Answer:
rational
Step-by-step explanation:
The correct statement is:
c. The other zero can be either rational or irrational.
A quadratic equation with integer coefficients can have two distinct zeros, and if one of the zeros is irrational, the other zero can be either rational or irrational.
The nature of the zeros depends on the specific values of the coefficients in the quadratic equation.
A quadratic equation with integer coefficients can be written in the form: \(ax^2 + bx + c = 0\), where a, b, and c are integers.
The solutions to this equation can be found using the quadratic formula:
\(\mathrm x = \frac{\mathrm{-b}\pm \sqrt{\mathrm b^2-4\mathrm a \mathrm c} }{2 \mathrm a}\)
If one zero is irrational, it means that one of the solutions obtained from the quadratic formula is an irrational number.
However, the other solution can still be either rational or irrational.
The discriminant, \(b^2 - 4ac\), determines the nature of the solutions.
If the discriminant is a perfect square, both solutions will be rational.
If the discriminant is not a perfect square, one solution will be irrational, and the other may be either rational or irrational.
Therefore, it is possible for the other zero to be rational or irrational, depending on the specific values of a, b, and c in the quadratic equation.
Thus, option (c) is the correct answer.
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Complete question =
Consider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero?
a. The other zero must be rational.
b. The other zero must be irrational.
c. The other zero can be either rational or irrational.
d. The zero must be non-real.
4x3 = -5x - 21 solve for x
To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:
1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:
4x3 + 5x = -21
2. Factor out x from the left-hand side of the equation:
x(4x2 + 5) = -21
3. Divide both sides by (4x2 + 5):
x = -21 / (4x2 + 5)
So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.
Cousteau is building a cubed cage for a parrot at his local zoo. Since the the cage's side length is 12 feet, its volume will be 12³ cubic feet. Can you help Cousteau write out 12³ in expanded form?
The expanded form of 12³ is given as follows:
12³ = 12 x 12 x 12 = 1728 cubic feet.
How to obtain the volume of a cube?The volume of a cube of side length a is given by the cube of the side length, as follows:
V(a) = a³.
This expression is equivalent to multiplying the side length of the object by itself twice, as follows:
V(a) = a x a x a.
The side length for this problem is given as follows:
a = 12 feet.
Hence the volume of the cube is given as follows:
V = 12³ = 1728 feet³.
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Which triangle is △ABC similar to and why?
Answer:
can we get a picture
Step-by-step explanation:
A jewelry company ordered 10 boxes of glass beads. There were 30 beads in each box. How
many glass beads did the jewelry company order?
glass beads
Answer:
300 glass beads
Step-by-step explanation:
There are 30 beads in each box so you multiply 30 by 10.
\(10*30=300\)
Please Help Marked for all my points and will Brainliest
Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches.
π,√6,2√6,√7
(a) Without using your calculator, approximate the decimal equivalent of each number to the nearest tenth.
(B) Order the ribbon sizes from least to greatest.
The requreid,
(a) Approximate values of the given numbers are π ≈ 3.1, √6 ≈ 2.4, 2√6 ≈ 4.8, and √7 ≈ 2.6.
(b) √6 < √7 < π < 2√6
(a)
π ≈ 3.1 (since π is between 3 and 4, and is closer to 3.1 than to 3.2)
√6 ≈ 2.4 (since 6 is between 4 and 9, and the square root of 6 is closer to 2.4 than to 2.5)
2√6 ≈ 4.8 (since 2√6 is approximately twice the value of √6, which is 2.4)
√7 ≈ 2.6 (since 7 is between 4 and 9, and the square root of 7 is closer to 2.6 than to 2.7)
(b)
Order from least to greatest:
√6 < √7 < π < 2√6
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Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer:
Step-by-step explanation:
m∠5 + m∠3 = m∠4 is always true, because in a triangle, the sum of all the angles is always 180°.m∠3 + m∠4 + m∠5 = 180° is always true, because in a triangle, the sum of all the angles is always 180°.m∠5 + m∠6 =180° is not always true, since it depends on the specific diagram and the measure of m∠6.
I need help with this i cant cuaet understand this.
Answer:
CANNOT SEE CLEARLY
Step-by-step explanation:
A study that looked at beverage consumption used sample sizes that were much smaller than previous national surveys. One part of this study compared 20 children who were 7 to 10 years old with 5 who were 11 to 13. The younger children consumed an average of 8.2 oz of sweetened drinks per day while the older ones averaged 14.1 oz. The standard deviations were 10.8 oz and 8.2 oz respectively.
Required:
Do you think that it is reasonable to assume that these data are Normally distributed? Explain why or why not?
Answer:
Step-by-step explanation:
In statistics, about 68 percent of values come in one standard deviation of the mean by using a standard normal model. Approximately 95% of the data were all within two standard deviations from the mean. Almost all of the data are in the range of three standard deviations of the mean (roughly 99.7%).
The 68-95-99.7 law, also known as the Empirical Rule, is based on this evidence. 68 percent of the data values of a naturally distributed data collection of small children with a mean of 8.2 and a standard deviation of 10.8 would be between -2.2 and 19.0.
Within a mean of 14.1 as well as a standard deviation of 8.2, 68 percent of the data values in a usually distributed data collection of older children would be between 5.9 and 22.3.
However, we cannot conclude that the data is naturally distributed since the real actual data vary from the usual normal curve computed above.
Hence, various measures like either goodness of fit or theory testing, would be used for this.
A person starts walking from home and walks:
2 miles East
3 miles Southeast
6 miles South
7 miles Southwest
3 miles East
This person has walked a total of
miles
Find the total displacement vector for this walk:
If this person walked straight home, they'd have to walk
miles
This person has walked a total of 21 miles and the total displacement vector for this walk is 13.153 in northeast direction by the concept of distance and displacement.
What is distance and displacement?Unaffected by direction, distance describes an object's entire movement. Displacement, in contrast, refers to a shift in an object's position. Because of this, the primary distinction between distance and displacement is that one is a scalar and the other is a vector.
According to question let us determine the total distance 2 miles+3 miles+6 miles+7 miles+3 miles =21 miles
So, this person has walked a total of 21 miles
Now let us find displacement vector as follows:
Divide into parts: Each leg on the Southeast and Southwest diagonals is the hypotenuse, therefore multiply by (2) /2.
x-axis is given as 2+3*(√ (2) /2) +0 -7(√ (2) /2) +3 =1.464
Similarly, y-axis is given as 0- 3(√ (2) /2)- 6- 7(√ (2) /2) +0=-13.071
The coordinates of the given ques are as follows: <1.464, -13.071>
By Pythagoras theorem, the hypotenuse of the given coordinates is 13.153 in northeast which is our required displacement.
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Substitute 3 for x in new equation. Do you get a ture statement explain
Explain the parts of an algebraic expression and what algebraic expressions can represent.
Step-by-step explanation:
Answer: An algebraic expression is a mathematical expression that consists of variables, numbers, and operations. We can use algebraic expressions to represent unknown number situations involving addition, subtraction, multiplication, and division.
Answer:
Answer: An algebraic expression is a mathematical expression that consists of variables, numbers, and operations. We can use algebraic expressions to represent unknown number situations involving addition, subtraction, multiplication, and division.
Step-by-step explanation:
Its The sample
EDG
What is the greatest common factor of 6 and 35
Answer:
1
Step-by-step explanation:
No other number is a common factor
Answer:
1
Step-by-step explanation:
greatest common factor of 6 and 35 is 1.
ω∞ω↑∈Ф
HELP PLEASEEEEEEEEEEE!! ILL MARK BRAINLIEST
Answer:no 3*little5 is not same as 5*little3
Step-by-step explanation:3*little5 is 3x3x3x3x3,5*little3 is 5x5x5
Answer:
They are DIFFERENT.
Step-by-step explanation:
3^5 (exponential form) means
3×3×3×3×3 (this is the repeated multiplication)
So the standard form is 243.
The other term is:
exponential: 5^3
rep mult.: 5×5×5
standard form: 125
243 NotEqual 125
They are not the same. 3^5 and 5^3 are different.
Solve for the length of the unknown side in the following right triangle. (Side AC is the hypotenuse.) Round your answer to two places, where applicable. Side AB Side BC Side AC ? 12 19
The length of the unknown side or, the length of AC = 22.62.
To calculate the length of the unknown side in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides or, in familiar algebraic notation, a2 + b2 = c2.
In this Question, side AC is the hypotenuse, so we can use the Pythagorean theorem to find the length of side AC:
AC^2 = AB^2 + BC^2
We know that AB = 12 and BC = 19, so we can substitute these values into the equation:
AC^2 = 12^2 + 19^2
AC^2 = 144 + 361
AC^2 = 505
To find the length of AC, we can take the square root of 505:
AC = √505
Rounded to two decimal places, the length of AC = 22.62.
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conver z= -12 - j5 to polar form
The polar form of the complex number z = -12 - j5 is z = 13∠arctan(5/12).
To convert the complex number z = -12 - j5 to polar form, we need to find the magnitude (r) and the angle (θ) of the complex number.
The magnitude (r) of a complex number is given by the formula:
r = √(Re(z)^2 + Im(z)^2)
where Re(z) represents the real part of z and Im(z) represents the imaginary part of z.
In this case, Re(z) = -12 and Im(z) = -5, so we can calculate the magnitude:
r = √((-12)^2 + (-5)^2)
r = √(144 + 25)
r = √169
r = 13
To find the angle (θ) of the complex number, we can use the tangent function:
θ = arctan(Im(z) / Re(z))
In this case, θ = arctan((-5) / (-12))
θ = arctan(5/12)
Now, we can express the complex number z in polar form as z = r∠θ, where r is the magnitude and θ is the angle:
z = 13∠arctan(5/12)
Therefore, the polar form of the complex number z = -12 - j5 is z = 13∠arctan(5/12).
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There are 12 more apples than oranges in the basket of 36 apples and oranges. How
many apples are there in the basket?
Step-by-step explanation:
Required Answer:-Total number of fruits=36Let
the number of oranges =x
The number of apples=x+12
ATQ\({:}\leadsto \)\(\sf x+x+12=36 \)
\({:}\leadsto \)\(\sf 2x+12=36 \)
\({:}\leadsto \)\(\sf 2x=36-12 \)
\({:}\leadsto \)\(\sf 2x=24 \)
\({:}\leadsto \)\(\sf x={\dfrac {24}{2}}\)
\({:}\leadsto \)\(\sf x=12 \)
Number of Apples =12+12=24Answer:
24 apples
Step-by-step explanation:
apples = x
oranges = y
y+12 = x
x+y = 36
y+y+12 = 36
2y = 24
y = 12
x = 24
PLS GIVE BRAINLIEST
ƒ(1) = −6
f(2)=-4
f(n) = f(n-2) + f(n-1)
f(3) =
Answer:
-10
Step-by-step explanation:
if we put f(n)=3 , Then
f(3)=f(3-2) + f(3-1)
= f(1) + f(2)
= -6+(-4). [since f(1)= -6 and f(2) = -4)
= -6-4
= -10
-13 1/5 times 4 2/5 hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhiiiii
Answer: Exact form - 1425/25
decimal form -58.08
mixed number form -58 2/25
Step-by-step explanation:
During practice, the players on a softball team warm up by running the bases. This graph shows the relationship between the number of hours, x, of practice the players attend and the number of minutes, y, the players spend running the bases.
How many minutes do the players spend running the bases during each hour of practice?
The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
In the context of this problem, the variables x and y are given as follows:
Variable x: number of hours.Variable y: time spent running the bases.The equation for the constant is given as follows:
k = y/x.
Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.
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Can someone help me with this question
←
Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Suppose the outcomes are equally likely. Compute the
probability of the event E="an even number less than 9."
P(E)= (Type an integer or a decimal. Do not round.)
The probability of the event even number less than 9 is 0.4
Calculating the probability of the event even number less than 9From the question, we have the following parameters that can be used in our computation:
Sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
From the above, we have
Sample size = 10
In the sample space, there are 4 even numbers less than 9
This means that
P(E) = 4/10
Evaluate
P(E) = 0.4
Hence, the probability of the event even number less than 9 is 0.4
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A student survey was conducted at a major university, and data were collected from a random sample of 750 undergraduate students. One variable that was recorded for each student was the student's answer to the question: "What region of the country did you live in just prior to enrolling in this university? Northeast/Southeast/Northwest/Southwest/Midwest/Outside the U.S." These data would be best displayed using which of the following?
a. Pie Chart
b. Histogram
c. InterQuartile Range
d. Stemplot
e. Boxplot
Answer:
Pie Chart
Step-by-step explanation:
The pie chart is a circular representation of data. It is divided into slices in order to show the distribution of data presented.
In a pie chart, the angle subtended by each slice is proportional to the magnitude of data represented.
Pie charts are most useful in the representation of categorical data such as the region of the country in which a student lived prior to enrolling in the university.
What is an example of "A one-to-one function of P onto Q is an isomorphism of P and Q "?
An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
How to Identify a One-to-One Function?An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).
Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.
Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.
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Can someone please help me solve this problem?
9514 1404 393
Answer:
true for all values of d; an infinite number of solutions
Step-by-step explanation:
Most folks find it convenient to eliminate the fractions as a first step. Here, we can do that by multiplying the equation by 12.
4(2d) +(d +3) = 3(3d +1)
9d +3 = 9d +3
This is true for all values of d. The equation has an infinite number of solutions.
For which points is the y-coordinate greater than -3
Answer:
d,c,a
Step-by-step explanation:
guess it helps
If you buy a meal from a restaurant that costs $15.00, and the tax is 7%, how much do you pay in taxes? explain pls
Answer: He pays $1.05 in tax
Step-by-step explanation: You multiply 7% by 15.00 (15.00 x 7%) and then you get your tax. If it asks how much the cost is plus tax, you just add the number you got by multiplying 15 by 7 and to the original price, $15.00.
What is the measurement of this angle ?
The measurement of the given angle is a 90 degree.
According to the statement
We have to find that the measurement of this angle.
So, For this purpose, we know that the
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
From the given information:
In the given figure, the measurement of the angle we have to find.
A 90-degree angle is a right angle and it is exactly half of a straight angle. It always corresponds to a quarter turn.
And from the figure it is clearly visible that the line of the angle exactly matches with the 90 degree.
Then the angle is 90 degree.
So, The measurement of the given angle is a 90 degree.
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solve for x: 6x<−24
enter answer as an inequality
Answer:
x<-4
Step-by-step explanation:
x is anything below -4 since 6x-4=-24 so anything below minus 4 would make x below -24
The distances between some planets are given below.
Planet Q is 3.6 × 10⁶ km from planet P.
Planet R is 1.6 × 10⁷ km from planet P.
Work out the shortest distance between planet Q and planet R.
Give your answer in standard form.
Answer:
To find the shortest distance between planet Q and planet R, we need to find the difference between their distances from planet P. The distance between planet Q and planet R is the distance of planet R from planet P minus the distance of planet Q from planet P.
The distance between planet Q and planet R is 1.6 × 10⁷ km - 3.6 × 10⁶ km = 1.2 × 10⁷ km.
In standard form, the distance between planet Q and planet R is 1.2 × 10⁷ km, or 1.2 × 10⁷ km.
Brainliest to right answer...plz don’t answer just for points I can’t fail this...
Answer:
Infinitely many solutions
True for all y values
Step-by-step explanation: