They show the decomposition of a multiplication expression into smaller parts
Volume is legnth times width times height so 3 dimentions
thee teacher probabl y wants you to factor the trinomial into 3 factors so
x^3+5x^2-24x
first factor out x
x(x^2+5x-24)
then factor
find what 2 numbers multiply to get -24 and add to get 5
the numbers are -3 and 8
x^2+5x-24 factors to
(x-3)(x+8)
the factored form is
(x)(x-3)(x+8)=volume
no dimention can be ≤0 so therefor
x≤0
x-3≤0
add 3
x≤3
x+8≤0
subtract 8
x≤-8
so the values for x is x<3
so if you had the volume, let's say 42 then
x^3+5x^2-24x=42
subtract 42 from both sides
x^3+5x^2-24x-42=0
factor and set each to zero to find the dimentions
Answer:
The trigonometric form of the complex number is 12(cos 120° + i sin 120°)
Step-by-step explanation:
* Lets revise the complex number in Cartesian form and polar form
- The complex number in the Cartesian form is a + bi
-The complex number in the polar form is r(cosФ + i sinФ)
* Lets revise how we can find one from the other
- r² = a² + b²
- tanФ = b/a
* Now lets solve the problem
∵ z = -6 + i 6√3
∴ a = -6 and b = 6√3
∵ r² = a² + b²
∴ r² = (-6)² + (6√3)² = 36 + 108 = 144
∴ r = √144 = 12
∵ tan Ф° = b/a
∴ tan Ф = 6√3/-6 = -√3
∵ The x-coordinate of the point is negative
∵ The y-coordinate of the point is positive
∴ The point lies on the 2nd quadrant
* The measure of the angle in the 2nd quadrant is 180 - α, where
α is an acute angle
∵ tan α = √3
∴ α = tan^-1 √3 = 60°
∴ Ф = 180° - 60° = 120°
∴ z = 12(cos 120° + i sin 120°)
* The trigonometric form of the complex number is
12(cos 120° + i sin 120°)
<span>Part 1.
Given that a small company did an analysis of their pay scale versus years of
experience and found that the line of best fit was y = 2035.6x + 36,000.
The 36,000 in the context of the problem mean that if they had 0 years of experience their salary would be 36,000.
For any linear equation of the form y = mx + c, The value of c is the value of the function when the independent variable, x, is 0.
Part 2.
Given that Harris is building a deck around his pool and that his contractor charges
$525 for labor plus an additional $4.75 per square foot for materials.
Recall that the equation of a line is given by y = mx + c, where m is the rate at which the independent value, x, is changing and c is the fived initial value.
Given that the contractor charges a fixed labour cost of $525 and additional rate of $4.75 per square foot for materials, therefore, the equation that can be used to determine the cost (y), in dollars, for a
deck with an area of x square feet is given by y = 4.75x + 525
Part 3.
Given that Ted researched the price of airline tickets and discovered a
correlation between the price of a ticket and the number of miles
traveled and after recording his data on a scatter plot, he determined the
equation for the line of best fit is y = 300 + 0.45x.
The 0.45 in the equation
represent the number of miles traveled
</span>For any linear equation of the form y = mx + c, The value of m is
the <span><span>rate at which the independent value, x, is changing.
</span>
Part 4.
The product of two or more numbers is the multiplication of the numbers. The expression that best represents the product of quantities a, b, and H is given by abH
Part 5)
Given that the price of a gallon of milk was $2.65. After the price rose y dollars after
the last hurricane, the price becomes 2.65 + y. After the price dropped $0.15, the price becomes 2.65 + y - 0.15 = 2.5 + y. After the price rose again by
$0.05, the price becomes 2.5 + y + 0.05 = 2.55 + y.
Therefore, the expression that represents the current price of milk is given by 2.55 + y
Part 6)
Given that the function C = 12x + 1500 models the cost of consumable computer
supplies for a school district.
Given that in the equation, C represents the cost
(in thousands of dollars), and x represents the number of years since
2015.
2030 is 15 years since 2015, thus, the value of x in the model is 15.
Therefore, according to the model, the cost of </span><span>consumable computer
supplies for the school district for the year 2030 will be 12,000(15) + 1,500,000 = 180,000 + 1,500,000 = $1,680,000.
Part 7.
There are 12 months in 1 year, thus, there will be (1)(x) / 12 = x / 12.
Therefore, the expression that represents how many years are in x months is given by x / 12
Part 8.
Given that Henry and Holly catch crawfish which they sell to a local Cajun
restaurant and that the restaurant pays them $3.80 a pound for live crawfish
that are large enough.
Given that 5% of the crawfish die before they can deliver
them to the restaurant and 7% of the live crawfish are too small.
Thus, the percentage of a pound of crawfish sold is given by (1 - 0.05)(1 - 0.07) = 0.95 x 0.93 = 0.8835 = 88.35%
Let x represent the number of pounds of crawfish they catch, therefore, an expression which represents how much money they make per pound of crawfish they catch is given by 88.35% of 3.80 = 0.8835(3.80) = 3.357x
Part 9.
Given that Olivia is growing roses and keeps track of how much fertilizer (in
ounces) she adds to the soil and how many blooms each rose bush has.
Given that a linear relationship that can be modeled by the equation y =
1.345x + 4 is established.
From the model it can be seen that Olivia's rose bush will have 4 blooms when x is 0, i.e. when she adds no fertilizer to the soil.
Part 10.
Given that Olivia is growing roses and keeps track of how much fertilizer (in
ounces) she adds to the soil and how many blooms each rose bush has.
Given that a linear relationship that can be modeled by the equation y =
1.345x + 4 is established.
The 1.345 in the contex of the problem mean that for every additional bloom on the rose bush she added 1.345 ounces of fertilizer.</span>
For any linear equation of the form y = mx + c, The value of m is
the <span>rate at which the independent value, x, is changing.</span>
