Distance covered by train in 1min.
[tex]\sf\large\underline{Solution:-}[/tex]
Let the distance covered by train in 1 min be [tex]\sf{x}[/tex] m.
So, if train covers 20 km in 60min then it covers [tex]\sf{x}[/tex] m in 1 min.
It can be written as,
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}}[/tex] [tex]\sf{=\frac{x}{1}}[/tex](by cross multiplication)
[tex]\rightarrow[/tex][tex]\sf{20\: = \: 60x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{1}{3}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{0.33= x}[/tex](approx)
Therefore, distance covered by train in 1 min= 0.33km (approx).
_______________________________
Hope it helps you:)
oshua wants to buy a flat-screen TV that costs $625. He saves $62.50 each week to buy the TV. In how many weeks will he have enough money to make his purchase?
Answer:
ten weeks
Step-by-step explanation:
62.50 multiped by 10 moves the decimal over 1 to the right which makes it 625 :)
Eli planted 14 out of his 20 tomato plants so far in his garden. What percentage of his tomato plants has he planted?
Answer:
70%
Step-by-step explanation:
First we express this as a fraction:
14/20
Then we express it as a decimal: (by doing 14÷20)
0.7
Now we express it as a percentage by multiplying the decimal by 100:
0.7×100%
70%
Answer:
70%
Step-by-step explanation:
GIven:
Eli planted 14 out of his 20 tomato plants so far in his garden. What percentage of his tomato plants has he planted?
Solve:
14/20 x 100
0.7 x 100
70%
Hence, 70% of his tomato plants he planted.
~Lenvy~
Is a 779 a good MI score
Answer:
yes
explanation:
Your score falls within the range of scores, from 740 to 799, that is considered Very Good. A 779 FICO Score is above the average credit score. Consumers in this range may qualify for better interest rates from lenders.
Olivia borrowed $5,000 for 5 years at 5% simple interest.
Answer:
The answer is $1250
Step-by-step explanation:
Solution,
Principle (P) = $ 5,000
Time (T) = 5 years
Rate(R) = 5 %
Simple Interest (I) = ?
Now,
We have,
Simple Interest (I) = P×T×R/ 100
= 5,000×5×5/100
= $1250
the length of a rectagle is twice its width. if the perimeter of the rectangle is 36in, find its length and width
Answer:
Perimeter=36in
Length of one side=12
Length of the other side=12
Width of one side=6
Width of the other side=6
Step-by-step explanation:
6*2=12, so if the length is 12 half would be six. All of them added up is 36
Answer:
Length = 12inWidth = 6inStep-by-step explanation:
[tex]perimeter \: of \: a \: rectangle = 2(2x) + 2(x) \\ 36in = 4x + 2x = 6x \\ \frac{36in}{6} = \frac{6x}{6} \\ x = 6in \\ 2x = 2 \times 6in = 12in[/tex]
Mark me brainliest!
14. You deposit $500 in a savings account that
carns 7% interest compouncted anually.
A.) write a function that represents the balance
after t years
B.) What is the balance after 2 years?
Answer:
A) A(t) = 500e^(0.07)(t)
B) 575.137
Step-by-step explanation:
A silo of a barn consists of a cylinder capped by a hemisphere. The
height of a cylinder is 60 feet and its diameter is 30 feet. What is the approximate volume of the entire silo
The approximate volume of the entire silo which consists of a cylinder capped by a hemisphere is 42,390 cubic feet
Volume of the silo
Volume of a cylinder = πr²h
where,
π = 3.14Radius, r = diameter / 2= 30 ft / 2
= 15 ft
Height, h = 60 ftVolume of a cylinder = πr²h
= 3.14 × 15 × 15 × 60
= 42,390 cubic feet
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A point located at (1, 8) is reflected over the x-axis. What are the coordinates of the image?
(-1, 8)
(8, 1)
(-1, -8)
(1, -8)
Answer:
(1, -8)
Step-by-step explanation:
In this case, we are reflecting. Since we are reflecting over the x axis, the only thing that will change will be the y.
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The x is staying the same because it is not moving. The y, however, is changing sides.
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Since the y is positive in its original spot, when you reflect over the x axis, you will have a negative y value, which is why it is a -8.
----------------------------------------------------------------------------------------------------------
I hope this helps!
-No one
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
A) The transformations can be a vertical translation and an horizontal translation.
B) K = 8 and K' = 16
C) g(x) = f(x + 8)
g(x) = f(x) + 16.
Which type of transformation could be used?
A ) By looking at the graph, we see that g(x) can be a translation to the left by K units or up by K' units.
B) In the case the translation is to the left, we can see that it the graph is moved 8 units, so K = 8.
In the case that the translation is up, we can see that it is for 16 units, so we have k' = 16.
C) How to write the equations?
An horizontal translation is written as:
g(x) = f(x + K).
Because the translation is to the left, we have that K is positive, then in our case we have:
g(x) = f(x + 8).
For the vertical translation the formula is:
g(x) = f(x) + K'
In our case, we have:
g(x) = f(x) + 16
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Answer:The transformations can be a vertical translation and an horizontal translation.B) K = 8 and K' = 16C) g(x) = f(x + 8) g(x) = f(x) + 16.Which type of transformation could be used?A ) By looking at the graph, we see that g(x) can be a translation to the left by K units or up by K' units.B) In the case the translation is to the left, we can see that it the graph is moved 8 units, so K = 8.In the case that the translation is up, we can see that it is for 16 units, so we have k' = 16.C) How to write the equations?An horizontal translation is written as:g(x) = f(x + K).Because the translation is to the left, we have that K is positive, then in our case we have:g(x) = f(x + 8).For the vertical translation the formula is:g(x) = f(x) + K'In our case, we have:g(x) = f(x) + 16
Step-by-step explanation:
The measure of an angle is 107.4 what is the measure of its supplemental angle ?
Answer:
72.6
Step-by-step explanation:
180-107.4 = 72.6
Leon and Omar went to grab ice cream after track practice. They each chose a container shaped like a cone or a cylinder. The dimensions of each container are shown in the drawing.
The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.
What is volume?Volume is the amount of space occupied by a three dimensional shape or object.
Let us assume the cone and cylinder has a radius of 7 cm and height of 10 cm, hence:
Volume of the cone = (1/3) * π * radius² * height = (1/3) * π * 7² * 10 = 513.33 cm³
Volume of the cylinder = π * radius² * height = π * 7² * 10 = 1540 cm³
The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.
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7. The area of the parallelogram is 450 m2. What is
the height?
A. 25 m
B. 36 m
C. 50 m
D. 72m
please help me I will mark BRAINLIEST
Answer:
See attached diagram
a) Points shown in blue
b) correlation is negative since the y-values decrease as the x-values increase.
c) Line of best fit needs to have the same number of points above as below.
If 12Kg of chicken feed cost 20 how much would 5kg cost?
and what is the unit rate? ( price per 1 kg)
Step-by-step explanation:
if you 12kg cost 20 what about 5kg that will be 5kg×20÷12kg= 8.33 when you round of to the nearest hundredth this is the price of 5kg
sorry but i dont think i know how to answer the other question i have done what i only know thankyou
3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations described below. a. The account pays 3% annual interest compounded monthly. b. The account pays 4% annual interest compounded continuously.
Answer:
Part A)
About $3767.34.
Part B)
About $3692.47.
Step-by-step explanation:
Part A)
Recall that compound interest is given by the formula:
[tex]\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.
To obtain $4000 after two years, let A = 4000 and t = 2.
Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.
Substitute and solve for P:
[tex]\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}[/tex]
In concluion, about $3767.34 should be deposited.
Part B)
Recall the formula for continuous compound:
[tex]\displaystyle A = Pe^{rt}[/tex]
Where e is Euler's number.
Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:
[tex]\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}[/tex]
In conclusion, about $3692.47 should be deposited.
camilo uses 32 ounces of filling to make empanadas. he puts 8 empanadas on each of 3 trays. Write a fraction to show how many ounces of filling camilo uses in each empanada. Please reply quickly!
Answer:
32/4
Step-by-step explanation:
how do i solve (2[tex](\frac{2}{3} r^{2} s^{7} )^{2} * (\frac{1}{6} r^{3}s)[/tex]
Answer:
5x+1=7
Step-by-step explanation:
The length of the base of an isosceles triangle is x. The length of a leg is 3x−6. The perimeter of the triangle is 65. Find x.
Answer:
x = 11
Step-by-step explanation:
Hello!
In an isosceles triangle, the two legs are congruent by the property Base angle Theorem. It is isosceles when both angles on the base are congruent.
So, since the base is x, and the measure of one leg is 3x - 6, we know that the other leg is also 3x - 6 in length.
The equation for perimeter is : leg + leg + base = Perimeter
We can plug in 65 for the perimeter because it's given
Solve for x:
x + 3x - 6 + 3x - 6 = 657x - 12 = 657x = 77x = 11The value of x is 11.
Help? Anything can help I’m in a rush
Answer: A vertical line from (-5 , 4 ) to (5 , 4)
Step-by-step explanation: The y axis is the vertical one. Go up 4 and draw a line connecting all the points with 4 in the coordinates.
Hope that helps :)
Answer:
Step-by-step explanation:
go up 4 lines on the y-axis then draw a straight line from left to right on y=4
I don't know if you can see the picture, but I drew a line on the picture you provided...
Please 5 stars if correct!!!
I hope this helps
Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 'of an inch, it is 4 3/4 'inches.
a) What is the largest the actual height the plant could be?
b) What is the smallest the actual height the plant could be?
c) How large could the percent error in Jada’s measurement be?
Answer:
See below.
Step-by-step explanation:
a) 4 7/8 inches
b) 4 5/8 inches
c) 12.5%
An arrow is shot vertically upward at a rate of 190 feet per second from ground level. Use the projectile formula
h
=
−
16
t
2
+
v
0
t
+
h
0
h
=
-
16
t
2
+
v
0
t
+
h
0
to determine when the height of the arrow will be 471 feet.
The height of the arrow will be 471 feet at 8.35s and 3.53s
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
h represent the height of the arrow after t seconds.
h(t) = -16t² + v₀t + h₀
v₀ is the initial velocity = 190 ft/s, h₀ is the initial height = 0m, hence:
h(t) = -16t² + 190t
At 471 feet:
471 = -16t² + 190t
0 = -16t² + 190t - 471
t = 8.35 or 3.53
The height of the arrow will be 471 feet at 8.35s and 3.53s
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What common donminator of 1/3 and 3/4
Answer:
12
Step-by-step explanation:
The least common denominator (LCD) of 1/3 and 3/4 is 12, because if you multiply the denominators of both fractions, 3 * 4 = 12.
This would change the fractions to-
1/3 * 4/4 = 4/12
3/4 * 3/3 = 9/12
I hope this was helpful! Have a lovely day!! :)
can someone please help me
Like the given triangle is an isosceles triangle, the value of ∠ABC is 72°.
Types of TrianglesThere are 3 main classifications for triangles refer to its sides.
Equilateral triangle - This triangle presents all sides with the same dimensions and the all angles equal to 60°.Isosceles triangle - This triangle presents two sides with the same dimensions and it has two angles with equal size.Scalene triangle - This triangle presents all sides with different dimensions and it has all angles no equal size.The figure shows that the given triangle is an isosceles triangle because it has two equal sides (AB=AC). If it is an isosceles triangle, this triangle presents two sides with the same dimensions (AB=AC). and it has two angles with equal size(∠ACB=∠ABC).
Knowing the sum internal angles of triangle is 180°. You can write:
3x+6x+6x=180
15x=180
x=12
Like ∠ABC=6x, then ∠ABC=6*12=72°.
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Whats 5-5-5-5-5-5x5757575
Answer:
-28787890
Step-by-step explanation:
solve plssss before i dieee i give points
Answer:
should be 66% of children and 1650 children in the town
Step-by-step explanation:
what is the area of this object?
Answer: no idea
Step-by-step explanation:
which fraction is larger: 3/10 or 2/7
Plot on a number line
Answer:
3/10 is bigger
Step-by-step explanation:
covert into a decimal so 0.3 is bigger than 0.2857
If tomorrow i said, "the day before yesterday was saturday",then what is today?
Answer:
Monday
Step-by-step explanation:
If day before yesterday was Saturday, so today is Monday.