The number of roots a polynomial will have can be determined by its degree, assuming that we are considering all possible roots including complex roots and counting each root according to its multiplicity.
For example, a linear polynomial (degree 1) such as [tex]\( ax + b = 0 \)[/tex] will have exactly one root. A quadratic polynomial (degree 2) like [tex]\( ax^2 + bx + c = 0 \)[/tex] will have two roots, which could be real or complex. Similarly, a cubic polynomial (degree 3) will have three roots, and so on.
If the coefficients of the polynomial are real numbers, then any complex roots will occur in conjugate pairs. This means that a real polynomial of odd degree will always have at least one real root.
To summarize, the number of roots of a polynomial equation is equal to the degree of the polynomial, provided that:
1. We include all real and complex roots.
2. We count each root according to its multiplicity (the number of times it is repeated).
3. The polynomial is non-constant (degree greater than 0).
3 is less than or equal to x, and x is less than or equal to 9
The musical frequency of notes is decreasing between beat numbers ___ and ___
13 Pts
PLEASE SOMEONE HELP ME WITH THIS QUESTION
PLZ EXPLAIN
THANK U
which pair of triangles is congruent by AAS?
Answer:
Triangles PQT and RQT are congruent (option D)
Step-by-step explanation:
The AAS or Angle- Angle- Side Theorem says that if two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.
So, triangles PQT and RQT are congruent.
Both triangles have angle Q as right angle and angle P and R are also equal. And both have side QT common.
So, these are congruent via AAS.
Which statement is true about the product of a non-zero rational number and an irrational number?
A) The product of a non-zero rational number and an irrational number is always a rational number.
B) The product of a non-zero rational number and an irrational number is never an irrational number.
C) The product of a non-zero rational number and an irrational number is sometimes a rational number.
D) The product of a non-zero rational number and an irrational number is always an irrational number.
The answer is defiantly D
If t(n) 2n+3 what is the 3rd term
Which of the following is not an identity?
A. cos^2 x csc x - csc x = -sin x
B. sin x(cot x + tan x) = sec x
C. cos^2 x - sin^2 x = 1- 2sin^2 x
D. csc^2 x + sec^2 x = 1
***i don't really get this one :( @terenzreignz? what do u think?,
The number 64 is a perfect
A.square and cube
B.square
C.cube
What is the 4th term in the sequence of
c(n)=-7+6(n-1)
....Please help ME!!!
The width of Zorn's patio is labeled in the diagram below. If the perimeter of the patio is (30x + 26) feet, what is the length of the patio?
2x^2=450
Determine which statement is true about the solutions to the equation.
The solutions are -15 and 15 and both are reasonable side lengths.
The solutions are -30 and 30 and both are reasonable side lengths.
The solutions are -30 and 30 but only 30 is a reasonable side length.
The solutions are -15 and 15, but only 15 is a reasonable side length.
Answer:
the answer is (8x+9)
Step-by-step explanation:
Natalie opened a bank account that earns 2.5% simple interest. If her account earned $180 over the next ten years, how much was Natalie’s initial deposit when she opened the account?
Answer: $720.
Step-by-step explanation:
The formula to find the simple interest is given by :-
[tex]I=Prt[/tex], where P is the principal amount , r is the rate of interest in decimal and t is the time in years.
Given : Rate of interest : r= 0.025
Simple interest : I= $180
Time : t=10
Let P be the Natalie’s initial deposit when she opened the account, then we have:-
[tex]180=P(0.025)(10)\\\\\Rightarrow\ P(0.25)=180\\\\\Rightarrow\ P=\dfrac{180}{0.25}=\dfrac{18000}{25}=720[/tex]
Hence, the Natalie’s initial deposit when she opened the account was $720.
helppppppppppppppppppppppppp
ANSWER THIS BEFORE 3 MINUTES, AND I WILL GIVE YOU BRAINIEST AND 15 POINTS!!!
PROBLEM:
In a heptagon, the degree measures of the interior angles are
x, x, x-2, x-2, x + 2, x + 2 and x + 4 degrees. What is the degree measure of the largest interior angle?
The largest interior angle of the heptagon, given the angle measures as x, x, x-2, x-2, x+2, x+2, x+4, is 132 degrees after solving for x.
The problem is to determine the degree measure of the largest interior angle in a heptagon. The degree measures of the interior angles are given as x, x, x-2, x-2, x+2, x+2, and x+4 degrees. To solve this, we first use the fact that the sum of the interior angles of a heptagon (7-sided polygon) is given by the formula (n-2) 180 degrees, where n is the number of sides. So, for a heptagon, the sum is
(7-2) 180 = 900 degrees.We then set up the equation based on the given interior angles: 3x + (2x - 4) + (2x + 4) + (x + 4) = 900. Simplifying, we get 7x + 4 = 900. Solving for x, we find x = 896/7 = 128 degrees. The largest interior angle is x + 4, which equals
128 + 4 = 132 degrees.y+15 <3 for inequality
Two isosceles triangles have the same base length. the legs of one of the triangles are twice as long as the legs of the other. find the lengths of the sides of the triangles of their perimeters are 23 cm and 43 cm.
Final answer:
To find the lengths of the sides of two isosceles triangles with equal bases and perimeters of 23 cm and 43 cm, we calculate based on the known relations. The smaller triangle has sides of 10 cm and 3 cm, while the larger triangle has sides of 20 cm and 3 cm.
Explanation:
The problem involves two isosceles triangles with the same base length, but the legs of one triangle are twice as long as the other. One triangle has a perimeter of 23 cm, and the other has a perimeter of 43 cm. To solve this, let's denote the common base of both triangles as b, the legs of the smaller triangle as l, and the legs of the larger triangle as 2l.
For the smaller triangle, the perimeter P is given by P = b + l + l or P = b + 2l. For the larger triangle, the perimeter P is P = b + 2l + 2l or P = b + 4l. Since the perimeters are 23 cm and 43 cm respectively, we can set up two equations: b + 2l = 23 and b + 4l = 43.
Solving these simultaneous equations, subtract the first from the second to find 2l = 20, so l = 10. Substituting l = 10 into the first equation gives us b + 20 = 23, thus b = 3.
Therefore, the sides of the smaller triangle are 10 cm (legs) and 3 cm (base), and the sides of the larger triangle are 20 cm (legs) and 3 cm (base).
A 32 ft ladder liens against a building so that the top of the ladder touches the building at a point 23 ft above the ground. To the nearest 10th of a foot how far from the bottom of the building is the bottom of the ladder
A. 27.5 ft
B. 39.4 ft
C. 22.2 ft
D. 30.1 ft
Okay so I’m thinking between C and B. I’m more so C because I did 32 as c and 23 as be so... or it could be the other way around
I just know it’s Pythagorean theorem help. Sending stars
Part A: Explain why we do not measure the rate at which water flows out through a shower head in cubic meters per second? In your explanation, use reasoning based on appropriate units to model this situation. (5 points) Part B: What are the two quantities that should be measured to find the rate at which water flows out of a shower head? Explain how the rate can be determined. (5 points)
The units to measure the rate of water flow from a shower are smaller than cubic meters per second due to the typical small value of this rate. To determine the rate, you need to know the cross-sectional area of the outlet and the water speed, multiplying the area by the speed.
Explanation:Part A: We do not measure the rate at which water flows out through a shower head in cubic meters per second because the typical rate of water flow from a shower is much smaller compared to one cubic meter per second. Using such a large unit for a typically small value would result in decimal figures that are often difficult to comprehend. For instance, a regular shower might output 0.01 cubic meters per minute, which convert to a very small number in cubic meters per second; hence cubic centimeters per second or liters per minute are more practical units.
Part B: To calculate the rate of flow from a showerhead, you need to know two quantities: the cross-sectional area of the outlet (which can be calculated if you know the diameter), and the speed at which the water is moving. The rate of flow (volume per unit time) can then be determined by multiplying the area by the speed of the water. Based on the given data from your textbook - a faucet with a 1.80-cm diameter and a speed of 0.500 m/s - the flow rate can be determined using the formula for the volume of a cylinder (Area of the base x Height), where in this case the 'height' would be the speed.
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Haruka hiked several kilometers in the morning. She only hiked 666 kilometers in the afternoon, which was 25\%25%25, percent less she had hiked in the morning.How many kilometers did Haruka hike in all?
Answer:
its 14 in all actually
Step-by-step explanation:
Let f(x)=x^2−3x−4 .
What is the average rate of change from x = 7 to x = 10?
Enter your answer in the box.
HELP PLS
Let f(x)=2/5 x^2−2 .
The function g(x) is a vertical stretch of f(x) by a factor of 2.
What is the equation of g(x)?
Enter your answer in the box.
Answer:
We have then:
f(x) = 2/5x^2-2 The function g (x) is a vertical stretch of f(x) by a factor of 2:
g(x) = 2f (x)
g(x) = 2 (2/5x^2-2)
g(x) = 4/5 x^2-4 is a required equation.
will give medal to best answer!
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.
C = 38°, a = 19, c = 10,
Answer:
No triangle is formed
Step-by-step explanation:
took test
What is 1,400,000 multiplied by 3.5x10^5 expressed in scientific notation?
The answer is [tex]\( 4.9 \times 10^{11} \)[/tex].
To solve the given mathematical problem, we will multiply the two numbers and then express the result in scientific notation.
First, let's multiply 1,400,000 by 3.5x10^5 without converting them to scientific notation:
[tex]\[ 1,400,000 \times 3.5 \times 10^5 \][/tex]
[tex]\[ = 1400000 \times 3.5 \times 10^5 \][/tex]
[tex]\[ = 4900000 \times 10^5 \][/tex]
Now, we have the product 4900000. To express this in scientific notation, we must write it as a number between 1 and 10 multiplied by a power of 10. The number 4900000 can be written as 4.9 followed by 11 zeros, which in scientific notation is [tex]\( 4.9 \times 10^{11} \)[/tex].
Therefore, the final answer, expressed in scientific notation, is:
[tex]\[ \boxed{4.9 \times 10^{11}} \][/tex]
For what values of x is x2 + 2x = 24 true?
–6 and –4
–4 and 6
4 and –6
6 and 4
Answer:
C. is the correct answer i took the quiz
Step-by-step explanation:
Write three to five sentences explaining which levels of production provide Alonzo’s Cycling with the maximum profit.
The optimal level of production for Alonzo's Cycling is at the point where the profit reaches its peak before starting to decline with further increases in production. This is the level of production that Alonzo's Cycling should aim for to achieve the marginal profit.
To determine which levels of production provide Alonzo's Cycling with the maximum profit, one must consider both the fixed costs and the variable costs associated with production.
The profit for each level of production is calculated by subtracting the total costs (fixed costs plus variable costs) from the total revenue generated by sales. The level of production at which profit is maximized is where the difference between total revenue and total costs is the greatest.
This can be found by analyzing the marginal cost and marginal revenue of production. When marginal revenue equals marginal cost, and if the additional production leads to a decrease in profit, that is the point of maximum profit.
Beyond this point, producing more units would decrease the total profit due to the law of diminishing returns, where the cost of producing additional units exceeds the revenue they generate.
Therefore, the optimal level of production for Alonzo's Cycling is at the point where the profit reaches its peak before starting to decline with further increases in production. This is the level of production that Alonzo's Cycling should aim for to achieve the maximum profit.
In triangle QRS, QR is congruent to SR and RT bisects QS. What justification can you give for QRT congruent to SRT and give the Triangle Congruence Postulate that supports your reason.
Answers:
Midpoint Theorem, SSS
Given, SSS
Definition of a segment bisector; SSS
Definition of an isosceles triangle, SAS,
Find the value of a and b
Answer:
The value of a is 14 unit and the value of b is [tex]6\sqrt{2}[/tex] unit
EXPLANATION:
Draw a perpendicular line from vertex B to DC at E.
Labeling the diagram as shown in the attachment:
Now, as you can see from the Figure as shown in the attachment that [tex]ABDE[/tex] represents the rectangle because a rectangle is a quadrilateral with four right angles and their opposite sides would be parallel.
Therefore, we have the sides [tex]AB=DE=8[/tex] unit , and [tex]AD=BE=6[/tex] unit.
Consider the right triangle BEC
BY 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
therefore, the length of side, [tex]BE=EC=6[/tex] unit
Using trigonometric ratio; to find the value of b:
[tex]\sin \theta =\frac{perpendicular}{Hypotenuse}[/tex]
∴ using trigonometric sine ratio in triangle BEC, we have
[tex]\sin 45^{\circ} =\frac{6}{b}[/tex] or
[tex]\frac{1}{\sqrt{2} }= \frac{6}{b}[/tex]
On Simplify:
[tex]b=6\sqrt{2}[/tex] unit
and the value of a = DC = DE+EC=8+6=14 unit
Therefore, the value of a is 14 unit and b is [tex]6\sqrt{2}[/tex] unit
Shari plans to bake cherry pies and sell them for $9.50 each how much pies dose she have to sell to make $100 profit
What are the zeros of the quadratic function f(x) = 2x2 + 8x – 3? x = –2 – and x = –2 + x = –2 – and x = –2 + x = 2 – and x = 2 + x = 2 – and x = 2 +
Does this set of ordered pairs represent a function? Why or why not?
{(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}
A. Yes, because there are two x-values that are the same.
B. No, because two of the y-values are the same.
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
Final answer:
The set of ordered pairs represents a function Yes, because every x-value corresponds to exactly one y-value(C).
Explanation:
The set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents a function because every x-value corresponds to exactly one y-value. In a function, each input (x-value) has only one output (y-value). The set does not have two different y-values for the same x-value, so option D is incorrect. Therefore, option C is the correct answer.
(C). Yes, because every x-value corresponds to exactly one y-value.
You can see that each unique x-value corresponds to exactly one y-value, and there are no repeated x-values. Therefore, this set of ordered pairs represents a function.
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Katie decides to sell lemonade to make some money. Katie’s mom said she will double the amount of money she makes. If Katie sells 66 cups of lemonade at $0.75 each, how much money does she make?
The answer is $99! :)