Answer:
[tex]2x^2+4x+2[/tex]
Step-by-step explanation:
[tex]2x^3+6x^2+6x+2[/tex] divide by x+1
Divide the first term of numerator by the first term of denominator and put it at the top. then multiply the answer by x+1 . write the expression at the bottom and subtract it. Repeat the process till we get remainder.
[tex]2x^2+4x+2[/tex]
-------------------------------------------------------
[tex]x+1[/tex] [tex]2x^3+6x^2+6x+2[/tex]
[tex]2x^3+2x^2[/tex]
-----------------------------------------(subtract)
[tex]4x^2+6x[/tex]
[tex]4x^2+4x[/tex]
-------------------------------------------Subtract
[tex]2x+2[/tex]
[tex]2x+2[/tex]
------------------------------------------Subtract
0
you have a bottle of water with a leak. after 2 seconds there is 28 ounces left in the bottle. after 6 seconds there are 20 ounces left in the bottle. how much water was in the bottle initially
Answer:
32!
Step-by-step explanation:
List the members of these sets.
a.{x | x is a real number such that x2 = 1}
b.{x | x is a positive integer less than 12}
c.{x | x is the square of an integer and x < 100}
d.{x | x is an integer such that x2 = 2}
The sets are:
a) {-1, 1}b) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}c) {1, 4, 9, 16, 25, 36, 49, 64, 81}d) {∅}.How to find the elements of each set?
We need to find all the values of x that meet the given restrictions for each set.
a) Here we know that x is a real number and we must have:
x^2 = 1
Solving for x:
x = ±√1 = ±1
Then this set is:
{-1, 1}
b) Here x is a positive integer smaller than 12, this is just:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
c) In this case x is a square number, and it must be smaller than 100, so let's find all the square values smaller than 100.
1^2 = 12^2 = 43^2 = 94^2 = 165^2 = 256^2 = 367^2 = 498^2 = 649*9 = 8110*10 = 100 (from this onwards, the squares don't meet the criteria).Then this set is:
{1, 4, 9, 16, 25, 36, 49, 64, 81}
d) Here x must be an integer, such that x^2 = 2
Solving the equation we get:
x = ±√2
But √2 is an irrational number, so there is no integer number that meets this restriction, this means that we have an empty set, this is written as:
{∅}.
If you want to learn more about sets, you can read:
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Solve p−|5|×|−3|=−20
Answer:
-5
Step-by-step explanation:
The solution of the equation p − |5| × |−3| = − 20 will be negative 5.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute equation is given below.
p − |5| × |−3| = − 20
Simplify the equation, then we have
p − |5| × |−3| = − 20
p − 5 × 3 = − 20
p − 15 = −20
p = − 5
The solution of the equation p − |5| × |−3| = − 20 will be negative 5.
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Write the expression(4x-2)·6(2x 7) in the standard form of a quadratic expression, ax² bx c what are the values of the couiffeciant?
What consecutive numbers have a sum of 133?
During a sale at a bookstore, a customer buys one book at full price. The customer is given a 25 percent discount on a second book of equal or less value. If George buys two books that value full prices of $17 and $8, by what percent is the total cost of the two books reduced during the sale?
Translate the sentence into an equation using n as the unknown number. Then solve the equation for n. Two times a number increased by 5 is 15. a. 2n(5) = 15 n = 1.5 c. 2n + 5 = 15 n = 20 b. 2n + 5=15 n = 5 d. n + 5 = 15 n = 10 Please select the best answer from the choices provided A B C D
The mass of a proton is approximately 1.67 x 10−24, and the mass of an electron is approximately 9.11 x 10−28. Find the approximate ratio of the mass of the proton to the mass of the electron.
what would is be in fraction form 1/1833 or 1833/1
List -0.3 , 0.5 ,0.55 ,-0.35 from least to greatest
Seascapes rent small fishing boats for a day-long fishing trips. each boat can carry only 1200 lb of people and gear for safety reasons. Assume the average weight of a person is 150 lb. each group will require 200 pounds of gear for the boat plus 10 lb of gear for each person.
A) create any quality describing the restrictions on the number of people that can possibly fit in a rented boat.
B) several groups of people wish to rent a boat Group one has 4 people group two has 5 people group three has 8 people. Determine which of the groups, if any, can safely run a boat what is the maximum number of people that may rent a boat.
A. We are given that each person weighs 150 lb, each gear
per person weighs 10 lb, and a total of 200 pounds of gear for the boat itself.
Since each person only carries one gear, therefore total weight per person in 160 lb (weight of person + weight of gear).
So let us say that x is the number of persons, the inequality equation is:
160 x + 200 ≤ 1200
B. There are three groups that wish to rent the boat.
> Solve the inequality equation when x = 4
160 (4) + 200 ≤ 1200
840 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 5
160 (5) + 200 ≤ 1200
1000 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 8
160 (8) + 200 ≤ 1200
1480 ≤ 1200 (FALSE)
So only the 4 people group and 5 people group can safely run the boat.
C. Find the maximum number of people that may safely use the boat, solve for x:
160 x + 200 ≤ 1200
160 x ≤ 1000
x ≤ 6.25
Therefore the maximum number of people that can safely use the boat is 6 people.
A mathematical inequality is created to determine that a maximum of 6 people can rent a boat based on the safety weight limit of 1200 lb. Of the groups provided, only groups with 4 or 5 people can safely rent the boat, while the group with 8 people cannot due to exceeding the weight limit.
To determine the restrictions on the number of people that can possibly fit in a rented boat given the safety weight limit, we start by creating an inequality. Let p represent the number of people, then the total weight of the people is 150 lb times p, and the total gear weight is 200 lb for the boat plus 10 lb per person. The inequality can be represented as:
150p + 10p + 200 \<= 1200
Simplifying the inequality gives us:
160p \<= 1000
Dividing both sides by 160:
p \<= 1000 / 160
p \<= 6.25
Since we cannot have a fraction of a person, the maximum number of people allowed is 6.
For part B, we evaluate if the groups mentioned can safely rent a boat:
Group 1 (4 people): 150(4) + 10(4) + 200 = 840 lb \<= 1200 lb - they can rent.
Group 2 (5 people): 150(5) + 10(5) + 200 = 1000 lb \<= 1200 lb - they can rent.
Group 3 (8 people): 150(8) + 10(8) + 200 = 1480 lb > 1200 lb - they cannot rent as it exceeds the limit.
The maximum number of people who may rent a boat based on the given restrictions and average weights is 6 people.
.help me thanks much
Suppose that there is a positive correlation between the variables k and I. If l is 75when k is 7, which of these is most likely to be the value of l when k is 14.
Answer:
l = 150
Step-by-step explanation:
The numbers k and have a positive correlation, to know the correlation between these two variables we have to use the values they give us:
When l = 75 the k = 7
The correlation between the two numbers is division. So this can be written as:
correlation: I = 75/7 k
So if we substitute k=14
l = 75/7 * 14
l = 150
We can also get this number by rule of three:
75/7 = x/14
75/7 *14 = l
1050/7 = l
150 = l
SOMEONE PLEASE HELP!
A store allows customers to fill their own bags of candy. Troy decides he only wants chocolate-covered pretzels and gumdrops. Chocolate-covered pretzels sell for $0.89 per pound, and gumdrops sell for $0.65 per pound. Troy’s bag weighs 1.8 pounds and it cost $1.29.
A. 0.5 pounds of pretzels; 1.3 pounds of gumdrops
B. 0.9 pounds of pretzels; 0.9 pounds of gumdrops
C. 1.3 pounds of pretzels; 0.5 pounds of gumdrops
D. 0.8 pounds of pretzels; 1 pound of gumdrops
Find the next two terms in the sequence. 0,1,4,9. . . A.13,18 B,16,25 C.13,17 D.16,23
Answer:
16 & 25
Step-by-step explanation:
had the same question (;
Solve for x.
−32>−5+9x
Enter your answer, as an inequality, in the box
The solution to the inequality -32 > -5 + 9x is x > -3.
To solve the inequality -32 > -5 + 9x, we'll isolate the variable x by first getting rid of the constant term (-5) on the right side.
1. Add 5 to both sides:
-32 + 5 > 9x
-27 > 9x
2. Divide both sides by 9 to solve for x:
-27/9 > x
-3 > x
Therefore, x is greater than -3. In interval notation, this can be written as (-∞, -3). In inequality notation, it's expressed as x > -3.
We started by isolating the variable x by adding 5 to both sides, then divided by 9 to solve for x. Remember, when dividing or multiplying by a negative number, the direction of the inequality sign flips. Thus, the final solution is x > -3.
Joe sold 15 T-shirts for a total of $82.50.
What is the unit price?
Simplify an expression
Answer:
[tex]\frac{20+2k}{3k+12}[/tex]
Step-by-step explanation:
Since there is no equals sign here, we are not solving this. The only way to simplify is to get a common denominator and write the expression as a single expression. We can begin by noting that the second term has a k in the numerator and in the denominator, and those cancel each other out. That is the first simplification we can perform. That leaves us with:
[tex]\frac{4}{k+4}+\frac{2}{3}[/tex]
In the first term, the denominator is k + 4, in the second term it is just 3. Therefore, the common denominator is 3(k+4). We are missing the 3 in the denominator of the first term, so we will multiply in 3/3 by that term. We are missing a (k + 4) in the second term, so we will multiply in (k + 4)/(k + 4) by that term:
[tex](\frac{3}{3})(\frac{4}{k+4})+(\frac{k+4}{k+4})(\frac{2}{3})[/tex]
Multiplying fractions requires that I multiply straight across the top and straight across the bottom. That gives me:
[tex]\frac{12}{3k+12}+\frac{2k+8}{3k+12}[/tex]
Now that the denominators are the same, I can put everything on top of that single denominator:
[tex]\frac{12+2k+8}{3k+12}[/tex]
Th final simplification requires that I combine like terms:
[tex]\frac{20+2k}{3k+12}[/tex]
Find the product: 5(−3)(−2)
PLEASE HELP ASAP!
what is an equation for the number of $0.60 bagels that can be purchased with d dollars
Find 3 solutions for 2x+y=10
Which of these is correct?
A) 30,792 is greater than 31,875.
B) 31,875 is greater than 32,496.
C) 31,875 is greater than 30,792.
D) 32,496 is less than 31,875.
What does negative 2 over 3 > −1 indicate about the positions of negative 2 over 3 and −1 on the number line?
Answer:
Step-by-step explanation:
Hugo’s friends bought used books at the yard sale Sonia paid 2.25 John paid 6.00 and Keisha paid 3.75 how many books did each friend buy
Answer:
Sonia , John and Keisha bought 3,8 and 5 books respectively.
Step-by-step explanation:
given ,
Sonia paid 2.25 to buy book in yard sale
John paid 6 to buy book in yard sale
Keisha paid 3.75 to buy book in yard sale
cost of 1 book is equal to 0.75 cent
books bought each of them will be equal to
Sonia = [tex]\dfrac{2.25}{0.75}[/tex] = 3 books
John = [tex]\dfrac{6}{0.75}[/tex] = 8 books
Keisha = [tex]\dfrac{3.75}{0.75}[/tex] = 5 books
Hence, Sonia , John and Keisha bought 3,8 and 5 books respectively.
At a certain college, there are 600 freshman, 400 sophomores, 300 juniors, and 200 seniors. if one student is selected at random, what is the probability that the student is a sophomore?
Find the difference quotient and simplify your answer. f(x) = 7x − x2, f(7 + h) − f(7) h , h ≠ 0
The difference quotient for the function f(x) = 7x - x² is (7h - h²) / h.
Explanation:The difference quotient is used to find the rate at which a function changes over a small interval. To find the difference quotient for the given function f(x) = 7x − x², we substitute f(7 + h) and f(7) into the formula: [f(7 + h) - f(7)] / h. Simplifying the expression, we get [(7(7 + h) - (7 + h)²) - (7(7) - 7²)] / h. Expanding and simplifying further, we have [(49 + 7h - h²) - (49 - 49)] / h, which becomes (7h - h²) / h.
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Fred completen 10 math problems This is 40 percent of the number of math problems he has to do How many math problems must he do
Answer:
15 more/ 25 problems in total
Step-by-step explanation:
Evaluate the expression. (26÷13)⋅(−7)+14−4 Enter your answer in the box
The value of the expression (26 ÷ 13) ⋅ (−7) + 14 − 4 will be negative four.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ (26 ÷ 13) ⋅ (−7) + 14 − 4
Simplify the expression, then the value of the expression will be
⇒ (26 ÷ 13) ⋅ (−7) + 14 − 4
⇒ (2) ⋅ (−7) + 14 − 4
⇒ −14 + 14 − 4
⇒ − 4
Then the value of the expression (26 ÷ 13) ⋅ (−7) + 14 − 4 will be negative four.
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5 x 2 x (-4) + 6 divided by 2
43
-37
-23
-17
A box measures 2 cm x 0.09 m x 20 mm. what is its volume in cubic centimeters?
Final answer:
To find the volume of the box, convert all dimensions to centimeters and then use the formula length x width x height. The volume is 36 cm³.
Explanation:
To calculate the volume of a rectangular box with dimensions in different units, we must first convert all dimensions to the same unit of measure. In this case, we will convert meters and millimeters to centimeters:
0.09 m = 0.09 * 100 cm = 9 cm
20 mm = 20 / 10 cm = 2 cm
Now we can calculate the volume using the formula for the volume of a rectangular box, which is length × width × height:
Volume = 2 cm × 9 cm × 2 cm = 36 cm³
Two consecutive integers have a sum of 81 . find the integers.