[tex] \large\underline{\sf{Solution-}}[/tex]
Given Logarithmic expression is
[tex]\rm \longmapsto\: log_{ \sqrt{3} }(729) [/tex]
Let first factorize 729
[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:729 \:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:243 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:81\:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:27 \:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:9\:\:}}\\\underline{\sf{}}&{\sf{\:\:3 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]
So,
[tex] \purple{\rm \longmapsto\:729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3}[/tex]
[tex] \purple{\rm \longmapsto\:729 = {3}^{6} }[/tex]
[tex] \purple{\rm \longmapsto\:729 = {( [{ \sqrt{3} ]}^{2}) }^{6} }[/tex]
[tex] \purple{\rm \longmapsto\:729 = {( \sqrt{3} )}^{12}}[/tex]
So,
[tex]\rm \longmapsto\: log_{ \sqrt{3} }(729) [/tex]
can be rewritten as
[tex]\rm \: = \: log_{ \sqrt{3} }( {( \sqrt{3}) }^{12} ) [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ log_{a}( {a}^{x} ) \: = \: x \: }}}[/tex]
So, using this identity, we get
[tex]\rm \: = \: 12[/tex]
Hence,
[tex] \green{\rm\implies \:\boxed{\tt{ \: \: log_{ \sqrt{3} }(729) \: = \: 12 \: \: }}}[/tex]
Write 6^7 + 6^5 + 11 in base six. Use the digits 0, 1, 2, 3, 4, 5
Answer:
Sorry I don't remember the answer
Simplify to create an equivalent expression
-5(3p+3) + 9(-7+p)
The answers are:
A)-5p-78
B)-6p-78
C)-6p-48
D)-6p+78
a man earned $180 for working 14 hours. How many hours must he work to earn 300
Answer:
it would be roughly 24 hours
Step-by-step explanation:
180÷14
12.8571428571
simplify to 12.85
12.85× X = 300
X=24
Ken bought a new car and had to borrow $6,500 from the bank. The bank charged
Ken 3.7% in simple interest for the 5 years Ken had the bank loan. What's the total
amount Ken will have to repay the bank?
Answer: 65005.037
Step-by-step explanation:
I=?
P=6,500
R=037
T=5 years
I= 6,500+037+5= 65005.037
HELP PLEASE!!
Write a recursive rule for an=1/3•4^n-1
A.) an=1/3•an-1
B.) an=4•1/3an-1
C.) an=1/3•4an-1
D.) an=4•an-1
Answer:
D.) an = 4 * an-1
Step-by-step explanation:
a(n) = (1/3) * 4^(n-1)
a(n-1) = (1/3) * 4^(n-1-1) = (1/3) * 4^(n-2)
Thus,
a(n) = (1/3) * 4 * 4^(n-2) = 4 * [(1/3) * 4^(n-2)] = 4 * a(n-1), so that
a(n) = 4 * a(n-1).
plzz help me with this question
Answer:
The answer to this question is C
[tex]y = \frac{3}{2} x + 7 \\ \\ y = \frac{1}{2}x + 1 [/tex]
write the equation of the line parallel to the given line y = 2x - 4
Answer:
y=2x-8
Step-by-step explanation:
Plot the line and use the parallel slope to create the line and then find the y-intercept
What is a correct congruence statement for the triangles shown?
Enter your answer in the box.
ΔQDJ=Δ____
Answer:
GAP but if not that AGP
Step-by-step explanation:
Answer:
ΔQDJ ≅ GAPStep-by-step explanation:
Use the order of corresponding vertices.
Q and G, D and A, J and P are corresponding considering the marks on the lines.
ΔQDJ ≅ GAPAn insect's head accounts for approximately 60% of its total mass. If the insect weighs 40 g, what is the mass
of its head?
Answer:
24 g
Step-by-step explanation:
60/100x40
2400/100
24
Do the ratios 2/1 and 18/10 form a proportion?
Answer:
2
9/5
Step-by-step explanation:
2/1 = 2
18/10 (divide by 2 up and down) = 9/5
Simplity using properties of exponents. Write your answer using a
single whole number exponent and the same base as given in the
expression below.
Simplifying Expressions Using the Properties of Exponents (Four Examples)Daniel Ozimek
in fiq Q.3 measure the angle which the ladder makes with (I) the ground (2) the wall
Step-by-step explanation:
for measuring the angle use the protractor !
LY!
Fill in the missing numbers to complete the pattern:
2.6, 3.1,
4.6, 5.1
Jones needs to travel from Town A to Town B in 2 hours. If the distance between between two towns is 320km. At what speed will Jones need to drive?
Answer:jone cần lái xe với tốc độlà:
Step-by-step explanation: 320/2=160(km/h)
PLEASE HELP ME!! I’ll give brainliest!!
Rena sells candles. The graph shows the number of candles sold and the
income from the sales. It represents a linear function.
Which statement best describes Rena's income from selling these candles?
A. She gets $6 per candle.
B. She gets $6.50 per candle.
C. She sells 6 candles per dollar.
D. She sells 6.5 candles per dollar.
Answer:
B.) She gets $6.50 per candle.
Step-by-step explanation:
19.5 (the price of 3 candles) divided by 3 is 6.5.
Which expression is equivalent to 5 to the power of 6
5^6
Answer:
5^6
5^6 is the same thing as
5^6=5×5×5×5×5×5
=5×5=25×5=125×5=625×5=3125×5=15625
5^6= 15625
Answer:
125 * 125
Step-by-step explanation:
do 125 x 125 = 15625
Solve the equation. 9 ( − 2 ) =
Answer:
- 18
Step-by-step explanation:
9 ( - 2 )
= 9 x ( - 2 )
= - 18
Therefore, - 18 is the answer of the given equation.
Answer:
-18
Step-by-step explanation:
the parentheses mean to multiply, so 9 times 2 is 18, but since it is a negative and a positive that you're multiplying, then it would be negative 18
What is the equation of the line in point slope form with a slope of m=-2/3 passing through the point (-5,-2)
Answer:
[tex]m=− 32 ≈−0.666666667[/tex]
Step-by-step explanation:
A cyclist rides her bike at a rate of 30 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answer:
48240Step-by-step explanation:
Part one
1 mile per hour = 1.60 kilometers per hour
30 miles per hour = ?
Step 1: Set up a fraction.
The units must be on the same level. And the rate in KM (kilometer) per hour will be a variable, "[tex]k[/tex]". It does not matter whether they are top or bottom.
[tex]\frac{1.60}{1} = \frac{k}{30}[/tex]
As you can see, 1 mile per hour and 30 miles per hour are at the same level, leaving the rest on the same level, as well.
Step 2: Solve
[tex]\frac{1.60}{1} = \frac{k}{30}[/tex]
Cross multiply1.60 × 30 = 48
1 × k = 1
Therefore, the rate is 48 kilometers per hour.
Part 2
This part is mainly the same as the first part. Fractions. However, since we've already found out the answer for part one, it will be simple.
Step 1: Multiply the result to 5.
48 × 5 = 240
Therefore, the cyclist will travel 240 kilometers in 5 hours.
Step-by-step explanation:
First, to make everything more clear, rewrite it like this-
1 mile = 1.6km
So we have to multiply 30 (miles) by 1.6 (km)
30 x 1.6 + 48
So it is 48km per hour, now we have to calculate how many km does she ride in 5 hours.
We have to multiply 48 by 5 which equals 240
So the answer is 240km
What is an equation of the line that passes through the points (2,6) and (1, 1)?
Answer: y=5x+b
Step-by-step explanation:
I used the slope intercept equation, which supplied me the solution.
m=5
b=0
Express the values below I’m scientific notation 52,800g, 255.6m, 0.04109cm!?
Answer:
1) 5.28 x 10^4 g
2)2.556 x 10^2 m
3)4.109 × 10^-2cm
Have a nice day!!!!!
Answer:
52,800 in scientific notation is [tex]5.28[/tex] × [tex]10^4[/tex].
255.6 in scientific notation is [tex]2.556[/tex] × [tex]10^2[/tex].
0.04109 in scientific notation is [tex]4.109[/tex] × [tex]10^{-2}[/tex].
HELP RN PLEASE!!!!!!!!
Step-by-step explanation:
this is the answer
hopes it helps
how to solve the attachment question?
Answer:
y = 100 - 0.08^ x
Step-by-step explanation:
Evaluate. 2 > 8 - 4/3h
Answer: h>9/2
Step-by-step explanation:
a line containing the points (4, y) and (-3, 2) has a slope of 3/2.
Answer:
y=14.5
Step-by-step explanation:
A slope of 3/2 means that for every unit it moves to the right, it will move 1.5 units up. The x of 4 is 7 more than the -3 of our other point. 7*1.5=12.5, and 12.5+2=14.5.
I need a answer PLEASE
Answer:
it's the third one. x=47/3
Step-by-step explanation:
if needed in decimal form: 15.666
mixed number form: 15 2/3
What is the answer for x?
Answer:
Step-by-step explanation:
The triangle’s angles add up to 180 degrees
so 40 + (16x + 2) + ∠C = 180
The straight angle is 180°
so ∠C = 180 - (23x + 7)
∠C = 180 - 23x -7
∠C = 173 - 23x
and then 40 + (16x + 2) +(173 - 23x) = 180
40 + 16x + 2 + 173 - 23x = 180
215 - 7x = 180
-7x = 180 - 215
-7x = -35
x = 5
please give me a brainliest answer
What is the significance of a correlation coefficient of − 0 . 97 ?
Answer:
The points all lie very close to the line of fit, and the
line is decreasing.
Step-by-step explanation:
Brainliest maybe
Answer: A.) The points all lie very close to the line of fit, and the line is decreasing.
Hooke’s Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 180 newtons stretches a spring 5 cm, how much will a force of 270 newtons stretch the same spring?
Answer:
7.5m
Step-by-step explanation:
Set up a proportion and cross multiply to find the unknown
Hope this helps
The elongation of spring by 170 newtons force maintaining the given ratio is 7.5 cm.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given question,
Elongation of spring in 180 newtons = 5 cm
The ratio of elongation to force applied = 5/180
The force the second time is 270 newtons.
Let's say the elongation at this time is x cm.
The ratio of elongation to force applied = x/270
Both ratios must be the same.
Therefore, x/270 = 5/180
x = 270/36 = 7.5 cm
Hence "The elongation of spring by 170 newtons force maintaining the given ratio is 7.5 cm".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ5
please help me with this
Answer:
Step-by-step explanation:
sum of angles of a triangle=180°
9x-2+3x-19+3x+6=180
15x-15=180
15x=180+15=195
x=195/15=13
m∠G=9x-2=9×13-2=117-2=115°