6x+3y=13
6x+3y-13=13--13
6x+3y-13=0
2. The sum of two cubes can be factored by using the formula q3 + b3 = (a + b)(a? - ab + b).
(a) Verify the formula by multiplying the right side of the equation.
(b) Factor the expression 8x3 + 27.
(c) One of the factors of 23 - bºis a - b. Find a quadratic factor of a3 - bº Show your work.
(d) Factor the expression x3 - 1.
Factorization involves breaking down an expression.
The factorized expression of [tex]8x^3 + 27[/tex] is [tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]The other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]The factorized expression of x^3 - 1 is [tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]The sum of cubes is given as:
[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]
(a) Verify the formula
Expand the expression on the right-hand side
[tex](a^3 + b^3) = a^3 -a^2b + ab^2 +a^2b - ab^2 + b^3[/tex]
Collect like terms
[tex](a^3 + b^3) = a^3 -a^2b +a^2b+ ab^2 - ab^2 + b^3[/tex]
[tex](a^3 + b^3) = a^3 + b^3[/tex]
The formula has been verified
(b) Factorized 8x^3+ 27
We have:
[tex]8x^3 + 27[/tex]
Express 27 as 3^3
[tex]8x^3 + 27 =8x^3 + 3^2[/tex]
Express 8 as 2^3
[tex]8x^3 + 27 =2^3x^3 + 3^3[/tex]
Rewrite as:
[tex]8x^3 + 27 =(2x)^3 + 3^3[/tex]
Given that:
[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]
The expression becomes
[tex]8x^3 + 27 =(2x + 3)((2x)^2 - (2x)3 +3^2)[/tex]
[tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]
(c)The other factor of 2^3 - b^3
By difference of cubes, we have:
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]
So, the equation becomes
[tex]2^3 - b^3=(2-b)(2^2+2b+b^2)[/tex]
This gives
[tex]2^3 - b^3=(2-b)(4+2b+b^2)[/tex]
Hence, the other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]
(c) Factor x^3 - 1
We have:
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]
Express 1 as 1^3 in x^3 - 1
[tex]x^3 - 1 =x^3 - 1^3[/tex]
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex] becomes
[tex]x^3 - 1^3=(x-1)(x^2+x+1^2)[/tex]
[tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]
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A passenger plane flew from Texas to Frankfurt and back. The round trip is 9900 km.
return trip took 4 hours less than the trip to Frankfurt because of the 50 km/hr wind over the ocean on the return trip. Assume there was no wind on the trip to Frankfurt. Let x km/hr represent the average speed of the plane in still air.
We want to find the average speed of the plane in still air, we will get that the average speed of the plane in still air is 355.3 km/hr
So we know that the total trip is 9900km, so from Texas to Frankfurt the distance is half of that:
9900km/2 = 4950km
Now, The speed of the plane in still air is x km/hr
The speed of the air is 50 km/hr, and it flows from Frankfurt to Texas.
So in the first part of the trip, the wind blows in opposite direction to the motion of the plane, thus the speed of the plane will be:
(x - 50) km/hr
While in the return trip the wind blows in favor of the plane, in this case, the speed is:
(x + 50)km/hr
Then if the first part of the trip lasts for T hours (the second for T - 4 hours) we can write the system of equations:
(x - 50)*T = 4950
(x + 50)*(T - 4) = 4950
Where I removed the units so it is easier to read.
If we isolate T in the first equation we get:
T = 4950/(x - 50)
Now we can replace this in the other equation to get:
(x + 50)*(4950/(x - 50) - 4) = 4950
If we multiply both sides by (x - 50) we get:
(x + 50)*4950 - 4*(x + 50)*(x - 50) = 4950*(x - 50)
Now we can solve this for x:
(x + 50)*4950 - 4*(x^2 - 2500) - 4950*(x - 50) = 0
100*4950 - 4*(x^2 - 2500) = 0
495000 - 4*x^2 + 10000 = 0
505000 = 4*x^2
√(505000/4) = x = 355.3
The average speed of the plane in still air is 355.3 km/hr
If you want to learn more about systems of equations, you can read:
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Can someone help me please?
Answer:
put your equation into fractions and then see what or which 1mathces with the image
Step-by-step explanation:
x-2/5=2/3-3x-2/6
solve for x
Solve
5 + 3 ( x - 1 ) = 5x - 6
PLEASE HELP ME SOLVE THIS!!!
Answer:
c. m < 13
Step-by-step explanation:
13 - 7 is equal to 6 so m must be less than 13 to be less than 6.
Which expression is equivalent to 1/4 (5x + 6)?
The expression which is equivalent to 1/4 (5x + 6) is; Choice A: {5(1/4)x} + {6(1/4)x}.
According to the question:
We are required to determine an expression which is equivalent to 1/4 (5x + 6).In a bid to expand the expression; we must multiply each term in the parenthesis by (1/4);
In essence; we have;
{5(1/4)x} + {6(1/4)x}Read more on multiplication;
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3.In the wild, a giant panda bear's diet consists primarily of bamboo, but in a zoo, the diet
includes other foods. On the first two days of the week, the giant panda bear at your zoo eats 34
pounds of highly nutritious biscuits and 37 pounds of bamboo, respectively.
Use inductive reasoning to create two possible sequences that describe the giant panda bear's
daily diet. Write the first five terms of each sequence.
First Sequence:
Second Sequence:
Describe the pattern you used to write each sequence. Which sequence do you think is more
likely? Explain your reasoning.
The sequence gives the order in which the the different types of foods are
given to the giant panda.
The possible first five terms of the sequences are;
[tex]\begin{tabular}{l|c|c|c|c|c|}Sequence Term& 1&2&3&4&5\\First Sequence&Biscuits&Bamboo&Biscuits&Bamboo&Biscuits\\Second Sequence&Biscuits /Bamboo&Bamboo&Bamboo/Biscuit&Bicuits &B/Bamboo\end{array}\right][/tex]
The sequence that is more likely is the First SequenceReasons:
Inductive reasoning is the reasoning based on the given observation
What the giant panda bear at the zoo eats on the first two days of the week are;
First day; 34 pounds of highly nutritious biscuits
Second day; 37 pounds of bamboo
Given that the number of terms in the sequence = 5
By inductive reasoning, we have;
[tex]\begin{tabular}{l|c|c|c|c|c|}Sequence Term& 1&2&3&4&5\\First Sequence&Biscuits&Bamboo&Biscuits&Bamboo&Biscuits\\Second Sequence&Biscuits /Bamboo&Bamboo&Bamboo/Biscuit&Bicuits &B/Bamboo\end{array}\right][/tex]
The pattern used to write the First Sequence is as follows;
Alternating diet of biscuit and bamboo, such that the panda has a balanced diet during the 5 periods of the sequence.The pattern used to create the Second Sequence is as follow;
Alternating days in which the panda has a mixed diet of biscuit and bamboo, followed by alternating single meal of bamboo and biscuit.The sequence that is more likely is the First Sequence
The reason why the first sequence is more likely is that it ensures that the panda eats adequate amount of each diet, thereby making the panda healthier, and cleaning the zoo much easier.Learn more about inductive reasoning here:
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Let f(x) = x+2/x+6
f^-1(-6) =
We can explicitly find the inverse. If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then
[tex]f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x[/tex]
Solve for the inverse :
[tex]\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x[/tex]
[tex]\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x[/tex]
[tex]1 - \dfrac4{f^{-1}(x) + 6} = x[/tex]
[tex]1 - x = \dfrac4{f^{-1}(x) + 6}[/tex]
[tex]f^{-1}(x) + 6 = \dfrac4{1-x}[/tex]
[tex]\implies f^{-1}(x) = \dfrac4{1-x} - 6[/tex]
Then when x = -6, we have
[tex]f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}[/tex]
Alternatively, we can first solve for x such that [tex]f(x) = -6[/tex]. Then taking the inverse of both sides, [tex]x = f^{-1}(-6)[/tex]. (The difference in this method is that we don't compute the inverse for all x.)
We have
[tex]\dfrac{x+2}{x+6} = -6[/tex]
[tex]x + 2 = -6 (x + 6)[/tex]
[tex]x + 2 = -6x - 36[/tex]
[tex]7x = -38[/tex]
[tex]\implies x = \boxed{-\dfrac{38}7}[/tex]
-2(x-6)=6 help me out
Answer:
x = 9
Step-by-step explanation:
i took the quiz
[tex]\mathfrak{-2(x-6)=6} [/tex]
[tex]\mathfrak{-2x+12=6} [/tex]
[tex]\mathfrak{-2x=6-12} [/tex]
[tex]\mathfrak{-2x=-6} [/tex]
[tex]\boxed{\mathfrak{x=3} }[/tex]
1/2 2/5 6/10 least to greatest
Answer:
2/5, 1/2, 6/10
Step-by-step explanation:
did problem
Answer:
1. 2/5
2. 1/2
3. 6/10
Step-by-step explanation:
Hope this helps
May I get braineist pls
i have 100 points
i need some help!!
Answer:
Option D: [tex]\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}[/tex]
Step-by-step explanation:
GIven the following inequality statement:
[tex]\displaystyle\mathsf{7x\:+\:6\:\geq \:\frac{-x}{2}}[/tex]
Start by eliminating the fraction on the right-hand side.
Multiply both sides of the inequality statement by 2:
[tex]\displaystyle\mathsf{2(7x\:+\:6)\:\geq \:\bigg[\frac{-x}{2}\bigg](2)}[/tex]
2(7x + 6) ≥ -x
Next, distribute 2 into the terms inside the parenthesis:
14x + 12 ≥ -x
Subtract 12 from both sides:
14x + 12 - 12 ≥ -x - 12
14x ≥ -x - 12
Add x to both sides:
14x + x ≥ -x + x - 12
15x ≥ - 12
Divide both sides by 15 to isolate x:
[tex]\displaystyle\mathsf{\frac{15x}{15}\:=\:\frac{-12}{15}}[/tex]
[tex]\displaystyle\mathsf{x\geq -\frac{4}{5}}[/tex] or [tex]\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}[/tex]
Therefore, the correct answer is Option D: [tex]\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}[/tex]
Simplify the expression by combining like terms.
6x + 9 + 2x + 4
Does anyone know the answer?
Answer:
8x + 13
Step-by-step explanation:
"Like terms" means the same kind of algebraic expression...the 6x and the 2x are "like terms" because they both have an x in them. The 9 and the 4 are both constants, which means they are plain numbers. So 6x and 2x is 8x .
9+4 is 13 just like elementary school.
So all together,
6x + 9 + 2x + 4
6x + 2x + 9 + 4
8x + 13
We can rearrange the terms because the problem has all addition in between the terms.
9
11 (a) Grapes cost £2 per kilogram.
Calculate the cost of 380g of grapes.
Answer:
£0.76
Step-by-step explanation:
1kilogram = 1000grams
1000g of grapes costs £2
380g costs = (380 × 2)/ 1000
760/1000 = £0.76
Given an undirected graph G= (V, E) determined by the adjacency matrix as follows:
01001
10111
01010
01101
11010
The number of odd degree vertices of the graph is
Select one
A.2
B.4
C.3
D.1
if anyone knows the question please help me :(
The degree of a vertex is defined as the number of edges that touch the vertex. The (i, j)-th entry of the adjacency matrix tells you whether vertex i touches vertex j (1 if yes, 0 if no). Then the degree of vertex i is equal to the sum of the i-th row in the adjacency matrix.
• vertex 1 : degree = 0 + 1 + 0 + 0 + 1 = 2
• vertex 2 : degree = 1 + 0 + 1 + 1 + 1 = 4
• vertex 3 : degree = 0 + 1 + 0 + 1 + 0 = 2
• vertex 4 : degree = 0 + 1 + 1 + 0 + 1 = 3
• vertex 5 : degree = 1 + 1 + 0 + 1 + 0 = 3
So, the correct answer is A. 2.
point w is graphed at (n,1)
Answer:
find the vertical asymptote of the graph of f(×) = (×+3) +2.
I need help fast I forgot how to do this
Answer:
ABC & E are true statements about the graph
The ratio of the number of cups of red paint to the number of cups of yellow paint that Garcia mixed to make a shade of orange paint is 4:1.
Part A: Write a sentence to describe the number of cups of red paint that Garcia mixed with each cup of yellow paint. (4 points)
Part B: How many cups of yellow paint should Garcia add to each cup of red paint to make the shade of orange? Explain your reasoning. (4 points)
Part C: If Garcia purchased 6 cups of red paint for $42, what is the unit price per cup of red paint? (2 points)
Pls answer i need help
Answer:
Uggghhh
Step-by-step explanation:
I dont know
Answer:
Part A: Garcia mixed 4 cups of red with 1 cup of yellow.
Part B: 1/4 because 4 cups of red requires 1 cup of yellow, so 1 divided by 4 is 1/4.
Part C: $7
Hope this helps! :)
Step-by-step explanation:
A middle school took all of its 6th grade students on a field trip to see a symphony at a theater that has 4500 seats. The students filled 2205 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answer:
49%.
Step-by-step explanation:
2205 100 220500
........... x .......... = .................. = 49 (49%).
4500 1 4500
The theater filled up with 49% of seats with 6th grade students.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a middle school that took all of its 6th grade students on a field trip to see a symphony at a theater that has 4500 seats. The students filled 2205 of the seats in the theater.
Assume that the theater filled up [x]% of seats at the theater. Then, we can write -
[x]% = (2205/4500) x 100
[x]% = 0.49 x 100
[x]% = 49%
Therefore, the theater filled up with 49% of seats with 6th grade students.
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Someone help me pls
Answer:
248 is your answer
Step-by-step explanation:
The two angles are supplementary, therefore together they add to 360. So take 360 and subtract 112, you get 248. Hope this helps you :)
last month, a store sent 2,014 emails to customers about sales. the number of e-mails sent the month before was 2,104. Use one of the symbols <, >, or = to compare the two numbers to compare the two numbers of e-mails sent. Explain how you used the digits to determine your answer
Answer:
Last month (2,014) = (2,014) Month before last month
Your answer would be 2,014 = 2,014
The digits are all the same. Therefore, I concluded that the numbers were the same. This means that a equal sign should be used.
Hope this helps. Pls mark brainliest. :S
what is 1*1000000*5*6/3*1757/4*45567-4-6-8*5846584*0+1+2+3+4+5+6+7+8+9+10
Answer:
2.0015305e+15 is the answer
3.) Jason has one less dimes than quarters and twice as many nickels
as quarters. If he has a total of $4.40, how many of each type
coin does he have?
Answer:
10 quarters, 9 dimes, and 20 nickels.
Step-by-step explanation:
q - 1 = d, 2q = n or q = 1/2n
.25q + .10(q - 1) + .05(2q) = 4.40
.25q + .10q - .10 + .10q = 4.40
.45q - .10 = 4.40
.45q = 4.50
4.5/.45 = 10
He has 10 quarters, 9 dimes, and 20 nickels.
Decrease £110 by 50%
Answer:
£55
Step-by-step explanation:
50% is just another way to say 1/2. This means that 1/2 of £110 is £55.
5. What is the measure of Angle WVX in the given square?
Answer:
try 90°C for an answer, good luck
A = $2100, P = $1600, t = 8
r = %
Answer:
I want to say 900 many sorry if it's wrong
Faith earned $565 last week. She earned the same amount each
day. If she worked 5 days, how much did she earn each day? Draw
models to help you find the quotient.
Answer:
113 each day
Step-by-step explanation: i cant draw it out but just put it into a bubble or something sorry
Examine the figure. What is the measure of angle a?
Answer:
59Step-by-step explanation:
90+31=121
180-121=59
Answer:
a=59
basic fact:
angles on a straight line add up to 180
Step-by-step explanation:
we can ignore b for a start
31+90+a=180
121+a=180
121+59=180
a=59
10. Flora rented a space at the flea market.
Her space included electricity.
Booth Space
each day:$25
Electricity:$2
Which expression gives the total cost of
the day's rental if she used h hours of
electricity?
A. 25-2h
B. 25 + 2h
C.(25+2) x h
D. 25h+2
Answer:
It is D
Step-by-step explanation:
I am not exactly sure how to explain but i'll try.
The 2 dollars is added to her price, so it is not A.
The 25 dollars is every day, so it is mutlipled by x. So its not B.
The 2 dollars is not everyday like the 25 dollars, so its not C b/c its not everyday.
5x squared +1=4x-7 solve the equation using the quadratic formula
Answer:
Step-by-step explanation:
- B ± √ B2-4AC
x = ____________
2A
which will be
4 ± √ -144
x = _______
10
x =(4-√-144)/10=(2-6i)/5= 0.4000-1.2000