Is the binomial a factor of the polynomial nominal function?
Select Yes or No for each binomial.
I accidentally said “no” for the first two on the chart. I need everything on the chart answered. Thanks!
Answers
The factors for given equation f(x)=[tex]x^{3} +3x^{2} -25x-75[/tex].
(x-1) - No(x-3) - No(x+3) - Yes(x-5) - Yes(x+5) - YesStep-by-step explanation:
The given equation is f(x)=[tex]x^{3} +3x^{2} -25x-75[/tex] .
Add 0 at the end of the equation.
[tex]x^{3} +3x^{2} -25x-75[/tex] = 0.
Let us group the given equation,
[tex](x^{3} +3x^{2}) -(25x-75)[/tex] =0.
⇒ Group 1: [tex]x^{3} +3x^{2}[/tex] .
Group 2: [tex]- 25x +75[/tex] .
Pull out factor from each group,
⇒ Group 1: [tex](x+3)(x^{2})[/tex].
Group 2: (x+3) (-25).
Join the two group since both (x+3) is common in both groups.
[tex](x+3)(x^{2} -25)[/tex] =0.
One of the factor is (x+3).
Other factors are solved by the formula, [tex]a^{2}-b^{2} = (a+b) (a-b)[/tex] .
[tex](x+3)(x^{2} -25)[/tex] = (x+5) (x-5) .
The other factors are (x+5) and (x-5).
Related Questions
How many square centimeters are in a rectangle that measures 1 meter by 3 meters
Answers
Answer:
30,000 cm^2.
Step-by-step explanation:
The area = 3*1 = 3 square meters.
There are 100^2 = 10,000 cm^2 in a square meter
So the area in square centimeters is 3 * 10,000 = 30,000.
4y+3y=21 simplify as much as possible
Answers
Answer:
y=3
Step-by-step explanation:
Add the y and divide
7y=21
21/7=3
y=3
• Add the number that have the same variables. 4y+3y=7y
• 7y = 21 ...divide 7 on both sides and the 7’s will cancel each other out and leave left with....
• 21 divided by 7...
Answer: y = 3
please help me with this question.
Answers
Answer:
b. Shift left 3 units
Step-by-step explanation:
You're given
y = √(x + 3)
y = √(x - (-3))
y = √(x - amount_shifted)
amount shifted = -3
so shifted 3 units and the negative means it's shifted to the left
Solve the inequality for u
-5u+27 [less than or equal to] 2
Answers
Answer:
5≤u
Step-by-step explanation:
Put the words and numbers into an equation:
-5u+27≤2
Put all like terms on one side:
27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)
Simplify:
25≤5u
Solve:
5≤u
:)
scientific notation
how do I do this?
Answers
Answer:
Post the questions and I'll do my best to help
Step-by-step explanation:
There are 75 balloons in each package how many balloons are in 20 packages
Answers
Answer:
1,500
Step-by-step explanation:
75•20
Answer:1500
Step-by-step explanation: 75 times 20 = 1500
16. A farmer plants 0.4 of a field with wheat.
The field is 2.3 acres.
Part A
Shade the grids to model the multiplication. How do i shade the grid
Answers
Step-by-step explanation:
the farmer plants 0.4 of the total field which is 2.3 acres
⇒0.4×2.3= 0.92 acres
now draw a grid of area 2.3 acres and in that area shade 0.92 acres.Use a proper scale to draw the grid. It will a be pictorial representation of the proper and its solution.
Miss Isaac took her family out to eat at Jason’s deli.The meal came to $25.40.Miss Isaac wanted to tip the waitress 18% and sale tax is 5.5%.Find the total price of their meal after tax and tip
Answers
Explanation:
The 18% tip is 4.572
The 5.5% tax is $1.397
25.40 + 4.572 + 1.397 = 31.549 = 31.55 rounded up
The sum of 3 consecutive even numbers is 408. What is the largest of the numbers
Answers
Answer:135,136,137
Step-by-step explanation:
408 divided by 3=136
136-1=135
136+1=137
135,136,137
The largest number of the three consecutive even numbers that sum to 408 is 138.
Explanation:The problem is a classic arithmetic sequence problem in mathematics, where a common difference exists between each number. For consecutive even numbers, this difference is 2. If the sum of three consecutive even numbers is 408, we can form the equation 3n+6=408 (since the first number is 'n', the next is 'n+2', and the following is 'n+4'). Solving this equation gives us n=134, hence the sequence of numbers is 134, 136 and 138. The largest number in this sequence is 138.
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Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y + 2x3y4 + xy3?
Both the sum and difference have a degree of 6.
Both the sum and difference have a degree of 7.
The sum has a degree of 6, but the difference has a degree of 7.
The sum has a degree of 7, but the difference has a degree of 6.
Answers
Answer:
The option " The sum has degree of 6 , but the difference has a degree of 7 " is correct.
Step-by-step explanation:
Given that the sum and difference of the polynomials [tex]3x^5y-2x^3y^4-7xy^3[/tex] and [tex]-8x^5y+2x^3y^4+xy^3[/tex]
Now sum the given polynomials :[tex]3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)[/tex]
[tex]=3x^5y-2x^3y^4-7xy^3-8x^5y+2x^3y^4+xy^3[/tex]
[tex]=-5x^5y+0-6xy^3[/tex]
[tex]=-5x^5y-6xy^3[/tex]
Therefore [tex]3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)=-5x^5y-6xy^3[/tex]
In the simplified sum of the polynomials [tex]-5x^5y-6xy^3[/tex] we have the degree is 6
Now difference the polynomials[tex]3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)[/tex]
[tex]=3x^5y-2x^3y^4-7xy^3+8x^5y-2x^3y^4-xy^3[/tex]
[tex]=11x^5y-4x^3y^4-8xy^3[/tex]
Therefore [tex]3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)=11x^5y-4x^3y^4-8xy^3[/tex]
In the simplified difference of polynomials [tex]11x^5y-4x^3y^4-8xy^3[/tex] we have the degree is 7
Therefore the option " The sum has degree of 6 , but the difference has a degree of 7 " is correct
Answer:
The sum has a degree of 6, but the difference has a degree of 7.
Step-by-step explanation:
Tonya uses the greatest common factor and the distributive property to rewrite this sum: 96 + 36
Which expression does Tonya write?
4(24 + 9)
6(16 + 6)
12(8 + 3)
18(5 + 2)
Answers
Answer:
C) 12(8+3)
Step-by-step explanation:
Answer:C) 12(8+3)
Step-by-step explanation: i took the test
TIMEDDDDD PLEASE ANSWER 15 POINTS
Jolianne worked half as many hours as Andrew. Jolianne makes $10 per hour and has saved $27. Andrew makes $8 per hour and has no money saved. After getting paid, they have the same amount of money.
Andrew claims that only his table and equation are correct, but Jolianne claims that both tables and equations are valid. Which statement regarding their claims is true?
Andrew is correct because t cannot be used to represent the number of hours Jolianne worked.
Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did.
Jolianne is correct because if one lets t = hours Andrew worked, then his equation is valid. If one lets t = hours Jolianne worked, then Andrew worked twice as many so her equation is valid, too.
Jolianne is correct because when solving t in her equation, t = hours Jolianne worked, and when solving for t in Andrew’s equation, t = hours Jolianne worked so they are equal.
Answers
Answer:
Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did
Step-by-step explanation:
Let
x ----> number of hours worked by Jolianne
t ----> number of hours worked by Andrew
we know that
The number of hours worked by Jolianne multiplied by $10 per hour plus $27 saved must be equal to the number of hours worked by Andrew multiplied by $8
The linear equation that represent this situation is
[tex]10x+27=8t[/tex] ----> equation A
[tex]x=\frac{t}{2}[/tex] -----> equation B
substitute equation B in equation A
[tex]10(\frac{t}{2})+27=8t[/tex]
so
Andrew's table and equation is correct
Jolianne's table and equation are not correct, because Andrew did not work twice as many hours as she did
Answer:
the answer is B :)
Step-by-step explanation:
what two digit number is a multiple of 5 and has 3 less tens than ones
Answers
Answer:
25
Step-by-step explanation:
If a two digit number is a multiple of 5, then it ends with 0 or with 5.
If a two digit number ends with 0, then the number of ones is 0 and the number of tens must be 3 less that is impossible.
Hence, this two digit number must end with 5. If it ends with 5, then the number of ones is 5 and number of tens must be 5 - 3 = 2.
Therefore, the number is 25.
The question is about two-digit numbers that are multiples of 5 and have fewer tens than ones. Numbers such as 15, 25, 35, 45, 50, 65, 75, 85, and 95 satisfy these conditions.
Explanation:The subject of this question is a mathematical problem solving task regarding two-digit numbers and their properties. The most important criteria are that the number is a multiple of 5 and has less tens than ones. First, multiples of 5 are numbers that end in 0 or 5. Secondly, having less tens than ones implies that the digit in the ones place must be greater than the digit in the tens place.
An example of a number that fulfills these conditions would be 15. Here, the digit in the ones place (5) is greater than the digit in the tens place (1). Also, 15 is a multiple of 5 because it can be divided by 5 without leaving a remainder.
However, 15 is just one of many possible answers. Other numbers that satisfy these conditions are: 25, 35, 45, 50, 65, 75, 85, and 95.
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How many solutions dose the equation have 2(x+3)=12
Answers
[tex]
2(x+3)=12 \\
x+3=6 \\
x=3
[/tex]
Hope this helps.
Answer:
The answer is 1 solution.
Step-by-step explanation:
2(x+3)=12
First, do the multiplication by multiplying two times everything in the parentheses
2x+6=12
Then, subtract six from twelve.
2x+6=12
-6 -6
--------------------
2x=6
Finally, divide everything by two.
x=3
It has one solution, and the solution is x=3!
Which shapes have the same volumes as the given rectangular prism ?
Answers
search for the best and accurate answers
Which function has a range of vy s 5)?
of(x) = (x - 4)2 + 5
O (x) = -(x - 4)2 + 5
o f(x) = (x - 5)2 + 4
Of(x) = -(x - 5)2 + 4
Answers
Answer:
see the explanation
Step-by-step explanation:
Verify the range of each quadratic function
case 1) we have
[tex]f(x)=(x-4)^2+5[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The function is written in vertex form
The vertex represent a minimum
The vertex is the point (4,5)
The range is the interval [5,∞)
[tex]y\geq 5[/tex]
case 2) we have
[tex]f(x)=-(x-4)^2+5[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The function is written in vertex form
The vertex represent a maximum
The vertex is the point (4,5)
The range is the interval (-∞,5]
[tex]y\leq 5[/tex]
case 3) we have
[tex]f(x)=(x-5)^2+4[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The function is written in vertex form
The vertex represent a minimum
The vertex is the point (5,4)
The range is the interval [4,∞)
[tex]y\geq 4[/tex]
case 4) we have
[tex]f(x)=-(x-5)^2+4[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The function is written in vertex form
The vertex represent a maximum
The vertex is the point (5,4)
The range is the interval (-∞,4]
[tex]y\leq 4[/tex]
A cell phone plan cost $200 to start. Then there is a $50 charge each month.
1. what is the total cost (start up fee and monthly charge) to use the cell phone plan for 1 month?
2. what is the total cost for x months?
Answers
Answer:
1) $250
2) $200 + $50x
Step-by-step explanation:
1)
$200 (start up fee) + $50 * ( 1 month ) = $200 + $50 = $250
2)
$200 (start up fee) + $50 * ( x months ) = $200 + $50x
Hope this helps :)
please help me I can fail math
Answers
3. y=3x+1
4. y=-3x-3
Sam & Avery are making small and large birdhouses for a craft show. Small houses sell for $10 and large houses sell for $15. It takes Sam 3 hours to build small houses and 5 hours to build large houses. He only has 24 hours of building time. Avery only has time to decorate 12 houses of either size. How many small & large houses should be made to make the most money?
If Sam had 30 days instead of only 24 hours and Avery had time to decorate 100 birdhouses instead of only 12, discuss solution methods you used and why.
Answers
Answer:
8 small houses; 0 large houses80 small houses; 0 large housesStep-by-step explanation:
a) The maximum number of houses Sam can build in 24 hours is 8, so the constraint is in construction, not decoration. For each small house Sam constructs, he makes $10/3 = $3.33 per hour of work. For each large house Sam constructs, he makes $15/5 = $3.00 per hour. The most money is to be made by building only small houses.
Sam should make 8 small houses and 0 large houses in 24 hours.
__
b) If Sam works 8-hour days, then he can complete at most 80 small houses. The constraint remains in construction, so the answer is the same: build only small houses.
_____
If Sam works more than 16 2/3 hours per day, he can build 100 large houses or more, so the constraint moves to decoration. The decorator makes more money by decorating large houses, so all the effort should go to construction of large houses.
If Sam works between 10 and 16 2/3 hours per day, the best revenue will come from some mix. The problem statement is unclear as to how many hours Sam works in 30 days.
The garden view hotel is seventeen less than twice the height of the plaza hotel. If their combined height is 361 feet, how tall is the gardenview hotel?
Answers
The garden view hotel is 235 feet tall
Step-by-step explanation:
The given is:
The garden view hotel is seventeen less than twice the height of the plaza hotelTheir combined height is 361 feetWe need to find the height of the garden view hotel
Assume that the height of garden view hotel is x feet and the height of the plaza hotel is y feet
∵ The height of the garden view hotel = x feet
∵ The height of the plaza hotel = y feet
∵ The height of the garden view hotel is 17 less than twice the
height of the plaza hotel
- That means x is less than 2 × y by 17, equate x by the difference
of 2 × y and 17
∴ x = 2y - 17 ⇒ (1)
∵ Their combined height = 361 feet
∴ x + y = 361
- Find y in terms of x by subtraction x from both sides
∴ y = 361 - x ⇒ (2)
Substitute y in equation (1) by equation (2)
∵ x = 2(361 - x) - 17
- Simplify the right hand side
∴ x = 722 - 2x - 17
- Add like terms
∴ x = 705 - 2x
- Add 2x to both sides
∴ 3x = 705
- Divide both sides by 3
∴ x = 235
The garden view hotel is 235 feet tall
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The height of the Gardenview Hotel is 235 feet, which we found by first creating a system of equations using the information given and then solving by substitution.
To find the height of the Gardenview Hotel, let's create a system of equations based on the information given. Let G be the height of the Gardenview Hotel and P be the height of the Plaza Hotel. We are told that the Gardenview Hotel is seventeen less than twice the height of the Plaza Hotel, which we can express as G = 2P - 17. Additionally, we know their combined height is 361 feet, so G + P = 361.
Now we can solve the system of equations step by step:
Substitute the expression for G from the first equation into the second equation: (2P - 17) + P = 361.
Combine like terms: 3P - 17 = 361.
Add 17 to both sides of the equation: 3P = 378.
Divide both sides of the equation by 3 to find the height of the Plaza Hotel: P = 126.
Now use the value of P to solve for G using the first equation: G = 2(126) - 17.
Simplify to find the height of the Gardenview Hotel: G = 252 - 17.
Thus, the height of the Gardenview Hotel is 235 feet.
Whats the analysis of yieldsof 2x square+9x+10
Answers
Answer:
The roots of the equation are -2.5 and -2
Step-by-step explanation:
We are given a quadratic equation and we are supposed to find the roots of the equation.
y = [tex]2x^{2}+9x+10[/tex]
To find the roots put y= 0.
We can factorize the given equation to get the roots.
[tex]2x^{2}+ 4x + 5x + 10[/tex] = 0
2x ( x + 2 ) + 5 ( x + 2 ) = 0
( 2x + 5 )( x + 2 ) = 0
x = -[tex]\frac{5}{2}[/tex] and x = -2
Hence the roots of the quadratic equation are -2.5 and -2.
8 4583/5000 simplified
Answers
Answer:
it's already simplified :) your welcome
in 1982, a belt sold for $11.50 ten years later, the price of the belt increased by 80%. How much more did it sell for in 1992? How much would the belt cost in 1992?
Answers
Answer:
It sold for $9.20 more in 1992 than in 1982.
It sold for $20.70 in 1992.
Step-by-step explanation:
The price in 1982 was $11.50.
The price increased by 80% of $11.50.
We need to find 80% of $11.50.
To find a percent of a number, multiply the percent by the number.
80% of $11.50 =
= 80% * $11.50
= 0.8 * $11.50
= $9.20
It sold for $9.20 more in 1992.
The price in 1992 is the original price of the belt plus the amount of increase.
$11.50 + $9.20 = $20.70
It sold for $20.70 in 1992 than in 1982.
What is the simplified expression for the expression below?
1/2 (8x+4)+1/3(9-34)
5x + 5
7x + 1
Ox+7
3x + 5
Answers
Answer:
4x-19/3
Step-by-step explanation:
1/2(8x+4)+1/3(9-34)
8/2x+4/2+9/3-34/3
4x+2+3-34/3
4x+5-34/3
4x-19/3
Answer:
3x+5
Step-by-step explanation:
10.31988 to the nearest hundredth
Answers
Answer:
10.32
Step-by-step explanation:
10.31988
the 9 makes the 1 to a 2 so...
10.32
Answer 10.32
dr.smith prescribes gentamicin for a patient with a serious bacterial infection . if a 750 ml bag contains 300 mg gentamicin and the patient receives 300 ml how many mg of gentamicin did tge patient receive?
Answers
Answer:
120 mg
Step-by-step explanation:
750 ml 300mg
300 ml x mg
750 / 300 = 300 / x
x = (300 x 300) / 750 = 120 mg
The sum of 4 times a number and 15 is 47. Find the number.
Answers
Answer:
The number is 8.
Step-by-step explanation:
Write an equation then solve by isolating the variable.
let x be the number
4x + 15 = 47 Subtract 15 from both sides
4x = 47 - 15
4x = 32 Divide both sides by 4
x = 32/4
x = 8
Therefore the number is 8.
Answer:
8
Step-by-step explanation:
One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 ft.²
Answers
The one side of rectangle is 11 feet and other side is 19 feet.
Step-by-step explanation:
Given,
Area of rectangle = 209 square feet
Let one side of rectangle = w
other side of rectangle = 2w-3
Area of rectangle = One side * other side
[tex]209=w*(2w-3)\\209=2w^2-3w[/tex]
[tex]0=2w^2-3w-209\\2w^2-3w-209=0[/tex]
[tex]2w^2+19w-22w-209=0\\w(2w+19)-11(2w+19)=0\\(2w+19)(w-11)=0[/tex]
Either;
2w+19=0 =>2w=-19
Or,
w-11=0 => w=11
As length cannot be negative, therefore,
One side of rectangle = 11 feet
Other side of rectangle = 2w-3 = 2(11)-3 = 22-3 = 19 feet
The one side of rectangle is 11 feet and other side is 19 feet.
Keywords: rectangle, area
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You decide to begin selling glow sticks at the local star wars convention. Your cost for each glow stick is $2.02 plus you have to pay a fixed weekly fee of $190 for the booth. Your plan is to sell each glow stick for $3.60.
Answers
You would have to sell approximately 52 bracelets per week in order to pay your fee.
190 ÷ 3.60 = 52.7
This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.
To determine the profit you make from selling glow sticks at the Star Wars convention, you can calculate the profit per unit and the total profit considering the costs and selling price.
Here are the key values:
Cost per glow stick: $2.02
Fixed weekly fee for the booth: $190
Selling price per glow stick: $3.60
Now, let's calculate the profit per unit:
Profit per unit = Selling price per unit - Cost per unit
Profit per unit = $3.60 - $2.02 = $1.58
This means you make a profit of $1.58 for each glow stick you sell.
To find the total profit, you need to consider how many glow sticks you sell. Let's assume you sell 'x' glow sticks. Your total profit can be calculated as:
Total Profit = Profit per unit × Number of Units Sold
Total Profit = $1.58x
Now, you need to take into account the fixed weekly booth fee of $190. So, your total profit after deducting the booth fee will be:
Total Profit - Booth Fee = $1.58x - $190
This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.
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Can someone plzzz help me with numbers 8 and 9 plzzz show work plzzz
Answers
Answer:
For question 9: Angle 1= 20, angle 2= 70, angle 3= 70, angle 4= 20, angle 5= 20, angle 6= 70, and angle 7= 70.
Step-by-step explanation: