find the values of a, b and c in the equation below (x^5yz^4)^3/x^3yz= x^a y^b z^c
Answers
Answer: a = 12, b = 2, c = 11
Step-by-step explanation:
Using exponent rules we can distribute the exponent of 3 to the xyz.
This results in the numerator now being. [tex]x^{5*3}+y^{1*3}+z^{4*3}\\[/tex] This can be simplified to, [tex]x^{15}y^{3}z^{12}\\[/tex].
Now divide the numerator by the denominator subtracting the exponents.
Which equals, [tex]x^{12}y^{2}z^{11}[/tex]
So a = 12
b = 2
and
c = 11
The values of [tex]a, \ b,\ c[/tex] are [tex]12,\ 2,\ 11[/tex] .
What are exponent ?Exponent indicates that the base is to be raised to a certain power. So, it is the power of the base.
We have,
[tex]\frac{(x^5yz^4)^3}{x^3yz}=x^ay^bz^c[/tex]
Now simplify the above given equation;
[tex]\frac{(x^5*3y^1*3z^4*3)}{x^3yz}=x^ay^bz^c[/tex]
[tex]\frac{(x^{15}y^3z^{12})}{x^3yz}=x^ay^bz^c[/tex]
Now, Using the exponent rule;
[tex]\frac{a^n}{a^m} = a^{n-m}[/tex]
So,
[tex](x^{15-3}y^{3-1}z^{12-1})=x^ay^bz^c[/tex]
[tex](x^{12}y^{2}z^{11})=x^ay^bz^c[/tex]
Now,
As we see variables on both sides of equation are same (i.e. bases of powers are same), so now compare the powers of sides of variables;
⇒ [tex]x^{12}=x^a[/tex]
[tex]a=12[/tex],
And, [tex]y^2=y^b[/tex]
[tex]b=2[/tex]
And, [tex]z^{11}=z^c[/tex]
[tex]c=11[/tex]
So, the values of [tex]a, \ b,\ c[/tex] are [tex]12,\ 2,\ 11[/tex] which are find out using the exponent rule.
Hence, we can say that the values of [tex]a, \ b,\ c[/tex] are [tex]12,\ 2,\ 11[/tex] .
To know more about exponent click here
https://brainly.com/question/5497425
#SPJ3
Related Questions
Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the eastbound car has traveled 12 kilometers. If the two cars are now a straight-line distance of 15 kilometers apart, how far has the northbound car traveled?
Answers
Answer 3 kilometers
15 kilometers total minus 12 kilometers of the east bound car leaves only 3 kilometers for the northbound car to travel.
At a baseball game, 70% of people attending were supporting the home team, while 30% were supporting the visiting team. If 350 people attending the game supported the home team, what was the total number of people attending the game?
Answers
Answer:500 people
Step-by-step explanation:
70% = 0.70
.70x = 350
x = 350/.70
x = 500
How much water can fill this cylinder with diameter of 3m and height of 8cm
Answers
Answer:
0.565 m^3 to the nearest thousandth.
Step-by-step explanation:
The volume of the cylinder = π r^2 h
Here the radius r = 1/2 diameter
= 1/2 * 3 = 1.5 m
8 cm = 0.08 m.
So the volume = π (1.5)^2 * 0.08
= 0.565 m^3 to the nearest thousandth.
determine the diameter
Answers
Answer:
2.75 cm
Step-by-step explanation:
You can multiply the diameter by the scale factor to find the size of the diameter on a scale diagram.
55 * 0.05 = 2.75 cm
One cubic centimeter will hold 1 milliliter of water. How many milliliters will the aquarium hold? How many liters will it hold? LOADING... Click the icon to see the metric units of capacity. 40 cm 30 cm 50 cm The aquarium will hold nothing mL of water.
Answers
Answer:
The aquarium hold 60000 ml and in liters is 60 liters
Step-by-step explanation:
Length of aquarium = 40 cm
Breadth of aquarium = 30 cm
Height of aquarium = 50 cm
Volume of tank =[tex]Length \times Breadth \times Height[/tex]
Volume of tank = [tex]40 \times 30 \times 50[/tex]
Volume of tank =[tex]60000 cm^3[/tex]
Now , 1 cubic cm = 1 ml
60000 cubic cm = 60000 ml
Now 1000 ml = 1 l
60000 ml = [tex]\frac{60000}{1000}=60 liters[/tex]
So, the aquarium hold 60000 ml and in liters is 60 liters
Can anyone help me find the equation of the line that has been graphed?
Answers
Answer:
y=3/2x+6
Step-by-step explanation:
Slope-intercept form: y=mx+b
Slope: (y2-y1)/(x2-x1)
(-2, 3) and (2, 9)
6/4
3/2
Y intercept, (0, 6)
y=3/2x+6
Write a quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, −17).
f(x)=
Answers
Answer:
x^4 +y+1
Step-by-step explanation:
The quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, -17) is [tex]-17(x-1)^{2}[/tex].
What is vertex form of a quadratic function?The vertex form of a quadratic function is [tex]f(x) = a(x-h)^{2} + k[/tex] where a, h, and k are constants and (h, k ) is the vertex of the graph of the function.
According to the given question we have
The graph has the vertex is (1, 0) and passes through (2, -17)
Since, the general form of a quadratic function in a vertex form is
[tex]y = a(x-h)^{2}+ k[/tex]
substitute, h = 1 and k = 0 in the above equation
⇒ [tex]y = a(x-1)^{2} +(0)^{2}...(i)[/tex]
Also, the graph passes through the point (2, -17)
⇒ [tex]-17 = a(2-1)^{2}[/tex]
⇒ -17 = a or a = -17
Substitute the value of a in equation (i).
⇒[tex]y = -17(x-1)^{2}[/tex]
Therefore, the quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, -17) is [tex]-17(x-1)^{2}[/tex].
Learn more about quadratic function in vertex form here:
https://brainly.com/question/13921516
#SPJ2
Which expression represents the perimeter of the triangle shown below?
Answers
Answer:
a)2x2+x-1Step-by-step explanation:
perimeter is the sum of sides of a triangle or length of botder
Hey the question is attached pls answer
Answers
Answer:
55%
Step-by-step explanation:
We need to first find the total length of the side.
let remaining length be x
perimeter= 40cm
4 (s)=perimeter
4(7+x)=40
28+4x=40
4x=40-28=12
4x=12
x=12/4=3
total length= 7+3= 10cm
4+y= 10=
y=6
therefore, area of square= s*s= 10*10=100cm²
find areas of the two triangles (unshaded).
1/2*3*10= 15cm²
1/2*6*10= 30 cm²
15/100*100= 15%
30/100*100= 30%
shaded percentage= 100-(15+30)
= 100-45
= 55%
Which of the following is the midsegment of AABC?
Answers
Answer:
Option D is the correct answer
Step-by-step explanation:
[tex] \overline{LM} [/tex] is the mid segment of [tex] \triangle ABC [/tex]
What is the measure of ∠S?
Answers
Answer:
30
Step-by-step explanation:
These two triangles are similar, thus they have equal angle measures.
Answer:
30
Step-by-step explanation:
all the interior angles in the triangle adds up to 180
85 + 65=150
180-150=30
Please help with part b
Answers
Answer:
We have to use the summation in this case.
Step-by-step explanation:
total/frequency=mean
frequency= 2 + 8 + 4 + 10 + 6=30
0*2=0
1*8=8
2*4=8
3*10=30
4*6=24
total= 70
70/30= 7/3= 2.33333... ≈ 2 (goals cannot be in decimals!)
This should be the answer, I hope.
solve. Eight less than 7 times a number is 6. Find the number.
Answers
The word "less than" switches the order around.
So instead of 8 - 7n = 6, our equation is 7n - 8 = 6.
Solving from here, we add 8 to both sides to get 7n = 14.
Now divide both sides by 7 to get n = 2.
Answer:
The number is 2
Step-by-step explanation:
The fastest way to solve this it to retrace the steps. So.....
(7)(x)-8=6
6+8=14
14/7=2
Thus, 2 is your answer.
1) An $1,000 investment is made in a trust fund at an annual percentage rate of 12%, compounded monthly. How long will it take the investment to reach $2,000?
2)If a $100 deposit is made at a bank that pays 12% per year, compounded annually, determine how long it will take for the investment to reach $2000.
3)Kelly invests $5000 with a bank. The value of her investment can be determined using the formula Y=5000(1.06)^t, where y is the value of the investment at time t, in years. Approximately how many years will it take for Kelly's investment to reach $20,000?
4)$2000 is invested at 5% per year, compounded semi-annually. How long will it take for the investment to triple in value?
Answers
Answer:
33 years, 7 months
Step-by-step explanation:
Using the compound interest formula Accrued Amount = P (1 + r/n)^(nt)
where Accrued amount (A) is the expected future balance
A = $8000
P = principal; $5000
r = 1.4% = 0.014
t = number of years
n = number of times interest is compounded = 12 for monthly
Therefore
8000 = 5000 (1 + 0.014/12)^(12t)
Therefore
(1.001167)^12t = 8000/5000
(1.001167)^12t = 1.6
finding the log of both sides
12t x log 1.001167 = log 1.6
12t = log 1.6 / log 1.001167
12t = 402.98
t = 402.98/12
t = 33.58
hence time to increase the balance is 33 years, 7 months
100 points. Fun question to do.
1: Find something in your home (a product) that has a percentage on the label.
2: Describe your product (short description 1-2 sentences, explaining the
product, what it is, its purpose, etc.)
3: Answer the following: Explain what the percentage is referring to – what does
it tell you about the product? Why is it included on the label?
4: Make a visual model/picture of some kind that represents the percentage
listed on your product’s label.
Answers
Answer:
Step-by-step explanation:
1.Wound wash
2.It helps wounds
3a.to the materals
3b.to tell whats in the product.
2 It is a paste used to brush teeth and usually prevents a variety of dental issues
3.Stannous Fluoride - tells what’s it does and such
What is the sum of the geometric sequence 1, 3, 9, … if there are 14 terms?
Answers
A group of 80 students in a college are surveyed. They are asked which of Spanish or French they are studying. a) complete the Venn Diagram. b) How many students study ONLY French c) How many students study Spanish?
Answers
Answer:
a) Find attached the completed Venn diagram (2nd diagram)
b) 25
c) 46
A related Question found at brainly (ID 16765143):
A group of 80 students in a college are surveyed. They are asked which of Spanish or French they are studying. 71 of the students surveyed studies at least one of the two languages.
a) Complete the Venn diagram.
b) How many students study only french?
c) How many students study Spanish?
Step-by-step explanation:
Find attached the Venn diagram (1st diagram)
a) Total number of students in college = 80
Since 71 out of the 80 students surveyed studies at least one of the two languages, the number of students that studied neither French nor Spanish = 80-71 = 9
From the venn diagram:
Number of students that study Spanish = 14
Number of students that study French = 25
We need to determine if the values are for Spanish only and French only respectively or for at least Spanish and French respectively.
Estimated value for the middle term = 80-(14+25+9) = 32
From the above calculation, the number of students that study both Spanish and French is 32 and it is more than each set value. This implies the value given in the Venn diagram is for Spanish only and French only respectively.
Let number of students that study both Spanish and French = x
Spanish only = 14
French only = 25
the number of students that studied neither French nor Spanish = 9
Total:
14 + 25 + x + 9 = 80
48 + x = 80
x = Number of students that study both Spanish and French = 32
b) French only = 25
c) Number of students that study Spanish = students that study at least Spanish
= 14+x = 14+32
Number of students that study Spanish = 46
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!
Answers
A. subtract the bottom equation from the top equation
Step-by-step explanation:
The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.
// have a great day //
The linear question y=-2x+4 is represented on the graph below
(2,0)
(0,4)
(0,-1)
(4,-4)
Answers
Which of the following looks the most like a straight angle?
A. The letter I
B. The letter T
C. The letter X
D. The letter O
Answers
The letter I
hope it helps
Answer:
The letter l
Answer A is correct
hope this helps
brainliest appreciated
good luck! have a nice day!
Which statement best explains why this expression is equal to 9.4?
Answers
Answer:
Where is the answers, they might help.
Answer:
Any number multiplied by 0 is 0
Step-by-step explanation:
imagine math answer.
Solve for x. Enter the solutions from least to greatest.
x2 – X – 12 = 0
Answers
Answer:
x=-3 or 4
Step-by-step explanation:
what attributes of a solid figure should you identify to classify it as a polyhedron HELP ME ASAP PLEASE!!!!!!
Answers
Answer:
If all the sides of the solid are flat, then it is said to be a polyhedron
Step-by-step explanation:
Given: a polyhedron
To find: attributes of a solid figure to classify it as a polyhedron
Solution:
A polyhedron is a three-dimensional figure with flat faces as polygons. It has straight edges and sharp vertices. It is made by joining polygons together.
If all the sides of the solid are flat, then it is said to be a polyhedron but if the solid has at least one curved side, then it is not a polyhedron.
Please answer this math question !! Thank u !! 20 POINTS AND BRAINLIEST!!
Answers
Answer:
x=2, y=3
Step-by-step explanation:
y = 3
3x-y =3
Substitute y =3 into the second equation
3x -3 =3
Add 3 to each side
3x-3+3 = 3+3
3x=6
Divide by 3
3x/3 = 6/3
x =2
Answer:
(2,3)Step-by-step explanation:
y=3
3x-y=3
lets plug in 3 for y
3x-3=3
3x=6
x=2
the solution to this linear system of equations is:
(2,3)
Find the area of the circle use 3.14 for
Answers
Answer: 153.86 cm²
Step-by-step explanation: To find the area of the circle shown here, start with the formula for the area of a circle which is A = πr².
Notice that here, we're given the diameter instead of the radius.
Remember that the radius is equal to half of the diameter.
So the radius of this circle will be equal to half of 14 cm or 7 cm.
So plugging into the formula, we have (π)(7 cm)².
A common mistake is to plug 14 cm into the formula but remember
that we must plug in the radius and not the diameter.
Multiplying, (7 cm)² is equal to (7 cm)(7 cm) or 49 cm².
So we have 49π cm².
So the area of the circle shown here is 49π cm².
Now, remember that π is approximately equal to 22/7 or 3.14 so we
can estimate the area of the circle by plugging in 3.14 for π.
So we have (49)(3.14) which is equal to 153.86 cm².
So the area of the circle is approximately equal to 153.86 cm².
what is the remainder of 2 ^1026 divided by 5
Answers
Transform expression: 2^20535/2
Simplify root: √2^20535
Solution: 2^10275 x √2
Find the average speed of a car that is travelling 45 km in 5 hours. *
4 points
6 km/h
8 km/h
9 km/h
20 km/h
Answers
Answer:
8km/h
Step-by-step explanation:
Given:
Distance ,d = 45 kmTime taken, t = 5 hoursTo be calculated:
Calculate the average speed of a car ?
Formula used :
Average speed = Distance/Time
Solution:
We know that,
Average speed = Distance/Time
☆ Substituting the values in the above formula, we get
Average speed = 45 km / 5 h
= 9 km/h
Thus, the average speed of a car is 9 km/h .
What is the solution to this equation?
–5(s – 30) = –10
A. s = –4
B. s = 8
C. s = 28
D. s = 32
Answers
Answer:
s = 32
Step-by-step explanation:
–5(s – 30) = –10
Divide each side by -5
–5/ -5(s – 30) = –10/-5
s - 30 = 2
Add 30 to each side
s-30+30 = 2+30
s = 32
Answer:
D. s=32
Step-by-step explanation:
To solve the equation, we want to find out what s is. In order to do this, we have to get s by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
–5(s – 30) = –10
s-30 is being multiplied by -5. The opposite of multiplication is division. Divide both sides by -5.
–5(s – 30)/-5= –10/-5
s-30=-10/-5
s-30=2
30 is being subtracted from s. The opposite of subtraction is addition. Add 30 to both sides.
s-30+30=2+30
s=2+30
s=32
Let's check our solution. Substitute 32 in for s in the original equation. If our solution is correct, the left side of the equation should match the right side.
–5(s – 30) = –10
-5(32-30)=-10
-5(2)= -10
-10=-10
The statement above is true, so we know that s is equal to 32, and D is the correct answer.
The equation of the graphed line is 2x-3y=12 what is the x-intercept of the graph ?
Answers
Answer:
(6,0)
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
correct on edg :)
The highest and lowest scores on a test taken by 80 students are within 19 points of the average of the exam. The average for this exam was 72. Set up an equation to solve for the highest and lowest scores. Show your original equation and the process used to find the highest and lowest exam score.
Answers
Answer:
The highest score is 91 and the lowest score is 53
Step-by-step explanation:
The highest and lowest scores on a test taken by 80 students are within 19 points of the average of the exam. The average is 72.
1. The method used to solve this question, is the use of absolute values.
2. Let x be the value that we can use to represent the lowest and highest scores. The equation using absolute values is given as:
| x - 72 | = 19.
Therefore:
x - 72 = 19 (highest score) or
- (x - 72) = 19 (lowest score)
3. We have to find the value of x for which it is the highest or lowest score.
The highest score is given as:
x - 72 = 19
x = 19 + 72
x = 91
For lowest score:
-(x - 72) = 19
-x + 72 = 19
x = 72 - 19
x = 53
The highest score is 91 and the lowest score is 53