Place the indicated product in the proper location on the grid.
(3a + 2c )(9a 2 - 6ac + 4c 2 )
Answers
27a^3+8c^3
Explanation.
In this question you are expected to expand (3a+2c)(9a^2-6ac+4c^2
(3a+2c)(9a^2-6ac+4c^2
=(3a×9a^2 )-(3a×6ac)+(3a×4c^2 )+(2c×9a^2 )-(2c×6ac)+(2c×4c^2 )
27a^3-18a^2 c+12ac^2+18a^2 c-12ac^2+8c^3
27a^3+8c^3
The expansion of the expression, (3a+2c)(9a^2-6ac+4c^2) is 27a^3+8. This is what the question requires.
Answer:
The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]
Step-by-step explanation:
Given: Polynomial [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]
We have to place the indicated product in the proper location o the grid.
Consider the given product [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]
Using distributive property, Multiply each term of first bracket with each term of last bracket, we have,
[tex]=3a\cdot \:9a^2+3a\left(-6ac\right)+3a\cdot \:4c^2+2c\cdot \:9a^2+2c\left(-6ac\right)+2c\cdot \:4c^2[/tex]
Apply plus-minus rule [tex]+\left(-a\right)=-a[/tex] , we have,
[tex]=3\cdot \:9a^2a-3\cdot \:6aac+3\cdot \:4ac^2+2\cdot \:9a^2c-2\cdot \:6acc+2\cdot \:4c^2c[/tex]
Simplify, we have,
[tex]=27a^3-18a^2c+12ac^2+18a^2c-12ac^2+8c^3[/tex]
Adding similar terms, we have,
[tex]=8c^3+27a^3[/tex]
Thus, The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]
Location on grid is as shown below
Related Questions
Two or more lines on a graph together is known as a
Answers
If a force of 60 N is exerted on a 15 kg object, calculate the acceleration that the object undergoes. ________ m/s2 4 900 0.25 40
Answers
Then:
a=F/m
a=60/15=4 m/s²
Answer: The correct option is
(A) 4 m/s.
Step-by-step explanation: We are given that a force of 60 N is exerted on a 15 kg object.
We are to calculate the acceleration that the object undergoes.
From Newton's second law of motion, we have
[tex]F=ma,[/tex] where m is the mass of the object, a is the acceleration and F is the force exerted.
For the given object, we have
F = 60 N and m = 15 kg.
So, we get
[tex]F=ma\\\\\Rightarrow 60=15\times a\\\\\Rightarrow a=\dfrac{60}{15}\\\\\Rightarrow a=4.[/tex]
Thus, the required acceleration that the object undergoes is 4 m/sec.
Option (A) is CORRECT.
Which term describes what a manufacturer spends for goods or services?
a)cost
b)price
c)markup
Pleas help. Willl fan and medal!!
Answers
The term describing what a manufacturer spends for goods or services is cost. Cost is the expenses incurred by the manufacturer as a result of his business or undertaking. There are two types of cost of a manufacturer. The cost of goods sold and the operating expenses. The cost of goods sold are those cost incurred directly as a result of manufacturing. The operating expenses are those other expenses not indirectly involved with the manufacture of goods or services.
A machine packs at a constant rate of 2/3 of a box every 1/2 minuet. What’s is the number of boxes per minute that’s the machine packs?
Answers
2/3 of a box ------> 1/2 minutes
x of a box ---------> 1 minute
Clearing x we have:
x = (1 / (1/2)) * (2/3)
Rewriting:
x = 2 * (2/3)
x = 4/3
Answer:
the number of boxes per minute that the machine packs is:
x = 4/3
For a machine, the output force is 20 N, and the output distance is 4 m. Which must be true about the work input? A. It equals 80 J. B. It must be greater than 80 J. C. It must be less than 80 J.
Answers
Work = (20 N)*(4 m)
Work = (20*4) Nm
Work = 80 J
So 80 joules of work is the output. Ideally we'd expect 80 J to be the input but that's not the case. There will always be things like heat loss, leading to some level of inefficiency. So if we input some amount of work, say 100 J, then it might drop to 80 J of actual output work after the wasted energy is accounted for.
In short, you have to put more work in than the work you want out. This is why the answer is choice B) It must be greater than 80 J
10 POINTS + BRAINLIEST ANSWER
A box contains 30 pieces of chocolate, distributed as shown in the table below. Each piece is made of either white chocolate or dark chocolate, and each piece contains either cream filling or no filling. If one piece is selected at random, what is the probability that the piece is either white chocolate with cream filling or dark chocolate with no filling? (10 POINTS + BRAINLIEST ANSWER)
A. 8/30
B. 12/30
C. 20/30
D. 22/30
Answers
8/30
I need 20 characters
The probability of selecting a chocolate at random that is either white chocolate with cream filling or dark chocolate with no filling is [tex]\frac{8}{30}[/tex].
What is probability?Probability is the chance of happening an event or incident.
Given, the box contains 30 chocolates.
The number of chocolates that are white chocolate with cream filling is 5.
Therefore, the probability of selecting a chocolate at random that is white chocolate with cream filling is [tex]= \frac{5}{30}[/tex].
The number of chocolates that are dark chocolate with no filling is 3.
Therefore, the probability of selecting a chocolate at random that is dark chocolate with no filling is [tex]= \frac{3}{30}[/tex].
Now, the probability of selecting a chocolate at random that is either white chocolate with cream filling or dark chocolate with no filling is
[tex]= \frac{5}{30} + \frac{3}{30} \\= \frac{8}{30}[/tex]
Learn more about probability here: https://brainly.com/question/28001361
#SPJ2
PLEASE HELP QUICK!!!!
11PTS AND BRAINLIEST AVAILABLE TO CORRECT ANSWER
Answers
darren has 3/4 of a gallon of soil.he needs to plant 5 small plants.if he splits the soil evenly between the plants.how much soil will each plant get?
Answers
3/4 x 1/5 = 3/20 of a gallon
The population P(t) of a species satisfies the logistic differential equation dP/dt= P(2-(P/5000)) where the initial population 3,000 and t is the time in years. What is the lim t>infinity P(t)?
Answers
[tex] \frac{dP}{dt} = rP[1- \frac{P}{K}] [/tex]
where r = growth parameter and K = carrying parameter.
In order to write you equation in this form, you have to regroup 2:
[tex] \frac{dP}{dt} = 2P[1- \frac{P}{10000}] [/tex]
Therefore, in you case r = 2 and K = 10000
To solve the logistic differential equation you need to solve:
[tex] \int { \frac{1}{[P(1- \frac{P}{K})] } } \, dP = \int {r} \, dt [/tex]
The soution will be:
P(t) = [tex] \frac{P(0)K}{P(0)+(K-P(0)) e^{-rt} } [/tex]
where P(0) is the initial population.
In your case, you'll have:
P(t) = [tex] \frac{3E7}{3E3+7E3 e^{-2t} } [/tex]
Now you have to calculate the limit of P(t).
We know that
[tex] \lim_{t \to \infty} e^{-2t} -\ \textgreater \ 0 [/tex]
hence,
[tex] \lim_{t \to \infty} P(t) = \lim_{t \to \infty} \frac{3E7}{3E3+0} = 10^{4} [/tex]
The lim t>infinity P(t) is 5,000, which is the carrying capacity of the species.
Explanation:The logistic differential equation dP/dt = P(2-(P/5000)) models the population growth of a species. To find the lim t>infinity P(t), we need to find the stable population when t becomes very large. In this equation, the population growth rate is initially exponential, but as the population approaches its carrying capacity (Q), the growth rate slows down and levels off to zero.
Solving the differential equation, we find that the equation represents logistic growth. The solution to the equation is P(t) = Q / (1 + (Q/Po)e^(-rt)), where Po is the initial population, Q is the carrying capacity, and r is the growth rate.
In this case, the initial population is given as 3,000. To find the carrying capacity (Q), we set dP/dt = 0 and solve for P. Substituting the values into the equation, we find Q = 5,000.
As t becomes very large, e^(-rt) approaches 0, and the equation simplifies to P(t) = Q. Therefore, the lim t>infinity P(t) is 5,000, which is the carrying capacity of the species.
find the solution of this system of equations shown on the graph.
Answers
hope it helps
Please help asap!!!! 53 points!
Answers
The line above intercepts the y-axis at y = -2, which is b. The slope (m) = rise/run = (y2-y1)/(x2-x1 ); so for the point (-4, 2) to (-6, 4) is:
(4-2)/(-6--4) = 2/(-6+4) = 2/-2 = -1.
So one form of the equation would be:
y = -1x - 2
Now the other form of an equation is point-slope: y-k = m (x-h), where the point is at (h, k)
and if we pick -5 for x (bc 5 it listed in 3 of the answers), the y at x=-5 looks like around +3
so we get: y-k = -1 (x--5)...
y-3 = -(x+5)... therefore D) is the correct answer:
Simplify these 12 radicals:
1) √80 2) √64
3) √45 4) √54
5) √32 6) √36
7) √150 8) √20
9) √180 10) √72
11) √8 12) √50
Answers
[tex]4 \sqrt{5} [/tex]
2)
[tex]8[/tex]
3)
[tex]3 \sqrt{5} [/tex]
4)
[tex]3 \sqrt{6} [/tex]
5)
[tex]4 \sqrt{2} [/tex]
6)
[tex]6[/tex]
7)
[tex]5 \sqrt{6} [/tex]
8)
[tex]2 \sqrt{5} [/tex]
9)
[tex]6 \sqrt{5} [/tex]
10)
[tex]6 \sqrt{2} [/tex]
11)
[tex]2 \sqrt{2} [/tex]
12)
[tex]5 \sqrt{2} [/tex]
Which group of measurements could be the side lengths of a right triangle?
A.
57 in, 86 in, 95 in
B.
47 in, 76 in, 95 in
C.
57 in, 76 in, 95 in
D.
57 in, 76 in, 105 in
Answers
if the hypotenuse is H and other 2 sides are A and B, then equation is as follows;
H² = A² + B²
1. A - 57 in. B - 86 in.
H² = A² + B²
H² = 57² + 86²
H² = 3249 + 7396
H = √10645
= 103.17 in.
third side given is not 103 in therefore this is not a right angled triangle
2. A - 47 in. B - 76 in.
H² = A² + B²
H² = 47² + 76²
= 2209 + 5776
H = √7985
H = 89.3 in.
third side given is 95 in. therefore this is not a right angled triangle.
3. A- 57 in. + B - 76 in.
H² = A² + B²
H² = 57² + 76²
= 3249 + 5776
H = √9025
H = 95 in.
third side given is 95 in. therefore this is a right angled triangle.
4. A - 57 in. B - 76 in.
As calculated in the third equation with the same side lengths of A and B, hypotenuse should be 95 in. however the third side length given is 105 in. so this is not a right angle triangle
If 8900 is invested at 3.8%
Answers
If $8,900 is invested at 3.8% interest compounded quarterly, how much will the investment be worth in 13 yrs?
A.$14,551.87
B.$14,518.40
C.$14,452.92
D.$14,574.46
If it is, Here is your answer:
Just plug everything into the equation.
A(t) = P(1 + r/n)^(nt)
P is the principle (investment)
r is the interest rate expressed as a decimal
n is the number of times compounding occurs in a year
t is the number of years
A(13) = 8900(1 + 0.038/4)^(4+13) = 14551.87
Answer is (A): 14, 551.87
People who reach retirement age will have accidents and health issues. True False
Answers
Answer:
Its FALSE on odyssey
Solve the system of equations
1.8x-0.5y=-6.4
0.6x+2.1y=2.4
_______________________
x= ??
y= ??
Answers
{1.8 x - 0.5 y = -6.4
{0.6 x + 2.1 y = 2.4
In the first equation, look to solve for x:
{1.8 x - 0.5 y = -6.4
{0.6 x + 2.1 y = 2.4
1.8 x - 0.5 y = (9 x)/5 - y/2 and -6.4 = -32/5:
{(9 x)/5 - y/2 = -32/5
Add y/2 to both sides:
{(9 x)/5 = 1/10 (5 y - 64)
{0.6 x + 2.1 y = 2.4
Multiply both sides by 5/9:
{x = 1/18 (5 y - 64)
{0.6 x + 2.1 y = 2.4
Substitute x = 1/18 (5 y - 64) into the second equation:
{x = 1/18 (5 y - 64)
{2.1 y + 0.0333333 (5 y - 64) = 2.4
2.1 y + 0.0333333 (5 y - 64) = 2.1 y + (0.166667 y - 2.13333) = 2.26667 y - 2.13333:
{x = 1/18 (5 y - 64)
2.26667 y - 2.13333 = 2.4
In the second equation, look to solve for y:
{x = 1/18 (5 y - 64)
{2.26667 y - 2.13333 = 2.4
2.26667 y - 2.13333 = (34 y)/15 - 32/15 and 2.4 = 12/5:
(34 y)/15 - 32/15 = 12/5
Add 32/15 to both sides:
{x = 1/18 (5 y - 64)
{(34 y)/15 = 68/15
Multiply both sides by 15/34:
{x = 1/18 (5 y - 64)
y = 2
Substitute y = 2 into the first equation:
Answer: {x = -3, y = 2
What number is between 7/11 and 7/10
which one?
76/99
23/33
77/9
25/44
???? plz be sure its 56 points
Answers
20 POINTS!! EASY QUESTION! WILL MARK BRAINLIEST!! READ THE INFO! THEN FILL IN THE BLANKS!
The cost for a single class session for each dance class is below.
Clodagh’s Dance = $6.00
New Steps = $7.50
Stepping High = $6.50
The class hours are below.
Clodagh’s Dance = 3:00pm - 4:00pm
New Steps = 4:00pm - 5:30pm
Stepping High = 9:00am - 10:15am
How would these answers change if you were to write the unit rate in cost per hour?
Fill in the blanks!
Dance Classes | Total Hours for Each Payment | Cost Per Hour
| |
Clodagh’s Dance | $6.00 | $6.00
New Steps | $7.50 | _____
Stepping High | $6.50 | _____
Answers
To find the unit rate in cost per hour, you will write the amount of money over the total time for each class. Then divide the cost by the time to find the unit rate.
New Steps: $7.50/1.5 hours = $5 per hour
Stepping High: $6.50/1.25 hours = $5.20 per hour
Answer:
To find the unit rate in cost per hour, you will write the amount of money over the total time for each class. Then divide the cost by the time to find the unit rate.
New Steps: $7.50/1.5 hours = $5 per hour
Stepping High: $6.50/1.25 hours = $5.20 per hour
5. (10.01 MC) If sin θ = 1 over 4 and tan θ > 0, what is the value of cos θ? (1 point)
Answers
To find the value of cos θ when sin θ = 1/4 and tan θ > 0, use the Pythagorean identity. As the angle is in the first quadrant, cos θ is positive and equals the square root of 15/16 or √15/4.
If sin θ = 1/4 and tan θ > 0, we need to determine the value of cos θ. When the sine of an angle is positive and the tangent is positive, we know the angle must be in the first quadrant, where all trigonometric functions are positive. To find cos θ, we utilize the Pythagorean identity sin2 θ + cos2 θ = 1. Rewriting this identity for cos θ, we get cos2 θ = 1 - sin2 θ.
Substituting the given value of sin θ, we have:
cos2 θ = 1 - (1/4)2
cos2 θ = 1 - 1/16
cos2 θ = 15/16
Since θ is in the first quadrant, and cos θ is positive, the value of cos θ is the positive square root of 15/16:
cos θ = √(15/16)
cos θ = √15/4 or approximately 0.9682
Lena runs 2/3 mile each day she wants to know how many miles she has to run before she has has run a whole number
Answers
Find the slope of the line that contains the points named. C(3, 8), D(-2, 5) -3/5 3/5 5/3
Answers
Answer: [tex]\dfrac{3}{5}[/tex]
Step-by-step explanation:
The slope of a line passing through two points X(a,b) and Y(c,d) is given by :-
[tex]m=\dfrac{d-b}{c-a}[/tex]
Given points : C(3, 8) and D(-2, 5)
Then , the slope of a line passing through two points C(3, 8) and D(-2, 5) is given by :-
[tex]m=\dfrac{5-8}{-2-3}=\dfrac{-3}{-5}=\dfrac{3}{5}[/tex]
Hence, the slope of the line that contains the points C(3, 8) and D(-2, 5) is [tex]\dfrac{3}{5}[/tex]
.
What are two solutions of 3 + 4 |x/2 + 3| = 11?
Answers
4 abs(x/2 + 3) = 11 - 3
4 abs(x/2 + 3) = 8 Divide by 4
abs(x/2 + 3) = 8/4
abs(x/2 + 3) = 2
Solution 1
x/2 + 3 = 2 Subtract 3
x/2 = 2 - 3
x/2 = - 1 Multiply by 2
x/2 *2 = - 2
x = - 2
Solution 2
x/2 + 3 = - 2
x/2 = - 2 - 3
x/2 = - 5 Multiply by 2
x = -5 * 2
x = -10
Solutions
x = - 2 <<<< answer 1
x = -10 <<<< answer 2
If cos thetha =-0.96 and (sec thetha)(sin thetha)>0 find the value of tan thetha
Answers
=>
theta is either in the 2nd or third quadrant.
cos(theta)=-0.96
=>
sec(theta)=1/cos(theta)=-1/0.96 <0
Given sec(theta)(sin(theta)>0
=> cos(theta)sin(theta)>0
=> cos(theta) and sin(theta) have the same sign,
=> sin(theta)<0
=>
theta is in the third quadrant. => tan(theta)>0
Given cos(theta)=-0.96
=>
|sin(theta)|=sqrt(1-(-0.96)^2)=sqrt(0.0784)=0.28
=> sin(theta)=-0.28
Finally,
tan(theta)=sin(theta)/cos(theta)=-0.28/-0.96
=7/24
=0.29167 (to the fifth decimal place)
The range of typical total prices for an American tourist traveling on the European continent is $20.70 to $25.00. What is the average price?
Answers
We look for the average of the prices by means of the following expression:
P = (20.70 + 25) / (2)
P = 22.8 $
Answer:
the average price is $ 22.8
Answer:
(The other answer has missing a number.)
The full answer is: $22.85
Please help ASAP!!!! 52 points and will give brainliest for RIGHT answer!
Answers
A job applicant estimates that his chance of passing a qualifying examination is 2/3, and his chance of being appointed if he does pass is 1/4. What is the probability that he will receive the job?
Answers
2 * 1
- -
3 * 4
so 2 /12
1/6 when simplified
Hence, the probability that he will receive job is:
1/6
Step-by-step explanation:It is given that:
chance of passing a qualifying examination is 2/3=P
and chance of being appointed if he does pass is 1/4=P'
Now, we are asked to find the probability that he will receive the job.
We are asked to find the probability that he will receive the job.
The probability is calculated as:
Probability that he qualify exam×Probability that he is being appointed.
=P×P'
=(2/3)×(1/4)
=1/6
WILL MARK AS BRAINLIEST
Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of [tex]\frac{ \pi }{2} [/tex], and a vertical shift up 3 units.
y=__________
Answers
The amplitude is given by a, so a = 1.
The period is given by 2*pi/b, so 2*pi/b = pi/2, and b = 4.
The variable c gives the horizontal shift, of which there is none, so c = 0.
Finally, the vertical shift of 3 units means that d = 3.
So the equation is:
y = sin(4x) + 3
Answer:
y = sin(4x) + 3
Step-by-step explanation:
Two parallel lines are _____ coplanar.
never
sometimes
always
Two lines that lie in parallel planes are _____ parallel.
sometimes
always
never
Please explain the answers, I want to understand this better.
Answers
Answer:
1. always
2. sometimes
Step-by-step explanation:
Two lines are coplanar if they lie in the same plane or in parallel planes. There is ALWAYS a plane which contains two parallel lines (see first attached image for details).
Two lines that lie in parallel planes are sometimes parallel. For example, see at second image. Planes [tex]\alpha[/tex] and [tex]\beta[/tex] are parallel. Consider pair of lines [tex]a[/tex] and [tex]a_1[/tex] - they are parallel, but if you consider the pair of lines [tex]a[/tex] and [tex]b_1[/tex], you can see they are not parallel.
Answer:
always
sometimes
Step-by-step explanation:
By definition parallel lines are lines in a plane which do not meet, that means, they have to be coplanar. Coplanar means they are included in the same plane. Then, two parallel lines are always coplanar (imagine two parallel lines in a 3d space, there is always a plane that can contain them).
Two lines that lie in parallel planes are sometimes parallel. As stated before, if there is a third plane which contains the two lines, they can be parallel or cannot, but if there is no plane which contains them, they are not parallel.
5x - 20 = 2x + 10 How do you solve this problem?
Answers
3x = 30
x is 10
x=10
add 20 to both sides
5x= 2x + 30
subtract 2x from both sides
3x= 30
divide both sides by 3
x= 10
Hope this helps! :)
Jax solved an equation and justified his steps as shown below. What reason would justify step 2?
3x + 5 > 2 Step 1: Given
3x > -3 Step 2: ?
x> -1 Step 3: Division Property of Equality
a. Combine Like Terms
b. Division Property of Equality
c. Subtraction Property of Equality
d. Multiplication Property of Equality
Answers
In the problem that Jax solved he subtract 5 from both sides of the equation. This is an example of the subtraction property of equality.
The property states that if you subtract the same amount from both sides of an equation the equation remains the same.
Step 2 can be justified using the Multiplication Property of Equality. This property states that if we multiply or divide both sides of an inequality by the same number, the inequality will still hold true.
Explanation:Step 2 can be justified using the Multiplication Property of Equality. This property states that if we multiply or divide both sides of an inequality by the same number, the inequality will still hold true.
In this case, Jax divided both sides of the inequality by 3. This is a valid step because dividing both sides of the inequality by a positive number does not change the inequality. So, by dividing both sides by 3, Jax found that x > -1.