I assume you're referring to the product,
[tex]\log_{5t}(5t+1)\cdot\log_{5t+1}(5t+2)\cdot\cdots\cdot\log_{5t+n}(5t+n+1)[/tex]
Recall the change-of-base identity:
[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]
where c > 0 and c ≠ 1. This means the product is equivalent to
[tex]\dfrac{\log(5t+1)}{\log(5t)}\cdot\dfrac{\log(5t+2)}{\log(5t+1)}\cdot\cdots\cdot\dfrac{\log(5t+n+1)}{\log(5t+n)}[/tex]
and it telescopes in the sense that the numerator and denominator of any two consecutive terms cancel with one another. The above then simplifies to
[tex]\dfrac{\log(5t+n+1)}{\log(5t)}=\boxed{\log_{5t}(5t+n+1)}[/tex]
solve x 3+3(x+2)=-24
Answer: x =5
Step-by-step explanation:
[tex]x + 3 + 3(x + 2) = - 24[/tex]
[tex]x + 3 + 3x + 6 = - 24[/tex]
[tex]4x + 9 = - 24[/tex]
[tex]4x = - 24 - 9[/tex]
[tex]4x = - 33[/tex]
[tex]x = \frac{ - 33}{4} [/tex]
What is the exact distance from (-5,1) to (3,0).
Answer:
The distance between the two points is [tex]\sqrt{65} \ \text{units}.[/tex]
Step-by-step explanation:
In order to find the distance between two coordinate pairs, we can use the distance formula:
[tex]\displaystyle \bullet \ \ \ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Our coordinate pairs need to be labeled accordingly, so we can use this naming system:
[tex]\bullet \ \ \ (x_1, y_1), (x_2, y_2)[/tex]
This assigns a name to our points:
[tex]x_1 = -5[/tex][tex]y_1 = 1[/tex][tex]x_2 = 3[/tex][tex]y_2 = 0[/tex]Therefore, we can plug these into the formula and solve:
[tex]d=\sqrt{(3-(-5))^2+(0-1)^2}\\\\d=\sqrt{(8)^2+(-1)^2}\\\\d=\sqrt{8^2+1^2}\\\\d=\sqrt{64+1}\\\\d=\sqrt{65}[/tex]
Therefore, the distance between the two points is [tex]\sqrt{65} \ \text{units}[/tex].
I REALLY NEED HELp!!!!!!!!
Retail Price Quantity Total Price
Twister Pen .35 * 2 = $0.70
Mini Fish Eraser .50 * 1 = $0.50
Happy Cap Eraser .05 * 5 = $0.25
Erasing Grip .35 * 3 = $1.05
---------
Subtotal .7 + .5 + .25 + 1.05 = $2.50
Sales Tax Amount (unknown because we aren't given a tax value)
Total (also unknown for the same reason)
Retail Price Quantity Total Price
Twister Eraser .35 * 3 = $1.05
Astral Wonders Pencils .20 * 4 = $0.80
Criss Cross Critters .15 * 2 = $0.30
Traction Mechanical
Pencil .35 * 2 = $0.70
Muchin Mike Sharpener .50 * 2 = $1.00
----------
Subtotal 1.05 + .8 + .3 + 0.7 + 1 = $3.85
Sales Tax Amount (unknown because we aren't given a tax value)
Total (also unknown for the same reason)
Best of Luck!
Check whether (x – 1) (x +2) = x + 3 is a quadratic equation or not.
Answer:
no, it is not
Step-by-step explanation:
STEP 1: Simplify (x−1)(x+2).
[tex]x^2+x-2=x+3[/tex]
STEP 2: Move all terms containing x to the left side of the equation.
[tex]x^2-2=3[/tex]
STEP 3: Move all terms not containing x to the right side of the equation.
[tex]x^2=5[/tex]
STEP 4: Take the square root of both sides of the equation to eliminate the exponent on the left side.
[tex]x=[/tex]±[tex]\sqrt{5}[/tex]
STEP 5: The complete solution is the result of both the positive and negative portions of the solution.
[tex]x=\sqrt{5} ,-\sqrt{5}[/tex]
X: -3, 2, 7, 12
Y: 0, 2, 4, 6
Whats the slope ?
Answer:
The Slope in 7,2
Step-by-step explanation:
what is the maximum value of the function? explain what the maximum value of this represents in this situation. make sure to include information about the x-value and y-value in your explanation
wowwwww he just roasted youuuuuuuuuu!!!!!
find the quotient 8 divided by 1/7.
Answer:
56
Step-by-step explanation:
When we divide a number with a fraction, we change the sign into a multiplication sign, and we do the reciprocal. Then we multiply across.
WA store manager records the number of people who have been in his store compared to the number of hours the store has been open. He graphs the data on the scatterplot below and sketches a trend line.
Store Customers
A graph has hours open on the x-axis, and total customers on the y-axis. A trend line goes through points (1, 25) and (2, 50).
Based on the data collected, if the store has been open 7 hours, which scenario is most likely to be true?
After 1/2 hour, 1 customer had been in the store.
After 6 hours, 129 customers had been in the store.
After 7 hours, 175 customers had been in the store.
After 8.5 hours, 225 customers had been in the store.
Answer: After 7 hours, 175 customers had been in the store.
Step-by-step explanation:
Did the quiz, Trust me.
Answer:
ccccccccc!
Step-by-step explanation:
how many solutions are there to the equation below
6x+30+4x=10(x+3)
a)0
b) infinitely many
c) one
Answer:
b) infinitely many
hope it helps
What is the K for this story Problem? John bought 27 baseball cards for $9. How many baseball cards can he buy with $84?
Answer:
210
Step-by-step explanation:
9 divided by 27 = .33333 = .4
you would divide 9 by 27 because if you did 27 divided by 9 he would only have 3 cards
84 divided by .4 = 210
Solve the formula for the indicated variable.
B=yv+y, for v
The solution is v=?
Answer: v = B/y -1
B = yv + y = (v + 1)y
=> B/y = v + 1
⇔ [tex]v=\frac{B}{y}-1[/tex]
Step-by-step explanation:
Abigale drove 20 kilometers in 10 minutes, and Jordan drove 30 kilometers in 15 minutes.
Both Abigale and Jordan drove at a constant speed.
Did Abigale and Jordan drive at the same speed? Explain your reasoning.
Answer:
15
Step-by-step explanation: 20+10+3+30 =30
What is 1.452 rounded to the nearest hundredth
Answer:
1.450
Step-by-step explanation:
what grade ar4e you in I'm guessing 4th or 5th
If f(1) = 10, what is f(3)?
Answer:
30
Step-by-step explanation:
multiply each f by the same root numeral
The cost of a magazine is $x and the cost of a newspaper is $(x -3). The total cost of 6 magazines and 9 newspapers is $51. Write down and solve an equation in x to find the cost of a magazine,
See attachment for math work and set up. Use the substitution method to find x.
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION I NEED TO TURN IT IN TODAY
Answer:
The answer is 833.65384615385
Step-by-step explanation:
pls help me on this iready question I beg u
Answer:
We conclude that for 1/2 batch, Faird would require 3/8 cups of sugar.
Step-by-step explanation:
Suger needed for a full batch = 3/4Given that Farid is making 1/2 of batchWe need to determine the expression for the amount of sugar Freed needs to make 1/2 batch.
Let 'x' be the batch and 'y' be the amount of sugar
Suger needed for a full batch = 3/4 cup of a sugar
so
x = 3/4yBut, Farid is making 1/2 of the batch.
Thus, multiply both sides by 1/2
[tex]x\times \frac{1}{2}\:=\:\frac{3}{4}y\times \frac{1}{2}[/tex]
[tex]\frac{x}{2}=\frac{3y}{8}[/tex]
Therefore, we conclude that for 1/2 batch, Faird would require 3/8 cups of sugar.
According to the 2014 national population projections published by the U.S. Census Bureau, the U.S. population is projected to be 334.4 million in 2020 with an estimated growth rate of 0.79% per year. Assuming the growth rate remains constant, find the projected population in 2050.
Answer:
423,437,744
Step-by-step explanation:
Given that :
Projected population in 2020 = 334.4 million
Estimated growth rate (r) = 0.79%
Projected population in 2050 ;
Using the exponential growth function :
Estimated value = initial value(1 + growth rate)^time
Initial value = i
Time = 2020 - 2014 = 6 years
334.4 = i(1 + 0.0079)^6
334.4 = i(1.0079)^6
334.4 = i2.43087455521E−13
i = 3.189786E8
Initial population = 318. 978 million
Estimated Population in 2050:
2050 - 2014 = 36
Projected population = 3.189786E8(1.0079)^36
Projected population = 3.189786E8*1.3274801
= 423437743.82586
= 423437744 million
Find the measures of the exterior angles.
Answer:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.) FACTS: An exterior ∠ is equal to the addition of the two Δ angles not right next to it.
What is the value of the expression below?
2 [32 - (4-1) to the power of 3]
Enter your answer in the box.
Answer:
the answer is 10
Step-by-step explanation:
Luther starts jogging 8minutes on the first day and then increases his time by 4 minutes each day. How many minutes will he jog the fifth day?
Answer:
80?
Step-by-step explanation:
Answer:
(8+4)x5
Step-by-step explanation:
HEY THS IS WORTH 69 POINTS
The vertices of a rectangle are A(2, 0), B(5, 0), C(5, −2), and D(2, −2). Reflect the rectangle in the y-axis, and then rotate
the rectangle 180° about the origin. What are the coordinates of the image?
Answer:
A′(-2, 0), B′(-5, 0), C′(-5, 2), and D′(-2, 2)
Step-by-step explanation:
I did FLVS (Online School stuffs)
Answer:
A
Step-by-step explanation:
In a small private liberal arts college, 40 percent of the students receive financial aid, and 30 percent of the students that receive financial aid also are first generation college students. In addition, 25 percent of the students in the college own a hybrid car. What is the probability that a randomly selected student receives financial aid and is first generation college student
Answer:
P(A∩B) = 0.12
Step-by-step explanation:
Given:
Students receive financial aid P(A) = 40% = 0.4
Students receive financial aid and first generation P(B/A) = 30% = 0.3
Find:
Probability [Selected student receives financial aid and is first generation college student] P(A∩B)
Computation:
P(A∩B) = P(A) x P(B/A)
P(A∩B) = 0.4 x 0.3
P(A∩B) = 0.12
Paula ran 3 1/4 kilometers. Omar ran 4,200 meters. What is the total number of centimeters Omar and Paula ran?
Answer:
325000 + 420000 = 745000
Step-by-step explanation:
They ran 745000 centimeters all together
What is the 15th term of the sequence an =
-3n+50
D. 95
Answer:
= 105
Step-by-step explanation:
Answer:
here ya go
Step-by-step explanation:
a
9
=
105 I think
Can someone answer this I would really appreciate it thanks :)
Answer:
Y = 130
X = 20
Z = 110
Answer:
y= 130 degrees x= 20 degrees z= 110 degrees
Step-by-step explanation:
I solved top left triangle first. So, we know all triangles add up to 180 degrees and we have two on the angles so 85 + 45 = 130 then 180 - 130 = 50 so the missing angle near y is 50. Now to figure out Y then you just subract your answer (50) from 180 which you get 130. So y is 130 degrees. Then to figure out X, you just do 180 - 130 = 50, 50 - 30 = 20, so x is equal to 20 degrees. Then lastly to figure out z we know that the missing angle is 50 because its vertical to the other 50 degree so now you do 180 - 20 = 160, 160 - 50 = 110 degrees.
plz help i have a branliest
Answer:
Use a calculator lol
Step-by-step explanation:
Answer:
Step-by-step explanation:
s= 2, 2 and 11
I= 2, 5 and 3
u=2, 7 and 5
t= 2, 2, 3 and 3
b= 2, 2, 5 and 5
n= 2, 2, 19
p= 2, 3, 3 and 5
o= 2, 2 and 17
r= 3, 3 and 11
m= 2, 3, 3 and 7
d= 2, 3 and 7
e= 2, 2, 3 and 11
Which expression can be used to find The amount of money for camp leader spends on b books
Answer:
Part A: A. 7.50 x b
Part B: $90
Step-by-step explanation:
Part A: The cost of a book is $7.50, so the equation that is going to tell you the total cost of however many books purchased is equation A.
Part B: $90. If the cost of a book is $7.50 and the teacher purchases 12 books, you do $7.50 x 12= $90. You can check the equation by adding $7.50 12 times. You will get the same result.
Please help me please
Answer:
To be honest I don't know I just need some points 1+1=2
Step-by-step explanation:
What number is equivalent to 15 and 25
Answer:
yo are you talking about like absolute value? then it's | -15 | and | -25 |
Step-by-step explanation: