Simplify the following expression.
12a376c5
3a284c5
O A 4a6²c
OB.
9a62
OC. 4a62
OD. 9ab2cC
Answer:
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}=4ab^{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex]
Required
Simplify
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex]
To solve this, we apply the following law of indices:
[tex]\frac{m^x}{m^y} = m^{x-y}[/tex]
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex] becomes
[tex]\frac{12}{3}a^{3-2}b^{6-4}c^{5-5}[/tex]
[tex]\frac{12}{3}a^{1}b^{2}c^{0}[/tex]
[tex]c^0 = 1[/tex]; So, we have
[tex]\frac{12}{3}a^{1}b^{2}*1[/tex]
Finally,
[tex]4ab^{2}[/tex]
Hence:
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}=4ab^{2}[/tex]
1,Find the eighth term of the geometric sequence whose 1st term is 5 and whose 4th term is
1/25.
Answer:
Solution will be 1/15625
Step-by-step explanation:
Substitute the value of first term for ar^(4-1) for the third term with 1/25 on RHS, make r the subject (which is the common ratio)
you'll get r as 1/5
Now for the eighth term, replace the "4" in the formula with "8" and a with "5" and observe the magic.
Graph this function using intercepts: 27x–15y=1,350. Provide x and y intercepts
I really don't know how to do it myself and when I try to solve using a website they can't even do it
Answer:
graph attached
Step-by-step explanation:
27x - 15y = 1350
15y = 27x -1350
y = 27/15 x - 1350/15
y = 9/5 x - 90
y = mx + b y intercept (b) = -90
y=0 x = 90 * 5/9 = 50 x intercept
Step-by-step explanation:
Given function
27x – 15y = 1350Easy way to find x- and y-intercepts and graph the line:
x-intercept found when y = 0
27x - 15*0 = 135027x = 1350x = 1350/27x = 50y-intercept found when x = 0
27*0 - 15y = 1350-15y = 1350y = -1350/15y = - 90So the points are:
(0, -90) and (50, 0)Plot these two points on a coordinate plane and connect with a line
What's 7.3 and 23 as a precent and what's 2/5 as a precent
Answer:
730% 23% and 40%
Step-by-step explanation:
.......
Write a Play
Write a short play about the
adventures of characters x, y, m, b,
as they travel around the coordinate
plane. Have your characters meet
many friends and relatives along the
way. The purpose of your play is
to educate the audience about the
mathematics in this topic through
action, dialogue, staging, and props.
Answer:
math is a difficult subject
Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
20% tip on a bill of $36.04
The amount of the tip is approximately $
$7.00
O $7.20
0 $7.25
$7.50
Answer:
36.04
The amount of the tip is approximately $
$7.00
O $7.20
0 $7.25
$7.50
Step-by-step explanation:
What is the value of the expression? (10 1/4 +61) – (3 3/5 - 3 1/2) Enter your answer in the box as a mixed number in simplest form.
Answer:
71 3/20Step-by-step explanation:
This is easy. The first step here is to simplify the numbers inside the parentheses.
10 1/4 + 61 = 71 1/4
3 3/5 - 3 1/2 = 3 6/10 - 3 5/10 (We needed to get both with like denominators, so we raised the fractions to an equivalent denominator.)
3 6/10 - 3 5/10 = 1/10
Now, we will do the operation outside of the parentheses.
71 1/4 - 1/10 = 71 5/20 - 2/20 = 71 3/20
Answer is 71 3/20 Give three points that lie on a line with a
slope of -2/5
Answer:
The three points that lie on a line y = -2/5x with a slope -2/5 will be:
(0, 0)(5, -2)(10, -4)Please check the attached graph also.
Step-by-step explanation:
We know that the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Given
slope = m = -2/5
We suppose the line passes through the origin.
so b = 0
substituting m = -2/5 and b = 0 in the slope-intercept form
[tex]y = mx+b[/tex]
y = -2/5x + 0
y = -2/5x
Thus, the equation of line with the slope m = -2/5 and passes through the origin (0, 0) will be:
y = -2/5x
As the equation of line passes through (0, 0), thus the point (0, 0) lies on the line.
Putting x = 0 in the equation y = -2/5x
y = -2/5 × (0)
y = 0
Thus, (0, 0) is the point which also passes through the line
Putting x = 5 in the equation y = -2/5x
y = -2/5 × 5
y = -2
Thus, (5, -2) is the point which also passes through the line
Now, putting x = 10 in the equation y = -2/5x
y = -2/5 × 10
y = -4
Thus, (10, -4) is the point which also passes through the line.
Thus, the three points that lie on a line y = -2/5x with a slope -2/5 will be:
(0, 0)(5, -2)(10, -4)Please check the attached graph also.
Which equation represents the rectangular form of Theta = StartFraction 5 pi Over 6 EndFraction?
StartRoot 3 EndRoot x minus y = 0
StartRoot 3 EndRoot x + y = 0
StartRoot 3 EndRoot x minus 3 y = 0
StartRoot 3 EndRoot x + 3 y = 0
Answer:
D. StartRoot 3 EndRoot x + 3 y = 0 (or √3x + 3y = 0)Step-by-step explanation:
This is about converting polar coordinate to rectangular
Relationship between coordinates is:
x = r cosθy = r sinθthen
y/x = sinθ/cosθy/x = tanθWe have θ = 5π/6, finding the value of tan:
tan 5π/6 = tan (π - π/6) = - 1/√3 = - √3/3Substitute tan with its value:
y/x = -√3/3 3y = -√3x3y + √3x = 0√3x + 3y = 0Correct option is D
Answer:
I did option d !!
Step-by-step explanation:
All functions have a domain of R (all real numbers).
True
Or False
Answer:
True
Step-by-step explanation: Trust me
PLEASE ANSWER ASAP I WILL MARK BRAINLIEST WHEN ANSWERING PLZ PUT ANSWER IN ORDER PLS THANK YOU :)
1.) Dana has 5 times as many french fries as Abdullah and Abdullah has twice as many French Fries as Jonathan. If they have 26 French Fries all together, how many does Dana have? ALSO
2.) After finishing their fries, they pooled all their money to buy as much soda as they could. Dana had $5.12. Abdullah had $2.77 and Jonathan had only $4. If soda is $1.99 for a 2-liter bottle, how many bottles could they purchase?
Answer:
Dana has 20 French fries.
They can purchase 5 bottles.
Step-by-step explanation:
1.
Let x rep. the amount of French fries Johnathan has.
Let 2x rep. the amount of French fries Abdullah has.
Let 10x rep. the amount of french fries Dana has.
If :
x+2x+10x=26
13x=26
x=2
So Johnny boy has 2 french fries which means Dana has 10 times as much as that.
10(x)=10(2)
10x=20
Therefore Dana has 20 French fries.
2.
Well
5.12+2.77+4=$11.89
11.89/1.99= APPROX. 5.9
Note you can't buy a fraction of a bottle. We gotta round down for this question cause you can't just give less amount of cash to get an extra bottle even if it's very close. Unless your teacher said to round something.
Therefore they can only purchase 5 bottles.
PLEASE ANSWER! WILL GIVE BRAINLIEST!
ardith has 3/71 x 10^7 bytes of space remaining on a flash drive. she needs to copy some files each of which is about 8.2 x 10^4 bytes in size, onto the flash drive. about how many files can ardith copy onto the flash drive?
Answer:
5
Step-by-step explanation:
Given that:
Space left on flash drive = 3/71 * 10^7 bytes = 0.0422535 * 10^7 = 422535.21 bytes
Size of each file = 8.2 * 10^4 bytes = 82000 bytes
Number of files that can be copied :
(422535.21) / (82000)
= 5.1528684
Number of files that can be copied = 5 files
What is an equation of the line that passes through the point (-6, -3) and is
parallel to the line 5x – 3y = 9?
Answer:
Submit Answer
9514 1404 393
Answer:
5x -3y = -21
Step-by-step explanation:
The parallel line will have the same x- and y-coefficients, but a constant suitable for the given point.
5x -3y = constant
5(-6) -3(-3) = constant = -30 +9 = -21
The equation of the line is ...
5x -3y = -21
Find the value of x that makes mll n.
150°
(3x-15)
Answer:
[tex]3x - 15 = 150 \\ 3x = 165 \\ x = 55[/tex]
55° is the right answer.Consider the following ordered data.6 9 9 10 11 11 12 13 14(a) Find the low, Q1, median, Q3, and high.(b) Find the interquartile range.
Answer:
6 ; 9 ; 11 ; 12.5; 14
B.) 3.5
Step-by-step explanation:
Given the data:
6 9 9 10 11 11 12 13 14
a.) The low = 6 (lowest value in the dataset)
b.) Q1 = Lower quartile
Q1 = 1/4(n + 1)th term
n = sample size = 9
Q1 = 1/4(9 + 1) ; 1/4(10) = 2.5th term
Q1 = (2nd + 3rd term) / 2 = (9 + 9) / 2 = 9
Median Q2:
Q2 = 1/2(9 + 1) ; 1/2(10) = 5th term = 11
Upper Quartile Q3:
Q3 = 3/4(9 + 1) ; 3/4(10) = 7.5th term
Q3 = (7th + 8th term) / 2 = (12 + 13) / 2 = 12.5
Interquartile range (Q3 - Q1)
(12.5 - 9) = 3.5
The high = 14 (highest value in the dataset)
Billy was standing on a diving board that was 4 feet above the water. He dove into the pool which was 8 feet deep and touched the bottom. Which statement accurately describes this
situation?
Solve -9 < 4x+3 5 11.
A. x>-3 and xs 2
B. x>3 or xs 2
C. x>-3 or xs 2
D. x > 3 and xs3
3 tiles are red 6 tiles are green 3 tiles are blue a tile will be randomly selected from the bag. What is the probability that the tile selected will be green?
Answer:
80 percent
Step-by-step explanation:
Because there are green tiles so the possibility is 80 percent
Rachel and David were shopping for holiday gifts when they noticed a Thanksgiving sweater on the discount rack. Rachel really wanted the sweater, even though she wouldn’t be wearing it until Thanksgiving of 2021! Part A: If the original price of the sweater was $24.00, and the sweater is on sale for 60% off, what is the sale price?
Answer:
$9.60Step-by-step explanation:
Original price = $24Discount = 60%Discount amount:
$24*0.6 = $14.40Sale price:
$24 - $14.40 = $9.60Answer:
9.60
Step-by-step explanation:
i did the quiz
Find the slope of the line that contains the following points:
(5, 4) and (3, -4)
Answer:
slope = 4
Step-by-step explanation:
y2-y1/x2-x1 = slope
-4 - 4 / 3 - 5 = slope
-8/-2 = slope
8/2 = slope
4/1 = slope
4 = slope
Ema’s family has completed 60% of a trip. They have traveled 45 miles. How far is the trip?
Answer:
72 miles
Step-by-step explanation:
60% times 45 = 27
27 + 45 = 72
Answer is 72 miles
Answer:
Ema's Family would drive 72 miles
Step-by-step explanation:
Hope this helps :)
And I hope this is correct
A town in east Texas received 10 inches of rain in two DAYS. If it kept raining at this rate for a 31 day month, how much rain did the town receive? 11
This is equivalent to approximately 12.917 feet.
===================================================
Work Shown:
(10 inches)/(2 days) = (x inches)/(31 days)
10/2 = x/31
10*31 = 2*x ... cross multiply
310 = 2x
2x = 310
x = 310/2
x = 155
Keep in mind that this water is being drained on a fairly continuous basis. This means that not all of the water is sticking around (we'd hope not anyway) at the same moment in time.
Note: 155 inches = 155/12 = 12.917 feet approximately.
--------------------------
Alternative method:
If the town got 10 inches in 2 days, this means it rains at a unit rate of 10/2 = 5 inches per day.
Multiply that by 31 days and we get 5*31 = 155 inches of total rain.
Anna bought 120 feet of copper
wire. She cut it into 16 pieces of
the same length. How long is one
piece of copper wire?
Answer:
7 1/2 feet
Step-by-step explanation:
⚠️please help!!!⚠️
find the value of x then find the measure of the labeled angle
x°=.......°
(x-35)°=......°
Step-by-step explanation:
x° + (x - 34)° = 180°. (C-angles)
Thereforr 2x - 34 = 180 and x = 107.
x° = 107°.
(x - 34)° = 73°.
A 1/2-mile long train enters a 2-mile long tunnel traveling at a speed of 10 mi/h. How many minutes pass from the time the front of the first train car enters the tunnel until the rear of the last train car exits the tunnel?
Answer:
15 minStep-by-step explanation:
The distance required is the length of the tunnel added to the length of the train
d = 1/2 + 2 = 5/2 miless = 10 mile/hour = 10/60 mile/min= 1/6 mile/minTime is:
t = d/st = 5/2 : 1/6 = 5/2*6= 15 minI have three marbles in a bag. One is purple and the other two are green. What is the probability of pulling a green marble out of the bag?
Answer:
1/3 would be the chances you'd pick purple, because there's only 1 in 3 that's purple out of all 3 marbles.
With green it would be 2/3 because there's twice the number of green marbles than purple.
If there's 1 of purple and 1 of green, the probability would then be 1/2 of picking either colour.
I need help anyone can anyone help
Answer:
14
Step-by-step explanation:
The perimeter is the sum of the sides, so we have
2x+x+15+4x-7=57
= 7x+8
Subtracting 8 from both sides, we get
7x= 49
Dividing 7 from both sides, we get
x=7
Our sides are then 2x=14, x+15=22, and 4x-7=21. 14 is our answer
Answer:
The shortest length of the triangle is: 14
Hence, option B is correct.
Step-by-step explanation:
Given the triangle with the lengths
[tex]x+15[/tex][tex]4x-7[/tex][tex]2x[/tex]Given that the perimeter of triangle = P = 57
We know that the perimeter of a triangle is the sum of the lengths of the sides of a triangle.
so
[tex]P = (x+15)+(4x-7)+(2x)[/tex]
substitute P = 57
[tex]57 = (x+15)+(4x-7)+(2x)[/tex]
switch sides
[tex]\left(x+15\right)+\left(4x-7\right)+\left(2x\right)=57[/tex]
[tex]x+15+4x-7+2x=57[/tex]
Group like terms
[tex]x+4x+2x+15-7=57[/tex]
Add similar elements
[tex]7x+15-7=57[/tex]
[tex]7x=49[/tex]
divide both sides by 7
[tex]\frac{7x}{7}=\frac{49}{7}[/tex]
simplify
[tex]x=7[/tex]
Now, measuring the lengths by substituting x = 7
[tex]x+15 = 7+15 = 22[/tex][tex]4x-7 = 4(7)-7 = 28 - 7 = 21[/tex][tex]2x = 2(7) = 14[/tex]Therefore, the shortest length of the triangle is: 14
Hence, option B is correct.
HELP ME PLS I REALLY NEED HELP THIS MAH LAST QUESTION
Answer:
number 1
Step-by-step explanation:
Please help!!!!!!!!
Answer:
He rode 20 miles in 2 hours
Is there enough information to prove that the triangles are congruent?
If yes, provide the correct Triangle Congruence Postulate or Theorem and a
congruence statement,
If no, justify your answer.
Answer:
Yes, there is enough information to prove that the triangles are congruent.
ASA POSTULATE
Step-by-step explanation:
[tex] In\:\triangle PQR \: and \triangle TSR\\[/tex]
[tex] \angle PQR \cong \angle TSR...(given) \\[/tex]
[tex] QR\cong SR..... (given) \\[/tex]
[tex] \angle PRQ \cong\angle TRS\\(Vertical \: \angle s) \\[/tex]
[tex] \therefore \triangle PQR \cong \triangle TSR\\(ASA\: postulate) [/tex]
Answer:
YesStep-by-step explanation:
Given
One angle and a side of one triangle are congruent to same on another triangleAlso angle R is vertical and therefore equal for both trianglesWe have two angles and included side congruence which is ASA