Answer:
Step-by-step explanation:
[tex]x^{2} -6x[/tex]
A chopstick model of a catapult launches a marshmallow in a classroom. The path of the marshmallow can be modeled by the quadratic y = −0.07x^2 + x + 2.2, where y represents the height of the marshmallow, in feet, and x represents the horizontal distance from the point it is launched, in feet.
When the marshmallow hits the ground, what is its horizontal distance from the point where it was launched?
16.22 feet
−1.94 feet
7.14 feet
2.2 feet
The horizontal distance from the point where it was launched is; Option C: 7.14 feet
How to solve quadratic model of projectile functions?
Horizontal distance is defined as the distance between two points measured at a zero percent slope.
We are told that the path of the marshmallow can be modeled by the quadratic equation;
y = −0.07x² + x + 2.2
The maximum point will occur when dy/dx = 0
Thus;
dy/dx = -0.14x + 1
At dy/dx = 0,
-0.14x + 1 = 0
1 = 0.14x
x = 7.14
This value of x is the x-coordinate of the vertex and it represents the horizontal distance from the point where it was launched.
Read more about Quadratic model of projectile functions at; https://brainly.com/question/15848058
#SPJ1
I need help with probability.
Answer:
Step-by-step explanation:
correct answer is 6 marbles, no doubt.
Can you justify that all sides and all angles are equal in a equilateral triangle?
The basic definition states that all the sides of an equilateral traingle is always same.
so equilateral traingle have same side and is justified according to the definition of the equilateral traingle.
Now secondly we have to prove that all angles of an equilateral traingle is same :
in the traingle PQR shown below PQ,QR,PR is the side of the traingle
we have to prove that ∠QPR = ∠PQR = ∠ PRQ.
As we know that all sides length of equilateral traingle are equal.
so PQ=QR=PR
Statement 1:
Angles opposite to equal sides QR and PR are equal so .
=> ∠QPR = ∠PQR
Statement 2:
Angles opposite to equal sides PR and PQ are equal so .
=> ∠PQR = ∠ PRQ.
combining statement 1 and statement 2.
=> ∠QPR = ∠PQR = ∠ PRQ and hence all three angles are same [Proved]
To know more about Equilateral traingle click on below link:
brainly.com/question/30068040#
#SPJ4
Jacinta says there are infinitely many rational numbers between 0 and 1. Do you agree? Explain.
Answer:
Yes
Step-by-step explanation:
Therese infinite amount of rational numbers between 0 and 1 because of decimals.
0.9
0.99
0.999
0.9999
.....
There's an infinite amount of decimals you can add. If the sequence repeats, it is rational.
which of the following is not an example of a binomial distribution? a.) the probability of a dart player missing the bullseye seven times in eight attempts. b.) the probability of rolling a die eight times and getting an odd number or a prime number four times. c.) the probability of a basketball player making a free throw seven times in ten attempts. d.) the probability of flipping a coin four times and never landing on tails.
The answer is B). "the probability of rolling a die eight times and getting an odd number or a prime number four times."
A binomial distribution is a statistical distribution that describes the probability of a certain number of successful outcomes in a fixed number of independent trials. In order for a situation to be a binomial distribution, the following conditions must be met:
There must be a fixed number of trials.
Each trial must have only two possible outcomes (e.g., success or failure).
The probability of success must be the same for each trial.
The first three answer choices all involve situations that meet these conditions and are therefore examples of binomial distributions. The fourth answer choice, however, involves rolling a die, which has more than two possible outcomes (1, 2, 3, 4, 5, or 6). This means that it is not a binomial distribution.
Learn more about binomial distribution here:
https://brainly.com/question/15278907
#SPJ4
x^2+4x-7 in the form (x+a)^2-b
The equation x² + 4x - 7 can be written in the form (x + a)² - b as (x + 2)² - 11
How to write equation in another form?x² + 4x - 7 in the form (x + a)² - b
Where,
b = constant
x² + 4x - 7
= (x + 2)² - 11
Hence,
x² + 4x - 7 = (x + 2)² - 11
Check:
(x + 2)² - 7
= (x + 2) (x + 2) - 7
= x² + 2x + 2x + 4 - 11
= x² + 4x - 7
Therefore, (x + 2)² - 11 is another form the equation x² + 4x - 7 can be written.
Read more on equation:
https://brainly.com/question/1958920
#SPJ1
What conditions would produce a negative z-score? Choose the correct answer below .
O A z-score corresponding to
O an area located entirely in the left side of the curve an area in the top 10 % of the graph
O a z-score for a negative area
O a z-score corresponding to an area located entirely in the right side of the curve
z-score in normal distribution is a standardized value of raw score,i.e., random variable X when mean is 0 and standard deviation is 1.
What is standard deviation?
The standard deviation is a metric that reveals the degree of variation (such as spread, dispersion, and spread) from the mean. Similar to variance, there is little variation when data points are close to the mean, but there is much variation when data points are widely scattered from the mean. The amount of departure from the average is determined by standard deviation. The most common measurement of dispersion, the standard deviation, is based on all values. Therefore, a change in even one value has an impact on the standard deviation's value. In the bell curve of z, a 'negative z-score' represents raw score below mean and 'positive a-score' means raw score is above mean.Since, the distribution of standard variate z~N(0,1) is always centered towards 'zero' mean and is symmetrical, negative z-score ,which represent raw score below mean, is always in the left side of the curve.Therefore, z-score corresponding to an area located entirely in the left side of the curve will produce a negative z-score. Also, area is never negative.To know more about z-score check the below link:
https://brainly.com/question/25638875
#SPJ1
Can you prove the triangles are congruent?
The triangles can be proven to be congruent. ΔADC ≅ ΔCBA based on the HL congruence theorem.
How to Prove that Two Triangles are Congruent by HL Congruence Theorem?The HL congruence theorem can be used to prove that two triangles are congruent if we can show that they are right triangles which have a pair of congruent hypotenuse and a pair of congruent legs.
Given the triangles in the image, ΔADC and ΔCBA, they have the following:
Both are right triangles because angles ADC and CBA are right angles.AC ≅ CA based on the reflexive property (congruent hypotenuses)DC ≅ AB because it is indicated they are congruent to each other [congruent legs].Therefore, both triangles are congruent by HL congruence theorem.
Learn more about the HL congruence theorem on:
https://brainly.com/question/2102943
#SPJ1
pls help me. i really need the answer quickly.
Answer:
x = 90
y = 58
z = 32
Step-by-step explanation:
A straight line is 180.
x = 180 =90 = 90
I looked at the small white triangle on the far right. I now that the sum of the 3 angles must add up to 180. I know that one angle is 90. I can figure out C from the large triangle.
Angle C is 180 -90 - 32 = 58
I now know 2 of the angle measurements for the small right side triangle:
58 and 90 I subtract these from 180 to find z
180 - 90 - 58 = 32
To find x. I know that a straight line is 180, I also know that I have a 90 and a 32 degree angle. I subtract these from 180
180 - 90 -32 = 58
Answer:
Your answer is x = 90° , y = 58° , z = 32°
Step-by-step explanation:
Looking at that right-angle triangle ABC we know that it has 3 angles that must add up to 180°.
The problem mentions that there is a square the inside the triangle.
Now within the triangle ABC there is 2 triangles and a square inside of it.
This is the information from looking at the triangle.
Angle 32° + x° + y° = 180°
Angle y° + 90° + z° = 180°
Angle x° seems to be perdicular to the triangle so must be 90°
Now we know 2 angles we can solve for angle y°
32° + x° + y° = 180°
32° + 90° + y° = 180°
122° + y° = 180°
y° = 58°
The square's four angle is all 90°. Substitute y to solve for z.
y° + 90° + z° = 180°
58° + 90° + z° = 180°
148° + z° = 180°
z° = 32°
How do you write 4 is greater than 3?
We write 4 is greater than 3 using Inequality sign as 4 > 3.
The first number in every inequality sign tells us how the first and second numbers relate to one another, so 4 > 3 means "4 is greater than 3."
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than symbol (>) is used when the first number exceeds the second number. The less than symbol (<) is used when the first number is less than the second number.
Learn more about Inequality sign:
brainly.com/question/948454
#SPJ4
find the endpoint and midpoint endpoint: (6, -4) midpoint: (5, -1)
Thus, ( 6 , 8 ) is the other endpoint.
What is Midpoint Formula?
Suppose the endpoints of a line segment are ( x 2 , y 2 ) and ( x 1 , y 1 ) . Also, suppose that the midpoint is ( x m , y m ) . To get ( x 2 , y 2 ) provided that the values of ( x m , y m ) and ( x 1 , y 1 ) are known, we can use the formula: ( x 2 , y 2 ) = ( 2 x m − x 1 , 2 y m − y 1 )
First, we have to determine the given values:
[tex]$$\begin{aligned}& \left(x_1, y_1\right)=(6, -4) \\& \left(x_m, y_m\right)=(5,-1)\end{aligned}$$[/tex]
Applying these points to determine the other endpoint:
[tex]$$\begin{aligned}& \left(x_2, y_2\right)=\left(2 x_m-x_1, 2 y_m-y_1\right) \\& \left(x_2, y_2\right)=(2(5)-4,2(1)-(-6)) \\& \left(x_2, y_2\right)=(6,8)\end{aligned}$$[/tex]
To learn more about Midpoint Formula visit:https://brainly.com/question/4728902
#SPJ1
How many solutions y 3x 5 has?
A linear equation y = 3x+5 with two variables hence has an infinite number of solutions.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given linear equation:
y = 3x+5
In this equation,
there are two variables, x and y.
And equation is one.
That means,
the number of unknowns > the number of equation
2>1.
The line y=3x+5 is a linear equation in two variables.
For every value of x, there is a unique value of y
Put x=0 ⇒ y=5
Hence, (0,5) is a solution
Put x=1, ⇒ y=8
Hence, (1,8) is a solution.
Put x=−1,⇒y=2
Hence, (−1,2) is a solution.
We so obtain varied values of y when preserving distinct values of x.
Therefore, infinitely many solutions are possible.
To learn more about the linear equation;
https://brainly.com/question/29739212
#SPJ4
How do you know if its a discontinuity?
The conditions for the discontinuity is illustrated as follows.
The term discontinuity in math is defined as the functions f(x) that are not continuous at a point of its domain.
If the function fall under the discontinuity if it satisfies any one of the following condition,
if the limit values are not sameIf any one of the limit value is not definedIf there is no limit in the functionFunction is not properly definedif the denominator of the function will fall on the value of zero,If the function will satisfies any one of these condition, then the function must discontinuous one.
To know more about Discontinuity here
https://brainly.com/question/28783981
#SPJ4
Why are measuring tools are necessary?
Measuring tools are necessary because its improve the quality and quantity of life while also making our lives easier and safer. It is debatable if the capacity for precise measurement of physical attributes has a significant survival value that gives humans an adaptive, evolutionary advantage honed over many years of natural selection.
what are measuring tools?A measuring instrument is a tool used to quantify anything tangible. Measurement is a key activity in the physical sciences, engineering, and quality control.
Measurement equipment that is frequently used includes thermometers, rulers, yardsticks, scales, beakers, protractors, clocks, and measuring tape. Understanding the proper way to use each instrument can make measurement more accurate , enjoyable. Each tool has a unique purpose.
To know more about measuring tools visit;-
https://brainly.com/question/22599655
#SPJ4
Which term should be inserted in X² − +16 to make it a perfect square?
64 should be added to the equation to make it perfect square. The correct option is A.
What is a perfect square?A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer. Perfect square trinomials are three-term polynomials with a quadratic equation of ax^2 + bc + c
In order to find the c, we must divide 16 in the equation 16x , and raise it to the power of 2.
This will be:
(16/2)²
= 8²
= 64
Therefore the answer is 64.
Learn more about perfect square at:
https://brainly.com/question/26119721
#SPJ1
Complete question
Which term should be inserted in X² − +16 to make it a perfect square?
A. 64
B. 6
C. 4
D. 2
help me PLEASEEEEEEEEE EE EE EE E
this is just base (b) times width (w) times height (h)
you can put them into an equation that looks like this:
b × w × h = area (a)
now lets put those numbers for the letters.
8 × 2 × 4 = a
a = 64
you're welcome :)
Graph the inequality on a coordinate plane.
2x - 5y< -10
Answer:
espero te sirva siuuuuuuuuuuu
A high school has a policy that students' phones must be kept away during class. A principal used
the school roster to poll a random sample of 50 students, and only 10% said that they ever had
their phone out during class. The next day, the principal observed classrooms and noticed that
approximately 25% of students had their phone out at some point during class.
Which of these is the most concerning potential source of bias in the principal's poll?
Choose 1 answer:
Answer:
Out of these potential sources of bias, the most concerning the potential source of bias in the principal's poll is probably response bias.
Step-by-step explanation:
There are several potential sources of bias in the principal's poll that could have led to the discrepancy between the poll results and the principal's observations. Some possible sources of bias include:
Self-selection bias: It is possible that students who were more likely to admit to using their phone during class were more likely to participate in the poll. This could have led to an overestimation of the percentage of students who use their phone during class.
Response bias: It is possible that students who participated in the poll were not entirely truthful in their responses. For example, students who do use their phone during class might have been reluctant to admit it, leading to an underestimate of the percentage of students who use their phone during class.
Sampling bias: The principal might not have selected a truly random sample of students for the poll, leading to a sample that is not representative of the entire student body. For example, if the principal only polled students from certain classes or certain grade levels, the results might not be representative of the entire school.
Observation bias: The principal's observations might not have been completely objective. For example, the principal might have been more likely to notice students who were using their phone during class, leading to an overestimate of the percentage of students who use their phone during class.
If students are not completely truthful in their responses, it will be difficult to accurately gauge the extent to which students are using their phones during class. It is important to try to minimize response bias as much as possible in any survey or poll.
He i the midpoint of AC which tatement bet decribe the relationhip between triumph ABD and CBD triangle ABD and CBD are congruent by the SSS congruence potulate
The option 1 "Triangles ABD and CBD are congruent by the SSS Congruence Postulate." is correct.
In the given question, DB is a median of ∆ADC.
We have to find which statement best describes the relationship between triangles ABD and CBD.
From the diagram we can see that
AD = CD
Since DB is median so it divide AC into two equal parts
So AB = CB
DB = DB (Common)
So, ∆ABD ≅ ∆CBD by SSS Congruence Postulate.
So, the option 1 "Triangles ABD and CBD are congruent by the SSS Congruence Postulate." is correct.
To learn more about SSS Congruence Postulate link is here
brainly.com/question/11804045
#SPJ4
The complete question is:
DB is a median of ∆ADC. Which statement best describes the relationship between triangles ABD and CBD?
(1) Triangles ABD and CBD are congruent by the SSS Congruence Postulate.
(2) Triangles ABD and CBD are similar by the SSS Similarity Postulate.
(3) Triangles ABD and CBD are congruent by the SAS Congruence Postulate.
(4) Triangles ABD and CBD are similar by the SAS Similarity Postulate.
Solve the following inequality for c. Write your answer in simplest form.
c-8<10c+3
-11/9 < c is the simplest form of the given inequality
What is Linear Inequality?
A linear inequality is a mathematical inequality that incorporates a linear function. A linear inequality contains one of the inequality symbols. It displays data that is not equal in graph form.
Solution:
In this question all that we have to do is to seperate the variable terms and the constant terms
It is showwn in the solution below
c - 8 < 10c + 3
-8-3 < 10c - c
-11 < 9c
-11/9 < c
as you can see after seperating the terms we can surely make an inequality
Refer to the Graph Attached
To learn more about Linear Inequality from the gievn link
https://brainly.com/question/24372553
#SPJ1
I have a lot of this but pls help me
Step-by-step explanation:
4. 5 Million
5. 6:10
Not sure about 3 tho I'm sorry !
A line goes from (1, 0) to (5, question mark). a horizontal line is at x = 5. what would the height need to be for this curve to be a density curve? one-fifth one-fourth one-half 1
As per the equation of line, the height density of the curve is 0.2
The standard form of the equation of a straight line is
=> y = mx + c
here m is the slope and c refers the intercept on the y-axis.
Here we have given that A line goes from (1, 0) to (5, question mark). a horizontal line is at x = 5.
And we need to find height need to be for this curve to be a density curve.
As per the given details,
here we have the point (1,0) and ( 5, ?)
There is an horizontal line at x = 5.
Then the height of the density of the curve is calculated as.
Here we have to recall that the area must equal 1 and that uniform density curves are rectangular.
=> base x height = 1
=> 5 x height = 1
=> height = 1/5
=> height = 0.2
To know more about Equation here.
https://brainly.com/question/10413253
#SPJ4
The shelter found homes for
10% of the cats they had. What is
10% of 40 cats?
Answer: 4 cats
Step-by-step explanation:
10% = 0.1
Take 40 times 0.1 = 4 cats
What is the natural domain of f x?
If only the rule y = f(x) is provided, the set of all real x for which the function is defined is assumed to represent the domain.
Given that,
We have to find what is the natural domain of f(x).
We know that,
Consider the relationship between the independent variable x and the dependent variable y, y = f(x). It is considered to be in the domain of the function f if a value for x successfully enables the construction of a single value y using another value for x.
If only the rule y = f(x) is provided, the set of all real x for which the function is defined is assumed to represent the domain.
For instance, all real x has a value of zero when y = x. This is sometimes referred to as the function's natural domain.
To learn more about domain visit: https://brainly.com/question/28135761
#SPJ4
A paper has an area of 96 square inches. What is the paper's area in square centimeters? Use the following conversion: 1 square inch is 6.5 square centimeters.
To convert an area measured in square inches to square centimeters, we need to multiply the area in square inches by the conversion factor that converts square inches to square centimeters. In this case, the conversion factor is 6.5 square centimeters per square inch. So, to convert the paper's area of 96 square inches to square centimeters, we multiply 96 square inches by 6.5 square centimeters per square inch, giving us 96 * 6.5 = 624 square centimeters. Thus, the paper's area in square centimeters is 624 square centimeters.
How many terms are there in the expression 5x 3xy?
There are four terms in the expression. Two are numbers and the remaining are variables.
What is mathematical expression?It is a mathematical statement express the relationship between two or more mathematical terms. In an expression there will be one or more mathematical symbols or operator such as addition, multiplication, division or subtraction sign. Beside this there are many other signs such as equal or inequal sign, integration sign, square root or cubic root sign etc.
Terms can be numbers, variables or variables with coefficient.
How many terms are in the expression?In the above question, we have four terms, and one symbol.
5 × 3xy
5 is number and it is called constant
3 is number but it acts as the coefficient of the variables x and y.
x and y are two variables.
there is a multiplication sign among these terms.
the above expression can be described as 5 is multiplied by 3xy.
hence, we have four terms.
To know more about Mathematical expression visit:
https://brainly.com/question/29176690
#SPJ4
"Four times the difference of a number and seven is at least -52."
The term "difference" relates to subtraction, thus since they are looking for an unknown number's "difference," we can utilize the variable "x." X-7
How to find the Calculation?Subtraction is an operation to find the difference of two numbers; yet, the outcome of subtraction is a difference.
The greater-than sign is represented by the letter >. Therefore, 9>7 is understood to mean "9 is greater than 7." The sign for less than is. (greater than or equal to) and are two more comparison symbols (less than or equal to).
The larger than, less than, and equal to signs are referred to as our "at least" signs.
7 divided by a number equals x-7.
Four times is four or four.
At the very least = -52 = Response negative 52
Connect them all,
x-7(4)<-52
4(x - 7) ≥ -52
4x - 28 ≥ -52
4x ≥ -24
x ≥ -6.
To Learn more About difference refer to:
https://brainly.com/question/148825
#SPJ1
How can you determine if the left and behavior of a polynomial function is rising or falling?
To determine if a polynomial function is rising or falling, take the derivative of the function and evaluate it at the given point. If the derivative is positive, then the function is rising; if the derivative is negative, then the function is falling.
To determine if a polynomial function is rising or falling, take the derivative of the function. The derivative of a function at a given point is the slope of the tangent line at that point. If the slope is positive, then the function is rising; if the slope is negative, then the function is falling. To find the derivative of a polynomial function, use the power rule. This states that if f(x) = x^n, then the derivative of f(x) is nx^(n-1). Once the derivative is found, evaluate it at the given point. If the result is positive, then the function is rising; if it is negative, then the function is falling.
Let's say we have a polynomial function f(x) = x^3. To find the derivative of this function, use the power rule. The derivative of f(x) = x^3 is 3x^2. Now let's evaluate the derivative at the given point x = 2. The derivative at x = 2 is 3(2)^2 = 12. Since 12 is positive, the function is rising at that point.
Learn more about polynomial here
https://brainly.com/question/11536910
#SPJ4
How do you find the length of a rectangular pyramid with the volume?
If the volume of a rectangular pyramid is known, we can determine the length of the pyramid if we get the base area or the base dimensions. Here the length of the pyramid is the height of the rectangular pyramid.
The volume of a right rectangular pyramid of base l×b and height h can be determined by the formula
V = l×b×h/3
Therefore we can obtain the length or height of the rectangular pyramid given the volume if we know other two dimensions or their product, that is the base area of the pyramid. In which case we can obtain the height be substituting.
To know more on pyramid
https://brainly.com/question/17615619
#SPJ4
What is the domain answer?
If a function f offers a means of successfully generating a single value y while using a value for x to that end, then that selected x-value is said to belong to the domain of f.
what is domain ?A function's domain is the collection of permitted values. Included in this collection are the x values for a function, such as f. (x). Such values are gathered together to demonstrate the variety of values that can be utilized as function input. Inputting an x value causes the function to return this set of values.
here
Take into account the relationship (0,7,0,8,(2,6),(1,6),(1,7),(2,9).
The relation is shown in this case as a set of sorted pairs. The range is the set of y -coordinates, which are (6 ,7 ,8 ,9), and the domain is the set of x -coordinates (0, 1, 2) .
To know more about domain visit :-
https://brainly.com/question/28135761
#SPJ4