6 = 2 • 3, so
6ˣ⁻³ = 2ˣ⁻³ • 3ˣ⁻³
Then in
2²ˣ = 6ˣ⁻³
we would have
2²ˣ = 2ˣ⁻³ • 3ˣ⁻³
2²ˣ / 2ˣ⁻³ = 3ˣ⁻³
2²ˣ⁻ˣ⁺³ = 3ˣ⁻³
2ˣ⁺³ = 3ˣ⁻³
Now take the logarithm of both sides. The base you choose doesn't matter.
log(2ˣ⁺³) = log(3ˣ⁻³)
Recall that log(aⁿ) = n log(a), so that the equation reduces to
(x + 3) log(2) = (x - 3) log(3)
Solve for x :
log(2) x + 3 log(2) = log(3) x - 3 log(3)
(log(2) - log(3)) x = - 3 log(2) - 3 log(3)
Recall that log(a) - log(b) = log(a/b), and log(a) + log(b) = log(ab), so that
log(2) - log(3) = log(2/3)
- 3 log(2) - 3 log(3) = - 3 (log(2) + log(3)) = - 3 log(6)
So, we get
log(2/3) x = - 3 log(6)
x = -3 log(6) / log(2/3)
As I mentioned, the base of the logarithm doesn't matter, x will always have the same value of about 13.257.
3/5n+15=10+2/5n what is n
[tex]\textsf{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3}{5}n +15=10+\dfrac{2}{5}n}[/tex]
[tex]\mathsf{\bf{SUBTRACT}\ \mathsf{by\ \dfrac{2}{5}n\ from\ both\ of\ your\ sides}}[/tex]
[tex]\mathsf{Like: \dfrac{3}{5}n+15-\dfrac{2}{5}n=\dfrac{2}{5}n+10-\dfrac{2}{5}n}[/tex]
[tex]\mathsf{\bf{CANCEL: \dfrac{3}{5}+\dfrac{2}{5}}}\textsf{out\ because that gives you\ 1}[/tex]
[tex]\textsf{Solve\ the set we have left over}[/tex]
[tex]\mathsf{Our\ new\ equation\ becomes: \dfrac{1}{5}n+15=10}[/tex]
[tex]\mathsf{\bf{SUBTRACT}}\textsf{ by 15 on both of your sides}[/tex]
[tex]\mathsf{\dfrac{1}{5}n+15-15=10-15}[/tex]
[tex]\mathsf{Cancel\ out: 15-15\ because\ that\gives\ you\ 0 }[/tex]
[tex]\mathsf{Keep: 10-15\ because\ it\ helps\ us\ solve\ for\ your\ n }[/tex]
[tex]\mathsf{10-15=-5}[/tex]
[tex]\mathsf{New\ equation: \dfrac{1}{5}n=-5}[/tex]
[tex]\mathsf{\bf{MULTIPLY}\mathsf{\ both\ sides\ by\ 5}}[/tex]
[tex]\mathsf{\dfrac{1}{5}n\times5=5\times-5}[/tex]
[tex]\mathsf{Cancel\ out\ \dfrac{1}{5}\times5 \ because \ it \ gives \ us \ 1}[/tex][tex]\mathsf{Keep: 5\times -5\ because\ it\gives\ us\ the\ value\ of\ your\ n}[/tex]
[tex]\mathsf{n =5\times-5}\\\mathsf{5\times-5 = -25}[/tex]
[tex]\textsf{Thus, \underline{\bf{n = -25}}}\checkmark[/tex]
[tex]\boxed{\boxed{\mathsf{Thus,\ your\ answer\ is: \boxed{\boxed{\bf{n =-25}}}}}}\checkmark[/tex]
[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Peter says, "If you subtract 12 from my number and multiply the difference by −7, the result is −175." What is Peter's number
Answer:
37
Step-by-step explanation:
let’s say peter’s number is x
(x-12)(-7) = -175
-7x + 84 = -175
-7x = -259
x = 259/7
x = 37
Answer:
The number is 37.
Step-by-step explanation:
-175 ÷ -7 = 25
25 + 12 = 37
You have to work backwards from -175 by doing the reverse of what peter did to get the original number.
Please answer give it too me now
Answer:
5/3
Step-by-step explanation:
HTH :)
Consider the two graphs above.
Which statement best describes the graphs?
A. Graph 1 represents a proportional relationship, but graph 2 does not.
B. Graph 2 represents a proportional relationship, but graph 1 does not.
C. Both graph 1 and graph 2 represent proportional relationships.
D. Neither graph 1 nor graph 2 represent a proportional relationship.
Answer:
B. Graph 2 represents a proportional relationship, but graph 1 does not.
Step-by-step explanation:
All proportional relationships pass through the origin. Graph 2 does but Graph 1 does not. Additionaly, Graph 2 is a straight line that represents a proportional relationship. Another way to find out if it is proportional is to find the constant of proportionality by dividing the y by the x in different parts of the line. The numbers should all have the same constant of proportionality.
Examples (all found in Graph 2):
15/3 = 5
10/2 = 5
5/1 = 5
10. What are the break-even points of the profit function (the values of x where profit equals 0)? Use the quadratic formula. (4 points: 2 points for each x-value)
Answer:
r = 50000
P (r) = 0.7r - 35000
Step-by-step explanation:
Given cost function is
C (r) = 0.85r + 35000
and revenue function is
R (r) = 1.55r
At break even point, revenue is equal to cost
R(x)= C(x)
1.55r = 0.85r+35000
Subtract 0.85 from both sides
0.7r = 35000
divide by 0.7 on both sides
r = 50000
Profit function
P(x)= R(x)- C(x)
P(r) = 1.55r - (0.85r+35000)
P(r) = 1.55r - 0.85r - 35000
P(r) = 0.7r - 35000
I need help NOW please!!!
Answer:
B)34
Step-by-step explanation:
Answer:
B.34°
supplementary angles
their sum is 180
180=146+x
x=180-146=34
Chick-fil-A offers its customers a choice of regular and diet soda. Last night, Chick-fil-A served 50 sodas in all, 27 of which were regular. What percentage of the sodas were regular?
Answer:
54%
Step-by-step explanation:
We know Chick-fil-A served 50 sodas in all, 27 of which were regular. The fractional form of this is 27/50. Now, we can convert this to a fraction with a denominator with 100, then a percentage. 27/50 is equal to 54/100.
54/100 is 54%
Answer:
is 54.the max is 100 percent.the percentage of regular sodas is 54 percent.you do this by timing 50 and 27 by 2 to get 100 and 54.
Step-by-step explanation:
Clare knows that Priya has a bunch of nickels and dimes in her pocket and that the total amount is $1.25. Find one possibility for the number of nickels and number of dimes that could be in Priya's pocket. Write an equation that describes the relationship between the number of dimes and the number of nickels in Priya's pocket. Explain what the point (13,6) means in this situation. Is the point (13,6) a solution to the equation you wrote? Explain your reasoning.
Answer:5x + 10y = 125
Step-by-step explanation
Number of nickel = x
Number of dime = y
Nickel = 5 cent
Dime = 10 cent
Total value = $1.25
Total value should be converted to cent since both dime and nickel are both in cent
= $1.25 * 100 = 125 cents
Therefore,
5x + 10y = 125 cents
3(2x − 5) = 6x + k , whats the value of k?
Answer:
k=-15
Step-by-step explanation:
3(2x-5)=6x+k
open the bracket by multiplying the contents of the bracket by +3
6x-15=6x+k
collect.like.terms(C.L.T)
6x-6x-k=+15
-k=+15 or
-k=15
switch the signs equal to sign(=)
k=-15
State the equation that results when both sides of 2x - 3y = -4 are multiplied by -3.
Answer:
6x - 9y = -12
Step-by-step explanation:
2x - 3y = -4 multiply both sides by 3 by adding paranthesis to represent this
3( 2x - 3y ) = 3 (-4) Then use distributive property for the left side equation
6x - 9y = -12 Finally just multiply -4 by 3 and you get this equation
M<A=45
A. straight
B. obtuve
C. right
D. acute
Answer:
d. acute
Step-by-step explanation:
acute angles are anything less than 90 degrees :)
Eric earned 60 points on his last test. If there was 75 possible points, WHAT was his PERCENT grade?
Answer:
80
Step-by-step explanation:
Eric-- 60/75
Percentage of Eric ---- 60/75 *100
Eric got 80 percentage in his last test.
please help me i cant do this question
Answer:
Step-by-step explanation:
[tex]x^{\frac{1}{2} }[/tex] × [tex]x^{\frac{1}{4} }[/tex] = [tex]x^{\frac{1}{2} +\frac{1}{4} }[/tex] = [tex]x^{\frac{3}{4} }[/tex]
ME ajudem porfavor não aguento mais, tá muito dificil
questão: Determine o valor de x em...
Answer:
say it in English plZz
I can't understand Spanish or whatever ur saying sorry
What is the simplified value of the expression below?
Negative 2.6 + 5.8
–8.4
–3.2
3.2
8.4
Answer:
i did that quiz the answer is 3.2
Step-by-step explanation:
your welcome
Answer:
3.2
Step-by-step explanation:
The directions on a sewing pattern say to buy an extra 12.5% of fabric to account for error. Sam needs 2.75 yards of fabric to make a shirt, so he buys 2.4 yards. Choose the correct statement.
A.Sam bought the correct amount of fabric because he bought what was suggested.
B.Sam bought the correct amount of fabric because he needs less than 2.4 yards.
C.Sam did not buy the correct amount of fabric because he needs less than 2.4 yards.
D.Sam did not buy the correct amount of fabric because he should have bought 3.09 yards
Answer:
Sam should have bought 3.09 yards of fabric instead of 2.4 yards
So, Option D is correct.
Step-by-step explanation:
Total fabric needed by Sam = 2.75
According to directions on a sewing pattern they say to buy an extra 12.5%
So, extra fabric would be: 12.5% of 2.75
Solving
[tex]12.5\% \ of \ 2.75\\=\frac{12.5}{100}\times 2.75 \\=0.343[/tex]
Now adding 0.343 into 2.75 to get extra fabric quantity:
2.75+0.343
=3.09
Therefore Sam should have bought 3.09 yards of fabric instead of 2.4 yards
So, Option D is correct.
What is the solution of the equation p + r + 2 = 3r – 4 – 3p in terms of r?
Answer:
[tex]r=2p+3[/tex]
Step-by-step explanation:
Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept form. (-6,6), (6,2)
Point-Slope form = y-y1=m(x-x1)
Y-6 = -1/3 (x+6)
Slope-intercept form = Y=mx+b
y = -1/3 + 4
The equation of line is y= -2/3x + 2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
Points: (-6,6), (6,2)
Slope= (-2 - 6)/( 6 -(-6))
slope= -8 / 12
slope= -2/3
Now, using slope intercept form
y-b = m(x- a)
y- 6 = -2/3( x + 6)
y -6 = -2/3x - 4
y= -2/3x + 2
Hence, the equation of line is y= -2/3x + 2.
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
What is the value of the expression when a = –5 and c = –1
Answer:
1 times anything is always the number that is being multiplied so the answer would be 5
Step-by-step explanation:
Amy needs to fill a tank that has a capacity of 112L. She using a bucket to collect water from the tap. The bucket can hold 7L of water. How many trips she needs to make to fill half of the tank? *
Answer:
8 trips
Step-by-step explanation: divided 112 by 2 then I got 56 which I then divided that by seven which gave me the answer of 8
Ali was earning $15 per hour before receiving a 10% raise. What is Ali’s new hourly rate? Write and solve an equation.
Answer:
12.56
Step-by-step explanation:
A was earning $15 per hour before receiving a 10% raise. What is Ali’s new hourly rate? Write and solve an equation.
what is the difference between twice a number that is 5 more than it is 3
NEED THIS IN NUMBER FORM
Answer:
The difference between twice a number and a number that is 5 more than 3. Write an equation that could be used to find the value of the number n,
Answer:
2n-8
Step-by-step explanation:
twice a number = 2n
5 more than 3 is 8
difference means subtraction
(2x+5+8)/x-2 there should be a remainder left, pls help
Answer: 13/2
Decimal answer 6.5
im sorry if it was wrong it was what I got
Step-by-step explanation:
how many sig figs does 5 280 feet have ?
Answer:I think 3
Step-by-step explanation: All numbers not zero, so 5 2 8
Please help will give brainlist
Answer:
g(10) = 31
f(-3) = -2
h(2) = -7
j(7) = 333
j(3) = 17
I hope the last 2 were for the same function lol
A recipe calls for 2/3 of cups of milk for 11 cookies. How many cups of milk are needed to make 165 cookies?
Answer:
10 cups of milk
Step-by-step explanation:
Make a proportion, where x is the number of cups of milk for 165 cookies:
[tex]\frac{2/3}{11}[/tex] = [tex]\frac{x}{165}[/tex]
Cross multiply and solve for x:
11x = 110
x = 10
So, 10 cups of milk are needed to make 165 cookies
A.) Translation
B.) Rotation
C.) Reflection
D.) Dilation
Answer: Dilation
Step-by-step explanation: Dilations are when a shape is transformed into something bigger or smaller
A bowl of fruit contains a 4: 1 ratio of blueberries to strawberries. There is a total of 65 berries in the bowl. How many of them are blueberries and how many are strawberries?
9514 1404 393
Answer:
52 blueberries13 strawberriesStep-by-step explanation:
There are a total of 4+1 = 5 ratio units, so each one stands for 65/5 = 13 berries.
blueberries : strawberries = 4 : 1 = 52 : 13
There are 52 blueberries and 13 strawberries in the bowl.
A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?
8.8 pounds
12.7 pounds
61.6 pounds
89.1 pounds
Answer:
8.8 pounds
Step-by-step explanation:
28 kg/7 days =4 kg per day
2.2 pounds * 4 kg = 8.8 pounds
Answer:
A 8.8 pounds
Step-by-step explanation:
(2 x 1058) * (2 x 10-27)