The required expression in terms of logarithm of prim numbers are;
[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]
[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]
Prime numbers are numbers that can only be divisible by 1 and itself.
From the given logarithmic expression, we will need to write 405, 8, and 81 as the product of prime numbers
405 = 3 * 3 * 3 * 3 * 5
405 = 3^4 * 5
8= 2* 2 * 2
8 = 2^3
81 = 3 * 3 * 3 * 3
81 = 3^4
The logarithm expression [tex]log_4405 \ and \ log_7(\frac{8}{81} )[/tex] can be expressed in terms of prime numbers as;
[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]
Similarly;
[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]
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A 12 foot fence on the property line casts a 25 foot shadow on the shortest day of the year, and the north side of the house is set back 60 feet from the property line.
Using similar triangles formed by the fence, and the house, the top of which the property line passes, the height of the house can be determined.
The height of the house is 28.8 feet.Reasons:
The given parameters are;
Height of the fence = 12 foot
Length of the shadow cast by the fence = 25 foot
Distance of the house from the property line = 60 feet
The maximum allowable height for the house.
Solution:
Using similar triangles, we have;
[tex]\displaystyle \frac{Height \ of \, fence}{Length \ of \ fence \ shadow} = \mathbf{\frac{Height \ of \, house}{Distance \ of \ house\ from \ property \ line}}[/tex]
Which gives;
[tex]\displaystyle \frac{12}{25} = \mathbf{\frac{Height \ of \, house}{60}}[/tex]
[tex]\displaystyle Height \ of \ house = \frac{12}{25} \times 60 = 28.8[/tex]
The height of the house = 28.8 feet
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Please find attached the drawing of the question created with MS Visio, obtained from a similar question online.
The number of ways to choose three different pizza toppings from a group of six is called a ?
Answer:
Uh, 16.
Step-by-step explanation:
We need to choose three different toppings. So here we need to find the number of ways in which we can choose three different toppings out off. 16. So a number of ways are takes three at a time, from a total of 16. That is civilians combination. Here are formula for combination is 16 factorial over three factorial into 16 minus three. Factorial this candidate and a 16 factorial over three factorial into 16 minus trees. 13. Authority in factorial, now 16. Factory converted on a 16 in 2 15 into 14 into 13. Factorial over three factorial into 30. In fact, a real as we can see that 13 factorial is common toward denominator and numerator so we can get through this. Now I remaining times are 16 into 15 into 14. Over three in Toto into one has three factories, three in tow, one So calculating this ticket. Find 60 Soviet 56 TVs to select three different topics. Talked to select three different toppings out off 16 on a bizarre
What is the slope in other words the answer
Answer:
gradient
Step-by-step explanation:
gradient is the same as steepness and slopes r steep so its gradient
Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression?
Answer:
(x-7)(x^2-5)
Step-by-step explanation:
can someone help please :)
5 - 6 - 9 - 8 - 5 - 4 + 5 - 5 -5 -5 - 32 = ?
5 - 6 = -1
-1 - 9 = -10
-10 - 8 = -18
-18 - 5 = -23
-23 - 4 = -27
-27 + 5 = -22
-22 - 5 = -27
-27 -5 = -32
-32 -5 = -37
-37 - 32 = -69
Answer = -69
A card game has 50 cards. After dealing 7 cards to each player, Tupi has 15 cards left over. Solve the equation 50 7p = 15 to find the number of players.
Solve the equations. 81^x^2=27^x
Answer: 81ײ=27× x = 6
what is 3 x 7 = x 3 ?
Answer:
7
Step-by-step explanation:
21=3x
x=7
Answer:
x = 7
Step-by-step explanation:
3 x 7 = x 3
21 = 3x
x = 21/3 = 7
Help please……………………………..
Answer:
Diagram number 3 is not a function.
Step-by-step explanation:
It isn't a function because C goes to 2 different numbers.
Explanation:
For choice (3), the input C maps to more than one output (The values 1 and 3 at the same time). A function must have each input map to one and only one output. So this is why relation (3) is not a function.
The other answer choices (1), (2) and (4) have each input point to exactly one output. So these are functions that can be ruled out.
Denise is buying four birthday cards for $11.16. Sales tax on the four cards is $0.68. Including sales tax, what is the cost of each card?
Answer:
$11.16 - $0.68 = $10.48 - price of four cards without tax
$10.48 : 4 = $2.62 - price of one card without tax
Cheers!
Answer:
the cost of each card including sales tax is 2.79
the cost of each card without sales tax is
11.16-0.68=10.48
10.48÷4=2.62
Step-by-step explanation:
A new bank customer with $3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.3% How much interest will the customer earn in 30 years
We must use the simple interest formula which is: A = P(1+rt) where
A = output amount , P = initial amount, r = rate as a decimal, and t = time.
so in this case we would write:
A(30) = P(1+rt) = 3000(1 + 0.013(30)) = 4170
We then see that A(30) is equal to $4170 at 30 years.
3(2x + 5) + 4(3c - 2)
Answer:
6x+12c+7
Step-by-step explanation:
3(2x+5)+4(3c-2)
3*2x+3*5+4*3c-4*2
6x+15+12c-8
6x+12c+7
Answer:
[tex]12c+6x+7[/tex]
Step-by-step explanation:
Use the distributive property to simplify the expression accordingly:
[tex](6x+15)+(12c-8)[/tex]
[tex]12c+6x+7[/tex]
100 POINTS
Given Point P(3,4), what is the resulting point after the following transformations?
Translate 3 up and 2 left
Rotation 180° around origin
Reflection over y-axis
Answer:
(1, -7)
Step-by-step explanation:
P(3,4)
3 up ---> y = 4 + 3 = 7
2 left ----> x = 3 - 2 = 1
new point (1, 7)
after 180 rotation around origin
point is (-1, -7)
now reflection over y-axis
(1, -7)
Answer:
[tex](1,-7)[/tex]
Step-by-step explanation:
Refer to the image below
what is 22 over 7 - 2 over 3 divided by 2
fill in the blank to make the fractions equivalent.
4/5 ?/15
Answer:
12/15
Step-by-step explanation:
times 4 by 3 because 5 is timesed by 3
Please help! Due in two hours!
Answer:
-175.26
Step-by-step explanation:
[tex]log_2\frac{z^8x^{10}}{r^{12}}=8log_2(z)+10log_2(x)-12log_2(r)=8*4.42+22.9-12*19.46=58.26-233.52=-175.26.[/tex]
18. Which is more, five-eighths of a dollar or four-ninths of a dollar?
I need hellllllllpppppppppp
Answer:
five-eighths of a dollar is more than four-ninths of a dollar
Step-by-step explanation:
If you convert the fractions into decimals:
5/8 = 0.625
4/9 = 0.44444444444...
0.625 is closer to 1 than 0.44444444444...
Hope that helped!
ticket sales for a local concert totaled $101,244 yesterday. After the ticket window closed today, the cashiers counted 968 tickets sold with a two-day total of $143,836. What is the cost of one concert ticket?
The cost of one concert ticket is approximately $148.59.
The tickets sales for the local sales is totalled $101, 244 yesterday.
ticket sales yesterday = $101244
He sold 968 tickets with a two-days total of $143, 836 (both yesterday and today)
The cost of one ticket can be calculated below:
cost of one ticket = 143,836 / 968
cost of one ticket = 148.590909091
cost of one ticket ≈ $ 148.59
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An experiment consists of drawing 1 card from a standard​ 52-card deck. What is the probability of drawing a club​?
Answer:
25%
Step-by-step explanation:
25%
there are 4 suits, and only 1 is of clubs
1/4 = 25%
What is the y-intercept of the graph of the equation y =(2x−3)^2+7
Answer:
(0,16)
Step-by-step explanation:
Hi there!
The y intercept is the value in which the parabola passes through the y axis
Therefore, the value of x at the y intercept is 0
So to find the value of the y intercept, substitute x as 0 in the equation.
y=(2x-3)^2 + 7
If x=0, then:
y=(2(0)-3)^2 + 7
Multiply
y=(0-3)^2 + 7
Subtract 3 from 0
y=(-3)^2 + 7
Raise -3 to the second power
y= 9 + 7
Add 9 and 7 together
y = 16
So the y intercept is the point (0,16)
Hope this helps!
solve the following equation
d) 0 = 12 + 2 ( m - 8 )
pls pls pls pls plz plz answer steps
[tex] \: \: \: \: \: \: \: \: [/tex]
[tex]m = 2[/tex]
Step-by-step explanation:
[tex]0 = 12 + 2(m - 8)[/tex]
remove the parentheses and distribute 2 through the parentheses[tex]0 = 12 + 2m - 16[/tex]
calculate the difference[tex]0 = - 4 + 2m[/tex]
move the variable to the left hand side and change its sign[tex] - 2m = - 4[/tex]
divide both sides of the equation by -2[tex] = m = 2[/tex]
hope it helps[tex] \: \: \: [/tex]
Answer:
m = 2
Step-by-step explanation:
0 = 12 + 2 ( m - 8 )
→ Expand the brackets
0 = 12 + 2m - 16
→ Add 16 to both sides
16 = 12 + 2m
→ Minus 12 from both sides
4 = 2m
→ Divide both sides by 2
2 = m
W/11+10=10 w/11=0. W=
Answer:
w/11+10=10w/11=0•w=10
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!2
Answer: B
Solution: Because the line is a dotted line. so print (-3, -1) and (3, 3) , (0, 0) are not the solution, so , answer is (0, 5) choice B.
Answer:
C
Step-by-step explanation:
first way: (easier way)
Plot the points out, points in the blue region are solutions. points on the dotted line are not solutions since it is a dashed line.
(0,5 is in the blue region)
second way:
find the equation of the in-equality:
the line that divides solutions and non-solutions passes through 3,3 and -3,-1
y=mx+b
m=change in y/change in x = (-1-3)/(-3-3) = 2/3
y=2/3x+b
plug x=3, y=3 (from the point "3,3")
3=2/3*3+b
3=2+b
b=1
y=2/3x+1 is the solution of the line.
the in-equality is
y(?)2/3x+1
plug in -5,5, which is a solution (looking at the graph)
5>-7/3
so use >, and not <
y>2/3x+1 is the equation of the in-equality, now just plug the answer choices in to see that
x=0,y=5 is a solution
How do you find the quotient in the equation 8÷304
Answer:
304 divided by 8 in decimal = 38
304 divided by 8 in fraction = 304/8
304 divided by 8 in percentage = 3800%
Step-by-step explanation: You just simply divide.
someone help me please :D ill give brainliest and 32 points :))
Answer:
Could you please show me the question?
Step-by-step explanation:
4. Answer a through c
Answer:
Hello is this math i can help you with your answer
is this the correct answer
Answer:
Step-by-step explanation:
correct.
Answer:
see attached
Step-by-step explanation:
The requested plot is only for that portion of the line that exists between the two points shown.
pls help will mark as brainlist
Step-by-step explanation:
total angle= 360°.
sides = 360/36 = 10 (decagon).
total angle= 360°
sides = 360/120 = 3(triangle).
hope this helps you to.
x³+2/3x²-2x-4/3 factorizing
Answer:
(x+2/3) (x^2 - 2)
Step-by-step explanation:
First we can seperate the problem
(x^3 + 2/3x^2) + (-2x - 4/3)
We factor x^2 out of the first parenthesis
x^2(x + 2/3) + (-2x - 4/3)
and factor -2 out of the second
x^2 (x+2/3) +-2 (x +2/3)
then we rewrite it as
(x+2/3) (x^2 -2)
-- Gage Millar, alg1/2 tutor