Which statement best describes the graph of x3 − 3x2 − x + 3?
It starts down on the left and goes up on the right and intersects the x-axis at x = −1, 2, and 3.
It starts down on the left and goes up on the right and intersects the x-axis at x = −1, 1, and 3.
It starts up on the left and goes down on the right and intersects the x-axis at x = −1, 2, and 3.
It starts up on the left and goes down on the right and intersects the x-axis at x = −1, 1, and 3.
It starts down on the left and goes up on the right and intersects the x-axis at x = −1, 1, and 3.
Which statement best describes the graph?
We want to describe the graph of:
[tex]y = x^3 - 3x^2 - x + 3[/tex]
We can see that the y-intercept is y = 3, and the x-intercepts can be seen in the graph below, these are at: x = -1, x = 1 and x = 3.
We also can see that it is cubic, so it starts down.
Then the correct option is the second one:
"It starts down on the left and goes up on the right and intersects the x-axis at x = −1, 1, and 3."
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What is the solution to the system of equations graphed below?
a. (2,-3)
b. (-3,2)
c. (-2,3)
d. (3,-2)
The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas? (Approximate to the nearest hundredth inch.)
10.62 inches
10.63 inches
10.64 inches
10.65 inches
The area of the square canvas is the square of its side length
The length of the side of the square canvas is 10.63 inches
The area the square canvas can hold is given as:
[tex]Area=113in^2[/tex]
The canvas has a square as its shape, and the area of a square is:
[tex]Area = L^2[/tex]
Where:
L represents the length of the shape (i.e. the square canvas)
So, we have:
[tex]L^2 = 113[/tex]
Take square roots of both sides
[tex]L = \sqrt{113[/tex]
Take the square root of 113
[tex]L = 10.63[/tex]
Hence, the length of the side is 10.63 inches
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The sum of the roots of 5 - 2m - 3m2 = 0 is:
Find the value of y. Look at image attached
What is the sum of the measures of the exterior angles in a heptagon? Explain
When constructing inscribed polygons how can you be sure the figure inscribed is a regular polygon
Angle c and angle d are supplementary, the measure of angle d is eight times the measure of angle
c. find measure of angle c and measure of angle d
Answer:
160
Step-by-step explanation:
A mother has 3 kids. Kid A is half the mother's current age. Kid B is 4 years younger than Kid A. In 3 years, Kid C will be 1/5 of his mother's age (not her current age). The sum of all their current ages is the mother's current age.
How old is the mother currently?
How old is each of her kids?
Final answer:
The mother is currently 40 years old. Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.
Explanation:
Let's denote the mother's current age as M. Kid A's age is A = M/2. Kid B is 4 years younger than Kid A, so B = A - 4 = M/2 - 4. Kid C will be 1/5 of his mother's age in 3 years, so if we denote Kid C's current age as C, we have C + 3 = 1/5(M + 3). The sum of all their current ages is the mother's current age, so M = A + B + C. With these equations, we can solve for M, A, B, and C.
We substitute A and B into the mother's age equation: M = M/2 + M/2 - 4 + C. Rearranging terms, we get M - 4 = C. Now we have two expressions for C: M - 4 and 1/5(M + 3) - 3. Setting them equal to each other, we get M - 4 = 1/5(M + 3) - 3. Solving for M, we find that M = 40 years old.
Now we can find Kid A, B, and C's ages using the mother's age. Kid A is half the mother's age, A = M/2 = 20 years old. Kid B is 4 years younger than Kid A, B = A - 4 = 16 years old. Kid C's age can be found by the substitution, C = M - 4 = 36 years old. So the mother is 40 years old, Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.
Solve the quadratic equation by completing the square.
x^2-10x+15=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
Which of the following is unnecessary when multiplying these polynomials?
(2x^3+2x^2-3x)(9x^2-4x+5)
A)use of the distributive property
B)use of the multiplication property of exponents
C)combine like terms
D)find the GCF
Shape 1 and shape 2 are plotted on a coordinate plane. Which statement about the shapes is true?
Two integers that vary in sign
How do we refer to self-contained state actions: monadic. dyadic. triadic. k-adic?
In mathematics, self-contained state actions are known as k-adic. Monadic, dyadic, and triadic are specific cases of k-adic functions.
Explanation:In mathematics, self-contained state actions are known as k-adic. The term 'k-adic' refers to functions that take k inputs and produce a single output. Monadic, dyadic, and triadic are specific cases of k-adic functions, where k is 1, 2, and 3, respectively. Thus, it typically refers to a numeral or number system that is based on the value of k, which can be any positive integer.
In such systems, numbers are represented using a base of k, and each digit holds its own place value. K-adic expansions are useful in number theory and algebraic number theory, providing insights into number properties and relationships in various mathematical contexts.
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Eight less than a number is seventy-five. What is the number? -67 67 83
8-75 = x
x=8+75
x= 83
the number is 83
Which of the following questions describes the equation w + 9 = -17? What number, A. when decreased by nine, is equal to negative seventeen?
B. What number, when added to negative seventeen, equals nine?
C. What number, when increased by nine, results in negative seventeen?
D. What number, when subtracted from nine, equals negative seventeen?
At what value of x does the graph of the function f(x) have a vertical asymptote?
F(x) = 5X/ 2X-6
The profit in manufacturing x refrigerators per day, is given by the profit relation p = ¡3x2 + 240x ¡ 800 dollars. a how many refrigerators should be made each day to maximise the total profit? b what is the maximum profit?
Final answer:
The firm should produce 40 refrigerators per day to maximize profit, resulting in a maximum profit of $4,000. A flat tax would reduce profit without affecting price directly, while a per unit tax could increase prices and alter the profit-maximizing output and profit levels.
Explanation:
Maximizing Profit and Effects of Taxes on a Firm's Profit
The profit that a firm makes from manufacturing x refrigerators per day is given by the profit function p = -3x^2 + 240x - 800, where p stands for profit. To maximize the total profit, we need to find the vertex of this quadratic function, which represents the highest point of the parabola on a graph. The x-coordinate of the vertex can be found using the formula -b/(2a), where a is the coefficient of x^2 and b is the coefficient of x. Substituting the values from the profit function, we get x = -240/(2*(-3)), which simplifies to x = 40. Thus, the firm should produce 40 refrigerators per day to maximize profit.
To find the maximum profit, we substitute x = 40 back into the profit function: p = -3(40)^2 + 240(40) - 800. After calculating, the maximum profit comes out to be $4,000 per day.
If a tax of $1,000 per day is imposed on the firm, this would lower the profit by the amount of the tax, without directly affecting the price. It's uncertain how the firm might react—whether they decide to increase the price to compensate or not is a strategic decision.
A tax of $100 per unit would likely cause the firm to increase the price by at least $100 to maintain their profit margins. The new profit function would be p = -3x^2 + (240-100)x - 800, which would also affect the profit-maximizing output. After recalculating with the new function, the firm would adjust its output and profit accordingly.
Carly and janiya put some money into their money boxes every week. the amounts of money (y), in dollars, in their money boxes after certain amounts of time (x), in weeks, are shown by the equations below:carlyy = 60x + 40janiyay = 50x + 80after how many weeks will carly and janiya have the same amount of money in their money boxes and what will that amount be? 5 weeks, $280 5 weeks, $340 4 weeks, $280 4 weeks, $340
Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4)? a 180 rotation about the origin a 90 counterclockwise rotation about the origin and a translation down 4 units a 90 clockwise rotation about the origin and a reflection over the y-axis a reflection over the y-axis and then a 90 clockwise rotation about the origin
Answer:
C. a 90 clockwise rotation about the origin and a reflection over the y-axis
Step-by-step explanation:
The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x) = 9x – 2. Which expression represents the profit, (k – h)(x), of producing soccer balls?
Andrea and raleigh are each rolling a fair, six-sided die. they roll their dice simultaneously, individually keeping a sum until someone reaches 100; whoever reaches 100 first wins. (if they reach 100 on the same roll, it's a tie.) andrea's die has sides 1, 2, 3, 4, 5, and 6. raleigh's has sides 1, 1, 1, 6, 6, and 6. who is more likely to win?
Let An be the likely number of rolls for Andrea to arrive at 100 or more, given that she is n away from the target of 100 (which means her current total is 100 - n ). Then we get the recurrence relation
An = 1 + (1/6) (An-1 + An-2 + An-3 + An-4 + An-5 + An – 6)
and the initial conditions A0 = A-1 = A-2 = A-3 = A-4 = A-5 = 0. This results in A100 = 29.0476 as the amount of expected rolls that Andrea has to make.
Now let Rn to be expected amount of rolls for Raleigh to arrive at 100 or more, given than he is also n away from the target of 100. Now the recurrence relation is:
Rn = 1 + (1/2) (Rn-1 + Rn-6)
with the initial conditions R0 = R-1 = R-2 = R-3 = R-4 = R-5 = 0. This gives us R100 = 29.1837 as the expected amount of rolls for Raleigh.
Therefore Andrea has to make less number of rolls thus she is expected to win.
Winner: Andrea
Bill is riding his bicycle. He takes 5 hours to ride 62.5 kilometers. What is his speed?
A box contains 13 red hats, 15 white hats, 18 blue hats, and 14 brown hats. Nina randomly chooses a hat from the box.
What is the probability that it will NOT be white? Write your answer as a decimal.
13 + 15 + 18 +14 = 60 total hats
15 are white
60-15 = 45 hats that are not white
45/60 reduces to 3/4
3/4 =0.75 probability the hat will not be white
1) What kind of figure is formed by the cross section below?
square
rectangle
circle
ellipse that is not a circle
If only 4.5% of the non- historically protected have a field stone and mortar foundation, how many homes is this?
What is the equation in point−slope form of the line passing through (−2, −5) and (2, 3)?
a) (y + 2) = −2(x + 5)
b) (y − 2) = 2(x − 3)
c) (y − 3) = 2(x − 2)
d) (y + 3) = −2(x + 2)
Point B is between A and C. If AB = 6 cm and BC = 11 cm, what is AC?
Which function is shown in the graph below?
Answer: The correct option is 2.
Explanation:
From the given figure it is easily noticed that the graph intersect the y-axis at y=9 , therefore the y-intercept is (0,9).
To find the equation of the curve put x=0 in each option, If we get y=9 then that option is true.
Option 1:
[tex]y=(\frac{1}{2})^{(x+3)}-1[/tex]
[tex]y=(\frac{1}{2})^{(0+3)}-1=\frac{1}{8}-1=\frac{-7}{8}[/tex]
Option 2:
[tex]y=(\frac{1}{2})^{(x-3)}+1[/tex]
[tex]y=(\frac{1}{2})^{(0-3)}+1=8+1=9[/tex]
Option 3:
[tex]y=(\frac{1}{2})^{(x-1)}+3[/tex]
[tex]y=(\frac{1}{2})^{(0-1)}+3=2+3=5[/tex]
Option 4:
[tex]y=(\frac{1}{2})^{(x+1)}-3[/tex]
[tex]y=(\frac{1}{2})^{(0+1)}-3=\frac{1}{2}-3=\frac{-5}{2}[/tex]
Only the equation in option 2 have the y-intercept (0,9), therefore the correct answer is option second.
Answer:
Its B
Step-by-step explanation:
Allen bought 1,350 shares of stock for $12 per share. If he sold all his shares for $27,000, how much profit on each share did he make?