Answer:
1. Expanded form of [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)
2.Exact solution x = -0.376
Step-by-step explanation:
Solution:
First we have to write the Expanded Form of [tex]a^{2} . b^{3}[/tex], Let's do it.
1) [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)
Hence,
Expanded form of [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)
2) [tex]4^{5x} = 3^{x-2}[/tex]
Now, we have to find out the exact solution of the above equation:
In order to equate the exponents, we need to make sure the bases are same. Or we simply can use logarithm to solve the above equation.
So,
We are using logarithm to solve this equation.
Let's break this down:
[tex]4^{5x} = 3^{x-2}[/tex]
Taking log on both sides.
log[tex]4^{5x}[/tex] = log[tex]3^{x-2}[/tex]
[tex]5xlog(4)[/tex] = [tex](x-2)log(3)[/tex]
Dividing both sides by log(4)
[tex]5x[/tex] = (x-2) [tex]\frac{log(3)}{log(4)}[/tex]
value of log(3) = 0.4771
value of log(4) = 0.6020
[tex]5x[/tex] = (x-2) [tex]\frac{log(0.4771)}{log(0.6020)}[/tex] =
5x = (x-2)0.792
5x = 0.792x - 1.584
by rearranging the equation, we get:
0.792x - 5x = 1.584
x(0.792 - 5) = 1.584
x(-4.208) = 1.584
x = -1.584/4.208
x = -0.376
Exact solution x = -0.376
Lou buys 20 pounds of apples for $40. How many pounds can she buy for one dollar?
Answer:
She can buy 2 pounds per dollar.
Step-by-step explanation:
0.05x =0.5 can someone please helppppp!!!!!!!!!!
Answer:
x equals 10
Step-by-step explanation:
you are moving the 5 from the hundredth value to the tenth, meaning it is becoming a higher number. for this one, just multiply by 10.
helppppppppppppppppp
Answer:
library-6
auditoriam-54
Are the lines y=4 and x=-3 perpendicular
Answer:
Yes, because y=5 will intersect the y axix (giving a horizontal line) and x =-3 will intersect the x axis (giving a vertical line). They will intersect at angle 90.
Step-by-step explanation:
Please gimme brainliest
Answer:
Yes
Step-by-step explanation:
When you graph y=4 it is a horizontial line going straight forever. You would mark a dot on postive four on the y-axis. For x, do the same thing mark on the negative three on the x-axis. But this one will be vertical.
REMEMBER-
Although the x-axis is horizontial when there is no Y (x,y) it will be vertical. And it is opposite for the Y.
Jordan found cloth for $7.50 per yard. How much would his total cost be if he needed 12 yards of cloth?
7. At an online retailer, the price of the camera is discounted 15% to $212.50. What was the
price of the camera before the discount?
Answer:
$250
Step-by-step explanation:
discounting 15 percent is the same as marking something for 85 percent. This is the same as multiplying by .85
set up equation and solve
.85x=212.50
x=250
Help please!!! will give brainliest
Answer:
Step-by-step explanation:kytiyfkutfdc
Help me out here pleaseeeeeee
Answer:
option C
Step-by-step explanation:
(6+3)= 9
9 × 4= 36
36-2= 34
hope it helps! please make me brainliest..
Thank you! Have a good day ahead!
Answer:
(6+3)*4-2
Step-by-step explanation:
(6+3)*4-2
9*4-2
36-2
34
PEMDAS
Parenthesis
Exponents
Multiply
Divide
Add
Subtract
4 2/3 ÷ 7 = ?
help pleaseee
Answer:
0.66666666666
Step-by-step explanation:
this is a real answer
The sum of seven and the quotient of a number x and eight.
32. A volleyball team played 25 games. The ratio of games won to
games lost was 6:4. How many games did the team win?
Number of volleyball games team win is 15 games
Given that;Number of volleyball games = 25 games
Won to lost ratio = 6:4
Find:Number of volleyball games team win
Computation:Number of volleyball games teams win = 25[6 / (6+4)]
Number of volleyball games teams win = 25[6 / 10]
Number of volleyball games team win = 15 games
Learn more:https://brainly.com/question/24140426?referrer=searchResults
what is the remainder and quotient of 11/3
Answer:
The remainder of 11 divided by 3 is 2. The quotient is 3.
Step-by-step explanation:
3 goes into 11 three times. 3 x 3 = 9. 11 - 9 = 2. 3 can't go into 2 so bring the two up and you get your answer of 3 r 2.
Pls help 10 easy points!!!
Answer:
D
Step-by-step explanation:
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $53,533. The variable costs will be $12.50 per book. The publisher will sell the finished product to bookstores at a price of $24.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
9514 1404 393
Answer:
4,556
Step-by-step explanation:
Revenue from the sale of n books is ...
R = 24.25n
Production cost for n books is ...
C = 53533 +12.50n
These are equal for ...
24.25n = 53533 +12.50n
11.75n = 53533
n = 53533/11.75 = 4556
The publisher must produce 4556 books so sales will equal production cost.
for the linear function f, the graph of y=f(x) in the xy-plane passes through the points (0,2) and (9,9). what is the slope of y=f(x)?
Answer:
[tex]slope = \frac{(y _{2} - y _{1})}{(x _{2} - x _{1})} \\ = \frac{(9 - 2)}{(9 - 0)} \\ = \frac{7}{9} \\ hence \: slope \: is \: \frac{7}{9} [/tex]
A marathon runner's time was 2% longer Tuesday than Monday. How much time did he log on Tuesday when compared to Monday.
A. y= 1.02x
B. y=(1 - 0.2)x
C. y= 1.2x
D. y= 0.02x
Answer:
B.
Step-by-step explanation:
I just guesses
Henry went clothes shopping and bought 3 pairs of shorts for $22.99 each, 2
shirts for $32.99 each and one pair of shoes for $54.99. What is the most
reasonable estimate of the total amount he spent on all the clothing?
A. $135
B. $184
C. $190
D. $223
Answer:
C
Step-by-step explanation:
Maria wants to add to her CD collection. If a CD costs $12, which expression shows the cost of d CDs? A. 12 - d B. 12 ÷ d C. 12 + d D. 12 × d
Step-by-step explanation:
Cost of CDs
= Number of CDs * Cost of one CD
= d * $12
= $12d. (D)
The answer is using multiplication as we have a unit rate and we wish to find the total.
Answer:
D. 12*d, or 12d
Kelsea and Landon are playing in a park standing 100 feet away from each other. They both see a bird flying above them. The angles of elevation from each person to the bird are shown. How high is the bird from the ground? Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
use an ASA triangle with law of sine
since we know that 180 = 20 +45 + C .. solve for C = 115°
now use law of sines c/ sin(C) = b/sin(B) .. and solve for b
Sin(20)*100/sin(115) = b
b = 37.73774 ft
that's the hypotenuse of the 45 triangle
SOH CAH TOA to remember how trig functions fit
use b*Cos(45) = adj
26.6846 = adj
The bird is 26.7 ft. from the ground
Clare subscribes to an online music streaming service
for a yearly fee of $96. Starting next month, there will
be a 12% increase in the fee.
The ad for another music streaming service is shown
below. Should Clare switch? Explain.
Answer:
She should go with service 2 because it is, cheaper. Service 1 cost $107.52, but service 2 cost only $105.
Step-by-step explanation:
Cost now+increase$=new cost
(Part=percent*whole)
Increase=percent increase*cost now
i=12%*$96
i=0.12*96=$11.52
$96+11.52=107.52
Service two⬇️
8.72*12=$105
Yes Clare should switch to service 2 because; cheaper it costs only $105 which is lesser than $107.52
How to Calculate Yearly Fee?
To find the new cost, we will use the expression;
New Cost = Present Cost + increase
However,
Increase = percentage increase * present cost
Increase = 12% * $96
Increase = 0.12 * 96
Increase = $11.52
Thus;
New Cost = $96 + 11.52
New Cost = $107.52
For Service two;
We are told that digital streaming costs $8.75 per month. Thus;
Cost = 8.75 * 12
Cost = $105
Read more about Yearly fee at; https://brainly.com/question/25109150
#SPJ2
I will mark you brainliest if you go subscribe to seema beauty care and more on y o u t u b e and put the screenshot in answer.
Step-by-step explanation:
Just subscribed wish you the best on your channel!!!
Ruby misses 4% of the free throws she attempts in a season. How many total free throws did she attempt if she missed 46?
how many times can 200 go into 4879
Answer:
24
Step-by-step explanation:
A set of data is summarized by the stem and leaf plot below.
Stem Leaf
1 0 0 2 2 4 5 5 5 6 7 8 8 9 9 9 9
2 0 0 0 3 3 4 5 8 8
3 0 0 1 1 3 4 5 5 5 6 6 6 6 7 7 8 8 8 9 9
4 1 2 2 3 3 3 5 5 6 6 7 8 8 9 9
The value 52 appears _________time(s) in the data set. The value 47 _________appears time(s) in the data set.
Answer:
0 ; 1
Step-by-step explanation:
Given the dataset :
Stem _____ Leaf
1 _______ 0 0 2 2 4 5 5 5 6 7 8 8 9 9 9 9
2 _______0 0 0 3 3 4 5 8 8
3 _______0 0 1 1 3 4 5 5 5 6 6 6 6 7 7 8 8 8 9 9
4 _______ 1 2 2 3 3 3 5 5 6 6 7 8 8 9 9
The value 52 appears 0 times in the dataset
This is because the stem does not contain the digit 5.
The value 47 appears 1 time(s) in the data set ; stem of 4, leaf 7
I need help with my wirk
Answer:
50
Step-by-step explanation:
22 is 44% of 50. It's 50 because it's techincally half if you look at it. I don't know how to really explain that well. But the answer is 50, trust me.
HELP ASAP.
WILL GIVE BRAINLIEST
Answer:
yay
Step-by-step explanation:
ty
A scale drawing of a living room is shown below:
What is the area of the actual living room in square feet? Round your answer to the nearest whole number.
17 ft2
41 ft2
495 ft2
103 ft2
Answer:
103 ft.
Step-by-step explanation:
Answer:
TrIaNgLe
Step-by-step explanation:
You have a square that has a side length of $1$ centimeter. Each minute, $2$ centimeters are added to the side length. After $10$ minutes, what will be the difference between the area of the last square and the area of the initial square in square centimeters (do not include the units in your answer)?
Answer:
Difference in area of the last square and the initial square = 440 cm²
Step-by-step explanation:
Length of the side of a square = 1 cm
Area of the square = (side)² = 1 cm²
Addition of side length every minute = 2 cm
After x minutes length of each side of the square = (1 + 2x) cm
If x = 10 minutes
Length of each side of the square = [1 + 2(10)]
= 21 cm
Area of the square after 10 minutes = (21)²
= 441 cm²
Therefore, difference in area of the last square and area of the initial square
= 441 - 1
= 440 cm²
Where another question helpppppppp plssssss
Answer:
41.1 = dekagrams
4.14 = hectograms
0.414 = kilograms
Answer:
I agree with the other person
Step-by-step explanation:
What is X 2(x+5)=3x+1
Answer:
X = 9
Step-by-step explanation:
