ln(r^2s^10 4√r^2s^10) is equal to Alnr+Blns Where A equals and B equals
[tex]\textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \ln\left( r^2s^{10}\sqrt[4]{r^2s^{10}} \right)\qquad \qquad \stackrel{\textit{let's for a second make}}{z = r^2s^{10}} \\\\\\ \ln\left(z\cdot \sqrt[4]{z} \right)\implies \ln\left(z\cdot z^{\frac{1}{4}} \right)\implies \ln\left(z^{1+\frac{1}{4}} \right)\implies \ln\left(z^{\frac{5}{4}} \right)[/tex]
[tex]\stackrel{\textit{and substituting back}}{\ln\left( \left[ r^2s^{10} \right]^{\frac{5}{4}} \right)}\implies \ln\left( r^{2\cdot \frac{5}{4}} ~~ s^{10\cdot \frac{5}{4}} \right)\implies \ln\left( r^{\frac{5}{2}}~~s^{\frac{25}{2}} \right) \\\\\\ \ln\left( r^{\frac{5}{2}} \right)~~ + ~~\ln\left( s^{\frac{25}{2}} \right)\implies \stackrel{A}{\cfrac{5}{2}}\ln(r)~~ + ~~\stackrel{B}{\cfrac{25}{2}}\ln(s)[/tex]
Janet just mulched her yard and had 2 1/4 bags of mulch left. She divided it evenly and gave 3/8 of a bag to each of the people on her block. How many people live on Janet's block?
Answer:
6 people
Step-by-step explanation:
2 1/4 = 9/4 = 18/8
She gave 3/8 of a bag to each of the people => she gave 18/8 : 3/8 = 6 people
So, there are 6 people that live on Janet's block (maybe 7 if count Janet herself)
Answer:
6
Step-by-step explanation:
2.25 divided by 3/8 (0.375)
To double check multiply 3/8 by 6 and you'll get 2.25 (2 1/4).
can 8 11 and 14 be sides lengths of a triangle
Answer:
yes
Step-by-step explanation:
For the lengths to be the sides of a triangle.
The sum of any 2 must be greater than the third.
8 + 11 = 19 > 14
8 + 14 = 22 > 11
11 + 14 = 25 > 8
Then the 3 lengths can form the sides of a triangle
Answer:
Yes, it can be the sides of a scalene triangle.
Step-by-step explanation:
Because the sides and the angles of a scalene triangle are different.
Can a triangle have sides with the given lengths?
(a) 4, 7, 10
(b) 8, 9, 17
Answer:
yes it can be scaline triangle
What kind of triangle is never wrong?
obiously
right angle triangle
because it has always 90°
Point M( -3, -2) is rotated 270° counterclockwise and then reflected over the x-axis. What are the coordinates of M'?
Rotation involves moving a point around a center
The coordinates of M" are (-2,-3)
How to determine the coordinates of M'The pre-image M is given as:
M =(-3,-2)
The rule of 270 degrees counterclockwise rotation is:
[tex](x,y) \to (y,-x)[/tex]
So, we have:
M' = (-2,3)
The rule of reflection over the x-axis is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
M" = (-2,-3)
Hence, the coordinates of M" are (-2,-3)
Read more about rotation at:
https://brainly.com/question/4289712
If you deposit $8300 earning 2% interest compounded continously, how much would you have after 6 years?
A pole 12 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Xin measures the distance from
the pole to the stake and from the pole to the tower, as shown in the diagram below.
Find the length of the guy wire, to the nearest foot.
Answer:
122ft
Step-by-step explanation:
(Note that this is just a logical guess, I do not remember learning how to do this)
We are given the length of the pole and the length of the guy wire after the pole. This gives us a right angle triangle where we know two of the sides. We can the other two sides into the Pythagorean theorem to solve for the diagonal side
recall:
[tex]{a}^{2} + {b}^{2} = {c}^{2} [/tex]
plugged in 12ft and 2ft we get:
[tex] {(12)}^{2} + {(2)}^{2} = 148[/tex]
to solve for the diagonal side we take the square root of 148
[tex] \sqrt{148} = 12.17[/tex]
so now we know that 12.17 ft of wire is equivalent to 2 feet on the ground.
[tex] \frac{12.17ft \: wire}{2 \: ft \: ground} [/tex]
We have a total of 20 feet, so we multiply this proportion by 20:
[tex] \frac{12.17}{2} \times 20 = 121.7[/tex]
we are asked to give to the nearest foot so we round up to 122ft
Trey weighs 7 pounds less than his brother. Together they weigh 119 pounds. How much does Trey weigh?
Answer:
56
Step-by-step explanation:
T+B = 119
T=B-7
B-7 + B = 119
2B = 126
B = 63 years old
T= 63-7 = 56 years old
What is the equation for the line in slope-intercept form?
Answer:
the equation is y = 8x
Step-by-step explanation:
so rn we know that the y-intercept 0 so we can write:
y = mx
now to find the slope we need to use the equation y2 - y1/ x2 - x1
lets use the points
(2, 16) and (-2, -16) sooo
16 - (-16) / 2 - (-2)
32/4
8
What is an equation of the line that passes through the points (6,2) and
(7, 1)?
(Giving brainliest )
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{6}}}\implies \cfrac{-1}{1}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{-1}(x-\stackrel{x_1}{6}) \\\\\\ y-2=-x+6\implies y=-x+8[/tex]
B --2x > 10
( it's a line under the more or less that sign)
Answer:
Step-by-step explanation:
A company is using the first two years of its profits to predict what will happen in the future. The profit, p(x), in millions, can be modeled by
the function p(x) =x^2 + 4x + 5, where x, represents the number of years after 2020
- In what year did the company have the largest profit and what was the amount?
Answer:
2022
9 million
Step-by-step explanation:
[tex]p(x) =-x^2 + 4x + 5[/tex]
To find the value of x when the maximum profit occurs, differentiate the function:
[tex]\implies p'(x)=-2x+4[/tex]
set it to zero and solve for x:
[tex]\implies p'(x)=0[/tex]
[tex]\implies -2x+4=0[/tex]
[tex]\implies x=2[/tex]
Therefore, the year in which the company had its largest profit was
2020 + 2 = 2022
Input found value of x into the function:
[tex]p(2) =-(2)^2 + 4(2) + 5=9[/tex]
Therefore, the amount was 9 million
What is the area of the polygon
Answer:
42m2
Step-by-step explanation:
9x4=36m2
3x2x0.5=3m2x2=6m2
36+6=42m2
please help me with this question
Answer:
$37.50
Step-by-step explanation:
Fernando had to pay $1.40 in sales tax when he purchased a shirt. If the sales tax rate is 7%, how much did his shirt cost? please show step by step
Sam is having a party and he will make 14 hamburgers. Each hamburger requires 2 7 pounds of meat. How much meat does Sam need in total for the party?
Answer:
I really don't know i need the answer as well
Step-by-step explanation:
HELP PLEASE-
NEED QUICK
Answer:
20 is A 3.7
21 is D 18.7
22 is C 8.8
23 is A 3.6
24 is D 11.6
25 is A 2.7
I hope this helps!!
Find each unknown angle measurement.
Answer:
angle(2) = 118 degree
angle(3) = 118 degree
angle(4) = 62 degree
Step-by-step explanation:
To find angle 2 :
[tex]62 + angle{2} = 180 \\ angle{2} = 180 - 62 = 118 \: degree[/tex]
The rule (head to head):
angle(2) = angle(3) = 118 degree
And the last one is angle(4) which is the same thing:
angle(4) = angle(1) = 62 degree
2xy (8x-3y) the answer?
The starting and stopping point for Amir’s run this morning are 0.5 inch apart on the map. If each inch on the map represents 3 miles, how far did Amir run?
Answer:.
1.5 miles
Step-by-step explanation:
1 inch = 3 miles
0.5 inches = X miles
X=3(0.5) = 1.5
Please help! 20 points thanks :)
Answer:
D) There is not enough info to tell (sike maybe not the asnwer)
B) b (bbbbbbbbbbb)
Step-by-step explanation:
SiiiKE, not D) I think but My first thought is D but I know it is not D unless it is another answer BUT I think it is B My final answer is B) b
A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split the bill and tip evenly among themselves. One of the friends used the equation One-fourth (t 34) = StartFraction 40 over 4 EndFraction to represent the situation, where t represents the total amount of the tip. Which describes the amount each friend paid for the food and for the tip? Each friend paid $8. 50 for the food and $1. 50 for the tip. Each friend paid $10. 00 for the food and $6. 00 for the tip. Each friend paid $8. 50 for the food and $6. 00 for the tip. Each friend paid $10. 00 for the food and $1. 50 for the tip.
The amount each friend paid for food is $8. 50 for the food and $1. 50 for the tip.
What is division?The division is one of the most basic mathematical operators. It is used when a number is to be distributed equally in n number of parts.
As it is given that the total of 4 friends went to the lunch, the total amount paid by them is $40, but the food bill was just $34, therefore, the rest of the amount was paid in the tip. If we calculate the tip,
Tip = Total spent - Food bill
Tip = $40 - $34
Tip = $6
Now, as it is that the total amount spend by all on the food is $34, and it is to be divided among the four friends, therefore, the amount paid by each of the friends is,
[tex]\text{Total amount to be paid by each friend}=\dfrac{\text{Total amount spent by all on food}}{\text{Number of friends}}\\\\\text{Total amount to be paid by each friend}=\dfrac{\$34}{4}\\\\\text{Total amount to be paid by each friend}=\$8.5[/tex]
Further, the total amount tip by all is $6, and it is to be divided among the four friends, therefore, the amount paid by each of the friends is,
[tex]\text{Total amount to be paid by each friend}=\dfrac{\text{Total Tip}}{\text{Number of friends}}\\\\\text{Total amount to be paid by each friend}=\dfrac{\$6}{4}\\\\\text{Total amount to be paid by each friend}=\$1.5[/tex]
Hence, the amount each friend paid for food is $8. 50 for the food and $1.50 for the tip.
Learn more about Division:
https://brainly.com/question/369266
A bakery sold 119 cupcakes in one day. The head baker predicted he would sell 99 cupcakes that day.
Answer:
soln,
=119+99
=218 answer
Solve using log
Help would be much appreciated
Answer:
5.2812
Step-by-step explanation:
[tex]10^{x-3.6}-7=41[/tex]
Add 7 to both sides:
[tex]\implies 10^{x-3.6}=48[/tex]
Taking logs of base 10:
[tex]\implies \log_{10}10^{x-3.6}=\log_{10}48[/tex]
Apply log rule [tex]\log a^b=b \log a[/tex]:
[tex]\implies (x-3.6)\log_{10}10=\log_{10}48[/tex]
Apply log rule [tex]\log_aa=1[/tex]:
[tex]\implies (x-3.6)\times 1 =\log_{10}48[/tex]
Simplify and solve:
[tex]\implies x-3.6=\log_{10}48[/tex]
[tex]\implies x=\log_{10}48+3.6[/tex]
[tex]\implies x = 5.281241237...[/tex]
[tex]10^{x-3.6}-7=41[/tex]
Use the rules of exponents and logarithms to solve the equation.
[tex]10^{x-3.6}-7=41[/tex]
Add 7 to both sides of the equation.
[tex]10^{x-3.6}=48[/tex]
Take the logarithm of both sides of the equation.
[tex]log(10^{x-3.6})=log(48)[/tex]
The logarithm of a number raised to a power is the power times the logarithm of the number.
[tex](x-3.6)log(10)=log(48)[/tex]
Add 3.6 to both sides of the equation.
[tex]x=log(48)-(-3.6)[/tex]
Solve by first finding [tex]log(48)[/tex] then subtract [tex](-3.6)[/tex] from the answer:
1. [tex]log(48)=1.6812412373755872181499834821531[/tex]
Now just solve the equation:
[tex]1.6812412373755872181499834821531 - (-3.6)=5.2812412373755872181499834821531[/tex]
Your answer is C. [tex]5.2812412373755872181499834821531[/tex] or [tex]5.2812[/tex]
A formula for finding the perimeter of a rectangle is P = 2L + 2W. If you know the perimeter (P) and length (L) of a rectangle, which formula can you use to find the width (W)?
Answer:
p/2 - L = W
Step-by-step explanation:
P = 2L + 2W
Subtract 2L from both sides
P - 2L = 2W
Divide both sides by 2
p/2 - L = W
Answer:
p/2 - L = W
Step-by-step explanation:
What is the value of x?
\log _3x=4
Answer:
x = 81
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{3}[/tex] x = 4 , then
x = [tex]3^{4}[/tex] = 81
The sum of three numbers is 24. Twice the smallest number is 2 less than the largest number. The largest number is equal to the sum of the smallest and middle number. What are the three numbers?.
Known information:
the sum of three numbers: 24the smallest number is 2 less than the largest numberthe largest number is equal to the sum of the smallest and middle number.Let us set up some variables for our terms:
smallest number --> Smiddle number --> Mlargest number -- LLet us set up some equations in terms of our known information
S + M + L = 24S = L - 2L = S + MLet us set up everything in terms of L, because in the first equation, we will be able to get rid of all the other variables but L allowing us to solve the equation:
(S + M) + L = 24 ---> L + L = 24
2L = 24
L = 12
Since L = 12, we know that S = L - 2:
S = L - 2 = 12 - 2 = 10
Since now we know that L = 12, and S = 10, and L = S + M:
L = S + M
12 = 10 + M
M = 2
So our answer is 2, 10, 12
Hope that helps!
A group went together to the Clayton Art and Wine Festival. They bought 30 tickets. Child tickets are $2 each and Adult tickets are $4. 50 each. If they spent $107. 50 total, how many of each type of ticket did they buy?
Answer:
they bought 23 adult tickets and 2 child tickets
Step-by-step explanation:
the explanation is in the screenshot below
please mark brainliest
The sum of the squares of 4 consecutive integers is an even integer.
Answer:
yes
Step-by-step explanation:
Let's call the first integer n and let's compute.[tex]n^2 + (n+1)^2 + (n+2)^2 +(n+3)^2 = \\n^2 + \\n^2+2n+1 + \\\ n^2+4n+4 + \\\ n^2+6n+9+\\\ n^2+8n+16 =\\4n^2+20n +30 = 2 (2n^2+10n+15)[/tex]
Which is indeed of the form 2(something), so it is even.
