ANSWER TO QUESTION 1
Given
[tex]f(x)=5x^3+8x^2-7x-6[/tex]
We can use the factor theorem to determine if
[tex]x+2[/tex] is a factor of the polynomial or not.
According to this theorem, if [tex]x+2[/tex] is a factor of [tex]f(x)[/tex], then [tex]f(-2)=0[/tex].
How did we get the [tex]-2[/tex]?
We set [tex]x+2=0[/tex] and then solve to obtain [tex]x=-2[/tex].
So now let us plug in [tex]x=-2[/tex] in to the function to see if it will simplify to zero.
[tex]f(-2)=5(-2)^3+8(-2)^2-7(-2)-6[/tex]
[tex]f(-2)=5(-8)+8(4)+7(2)-6[/tex]
[tex]f(-2)=-40+32+14-6[/tex]
[tex]f(-2)=6-6[/tex]
[tex]f(-2)=0[/tex]
Since the result simplifies to zero, we conclude that
[tex]x+2[/tex] is a factor of
[tex]f(x)=5x^3+8x^2-7x-6[/tex]
ANSWER TO QUESTION 2
We have the function,
[tex]f(x)=5x^3+8x^2-7x-6[/tex]
We can use the remainder theorem to show that
[tex]x+1[/tex] is NOT a factor of the polynomial.
According to this theorem, if [tex]x+1[/tex] is not a factor of [tex]f(x)[/tex], then [tex]f(-1)\ne 0[/tex].
So now let us plug in [tex]x=-1[/tex] in to the function to see if it will simplify to non-zero number.
[tex]f(-1)=5(-1)^3+8(-1)^2-7(-1)-6[/tex]
[tex]f(-1)=5(-1)+8(1)+7(1)-6[/tex]
[tex]f(-1)=-5+8+7-6[/tex]
[tex]f(-1)=4[/tex]
[tex]f(-1)\ne0[/tex]
Since the result simplifies to a non zero number, we conclude that
[tex]x+1[/tex] is NOT a factor of
[tex]f(x)=5x^3+8x^2-7x-6[/tex]
In a company, 37% of 1500 employees are females.work out the number of males in the company.
Otylia simplifies the expression 4y + y to 4y2. Use the drop-down menus to complete the statements below to explain why Otylia's solution is correct or incorrect.
Hi, the answer is this...
Otylia's solution is: Incorrect
Because 4y+y is the same as 4y+1y
4y2 is the same as 4y x y
4y+y simplifies to 5y
Answer:
Otylia's solution is incorrect
Correct solution is 5y
Step-by-step explanation:
Otylia simplifies the expression 4y + y to 4y^2.
LEts simplify the expression 4y+y and check with Otylia's solution
4y and y are like terms
y or 1y are same
4y and 1y are like terms
To combine like terms, we add only the coefficient of y
So 4y + 1y = 5y
Otylia simplifies the expression 4y + y to 4y^2
4y^2 is not correct. So Otylia's solution is incorrect
28 points to answer this questio(these are my last points please help)
Answer:
It is not direct variation.
Step-by-step explanation:
In a direct variation, each y value divided by its corresponding x-value gives the same quotient, which is the constant of variation. Let's try two y-values and their corresponding x-values.
11/7 = 1.571428...
13/8 = 1.625
Since the two quotients above are different, there is no constant of variation, and the relation is not direct variation.
Answer:
It is not direct variation.
Step-by-step explanation:
In a direct variation, each y value divided by its corresponding x-value gives the same quotient, which is the constant of variation. Let's try two y-values and their corresponding x-values.
11/7 = 1.571428...
13/8 = 1.625
Since the two quotients above are different, there is no constant of variation, and the relation is not direct variation.
Step-by-step explanation:
This makes sense what they put
A coat that usually cost $120.00 is marked 1/3 off. What is the sale price of the coat
1/3 of $120.00 is $40.00, therefore the sale price will be $80.00 :-) xxx
Please help me!!! Giving first person all my points and brainliest!!!!!!
1. Yes they are congruent. You translate AB to move it over to CD. Specifically, shift 2 units to the right.
2. No, they are not congruent. QR is longer than MN. Congruent segments must be the same length.
3. No, they are not congruent. At first glance, they seem to be congruent after translation and reflection. However, XY is longer than UV, and those legs should be the same length for a pair of congruent triangles to be possible.
4. Yes they are congruent. You translate triangle ABC to move it over to triangle DEF (shift 1 to the left, 3 down).
Use distributive property to rewrite problem so it had only two factors. Then solve (25x9)+(75x9)=
ANSWER
[tex](25\times9)+(75\times9)=9(25+75)[/tex]
[tex](25\times9)+(75\times9)=9(100)[/tex]
[tex](25\times9)+(75\times9)=900[/tex]
EXPLANATION
According to the distributive property,
[tex](a\times b)+(a\times c)=a(b+c)[/tex]
This implies that,
[tex](25\times9)+(75\times9)=9(25+75)[/tex]
[tex](25\times9)+(75\times9)=9(100)[/tex]
The Right Hand Side of the equation now has 2 factors.
We solve now to obtain;
[tex](25\times9)+(75\times9)=900[/tex]
The distributive property allows you to factor out a common factor from both terms in an equation. In this case, you can rewrite the expression (25x9)+(75x9) using the distributive property as 9*(25+75), which simplifies to 9*100 or 900.
Explanation:The distributive property in mathematics is a property where each term inside a bracket is multiplied by the term outside the bracket. We can use the distributive property to rewrite the given expression (25x9)+(75x9).
First, recognize that both terms in the equation have a common factor of 9. By applying the distributive property, you can factor out the common factor of 9 to get 9(25 + 75). Next, simplify the expression inside the parentheses (25 + 75) to get 100. So, your expression is now 9*100. Finally, multiply 9 by 100 to get 900. So, (25x9)+(75x9) = 900.Learn more about Distributive Property here:https://brainly.com/question/6276874
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The mailman delivered a $22 check and three bills for $ 14 each today .What is the total in the mailbox?
HE WOULD HAVE 64$ IN TOTAL
Answer:
-64
Step-by-step explanation:
its actually, -64 not 64.
If an = n(n+2), what is a9?
20
99
108
120
an = n(n+2)⇒ a9 = 9(9+2) = 9 × 11 = 99
3 questions 40 points
The best graph that best fits your table is graph D.
For number 12, I don't see any graphs, but the graph would look like the graph I have below.
For number 11, A) y = 1/2x - 1 is correct. Here's the proof! (pic #2)
For number 10, the first graph is correct, here's the proof! (pic #3)
In an auditorium there are 9 rows of seats with 18 seats in each row. There are also 6 rows of seats with 24 seats in each row. How many seats are there I'm the auditorium
Answer:
306 seats
Step-by-step explanation:
The total number of seats in the auditorium is calculated by multiplying the number of rows by the number of seats in each row for both sets of rows, then adding both totals together. The total comes to 306 seats.
Explanation:This is a mathematics question focused on multiplication and addition, which are key fundamentals in arithmetic, often covered in middle school. To find the total number of seats in the auditorium, you need to multiply the number of rows by the number of seats in each row, then add these numbers together.
For the first part, there are 9 rows with 18 seats in each. By multiplying these numbers (9 * 18), we get 162.
For the second part, there are 6 rows with 24 seats in each. By multiplying these numbers (6 * 24), we get 144.
Then, to find the total number of seats in the auditorium. we add these two numbers together (162 + 144), which equals 306. Therefore, there are 306 seats in the auditorium.
Learn more about Arithmetic here:https://brainly.com/question/29116011
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The complete question is here:
In an auditorium there are 9 rows of seats with 18 seats in each row. There are also 6 rows of seats with 24 seats in each row. How many seats are there in the auditorium?
The hypotenuse of a right triangle measures 58 cm and one of its legs measures 42 cm. What is the length of the missing leg? 10 cm 16 cm 40 cm 71 cm
Select the property that this number sentence illustrates:
2 × 3 = 3 × 2
A.
associative property of addition
B.
associative property of multiplication
C.
commutative property of addition
D.
commutative property of multiplication
Answer:
D. Commutative Property of Multiplication
Step-by-step explanation:
Commutative Property of Multiplication states that two numbers can be multiplied in either order.
For this case we have to:
By definition, the commutative property of the multiplication establishes that, the order of the factors does not alter the product, that is to say:
[tex]a * b = b * a\\[/tex]
Therefore the expression given by:
[tex]2*3 = 3*2[/tex] represents:
The commutative property of multiplication
Answer:
Option D
Which graph represents the solution set of the compound inequality below? x + 3 < (4x – 12) < 20
x + 3 < 4x - 12 or 4x - 12 < 20
-x -x +12 +12
3 < 3x - 12 or 4x < 32
+12 +12 ÷4 ÷4
15 < 3x or x < 8
÷3 ÷3
5 < x
5 < x < 8
Graph: 5 o---------------o 8
Answer:
5<x<8
Step-by-step explanation:
x + 3 < (4x – 12) < 20
Solve the inequality
x + 3 < 4x – 12 < 20
We break the inequality
x+3<4x-12 and 4x-12<20
solve it separately
x+3<4x-12
subtract 4x on both sides
-3x +3< -12
subtract 3 on both sides
-3x < -15
divide by -3 on both sides
x> 5
4x-12<20
add 12 on both sides
4x <32
divide by 4
x<8
x>5 and x<8
so x lies between 5 and 8, 5<x<8
the graph is attached below
100 points (,: giving brainliest too! please help?
2. KL = LM
3. Definition of midpoint
4. L is the midpoint of KM
5. Transitive Property of Congruence
What is the change in value of the 5 digit in these two numbers? 658 201 and 675 201
What is the mode of the following numbers?
2, 5, 11, 7, 5
The mode of this set of numbers is 5.
The mode of a set of numbers, is the most common/frequent number within the set. Since there are two 5's but only one of each other number. Thus making 5 the mode.
How did speculative investing weaken the stability of the stock market
Write as an equation.
60 is 2 more than the product of 5 and N
A. 60=2+5+N
B. 60=2N+5
C. 60=2+5N
D. 60=2+5/N
If 60 is 2 more than the product of 5 and N:
The product of 5 and N is when they are multiplied, so 5N is going to be part of the equation.
We know that 60 is 2 more than 5N, so 5N + 2 would be 60.
We can make an equation with this:
60 = 2 + 5N
Therefore, the equation would be 60 = 2 + 5N.
Hope this helps! :)
The equation that can be used to depict the information 60 is 2 more than the product of 5 and N will be 60 = 2 + 5N
From the information given, 60 is 2 more than the product of 5 and N and this will be written as 60 = 2 + 5N.
To further solve the equation, we can solve for N and this will be:
60 = 2 + 5N
Collect like terms
5N = 60 - 2
5N = 58
N = 58/5
N = 11.6
Therefore, the value of N will be 11.6.
In conclusion, 60 is 2 more than the product of 5 and N and this will be written as 60 = 2 + 5N.
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https://brainly.com/question/11271694
PLEASE HELP
What are the steps for using a compass and straightedge to construct a square?
Drag the steps and drop them in order from start to finish.
Answer:
To construct the Square using a compass and straight edge, you have written the steps not in proper order. I am rearranging the steps for you
1. Construct horizontal H J¯¯¯¯¯
2. Construct a circle with point H as the center and a circle with point J as a center with each circle having radius HJ .
3.Label the point of intersection of the two circles above HJ¯¯¯¯¯ , point K, and the point of intersection of the two circles below HJ¯¯¯¯¯ , point L.
4.Construct KL¯¯¯¯¯ , the perpendicular bisector of HJ¯¯¯¯¯ , intersecting HJ¯¯¯¯¯ at point M.
5.Construct a circle with point M as the center with radius MJ .
6.Label the point of intersection of circle M and KL¯¯¯¯¯ closest to point K, point N, and the point of intersection of circle M and KL¯¯¯¯¯ closest to point L, point O.
7.Construct HN¯¯¯¯¯¯ , NJ¯¯¯¯¯ , JO¯¯¯¯¯ , and OH¯¯¯¯¯¯ to complete square HNJO .
An irrational number in-between 7.7 and 7.9
Best Answer:
7.8
Whats an irrational number again?
The side-by-side boxplots show the ages of all Oscar winners for Best Actress (females) and Best Actor (males). What percentage of Best Actress winners (among females) lie between Q1 = 28 and Q3 = 41?
A. 25%
B. 12%
C. 50%
D. 75%
The first quartile Q1 shows a partition of the first 25% of the data. In the same way the quartile Q3 shows a partition of 75% of the data.
Then, the difference Q3-Q1, also called the interquartile range shows the central 50% of the data.
Therefore the answer is option C:
The percentage of Best Actress winners (among women) between Q1 = 28 and Q3 = 41 is 50%.
Answer: Option C
Step-by-step explanation: i Just Took The Test
Casey has a total of $2.55 cents in dimes and quarter. If she has eight fewer quarters than dimes, how many of each coin does she have ?
approximate the number using a calculator 6^2.8
When you approximate 6 raised to the power of 2.8, you get a result of approximately 177.83 (rounded to two decimal places).
To approximate the number 6 raised to the power of 2.8 using a calculator, follow these steps:
1. Turn on your calculator and make sure it is in standard mode.
2. Enter the base number, which is 6.
3. Look for the exponent key on your calculator, which is usually denoted by the "^" symbol or a button labeled "Exp" or "EE".
4. Enter the exponent value, which is 2.8.
5. Press the equals "=" button to calculate the result.
Now, let's calculate it together:
6^2.8 ≈ 177.827941
Therefore, when you approximate 6 raised to the power of 2.8, you get a result of approximately 177.83 (rounded to two decimal places).
Keep in mind that different calculators may vary slightly in their display of decimal places, so the exact result may differ slightly depending on the calculator you are using.
Monique made several batches of soup for a potluck supper. Each batch required 3/4 of a pound of potatoes, and she used a total of 6 1/2 pounds of potatoes. How many batches of soup did Monique make?
If Monique used a total of 6 1/2 pounds of potatoes and each batch required 3/4 of a pound of potatoes, then you have to divide the total amount of pounds by an amount of pounds needed for one batch:
[tex]6\dfrac{1}{2}:\dfrac{3}{4}=\dfrac{13}{2}\cdot \dfrac{4}{3} =\dfrac{26}{3}=8\dfrac{2}{3}.[/tex]
Answer: [tex]8\dfrac{2}{3}.[/tex]
Answer:
Step-by-step explanation:It’s B and E
What is the integer best represent a debt of $20
i need some help with an algebra equation please help
Please help find the percent of increase?!
Subtract to find the difference:
2000 - 500 = 1500
Divide the difference by the original population:
1500 / 500 = 3
Multiply that by 100 to get the percentage:
3 x 100 = 300%
Clint picks 13 apples. Tim picks 5 fewer apples than clint picks. How many apples does clint pick
Final answer:
To find out how many apples Clint picked, we need to first determine how many apples Tim picked. Clint picked 13 apples.
Explanation:
To find out how many apples Clint picked, we need to first determine how many apples Tim picked. It is given in the question that Tim picked 5 fewer apples than Clint.
So, we can subtract 5 from Clint's total apples to get Tim's total apples.
Next, to find Clint's total apples, we can add the number of apples Tim picked to the 5 fewer apples. This will give us Clint's total apples.
Let's solve the problem step-by-step:
Clint picked 13 apples.
Tim picked 5 fewer apples than Clint, which is 13-5 = 8 apples.
Clint's total apples = Tim's apples + 5 fewer apples = 8 apples + 5 apples = 13 apples.
Therefore, Clint picked 13 apples.
Ford is the coach of a local baseball team that is currently losing by two runs. They are getting ready to take the field to start the bottom of the eighth inning. In the past, when losing by two runs, he has replaced the starting pitcher with a relief pitcher a total of 25 times in the eighth inning of the game. When in the same position, he has left the starting pitcher in the game 15 times.
In the situations when he has replaced the pitcher, they have lost 14 times and won 11 times. In the situations when he has left the starting pitcher in the game, they have lost 8 times and won 7 times.
Based on these numbers, if the goal is to win the game, should he replace the pitcher or not?
A.
Ford should leave the starting pitcher in the game.
B.
There is not enough information to determine if he should replace the pitcher or not.
C.
Ford should replace the pitcher.
D.
Neither option has any advantage.
Answer: A: Ford should leave the starting pitcher in the game.
I just used the other answer provided and it was wrong, at least on study island it was wrong.
I'd appreciate it if anyone helped! :)
Every week, Nina used 5 L of water from her rain barrel to water her plants. She did this until her rain barrel was empty. When Nina first started watering, her rain barrel contained 75 L of water.
Which sketch represents this situation? (Please don't mind the filled bubble at the bottom right corner.)
Answer:
Graph given on the top right side.
Step-by-step explanation:
Nina used 5 L of water from her rain barrel to water her plants every week.
She did this until her rain barrel was empty.
So barrel will be empty in the time = [tex]\frac{75}{5}=15[/tex] weeks.
Nina started watering when rain barrel contained 75L of water.
We draw a graph with water remaining on y-axis and weeks to get the barrel empty on x-axis.
Line representing this process will start from a point (0, 75) on y-axis and will end at x-axis at the point (15, 0).
Therefore, graph given on the top right side of the options is the correct answer.
The correct graph is the graph at the top right of the image given.
This is about interpreting graphs.From the graph, we see that the water remaining is represented on the y-axis while weeks it will take for the barrel to get empty is represented on the x-axis.
When she started watering, her rain barrel contained 75 L of water. This means that amount remaining when she started at 0 weeks was 75 L.This means that, the first coordinate will be; (0, 75). 0 on the x-axis and 75 on y-axis.
We are told that every week she used 5 L of water from her barrel.Since continued using 5 litres every week until the barrel was empty, it means that,Number of weeks it took for the barrel to be empty = 75/5 = 15 weeks
This means when, the water is finished, y-axis will be 0 L while x-axis will be 15 weeks and the coordinate here is (0, 15)Thus, the correct graph is the graph at the top right of the image given.Read more at; brainly.com/question/2050992