Answer:
The factored form of the polynomial is 11*(x+2)*(x-5/11). The root found was r = -2
Step-by-step explanation:
If you take a positive value of x, you will most likely obtain positive results, since 11x² + 17x ≥ 11 + 17 = 28 for x ≥1, which means that 11x²+17x-10 ≥ 28-10 = 18 > 0.
Therefore, we prove with negative values.
x = -1: 11*(-1)²+17*(-1) - 10 = -16x = -2: 11*(-2)² + 17*(-2) - 10 = 44-34-10 = 0Therefore, -2 is a root. We can find the other knowing that
p(x) = 11*(x-r₁)*(x-r₂) = 11*(x-(-2)) * (x-r₂) = 11*(x+2)*(x-r₂)
The independent term is 11*2*(-r₂) = -22r₂ = -10
thus, r₂ = -10/-22 = 5/11.
Therefore, p(x) = 11*(x+2)*(x-5/11)
To write 11x2+17x−10 in factored form we find two numbers whose sum is 17 and product is -110. The correct pair is 2 and -55 which leads to the factored form (11x - 55)(x + 2).
Explanation:The question involves factoring a quadratic expression, 11x2+17x−10. To re-write this expression in factored form, one needs to find two numbers, such that their sum equals to the coefficient of x, 17, and their product equals to the product of the coefficient of x² and the constant term (11*(-10)=-110). Diego started by listing all pairs of factors of the constant term, -10. The correct pair here, considering the product and the sum, are 2 and -55, because 2*(-55)=-110 and 2+(-55)=17. Therefore, our factored form will be: (11x - 55)(x + 2).
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PLEEESE HELLLLP!!!!!!!!!!!
Find the area of the trapezoid shown below and choose the appropriate result.
Answer:
A=2.6
Step-by-step explanation:
Please help me idk this
Answer:
C =12.56 inches
Step-by-step explanation:
The circumference is given by
C = 2*pi*r where r is the radius
C = 2* 3.14 * 2
C =12.56 inches
Answer:
4π
Step-by-step explanation:
The equation for circumference is 2πr
In order to find the circumference here, plug in the given radius
2π(2) = 4π
Como parte de la propuesta de investigación de Iris, ella planifica desplazar un objeto a 5 m con la fuerza de 20N. Al probar su experimento, Iris terminó realizando un trabajo de 100 unidades. ¿Cuál unidad de medida debe usar Iris para expresar el trabajo?
Answer:
Joule.
Step-by-step explanation:
Dado que las unidades empleadas son del Sistema Internacional, la unidad a emplear es el Joule, cuya definición es Newton multiplicado por metro.
You want to put a 6 inch thick layer of topsoil for a new 24 ft by 25 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answer:5
Step-by-step explanation:
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Bailey and Steve bought notebooks for science class.
Bailey bought 6 notebooks for $10.80.
steve bought 4 notes for $7.28
Who got the better deal? and explain :))
Answer: i believe it is bailey
Step-by-step explanation:
bailey bought 6 note books for 10.80
thats about $1.8 per notebook
bc 10.80 ÷ 6 = 1.8
if we take steve's which is 7.28 for, four note books
thats $1.82 per note book
7.28 ÷ 4 = 1.82
then we check what it would be if he bought 6 note books.
1.82 x 6 = 10.92
so bailey got the better deal. i think dont take my word for it
answer please quick
Answer:
The answer to your question is letter B
Step-by-step explanation:
Process
1.- Get two points of each line
Line 1 Line 2
Point A (0, 2) (5, 7)
Point B (-4, 0) (0, -4)
2.- Find the slope of each line
Formula slope = m = (y2 - y1) / (x2 - x1)
Line 1 m = (7 - 2) / (5 - 0)
m = 5/5
m = 1
Line 2 m = (-4 - 0) / (0 + 4)
m = -4/4
m = -1
3.- Find the equation of the lines
Formula y - y1 = m(x - x1)
Line 1 y - 2 = 1(x - 0)
y - 2 = x
y = x + 2
Line 2 y + 4 = -1(x - 0)
y + 4 = -x
y = -x - 4
4) Misty wishes to obtain 85 ounces of a 40% acid solution by combining a 72% acid solution with a 25% acid solution. How much of each solution should Misty use?
Answer:
27.13 ounces of one solution and 57.87 ounce of other solution
Step-by-step explanation:
Considering 'x' no. of ounces of one solution and 'y' no. of ounces of other solution.
Lets form the equations according to the given data.
-> she wishes to obtain 85 ounces by combining both solutions
x+y= 85
x = 85- y -->eq(1)
-> by combining a 72% acid solution with a 25% acid solution
0.72x + 0.25 y = 0.4 x 85 --> eq(2)
Substituting value of eq(1) in eq(2)
0.72(85-y) + 0.25 y = 34
61.2 - 0.72y + 0.25y = 34
-0.47y= 34-61.2
y= 27.2/0.47
y= 57.87 ounces
Plugging in eq(1)
eq(1)=> x = 85- 57.87
x= 27.13 ounces
Therefore, Misty should use 27.13 ounces of one solution and 57.87 ounce of other solution
What is this one..?
Answer: The last one (C)
Step-by-step explanation: Use the rule to convert
15
1
3
to a radical, where
a
=
15
,
x
=
1
, and n = 3 .
3 √ 15
the width of the rectangular garden is eleven feet less than the length. find the dimensions. if the area is 80 square feet
Answer:
the dimensions are;
Width = 14.5 ft
Length = 25.5 ft
Step-by-step explanation:
We are told that width is 11 feet less than length. Let Width be W and Length be L.
Thus;
W = L - 11
Area of rectangle is given by;
Area; A = 2W + 2L
Putting L - 11 for width, we have;
Area = 2(L - 11) + 2(L)
A = 2L - 22 + 2L
A = 4L - 22
Length = L
Width = W
Area = A
A =4L-22
We are told that Area is 80 square feet. Thus;
80 = 4L -22
Add 22 to both sides to give;
102 = 4L
Divide both sides by 4 to give;
102/4 = 4L/4
L = 25.5
Recall that; W = L - 11
Thus;
W = 25.5 - 11 = 14.5
So the dimensions are;
Width = 14.5 ft
Length = 25.5 ft
linear function passes through the points (2, 9) and (7, 34). What is the rate of change?
Answer:
5
Step-by-step explanation:
1. What is the factored form of the
trinomial x2 – 8x + 7 ?
A
(x - 7)(x - 1)
(x + 7)(x - 1)
(x + 7)(x + 1)
(x - 3)(x - 4)
Answer:
(x - 7) (x - 1) or option a
Step-by-step explanation:
(x - 7) (x - 1) =
x² - 7x - x + 7 =
x² - 8x + 7
Factorise the following:
a) x + 10x + 16
b) x + 7x + 12
c) x + 13x + 12
Answer:
A) (x + 2)(x + 8) B) (x + 3)(x + 4) C) (x + 1)(x + 12)
Step-by-step explanation:
I think that you meant to put x^2 on all of them
A) You can factor out an x, an 8, and a 2. (x + 2)(x + 8)
B) You can factor out an x, a 3, and a 4. (x + 3)(x + 4)
C) You can factor out an x, a 12, and a 1. (x + 1)(x + 12)
If these answers are correct, please make me Brainliest!
The Factorize value is
A) (x + 2)(x + 8)
B) (x + 3)(x + 4)
C) (x + 1)(x + 12)
What is Factorization?A number is swiftly factorised into smaller numbers or factors of the number using the factorization formula. A factor is a number that evenly divides the inputted number.
The process of dividing a number into smaller numbers that, when multiplied together, equal the original number is known as factorization.
Given:
A) x² + 10x + 16
Now, factorizing
x² + 8x + 2x + 16
x(x+ 8)+ 2(x+8)
(x + 2)(x + 8)
B) x² + 7x + 12
Now, factorizing
x² + 3x + 4x + 12
x(x+ 3)+ 4(x+3)
(x + 3)(x + 4)
C) x² + 13x + 12
Now, factorizing
x² + 12x + x + 12
x(x+ 12)+ 1(x+3)
(x + 12)(x + 1)
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The scores of two school basketball teams are recorded.
Team A scored the following points per game: 67, 45, 84, 55, 73, 36, 80, 62 and 38.
Team B scored the following points per game: 72, 47, 76, 34, 98, 76, 56, 54 and 63.
Answer:
(67 + 45 + 84 + 55 + 73 + 36 + 80 + 62 + 38)/9 = 60
The mean number of points is 60.
Step-by-step explanation:
Add up all of the points and divide it by the number of games played
Answer:
The scores of two school basketball teams are recorded.
Team A scored the following points per game: 67, 45, 84, 55, 73, 36, 80, 62 and 38.
Team B scored the following points per game: 72, 47, 76, 34, 98, 76, 56, 54 and 63.
Step-by-step explanation:
The water level, measured in feet above mean sea level, of Lake Lanier in Georgia, USA, during 2012 can be modeled by the function L(t) = 0.01441t 3 − 0.4177t 2 + 2.703t + 1060.1 where t is measured in months since January 1, 2012. Estimate when the water level was highest during 2012.
Answer:
May 4th, 2012.
Step-by-step explanation:
The highest level can be found with the help of the First Derivative and Second Derivative Tests. First and second derivatives of the function are, respectively:
[tex]l'(t) = 0.04323\cdot t^{2}-0.8354\cdot t +2.703[/tex]
[tex]l''(t) = 0.08646\cdot t - 0.8354[/tex]
The First Derivative Tests consists on equalizing the first derivative to zero and finding the critical points.
[tex]0.04323\cdot t^{2}-0.8354\cdot t +2.703 = 0[/tex]
Roots are [tex]t_{1} \approx 15.672[/tex] and [tex]t_{2} \approx 4.077[/tex]. just the second root offer a realistic solution and is test by the second derivative.
[tex]l''(4.077) = -0.482[/tex] (which leads to a maximum).
Given that a year has 365 days or 12 months, the highest water level occurs at day:
[tex]n = \frac{4.077}{12} \cdot (365\,days)[/tex]
[tex]n \approx 124[/tex] (May 4th).
HELP PLEASE ITS LATE
Answer:
0.83 ft
Step-by-step explanation:
If the diameter of the cylinder is 20 in, then half of that would be 10 in.
10 in is not quite a full foot, so 10/12 = 0.83 ft.
What the square root of 243
Answer:
9√3
Step-by-step explanation:
that’s the simplified square root of 243 :)
What steps should be taken to calculate the volume of the right triangular prism? Select three options. A triangular prism. The triangular base has a base of 8 meters and height of 14 meters. The height of the prism is 7 meters. Use the formula A = one-half b h to find the area of the base. Use the formula A = b h to find the area of the base. The area of the base, A, is One-half (7) (8) = 28 meters squared. The area of the base, A, is One-half (8) (14) = 56 meters squared. The volume of the prism, V is (56) (7) = 392 meters cubed.
9514 1404 393
Answer:
A, D, E
Step-by-step explanation:
Given:
A triangular prism 7 m high with a base triangle that has a base of 8 m and a height of 14 m.
Find:
3 steps among those listed that should be taken to compute the volume.
Solution:
The listed steps are ...
(a) Use the formula A = one-half b h to find the area of the base.
(b) Use the formula A = b h to find the area of the base.
(c) The area of the base, A, is One-half (7) (8) = 28 meters squared.
(d) The area of the base, A, is One-half (8) (14) = 56 meters squared.
(e) The volume of the prism, V is (56) (7) = 392 meters cubed
__
The formula for the volume is ...
V = Bh . . . . where B is the area of the base, and h is the prism height
The formula for the area of a triangle is ...
A = 1/2bh . . . . where b is the base of the triangle and h is its height
We need the area of the triangular base before we can use the volume formula, so the first step is (a). The next step is to fill in values in that formula, so the second step is (d). Finally, we fill in values in the volume formula, so the third step is (e).
Of the steps listed, we should use steps (a), (d), (e).
At a pond there were 24 ducks swimming. 5 ducklings to 1 adult duck.
How many ducklings were swimming at the pond?
Answer:
24 ducks were swimming at the pond.
which function has zeros at x= -2 and x=5
Answer:
x^2-3x-10
Step-by-step explanation:
If the zeros are -2 and 5, the equation (x+2)(x-5) is true. If you multiply those factors together you get x^2-3x-10.
You are running a concession stand at a basketball game. You are selling hot
dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the
end of the night you made a total of $78.50. You sold a total of 87 hot dogs and
sodas combined. You must report the number of hot dogs sold and the
number of sodas sold. How many hot dogs were sold and how many sodas
were sold:
Let x = the number of hot dogs sold
Let y = the number of sodas sold
write your answer as an ordered pair (x,y)
x= hot dogs
y= soda
Total sold
1 x + 1 y = 87 .............1
2 x 0.50 y = 78.50 .............2
Eliminate y
multiply (1)by -0.50
Multiply (2) by 1.00
-0.50 x -0.50 y = -43.50
2 x + 0.50 y = 78.50
Add the two equations
1 x = 35.00
/ 1
x = 35.00
plug value of x in (1)
1 x + 1 y = 87
35 + y = 87
y = 87 -35
y = 52
y = 52.00
x= 35 hot dogs
y= 52 soda
Final answer:
The number of hot dogs and sodas sold can be determined using a system of linear equations. By solving these equations, it was found that 35 hot dogs and 52 sodas were sold, represented as an ordered pair (35, 52).
Explanation:
Let's solve the problem of determining the number of hot dogs (x) and sodas (y) sold at a concession stand. Given that each hot dog costs $1.50 and each soda costs $0.50, and the total revenue is $78.50 for 87 items sold, we can set up two equations:
1.50x + 0.50y = 78.50 (The revenue equation)x + y = 87 (The total items equation)Now, let's use these equations to find x and y by substitution or elimination. If we multiply the second equation by 0.50, we get:
0.50x + 0.50y = 43.50Subtract this new equation from the first one to eliminate y:
1.50x + 0.50y = 78.50-(0.50x + 0.50y = 43.50)x = 35 (Number of hot dogs sold)Now, plug x back into the second original equation:
35 + y = 87
So, y = 52 (Number of sodas sold).
The answer as an ordered pair is: (35, 52), where 35 represents the number of hot dogs sold, and 52 represents the number of sodas sold.
Suppose Ms. Smith sells her 2018 Honda Fit next year. The original cost of the vehicle was $10,000. During the time she has owned the car she has taken $3,000 dollars of deprecation on it. Ms. Williams sells the car for $9,000. What is result of the transaction
Answer:
An ordinary gain of $2,000
Step-by-step explanation:
Cost of the vehicle(C)=$10,000
Depreciation(D)=$3,000
Selling price(S)=$9,000
Worth of the vehicle= Cost price - depreciation
=$10,000-3,000
=$7,000
Net worth= selling price - worth of the vehicle
=$9,000-$7,000
=$2,000
Answer:
transaction would be a profit of $ 2,000.
Step-by-step explanation:
Given:-
- The original cost of the vehicle, C = $ 10,000
- The depreciation of the vehicle until the time of selling, d = $3,000
- The price at which the vehicle is sold, S = $ 9,000
Find:-
What is result of the transaction
Solution:-
- Whenever an asset is bought the value of the asset depreciates. There are several tools and methods to estimate the amount of depreciation.
- After n years of possession of car / since manufactured the asset undergoes depreciation until its sold or salvaged.
- Here Ms Smith possessed her car for a certain amount of time t years.
- The accumulated depreciation at the time she sold her car was " d ".
- So at the point of selling her car the actual worth or value of her car was ( C* ):
C* = C - d
C* = $10,000 - $3,000
C* = $7,000
- Now her car's value is ( C* ). If she sells her for " S " higher than current asset worth then she will profit from it otherwise she would sustain a loss in her selling transaction. So the net asset worth she would have after selling her car would be:
Net Worth = S - C*
Net Worth = $9,000 - $ 7,000
Net Worth = $ 2,000
Answer: The net worth is a positive value that means she sold her car for higher value than its worth; hence, the transaction would be a profit of $ 2,000.
Give the digits in the thousands place and the tens place.
8,695
thousands:
tens:
Answer:thousands-8 5 in the tans place
Step-by-step explanation:
Answer:
Thousands: 8
Tens: 9
Step-by-step explanation:
Thousands, Hundreds, Tens, Ones
8 Thousands, 6 Hundreds, 9 Tens, 5 Ones
Bert wants to save $5742 so that he can buy the car he wants. If Bert can save $18 per day, how many days will it take him to save enough money?
Answer: It will take him 319 days
Step-by-step explanation:
5742 divided by 18 = 319
Answer:
319 daysStep-by-step explanation:
If he wants to save $5,742, and is saving $18 per day, you can simply simplify $5,742 by $18 and you get 319.
The number of words per page in a certain book is normally distributed with a mean of 340 words and a standard deviation of 20 words.
Approximately what percent of pages in the book are less than 360 words in length?
Answer:
Step-by-step explanation:
Since the number of words per page in the book is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = number of words per page.
µ = mean
σ = standard deviation
From the information given,
µ = 340 words
σ = 20 words
The probability that the number of pages in the book are less than 360 words in length is expressed as
P(x < 360)
For x = 360,
z = (360 - 340)/20 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.84
The percent of pages in the book that are less than 360 words in length is
0.84 × 100 = 84%
The number of mosquitoes in a field after a major rainfall is modeled by the function M defined by M(t)=−t3+12t2+144t , where t is the number of days after the rainfall ended and 0≤t≤18 . Using correct units, interpret the meaning of M′(15)=−171 in the context of the problem.
Answer: The rate at which mosquitoes are appearing in a field 15 days after the rainfall ended is -171. I believe this to be correct.
M'(15) = -171 means that after 15 days, the number of mosquitoes is decreasing at a rate of 171 mosquitoes per day.
Interpreting the FunctionThe function M(t) represents the number of mosquitoes in a field after t days have passed since a major rainfall. The derivative of this function, M'(t), represents the rate of change of the number of mosquitoes.
M'(15) = -171 means that after 15 days, the number of mosquitoes is decreasing at a rate of 171 mosquitoes per day. In other words, the population of mosquitoes is declining by 171 mosquitoes each day.
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What is the quotient of 20 and n
I need help with these two. It’s a project and it’s due tomorrow and need better understands to find the base and the perimeter of the base. Please I need help. My teacher gave me some details about project:
Goal: Determine the most affordable way to package 12 cans of soda.
Details:
● Height of each can: 5 inches
● Radius of each can: 2 inches
All cans must be packaged so that they are standing upright like such----->
Answer:
Option 3
Step-by-step explanation:
If the radius of the can is 2 inches, then the diameter must be 4 since the diameter is 2 times the radius. So we want to make it as small as possible. I think the best option is option 3 because it is tight and it is stacked nicely. The package wrapping will not have much to go around. I hope this helps! please mark me brainliest! Thanks!
A 150-inch pipe is cut into two pieces. One piece is four times the length of the other. Find the length of the shorter piece. The shorter piece is nothing inches long.
Answer:
Step-by-step explanation:150/4 = 37.5 inches small piece
150 - 37.5 = 112.5 large piece
37.5 * 4 = 150
Answer: the shorter piece is 30 inches long.
the longer piece is 120 inches long.
Step-by-step explanation:
Let x represent the length of the shorter piece.
Let y represent the length of the longer piece.
A 150-inch pipe is cut into two pieces. It means that
x + y = 150- - - - - - - -1
One piece is four times the length of the other. It means that
y = 4x
Substituting y = 4x into equation 1, it becomes
x + 4x = 150
5x = 150
x = 150/5
x = 30
y = 4x = 4 × 30
y = 120
the angle of depression from an eagle sitting on top of a flagpole to base tree is 63. If the flag pole is 18 feet tall, then what is the distance between the pole and tree?
here u go:
BC = 18 × 1.96
= 35.28 ft
Therefore the distance between the pole and the tree is 35.28 ft .
Helena lost her marbles. But then she found them and put them in 4 bags with m marbles in each bag. She had 3 marbles left over that didn’t fit in the bag.
how many marbles does Helena have.
Answer:
4m+3
Step-by-step explanation:
Helena had ...
m +m +m +m +3
marbles. This is more easily written as ...
4m +3 . . . . the number of Helena's marbles