The cheaper price among this set of orange sales is the one done by trader B, who sells 8 for N120.
How is the cheaper price determined?The cheaper price can be computed by finding out the price per unit.
Data and Calculations:Price of Set Unit Price
Sale of 6 oranges N100 N16.67 (N100/6)
Sale of 8 oranges N120 N15.00 (N120/8)
Thus, selling 8 oranges for N120 is cheaper than selling 6 oranges for N100, and N1.67.
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will give brainliest
The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).
How to simplify the addition between two rational equations
In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:
(n + 5) / (n² + 3 · n - 10) + 5 / (3 · n²) Given(n + 5) / [(n + 5) · (n - 2)] + 5 / (3 · n²) x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)1 / (n - 2) + 5 / (3 · n²) Associative and modulative property / Existence of the multiplicative inverse[3 · n² + 5 · (n - 2)] / [3 · n² · (n - 2)] Addition of fractions with different denominator(3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²) Distributive property / Power properties / ResultTo learn more on rational equations: https://brainly.com/question/20850120
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simply the following expression by combining like terms 5w + 7v - 8w + v - w + 2y
Si al invertir $60.000 se pierde un 8% ¿A cuánto asciende la pérdida?
Trabajando con porcentajes, concluimos que la pérdida es de $4800.
¿A cuánto asciende la pérdida?
Sabemos que la inversión inicial es de $60000, y de esta cantidad, se pierde un 8%.
Entonces la pérdida va a ser el 8% de $60000.
Podemos escribir las relaciones:
$60000 = 100%
x = 8%
Queremos resolver esto para x, tomando el cociente entre esas relaciones y resolviendo para x obtenemos:
x = $60000*(8%/100%) = $60000*0.08 = $4800
Así, concluimos que la pérdida es de $4800.
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Simplify the expression cos (tan-1(x/2)).
\cos (\tan \left( -1\right) (\frac{x}{2}))
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Combine multiplied terms into a single fraction
\cos (\tan \left( -1\right) \cdot \frac{x}{2})
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\cos (\frac{\tan \left( -1\right) x}{2})
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Solution
\cos \left( \frac{\tan \left( -1\right) x}{2}\right)
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Answer:
Step-by-step explanation:
[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]
Ritchie got a job at the movie theater. On the first day, he sold 5 adult tickets and 7 children tickets for a total of 104. On the second day he sold 7 adult tickets and 3 children tickets for a total of 98. What is the price for each ticket?
Answer:
A = $11; C = $7 tickets
Step-by-step explanation:
Using the given info, we can create a system of equations to find the price of adult and children tickets.
Thus, we have 5A + 7C = 104 and 7A + 3C = 98
The easiest method to solve would be elimination:
Answer:
adult: $11children: $7Step-by-step explanation:
The sales on the two days can be expressed using equations that can be solved for ticket prices.
SetupLet x and y represent the prices of adult and children's tickets, respectively. Then the sales revenue for the two days can be expressed in the equations ...
5x +7y = 1047x +3y = 98SolutionOne of the easiest solution methods is to use a graphing calculator. The first attachment shows the prices are $11 for an adult ticket; $7 for children tickets.
Using the matrix functions of a calculator, the augmented matrix of the equation coefficients can be reduced to row-echelon form. This, too, shows the solution to be (adult price, children price) = ($11, $7). See the second attachment. (The solution is the right-most column of the reduced matrix.)
Yet another solution method can use the coefficients from the equations written in general form:
5x +7y -104 = 07x +3y -98 = 0In this form, we define three products of "cross multiplication":
Δ1 = (5)(3) -(7)(7) = -34
Δ2 = (7)(-98) -(3)(-104) = -374
Δ3 = (-104)(7) -(-98)(5) = -238
Using those, we find the variable values to be ...
x = Δ2/Δ1 = -374/-34 = 11
y = Δ3/Δ1 = -238/-34 = 7
(adult price, children price) = ($11, $7)
__
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6. (a) In the given figure, AD and BC are two straight lines. If ZBAO = 50°, ZABO = 60° and ZPCD = 130° then find the values of x and y. 50 60% B 130
Answer: 70 and 60 degrees
Step-by-step explanation:
Angle AOB = 180 - 50 - 60 = 70 degrees so x is 70 degrees
Angle OCD = 180 - 130 = 50 so y = 180 - 70 - 50 = 60 degrees
What is the length of the hypotenuse of a 45°-45°-90° triangle with legs that are 8 cm long?
Answer:
Step-by-step explanation:
Use your 45-45-90 special triangle with side lengths 1, 1, sqrt(2).
The given triangle has legs length 8 (given) which is 8 times the size of our special 1-1-sqrt(2) triangle.
Therefore the length of the hypotenuse is 8 times the length of the hypotenuse in our special triangle
= 8 sqrt(2)
the sum of three consecutive integers is 78. what are the three Integers
Answer:
25, 26, and 27 are the three consecutive integers.
Step-by-step explanation:
Let the numbers be represented as x, x + 1 and x + 2.
We can write the equation:
[tex]x+(x+1)+ (x+2)=78[/tex]
Opening the brackets and simplifying:
[tex]x+x+1+x+2=78[/tex]
[tex]3x+3=78[/tex]
Subtract 3 from both sides.
[tex]3x=75[/tex]
Divide both sides by 3.
[tex]x=25[/tex]
Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.
∴ 25, 26 and 27 are the three consecutive integers.
Answer:
25 , 26 and 27
Step-by-step explanation:
anna bought a sweater at 40% off the original price. if she paid $12 what was the original price of the sweater?
Answer:
The original price was $30
Step-by-step explanation:
40% = 40/100 = 0.4
[tex]\frac{12}{0.4} =30[/tex]
Hope this helps
The human eye contains approximately 9.1 x 10^7 rod cells and 4.5 x 10^6 cone cells . Samuel subtracts 9.1-4.5 and says there are about 46,000,000 more rod cells than cone cells in the human eye . Use the drop - down menus to explain why Samuel is incorrect
Samuel is incorrect because he didn't subtract the power of the numbers.
How many more rod cells are there?The number of rod and cone cells in the human eye is written in scientific notation. Scientific notation is used in expressing large numbers in smaller numbers. To write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100
(9.1 x 10^7) - (4.5 x 10^6)
= (9.1 - 4.5) x 10^(7 - 6)
4.6 x 10 = 46
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A Big Year
By Bob Kowalski
Would you go to the ends of the earth to see a bird? What if it were a really special bird: one with beautiful feathers, an entrancing call, or a silly dance? What if seeing that one special bird would allow you to win a contest?
If that contest doesn't get you on television or win you any cash prizes, would you still do it? For those who participate in the "Big Year," the honor of beating the previous record is the only reward they get or even want.
A "Big Year" is a year in which a person attempts to see as many different species of birds as possible within a particular region. For most in North America who participate in a "Big Year," this region is the lower 48 American states, plus Alaska, Canada, and a couple of French islands off the Canadian coast.
You may be thinking that looking at birds is silly, but just think about the numbers of the recent record holders and the commitment it takes to get these numbers. One recent "Big Year" winner managed to see 744 birds in one year, missing the record by just one bird. Big Year birders travel by train, plane, boat, car, bicycle, and of course, by foot. They can cover over 150 thousand miles to get numbers of sightings this high. They can also spend a small fortune.
Just to clarify, the birds these contestants are counting are the number that they see in a particular year. You see, the contest is based on an honor system. No pictures or other evidence is required as proof of a sighting. Most birders take great pride in their reputation and their abilities to see or hear and then identify a bird. Usually, important sightings of the rare birds needed to get counts in the 700s are visited by hundreds of birders. It is pretty hard to cheat your way to a record-breaking year, but in general, few are interested in cheating.
This honesty comes from the fact that most people who want to break such a record know the greatest rewards are not necessarily in winning. Such rewards are in being able to commit a year of your life to doing something you love. Rewards are found in seeing amazing, inspiring creatures like the California Condor or the Magnificent Frigate bird. Rewards also come in spending time with people who, like you, want to spend their time looking to the skies and trees for glimpses of emerald, crimson, or cerulean blue feathered jewels.
You don't have to be able to travel a continent to have a big birding experience though. Have a big month. Or a big weekend. Set a personal record, learn to identify the species that live in your part of the world, or try to learn the calls of just two species of birds. You will soon find looking at birds isn't such a strange way to spend your time.
Extra! Extra! Backyard Birding
Many schools, families, and young birders across the country participate in the "Great Backyard Bird Count." While not as long as a "Big Year," the "Great Backyard Bird Count" happens every year. It depends on birders and families across the country to watch feeders and other areas in their yards and count the number of birds they see. Unlike the "Big Year," the goal is not to see who can count the most birds. Instead, participants in this event work together to help bird experts get a good idea of how birds are doing. Participants are given checklists and enter their sightings on a website. Called a "citizen-science" project, this event is open to anyone, requires no travel, and happens every year over one weekend in February.
Read this sentence from the article:
You may be thinking that looking at birds is silly, but just think about the numbers of the recent record holders and the commitment it takes to get these numbers.
Why would the author suggest that looking at birds is silly?
To create a sense of doubt in the reader
To distance himself from what seem to be rather strange people
To show readers that some people do not think birding is interesting
To suggest he has never birded himself but might someday
Ill give brainliest
The inference is that the author suggest that looking at birds is silly A. to create a sense of doubt in the reader.
What is an inference?It should be noted that that an inference simply means the conclusion that can be deduced based on the information given in a story.
In this case, A Big Year" is a year in which a person attempts to see as many different species of birds as possible within a particular region. For most in North America who participate in a "Big Year," this region is the lower 48 American states, plus Alaska, Canada, and a couple of French islands off the Canadian coast.
The inference is that the author suggest that looking at birds is silly is to create a sense of doubt in the reader. Therefore, the correct option is A.
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Four seniors and six juniors are competing for four places on a quiz bowl team.
What is the approximate probability that all four seniors will be chosen at random?
what’s the % ?
Answer:
.00476
Step-by-step explanation:
Factorise: a8 - b8
please solve this
Answer:
(a - b)(a + b)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )
Step-by-step explanation:
by repeated use of the difference of squares factorising method, that is
a² - b² = (a - b)(a + b)
given
[tex]a^{8}[/tex] - [tex]b^{8}[/tex]
= ([tex]a^{4}[/tex] )² - ([tex]b^{4}[/tex] )²
= ([tex]a^{4}[/tex] - [tex]b^{4}[/tex] )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis using difference of squares
= ( a² - b²)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis by difference of squares
= (a - b)(a + b)(a² + b² )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )
g. Exactly 14 proper subsets h. Exactly 15 proper subsets How many elements does A contain if it h a. 64 subsets? b. 31 proper subsets? c. No proper subset? d. 255 proper subsets?
I don't know what you mean by g. and h., so I'll just skip that part.
I'm assuming you're asking about some arbitrary finite set [tex]A[/tex].
a. If [tex]A[/tex] has 64 subsets, then [tex]A[/tex] has [tex]\log_2(64) = \boxed{6}[/tex] elements. This is because a set of [tex]n[/tex] elements has [tex]2^n[/tex] subsets/elements in its power set.
b. A proper subset is a subset that doesn't contain all the elements of the parent set. This means we exclude the set [tex]A[/tex] from its power set. The power set itself would have 32 elements, so [tex]A[/tex] would have [tex]\log_2(32) = \boxed{5}[/tex] elements.
c. The empty set is a proper subset of any non-empty set. However, if [tex]A=\emptyset[/tex], then it has no proper subsets. So [tex]A[/tex] must be the empty set and have [tex]\boxed{0}[/tex] elements.
d. By the same reasoning as in part (b), if [tex]A[/tex] has 255 proper subsets, then it has a total of 256 subsets, and [tex]\log_2(256) = \boxed{8}[/tex].
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].
Given the equation of circle be [tex]x^{2} +y^{2}-2x-8=0[/tex].
We are required to find the appropriate statements related to the equation [tex]x^{2} +y^{2}-2x-8=0[/tex].
[tex]x^{2} +y^{2}-2x-8=0[/tex] can be written as under:
[tex]x^{2} +y^{2} -2x+1-9=0[/tex]
[tex]x^{2} +1^{2}-2x+y^{2} -9=0[/tex]
[tex](x-1)^{2}+y^{2}[/tex]-9=0
[tex](x-1)^{2} +y^{2} =9[/tex]
[tex](x-1)^{2}+y^{2} =3^{2}[/tex]
Equation of a circle usually in the form [tex]x^{2} +y^{2} =a^{2}[/tex] in which a is radius.
From the comparison of both the equations we get that radius is 3 units.
From the equation point will be (1,0). It is on the x axis.
Hence the statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].
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Answer: 1,2,5 on edge
Step-by-step explanation:
see above ans for work
What is the answer to this equation?
Answer:W ^10
Step-by-step explanation:
The solution is in the
THE NICHOLS ARE BUYING A HOUSE SELLING FOR $245,000. THEY PAY A DOWN
PAYMENT OF $45,000 FROM THE SALE OF THEIR CURRENT HOUSE. TO OBTAIN A 15-
YEAR MORTGAGE AT 4.5% INTEREST, THEY MUST PAY 1.5 POINTS AT THE TIME OF
CLOSING. WHAT IS THE AMOUNT OF THE MORTGAGE, AND WHAT IS THE COST OF
THE 1.5 POINTS
The amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars
How to solve for the mortgage that is on this houseThe data from the questions says that the cost of the house = $245000
The down payment amount amount is 45000
Given that they already paid 45000 from the cost of the house, the mortgage would be 245000 - 45000
= $200000
The cost of 1.5 points is the same as the cost of 1.5% of the mortgage of this house.
This is calculated as 0.015 x 200000
= $3000
The conclusion is that the amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars
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Calculate the weight on earth of an object with a mass of 48kg
Answer: 470.4 N
Step-by-step explanation:
Concept:
1 kg on Earth = 9.8 N
Given information:
Mass = 48 kg
Find the weight on Earth
1 kg = 9.8 N
48 kg = 48 * 9.8 = [tex]\Large\boxed{470.4N\\}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Given: m space measured angle space B equals 18 degree, b = 9, and c = 20. Find m space measured angle space C degree to nearest whole number.
Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.
What is the measure of angle space C?
From the Rule of Sine;
sinA/a = sinB/b = sinC/c
Where A,B and C are the angles of the triangle and a, b and c are the corresponding opposing sides.
Given that;
Angle B = 18°side b = 9side c = 20Angle C = ?Using the rule of sine.
sinB/b = sinC/c
We substitute the given values into the equation
sin( 18° )/9 = sinC/20
We solve for C.
sin( 18° ) × 20 = sinC × 9
0.309016994 × 20 = sinC × 9
6.18033988 = sinC × 9
Divide both sides by 9
6.18033988/9 = (sinC × 9)/9
sinC = 0.686704431
C = sin⁻¹( 0.686704431 )
C = 43.3697°
C = 43°
Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.
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Knowing the first day Anna and Tamara stop for sightseeing and lost 2 hours of travel time and the second day, they gain 1 hour because they did not stop for lunch, write an algebraic expression that represents how many hours Anna and Tamara traveled the first two days. Let x be the number of hours driven.
The algebraic expression that represents the number of hours Anna and Tamara traveled the first two days is (2x - 1) hours.
How to write Algebraic Word Problems?
We are told that;
On the first day, Anna and Tamara stop for sightseeing and lost 2 hours of travel time.
On the second day, they did not stop for lunch and gained 1 hour.
Now, we are told that x is the number of hours driven per day. Thus, for two days, number of hours driven is expressed as 2x.
Now, since they lost 2 hours on the first day, then total hours travelled is;
2x - 2 hours
On the second day, they gained 1 hour. Thus;
Final total number of hours traveled = 2x - 2 + 1
Final total number of hours traveled = (2x - 1) hours
Thus, we can conclude that the algebraic expression that represents how many hours Anna and Tamara traveled the first two days is (2x - 1) hours.
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A two digit number has 6 more ones than tens. Twice the sum of the number and its reverse is 6 more than ten times the number. Find the number.
The number with the given properties is 17
How to determine the numbers?Let the tens be x and the units be y.
So, the number is 10x + y
The relationship between the digits is
[tex]y = x + 6[/tex]
The relationship between the number and the reverse is
[tex]2(10x + y + 10y + x) = 6 + 10 * (10x + y)[/tex]
Simplify the second equation
[tex]2(11x + 11y) = 6 + 100x + 10y[/tex]
Open the brackets
[tex]22x + 22y = 6 + 100x + 10y[/tex]
Substitute y = x + 6
[tex]22x + 22(x + 6) = 6 + 100x + 10(x + 6)[/tex]
Expand
[tex]22x + 22x + 132 = 6 + 100x + 10x + 60[/tex]
Collect like terms
[tex]22x + 22x - 100x - 10x = 6 + 60 - 132[/tex]
Evaluate the like terms
[tex]-66x = -66[/tex]
Divide by -66
x = 1
Substitute x = 1 in y = x + 6
[tex]y = 1 + 6[/tex]
y = 7
Recall that the number is 10x + y
So, we have
Number = 10 * 1 + 7
Evaluate
Number = 17
Hence, the number is 17
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A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?
Using the sample space and probability concepts, we have that:
A) All the possibilities for the sample space are: {{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.
B) The probability is: 7/8.
C) The probability is: 1/2.
D) The probability is: 1/4.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The sample space is the set that contains all possible outcomes, hence in this problem, considering G for girl and B for boy, it is given by:
{{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.
For item B, 7 outcomes have at most two boys, hence the probability is 7/8.
For item C, 4 outcomes have at least two girls, hence the probability is 4/8 = 1/2.
For item D, 2 outcomes have all the babies with the same sex, hence the probability is 2/8 = 1/4.
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If u spend $25 per day. How many days will it take you to spend $1,000
Answer:
4days atlases in the week
Quantity day
25------------------1
1000---------------x
We solve
[tex]\boldsymbol{\sf{x=\dfrac{1000\times1}{25}=\dfrac{1000}{25}=40 }}[/tex]
Answer: To spend $1,000 it will take 40 days.
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In two or more complete sentences write and solve an equation for the situation and explain how you will solve the equation. Fifty students were given a pre and post test for their math course. Overall, most students increased their scores by 20% points. The grades on the post test went up to 95%. What is the starting range for the grades on the test?
We conclude that the starting average grade is 79.17%
How to write the equation and solve it?There are 50 students, let's say that the grades are measured between 1% and 100%.
And the average grade of the 50 students is A.
We know that after it increased by 20%, the average of the grades is 95.
Then we just need to solve the percentage equation:
95 = A*(1 + 20%/100%) = A*(1.2)
95/1.2 = A = 79.17
We conclude that the starting average grade is 79.17%
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Answer:
75%
Step-by-step explanation:
You need to do the following equation: x+20≤95 and you will have the answer. (I am sorry if it is wrong but this is what my teacher told the answer was. I put this answer and got it correct.) Hope it helped. Have a nice day.
Patty pays $235 in advance on her account at the athletic club. Each time she uses the club, $6 is deducted from the account. Write an equation that represents the value remaining in her account after x visits to the club. Find the value remaining in the account after 5 visits.
a. V=235 - 6x; $1415
b. V= 6 - 235x; $205
c. V=235 - 6x; $1401
d. V=235 - 6x; $205
*show your work*
Answer:
205
Step-by-step explanation:
We start with 235, this will be our y-intercept.
6 Is deducted from our value every visit, making our slope -6.
Put the two into slope intercept form:
[tex]y=235-6x[/tex]
To find the value after 5 visits substitute x for 5:
[tex]y=235-6(5)[/tex]
Solve
[tex]y=235-6(5)\\y=235-30\\y=205[/tex]
Therefore you have 205 left in your account after 5 visits.
what is the value of x when the richter scale rating scale is 8.4?
The value of x when the richter scale rating scale is 8.4 is 251188643.151
What is a richter scale?A richter scale is a numerical scale that is used for expressing the magnitude of an earthquake in a geographical area
How the richter scale works?The richter scale takes the amplitude of the earthquake's largest seismic as an input and calculate (and display) the magnitude of an earthquake in the geographical area using a logarithmic function
How to determine the value of x?The formula of a richter scale is expressed as:
log(x) = n
Where n represents the scale rating of the scale
In this case, n = 8.4.
So, we have:
log(x) = 8.4
Express as an exponent
x = 10^8.4
Evaluate the exponent
x = 251188643.151
Hence, the value of x when the richter scale rating scale is 8.4 is 251188643.151
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The first five terms of a quadratic sequence are 3, 12, 25, 42, 63.
Find the nth term of this sequence.
Since we know the sequence is quadratic, we expect the [tex]n[/tex]-th term to have the general form
[tex]x_n = an^2 + bn + c[/tex]
Plug in the first 3 known values of the sequence to form a system of equations.
[tex]x_1 = 3 = a + b + c[/tex]
[tex]x_2 = 12 = 4a + 2b + c[/tex]
[tex]x_3 = 25 = 9a + 3b + c[/tex]
Eliminating [tex]c[/tex] gives
[tex](4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9[/tex]
[tex](9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11[/tex]
Eliminating [tex]b[/tex] gives
[tex](4a + b) - (3a + b) = 11 - 9 \implies a = 2[/tex]
Solving for [tex]b,c[/tex], we get
[tex]4a + b = 11 \implies b = 11-4\cdot2 = 3[/tex]
[tex]a+b+c=3 \implies c=3-2-3 = -2[/tex]
So, the [tex]n[/tex]-th term of the sequence is
[tex]x_n = \boxed{2n^2 + 3n - 2}[/tex]
what is (x+6) (x+6) expanded
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
When we expand a function, everything must be multiplied out evenly.
[tex](x+6)*(x+6)\\=x*x +x*6+6*x+6*6\\=x^2 + 6x + 6x+36\\x^2 +12x+36[/tex]
Answer: x² + 12x + 36
Hope that helps!
#LearnwithBrainly
Polynomials are mathematical expressions made up of many terms.
To simplify the polynomial to the maximum, all like terms must be grouped together and rearranged from highest to lowest power.
(x + 6)(x + 6)Distribute
x(x + 6) + 6(x + 6)x² + 6x + 6(x + 6)x² + 6x + 6x + 36Combining like terms.
x² + 12x + 36See more in:https://brainly.com/question/28184428Open Ended
a. Find the slope of the line that passes through the points (2,-5) and (-2,3).
b. What are the slope and y-intercept of the equation 2x - 5y = -10?
c. Find the x value so that the line through the points (x,-9) and (0,1) has a slope of -4.
d. Write the equation of a line that passes through the point (-1,5) and has a slope of -7. Your answer should be given in the form y = mx + b.
(PLEASE SHOW WORK, IT CAN BE SIMPLE I JUST NEED TO PUT IT IN FOR CREDIT)
a.
Solution Given:
Slope of the line passing through the point is
m= [tex] \frac{y_2-y_1}{x_2-x_1}=\frac{3-(-5)}{-2-2}=\frac{8}{-4}=-2[/tex]
slope=-2
b.
Solution given:
equation is
2x-5y=-10
2x+10=5y
y=2x/5 +10/5
y=2/5 x +3
comparing above equation with y=mx+c
we get
m=2/5
slope=2/5
c.
Slope of the line passing through the point is
m=[tex] \frac{y_2-y_1}{x_2-x_1}[/tex]
-4=[tex] \frac{1-(-9)}{0-x}[/tex]
-4=10/-x
doing criss cross multiplication
-4*-x=10
4x=10
x=10/4
x=5/2
slope=5/2
d.
we have
equation of line passing through the one point is
[tex] y-y_1=m(x-x_1)[/tex]
y-5=-7(x-(-1))
y=-7(x+1)+5
y=-7x-7+5
y=-7x-2 is a required equation:
The following diagrams show six lines with equations of the form y =mx +c
I have the answers but I do not know how to FIND the right one. Please help!
Answer:
understand the meaning of m > 0 and c > 0.
Step-by-step explanation:
The slope-intercept form of the equation of a line tells you its slope and its y-intercept.
y = mx +c . . . . line with slope m and y-intercept c
Slope (m)The slope is the rate of increase moving from left to right. It is positive (m>0) when the line slants upward to the right. It is negative (m<0) when the line slants down to the right.
m > 0: lines 3, 5, 6m < 0: lines 1, 2, 4Y-intercept (c)The y-intercept is where the line crosses the (vertical) y-axis. It is positive (c>0) when the line crosses above the x-axis, where y-values are positive. It is negative (c<0) when the line crosses below the x-axis. If the line passes through the origin, then c=0.
c > 0: lines 4, 5c < 0: lines 1, 3c = 0: lines 2, 6