To factor the expression x³ - 2x² - 9x + 18, use the grouping method to factor out a common binomial factor.
Explanation:To factor the expression x³ - 2x² - 9x + 18, we can first look for any common factors. Since there are no common factors among all the terms, we will use the grouping method to factor the expression.
Step 1: Group the terms in pairs.
(x³ - 2x²) - (9x - 18)
Step 2: Factor out the greatest common factor from each pair.
x²(x - 2) - 9(x - 2)
Step 3: Notice that we now have a common binomial factor of (x - 2).
(x² - 9)(x - 2)
Therefore, the factored form of the expression x³ - 2x² - 9x + 18 is (x² - 9)(x - 2).
The student is looking to factor the polynomial expression x^3 - 2x^2 - 9x + 18. This process typically involves finding whether factors like binomials divide the polynomial without a remainder, using methods like grouping, trial and error, or the Rational Root Theorem, followed by long or synthetic division.
Explanation:The student has asked to factor the expression x^3 - 2x^2 - 9x + 18.
To factor this expression, we can follow a systematic approach, which often starts with looking for common factors or applying techniques such as grouping, trial and error, or the use of the Rational Root Theorem. In this case, we may not see an immediate common factor, so we might try to group terms or apply synthetic division or the Rational Root Theorem to identify potential roots of the polynomial.
A factor of a polynomial is a binomial (or another polynomial) that divides the original polynomial without leaving a remainder. If we find such a factor, we can then divide the original polynomial by this factor to simplify the expression further. For example, if we discover that (x - 3) is a factor, then we can divide the polynomial by (x - 3) to find the other factors.
Unfortunately, without performing the actual factoring process or having additional information, we cannot factor this specific expression purely based on the question provided. If we had one root or factor given, we could use long division or synthetic division to further factor the expression, and then possibly factorize it completely into the product of binomials or another polynomial.
Please help! Numbers 16 & 17.. It will be much appreciated! :D
What is a soliloquy? ...?
What is the solution to the equation?
5(8 + 7) = 5 • x + 5 • 7
A.
x = 1
B.
x = 5
C.
x = 7
D.
x = 8
A surveyor, standing 100 ft. from the base of a building, measures the angle of elevation to the top of the building to be 75 degrees. How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?
4sin(x)−4=0
solve for x
Find the missing length. The triangle in each pair are similar.
Answer:
39 UNIT
Step-by-step explanation:
According to similar triangle.
Let's call NG "X"
45/27 = 65/x
X=( 65*27)/45
X= 1755/45
X = 39
A vehicle travels on a highway at a rate of 65 mi/h how long does it take the vehical to travel 25 mi?
Answer:
Step-by-step explanation:
A vehicle travels at a rate of 65 m/h, How long does it take the vehicle to travel at 25 miles?
Apply the "distance formula":
d = rt
25 = 65t
25/65 = t
5/13 hour = t
or
0.385 hour = t
or
23.08 minutes = t
The mean number of hours that Raphael worked over the past four weeks is 37.75. If he works 40 hours this week, what will the mean number of hours be that he will have worked over the five-week period?
What is the five-week mean?
An Antique vase is projected to be worth $1000 in 2 years and $1,300 after 5 years. If the value continues to appreciate at the same rate, what will it be worth in 8 years?
The value of the antique vase after 8 years with a consistent appreciation rate, it would amount to $1,600.
An antique vase:
Value after 2 years: $1,000
Value after 5 years: $1,300
To find the value after 8 years, we can assume a constant rate of appreciation:
In 8 years, the value will be: $1,000 + ($1,300 - $1,000) = $1,300 + ($1,300 - $1,000) = $1,600
What is d if p equals 15 in d=-3p^2+168p-315
A brownie recipe requires one and one third cups of sugar to one cup of chocolate chips. If four and two thirds cups of sugar is used, what quantity of chocolate chips will be needed, according to the recipe?
...?
Final answer:
To find the number of chocolate chips needed for four and two-thirds cups of sugar, we use the given ratio of 4/3 cups of sugar to 1 cup of chocolate chips and set up a proportion. Solving it gives us 3.5 cups of chocolate chips.
Explanation:
To determine the number of chocolate chips needed when using four and two-thirds cups of sugar according to the brownie recipe, we must first understand the ratio given in the recipe, which is one and one-third cups of sugar to one cup of chocolate chips. This ratio can be simplified to a fraction for easier calculation: 4/3 cups of sugar : 1 cup of chocolate chips.
With this ratio, we can set up a proportion to find the amount of chocolate chips needed for four and two-thirds cups of sugar:
(4/3 cups of sugar) / (1 cup of chocolate chips) = (14/3 cups of sugar) / (x cups of chocolate chips)To solve for x, we cross-multiply and solve the resulting equation:
(4/3) * x = (14/3) * 1x = (14/3) * (3/4)x = 14/4x = 3.5The quantity of chocolate chips needed is 3.5 cups when using four and two-thirds cups of sugar.
PLEASE HELP!!
Oscar entered y=−0.4^x+3y=−0.4^x+3 into an online graphing tool.
What function did he graph?
y=(−0.4)x+3y=(−0.4)x+3
y=(−0.4)x+3y=(−0.4)x+3
y=−(0.4)x+3y=−(0.4)x+3
y=−(0.4)x+3
During World War I, the Germans had a gun
called Big Bertha that was used to shell Paris.
The shell had an initial speed of 2.41 km/s at
an initial inclination of 61.5 to the horizontal.
The acceleration of gravity is 9.8 m/s2 .
How far away did the shell hit?
Answer in units of km
How long was it in the air?
Answer in units of s
To find the distance the shell hit and the time it was in the air, we need to determine the total time it takes for the shell to hit the ground. The horizontal component of the shell's initial velocity remains constant, while the vertical component is affected by gravity. By solving for the time using the vertical component, we can then multiply it by the horizontal component to find the distance and convert it to kilometers.
Explanation:To find the distance that the shell hit, we need to determine the time it was in the air. We can do this by finding the total time it takes for the shell to hit the ground. The shell's initial velocity is given as 2.41 km/s at an angle of 61.5 degrees. We can break down the initial velocity into its horizontal and vertical components. The horizontal component remains constant, while the vertical component is affected by gravity. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can solve for the time it takes for the shell to reach the ground.
Find the horizontal component of the initial velocity using the equation horz_vel = init_vel * cos(angle).Find the vertical component of the initial velocity using the equation vert_vel = init_vel * sin(angle).Using the vertical component, solve for the time it takes for the shell to reach the ground using the equation -vert_vel = 0 + 0 * t - 0.5 * acceleration * t^2.The time calculated in step 3 will give us the total time the shell was in the air.Multiply the total time by the horizontal component of the initial velocity to get the distance that the shell hit.Convert the distance from meters to kilometers by dividing by 1000.So, the shell hit a distance of [distance] km away and was in the air for [time] s.
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Simplify (8j3 + 5j2 – 3) – (5j3 + 7j2 – 12j + 7) ...?
Answer:
3j^3 - 2j^2 + 12j - 10
Step-by-step explanation:
I took the test and got a 100%
What is the best approximation of the sine of 50°?
A. 0.2624
B. 0.6428
C. 0.7660
D. 1.1918
A truck carried 3 1/3 ton of sand, but lost 1/4 ton of sand along the way. how many tons of sand were survived
A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal parts of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?
To maximize profit, the candy manufacturer should use mathematical linear programming. The decision variables are the amounts of Candy A (x) and Candy B (y). The profit function P = 285x + 260y is to be maximized subject to constraints arising from available stock of dark chocolate, caramel, and walnuts, leading to a typical linear programming problem.
Explanation:To solve this problem, we need to use Linear Programming, a mathematical model that helps in making optimal decisions. The candies are what we call decision variables. Our decision variables here are Candy A and Candy B.
Candy A: x kilograms (dark chocolate and caramel in equal parts).
Candy B: y kilograms (two parts of dark chocolate and one part of walnut).
We want to maximize the profit function P = 285x + 260y subject to constraints arising from the available stock of dark chocolate (DC), caramel (C), and walnuts (W).
DC constraint: A uses DC in equal parts, and B uses two parts DC. Therefore, x + 2y ≤ 360.C constraint: A uses equal parts C, x ≤ 430 (as B doesn't use C).W constraint: B uses one part W, y ≤ 210 (as A doesn't use W).
The next step is to solve these inequalities graphically or using mathematical methods to get values of x and y that maximize P while respecting constraints. This case, where we want to optimize a certain function with respect to constraints, is a typical linear programming problem in mathematics.
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Wendy wants $15,000 saved in 6 years to make a down payment on a house. How much money should she invest now at 4.65% compounded annually in order to meet her goal?
The graph of y = x2 is shown below.
If graphed on the same grid, which of the following could be the graph of y = 0.4x2?
Answer:
The answer is in the attachment.
Step-by-step explanation:
Coefficient in front of x^2 is 0.4. What that means is that for same increase of x now we will have less increse of y. If you picture that we can also say that graph would be wider. The graph will stay on positive side of y axis because x^2 is always positive and 0.4 times that is again always positive.
The answer is third graph (middle one)
what is the area of a right triangle with side lengths 6, 8, and 10? a. 48 b. 40 c. 30 d. 24
A car Purchased for $18,500. After each year, the resale value decreases by 30%. What will the resale value be after 4 years
Solve for x. Enter your answer in interval notation using grouping symbols.
x^2+4x<45 ...?
Which of the following is a result of shifting a circle with equation (x + 3)² + (y - 2)² = 36 left 3 units?
Answer:
The answer is [The x-coordinate of the center of the circle decreases by 3.]
Step-by-step explanation:
Which of the following is not a way to prove a quadrilateral is a parallelogram?
The way to not prove a quadrilateral is a parallelogram is; Show one set of opposite sides of the quadrilateral is congruent.
Parallelogram and CongruenceA parallelogram is a quadrilateral which has opposite sides to be congruent and parallel as the name implies and hence, opposite angles of the parallelogram are congruent.
However, showing one set of opposite sides of the quadrilateral is congruent is not a confirmatory test for a parallelogram, as it evades the parallel law of opposite sides of the Parallelogram.
Read more on parallelogram;
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A furniture company misprinted a sales ad for a living room set but honors the advertised price. For each customer who purchases the living room set, the company suffers a loss of $125. Write a function to represent the company's total loss. What is the value of the function for an input of 50, and what does it represent? ...?
half a pepperoni pizza plus three fourths a ham-and-pineapple pizza contains 765 calories. One fourth of a pepperoni pizza plus a whole ham-and-pineapple pizza contains 745 calories. How many calories are in each kind of pizza?
1. D (4,5)
2. C
3. D
4. A
5. C
6. D
7. B
8. C
9. A
10. B
OR
1. B (2,6)
2. A
3. A
4. C
5. D
6. A
7. A
8. B
9. C
10. A
Don't deny it, you came here for the answers ;)
Final answer:
A half pepperoni pizza contains 660 calories and a ham-and-pineapple pizza contains 580 calories.
Explanation:
Let's represent the number of calories in half a pepperoni pizza as x, and the number of calories in a ham-and-pineapple pizza as y. We can set up a system of equations to represent the given information:
0.5x + 0.75y = 765 -- Equation (1)
0.25x + y = 745 -- Equation (2)
We can solve this system of equations using the method of substitution:
From Equation (2), y = 745 - 0.25x
Substitute this value of y into Equation (1):
0.5x + 0.75(745 - 0.25x) = 765
Simplify and solve for x:
0.5x + 558.75 - 0.1875x = 765
0.3125x = 206.25
x = 660
Now substitute the value of x back into Equation (2) to find y:
0.25(660) + y = 745
Simplify and solve for y:
165 + y = 745
y = 580
Therefore, there are 660 calories in a half pepperoni pizza, and 580 calories in a ham-and-pineapple pizza.
is 87 a prime or composite
Answer:
Prime
Step-by-step explanation:
77 is composite
It has other factors besides 1 and itself
68 -composite
52-composite (it is even)
31 -prime
59-prime
21/80 in a simplified fraction
Miss fernandez built two rectangular gardens the length of garden a is 2 feet longer than twice its width the list of garden b is 1 foot less than the width of garden a the length of garden b is 2.5 times its width the two gardens have the same perimeter what are the dimensions of the gardens
Wally bakes muffins. in each batch of 12 muffins, he bakes 8 bluberry muffins write in simplest form the fraction of muffins that are not blue berry
Answer:
probably 4/12 = 1/3 muffins are not blueberry
Step-by-step explanation: