Determining whether each statement implies correlation or causation between two variables is as follows:
Correlation:Students with high scores in physics also got high scores in chemistry.A survey shows that people who own a TV also own an automobile.Causation:Watching more TV increases the bill for electricity.Drinking water helps flush out toxins.Vaccination reduces the chance of getting infected by the disease.How is correlation different from causation?Correlation indicates that one independent variable causes another dependent variable to change.
Causation indicates that one dependent variable or event is the direct result of the occurrence of the other event or independent variable.
Causation shows cause and effect - unlike correlation which points out two events simultaneously occur or two variables change at the same time.
Thus, correlation is a test of association in relationship, while causation focuses on cause and effect.
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The length of a rectangle is 2 ft more than twice the width. The area is 84 ft2. Find the length and width of the rectangle.
Lenght
Width
Answer:
let width=x
length = x + 2ft
Area = 82ft^2
Area= length×width
=(x+2)x
=x^2 +2x=82
x^2+2x-82=0
Use Quadratic Equation to get x.
x = -10.1(reject, length cannot be minus value or 8.11)
x = 8.11
width = 8.11ft
length = 10.11ft
A quality inspector visits two factories. She measures statistics for the mass of screwa produced at each factory.
- The screws from which factory have grealer mass?
Overall, the screws from Factory A have greater mass.
- Find the difference in means between the factories:
25.1-24.9=0.2
Find the ratio of the difference in means to the MAD of Factory A: 0.2/0.2=1 Find the ratio of the difference in means to the MAD of Factory B: 02/0.3}=0.67 Are the screws produced by the two factories substantially different?
The required percentage is 95% data lies between the given data.
What is percentage?
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.Let X be the lengths of screws.
X~ Normal (μ = 5.5, σ = 0.1)
P[5.3 < X < 5.7]
= P[(5.3-5.5)/0.1 < (X-μ)/σ < (5.7-5.5)/0.1]
= P[-2 < Z < 2] Z is a standard normal variable.
= 2*P[Z < 2] - 1
= 2*0.97725 - 1, from standard normal table.
= 0.9545
P[5.3 < X < 5.7] = 0.95
Hence, the required percentage is 95% data lies between the given data.
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please help, im sick and im having a mental breakdown right now.
Answer:
Step-by-step explanation:
SORRY CANT HELP YOU I AM ONLY IN 4 GRADE SO SORRY
Fred sells new and used kayaks.
He makes a 12.5% commission on every kayak he sells and he also gets paid $395.50 per week. a) Develop an equation for the way Fred is paid. b) Last month, the total value of the kayaks he sold was $17 400. Use the equation you’ve developed to find out how much Fred was paid for that month.
The total commission Fred was paid for that month is $2570.5.
Given that, Fred sells new and used kayaks.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the number of kayaks be x and the total amount of money Fred get paid per week be y.
A) An equation for the way Fred is paid.
So, equation is y =395.50 +12.5% of x
⇒ y=395.50 +0.125x
B) Last month, the total value of the kayaks he sold was $17400.
Here, x=17400
So, y=395.50 +0.125×17400
= $2570.5
Therefore, the total commission Fred was paid for that month is $2570.5.
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I need help with this question
wn measures (Example 1)
B 8 in.
2.
85%
12 in.
A 35°
14 in.
60°
C
Z
42 in.
t
S
Y
36 in.
Answer:
The answer is A
Step-by-step explanation:
took the test.
In a manufacturing process, a random sample of 36 bolts has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99 percent confidence interval for the true mean length of the bolt?
The 99 percent confidence interval for the true mean length of the bolt is CI = (2.8712, 3.1288)
How to find the confidence interval?Confidence Interval is used to tell us the degree of certainty or uncertainty that is existent in a sampling method.
The general formula for confidence interval is;
CI = x' ± z(s/√n)
where;
x' is sample mean
z is z-score at confidence level
s is sample standard deviation
n is sample size
We are given;
sample size; n = 36
Sample mean; x' = 3 inches
standard deviation; s = 0.3 inches
confidence level = 99%
z at 99% CL = 2.576
Thus;
CI = 3 ± 2.576(0.3/√36)
CI = 3 ± 0.1288
CI = (2.8712, 3.1288)
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Please help asap need it now
Using fractions and mathematical operations, the number of students in the class are 53, the number of juniors are 21 and 16 seniors did not attend the field trip
What are FractionsA fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
A)
From the information given, 3/5 of the students are seniors
However, we know that he has 32 seniors currently
Let's use the concept of percentage here
3/5 = 0.6. Expressing this in percentage = 60%
This we can say 60% of the students are seniors
60/100 = 32/ x
x = total number of students
x = 32 / 0.6
x = 160/3 = 53 students
We have 53 students in the class
B) The number of juniors in the class are
53 - 32 = 21
C) The number of seniors that did not go will be
3/5 * 40 = 24
40 - 24 = 16
16 seniors did not go
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. 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°
1. m∠5 + m∠6 = 180° - Pair of linear angles
2. ∠ 2+ ∠ 3 = ∠ 6 - Exterior Angle Theorem.
3. m∠2 + m∠3 + m∠5 = 180° - Sum of angles of Triangle
Exterior and interior angles of Triangle:
The angles that are created outside of a triangle are its external angles. In other terms, the angle created between one of a triangle's sides and its neighboring extended side is the triangle's exterior angle.
Each exterior angle of the triangle and its corresponding interior angle will form a pair of linear angles i.e the Sum of an Exterior angle and its corresponding interior angle is 180°.
A triangle's exterior angle is equal to the sum of its two opposite interior angles. This property of the triangle is known as Exterior Angle Theorem.
Here we have
∠2, ∠3, and ∠5 are the interior angles of a triangle
∠1, ∠4, and ∠6 are exterior angles of the same triangle
Let's assume that the given triangle is ΔABC
Can be represented as given in the picture
As we know the sum of angles in a triangle = 180°
=> m∠2 + m∠3 + m∠5 = 180° will be true
If we observe the given picture,
From line BC, m∠5 + m∠6 = 180° [ Pair of linear angles ]
From Exterior angle Property
=> ∠ 2+ ∠ 3 = ∠ 6.
Therefore,
The correct statements are
1. m∠5 + m∠6 = 180° - Pair of linear angles
2. ∠ 2+ ∠ 3 = ∠ 6 - Exterior Angle Theorem.
3. m∠2 + m∠3 + m∠5 = 180° - Sum of angles of Triangle.
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susan can type 4 pages of text in 10 minutes. assuming she types at a constant rate, write the linear equation that represents the situation.
Assuming that Susan types at a constant rate, the situation can be represented as a linear equation as:
n = 0.4t, where n represents the number of pages that Susan can type and t represents time in minutes in which Susan would type.
Number of pages Susan can type in 10 minutes = 4
The number of pages that Susan can type in 1 minute
= 4/10 = 0.4
Therefore, the number of pages that Susan can type in t minutes
= 0.4 × t = 0.4t
Hence, this can be represented in the form of a linear equation as
n = 0.4t
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You want to buy a $241,000 home. You plan to pay 15% as a down payment, and take out a 30 year loan for the rest.
The monthly payment will be 1,228.18.
What is principle amount?
The amount you owe at any one moment is the primary amount. When you first took out the loan, it is exactly your loan amount. The principle amount drops as you make EMI payments, and when it hits zero, your loan is closed.
The total price of the home is $241,000.
The down payment will be 15% among the total price.
Rest amount will be paid by taking loan for 30 years.
The down payment amount is
15% of $241,000 = $ 241,000×15/100 = $36,150.
Hence the loan amount is going to be the rest amount, that is,
$(241,000-36,150) =$204,850.
So the principle amount, P= $204,850.
Interest rate= 5% implies
interest, R= 5/100 = 1/20 = 1/12×1/20 (monthly) = 1/240.
Number of years, N= 30 years = 30×12 months = 360 months.
Hence the monthly payment will be
[ P × R × (1+R)N ] / [ (1+R)N - 1 ] = $1,099.68.
So the principle amount, P= $204,850.
Interest rate= 6% implies
interest, R= 6/100 = 1/12×6/100 (monthly) = 1/200.
Number of years, N= 30 years = 30×12 months = 360 months.
Hence the monthly payment will be
[ P × R × (1+R)N ] / [ (1+R)N - 1 ] = 1,228.18
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Every day, Aubrey's orange juice stand uses 2 bags of oranges. How many days will 4/5
of a bag of oranges last?
Answer:
please download the attached file and let me know if you need any further information about addmition in roots international and if so how to make food with clay
Step-by-step explanation:
ok inshallah and a have of safe Earth’s warm and and
[tex]85(94 + 611) < 64(85 - 54)[/tex]
it same like before the end
Answer: 2/5 days
Step-by-step explanation:
4 / 5 = 2d
4 / 10 = d
2 / 5 = d
The coordinates of the vertices of a rectangle are given by R(- 3, - 4), E(- 3, 4), C (4, 4), and T (4, - 4). Plot these points on the coordinate plane at the right and connect them to draw the rectangle. Then connect points E and T to form diagonal _ET . a. Use the Pythagorean Theorem to find the exact length of _ET . b. How can you use the Distance Formula to find the length of _ET ? Show that the Distance Formula gives the same answer.
Answer:
By Pythagorean theorem: [tex]ET=\sqrt{113}[/tex]
By distance formula: [tex]ET=\sqrt{113}[/tex]
Step-by-step explanation:
The given rectangle has vertices R(-3,-4), E(-3, 4), C(4,4), and T(4-4).
The points have been plotted on the coordinate plane as shown in the attachment.
A. Using the Pythagoras Theorem;
[tex]ET^2=EC^2+CT^2[/tex]
We substitute the side lengths to obtain:
[tex]ET^2=EC+CT^2[/tex]
[tex]ET^2=49+64[/tex]
[tex]ET^2=113[/tex]
Take positive square root to obtain:
[tex]ET=\sqrt{113}[/tex]
B. The distance formula is given by:
[tex]d=\sqrt{(x_{2}-x_{1)^2+(y_{2}- y_{1} )[/tex]
The endpoints of ET are at E(-3,4) and T(4,-4).
Using the distance formula;
[tex]ET=\sqrt{4--3)^2+(-4-4)^2}[/tex]
[tex]ET=\sqrt{(7)^2} +(-8)^2[/tex]
[tex]ET=\sqrt{49+64}[/tex]
[tex]ET=\sqrt{113}[/tex]
With the recent launch of Artemis there has been a new initiative to send manned missions to the Moon in hopes of one day colonizing it. The newly founded International Space Agency has decided to select one lucky person from the general population to join this venture. Instead of choosing people at random, however, they decide to administer a 50-question multiple-choice test to everyone who applies. Each question has only two choices (A or B) and only one correct answer. Answer the questions below and explain the steps you used to arrive at your answers (e.g., give calculations when applicable):
a) What is the probability that random guessing will lead to a passing (70% or higher) score?
b) Imagine that the Agency decided that 50 questions was too difficult and shortened the test to just 25 questions. To balance this out, they also changed the questions so they each have four options (A, B, C, and D), but still only one possible correct answer. What is the probability that random guessing will lead to a perfect score?
c) Based on the results, do you think the first or second version of the test is safer against examinees guessing to achieve a passing score? Explain your answer.
a) The probability that random guessing will lead to a passing score is of: 0%.
b) The probability that random guessing will lead to a perfect score is of: 3.35 x 10^-18.
c) The first version of the test is safer against examinees guessing to achieve a passing score.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.For item a, considering that for 50 questions, all are guessed among five answer, the values of these parameters are given as follows:
n = 50, p = 1/5 = 0.2.
The probability of passing is given as follows:
P(X ≥ 35).
Using a binomial distribution calculator, with the given parameters, we have that:
P(X ≥ 35) = 0%.
For item b, the parameters are given as follows:
n = 25, p = 1/4 = 0.2.
Hence the probability of a perfect score is given as follows:
P(X = 25) = 0.2^25 = 3.35 x 10^-18.
For item c, we have that the first version is safer against examinees guessing to achieve a passing score, as:
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Solve for m. -2m-4m-17=1 m=
m = -[tex]\frac{17}{7}[/tex]
Step-by-step explanation:Here are the steps to figuring out your problem:1. Combine like terms
-2m - 4m - 17 = 1m
-6m - 17 = 1m
2. Multiply by 1
-6m - 17 = 1m
-6m - 17 = m
3. Add 17 to both sides
-6m - 17 = m
-6m - 17 + 17 = m + 17
4. Simplify
Add the numbers:
-6m - 17 + 17 = m + 17
-6m = m + 17
5. Subtract m from both sides
-6m = m + 17
-6m - m = m + 17 - m
6. Simplify
Combine like terms:
-6m - m = m + 17 - m
-7m = m + 17 - m
Combine like terms:
-7m = m + 17 - m
-7m = 17
7. Divide both sides by the same factor
-7m = 17
[tex]\frac{-7m}{-7}[/tex] = [tex]\frac{17}{-7}[/tex]
8. Simplify
Cancel terms that are in both the numerator and denominator:
[tex]\frac{-7m}{-7}[/tex] = [tex]\frac{17}{-7}[/tex]
m = [tex]\frac{17}{-7}[/tex]
Divide the numbers:
m = -[tex]\frac{17}{7}[/tex]
Solution:m = -[tex]\frac{17}{7}[/tex]
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
An automobile uses 17 gal of fuel to go 570 mi. how many gallons are required to travel 890 mi? (round your answer to one decimal place.)
The automobile needs 26.5 gallons of gas to reach 890 miles.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, An automobile uses 17 gallons of fuel to go 570 mi.
∴ The automobile requires (17/570) gallons of gas to reach 1 mile.
∴ To reach 890 miles the automobile needs (17/570)×890.
= 26.5 gallons of gas.
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What linear equation does each graph represent?
Draw an equation into each box to match the graph with its equation.
The linear equation each graph is y = (1/5)x +3, y = 2x, y = -3x+5 and y = (1/3)x +5 respectively
How to determine what linear equation each graph represents?The equation of a line is of the form y = mx+c
Where m is the slope and c is the y-intercept
Graph 1
c = 3
m = 1/5 = 0.2
y = mx+c
Thus, the linear equation is y = (1/5)x + 3 or y = 0.2x + 3
Graph 2
c = 0
m = 2/1 = 2
y = mx+c
Thus, the linear equation is y = 2x+0 or y = 2x
Graph 3
c = 5
m = -3/1 = -3
y = mx+c
Thus, the linear equation is y = -3x+5
Graph 4
c = 5
m = 1/3 = 1/3
y = mx+c
Thus, the linear equation is y = (1/3)x+5 or y = 0.33x+5
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suppose that over a certain region of space the electrical potential v is given by the following equation. v(x, y, z)
12/√3 is the direction of the vector v .
What does a basic math vector mean?
A thing with both magnitude and direction is called a vector.
A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector.
Normalize (make length 1) the vector v = <1, 1, -1>.
||v|| = √(1^2 + 1^2 + (-1)^2) = √3.
So, the unit vector u is given by u = v/||v|| = <1, 1, -1>/√3.
To find the rate of change of the potential in the direction of the vector v, you should calculate the ∇f(6, 6, 5) and multiply by u.
=<df/dx, df/dy, df/dz>*u
= <4x-3y+yz, -3x+xz, xy> {at (6, 6, 5)} * u
= <36, 12, 36> · <1, 1, -1>/√3
= 12/√3.
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The complete question is -
Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 2x2 − 3xy + xyz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i + j − k.
27 students are learning to make ballon animals. There are 172 ballooons to be shared equally among the students.
Kara, Sammy, Liz, and Mark each took many samples from the same population of students. The number of students in each sample is shown in the table. Which person’s sampling distribution was most likely to closely approximate the population distribution. Kara: 83 | Sammy: 14 | Liz: 46 | Mark: 65
Answer:
B. Sammy
Step-by-step explanation:
Kara, Sammy, Liz and Mark each took many samples from the same population of students. But the number of students in the Sammy's sample is largest, hence their mean will have lest variation.
Which of the following graphs shows a dilation of the triangle from a fixed point?
The graph that shows a dilation among the given graphs is; Graph F.
What is dilation?Dilation in graphs simply means each side is multiplied by the same
scale factor. What this means is that the ratio of each dilated side to their respective old sides before dilation must be the same scale factor.
We can see that the pre-dilated image has 2 units along the y - axis and 4 units across the x-axis. After dilation, it now has 4 units along the y - axis and 8 units across the x-axis. This means the scale factor in both axis are; 4/2 = 2 and 8/4 = 2. They are both the same scale factors and as such this graph shows a dilation.
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John asks why the last step of Pólya's four-step problem solving process, looking back, is necessary since he has already given the answer. What can you tell him?
Select all the possible reasons the last step, looking back, is necessary below.
A. Looking back allows a student to check that the answer is correct.
B. Looking back allows a student to determine the best strategy to find the solution.
C. Looking back allows a student to understand the problem.
D. Looking back allows a student to check that the answer makes sense in context of the problem.
The reason why looking back is important in mathematical answers is that; Option D: Looking back allows a student to check that the answer is correct and makes sense in context of the problem.
How to confirm mathematical answers?We know that in mathematics, every problem has steps to solve it whether algebra, proportion, trigonometry, calculus, congruency, angles, logarithms, e,t,c
Now, since we know that every Maths problem has steps to solve them, then we can say that, in some instances, we definitely have to look back to be sure that the answer actually makes sense when we consider the solution being required.
Now, if we have to look back to check that the answer is actually correct and properly portrays the solution being demanded, then we can say that the appropriate option for looking back her is option D.
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Find the measure of the reference angle for a -319° angle.
The measure of the reference angle for the angle A = -319° is 41°
What is Reference Angle?
Every angle is measured from the positive part of the x-axis to its terminal line (the line that determines the end of the angle) traveling counterclockwise. For angles in the first quadrant, i.e., angles less than or equal to 90 degrees, the reference angle is equal to the original angle.
The reference angle is always positive
0° to 90°: reference angle = angle
90° to 180°: reference angle = 180° - angle
180° to 270°: reference angle = angle - 180°
270° to 360°: reference angle = 360° - angle
Given data ,
Let the reference angle be = R
Let the angle be represented as A
Now , the value of A is = -319°
And , The reference angle is always positive
So , the value of A = 319°
So , the angle lies in the first quadrant
Now , the reference angle is calculated by
R = 360° - A
Now , the value of the reference angle R = 360° - 319°
The value of R = 41°
Therefore, the value of R = 41°
Hence , The measure of the reference angle for the angle A = -319° is 41°
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Given BC ║ AD and BC ≅ AD
Proof m∠ BAC ≅ m∠ DCA
What is parallelogram side theorem?
The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.
Proof: We have AD || BC [Opposite sides of parallelogram ABCD]
∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]
Now, AB || CD [Opposite sides of parallelogram ABCD]
∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]
In ΔABC and ΔACD, we have
∠1 = ∠3 [From (i)]
∠2 = ∠4 [From (ii)]
and AC = CA [Common]
∴ ΔABC≅ ΔCDA [By ASA Congruence]
Hence Proved.
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ΔABC≅ ΔCDA By ASA Congruence, therefore m∠ BAC ≅ m∠ DCA, hence proved using parallelogram side theorem.
What is parallelogram side theorem?
The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.
Proof: We have AD || BC [Opposite sides of parallelogram ABCD]
∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]
Now, AB || CD [Opposite sides of parallelogram ABCD]
∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]
In ΔABC and ΔACD, we have
∠1 = ∠3 [From (i)]
∠2 = ∠4 [From (ii)]
and AC = CA [Common]
∴ ΔABC≅ ΔCDA [By ASA Congruence]
Hence Proved.
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The chart shows the average time spent reading per day for students in an 8th grade class.
The line plot is titled minutes of reading per day, and the horizontal axis is labeled minutes of reading per day. There are 5 dots at 30, 1 dot at 33, 5 dots at 35, 1 dot at 36, 1 dot at 37, 3 dots at 40, 1 dot at 44, one dot at 46, 1 dot at 47, and 1 dot at 50.
Which of the following describes this data set?
Categorical and bivariate
Categorical and univariate
Numerical and bivariate
Numerical and univariate
This data collection may be characterized as numerical and univariate.
How do you define numerical and univariate?If the collection of all potential values for a numerical univariate data is finite or countably infinite, the data is discrete. Usually, discrete univariate data are used in counting (such as the number of books read by a person). If the range of all potential values is a set of numbers, then a numerical univariate data is continuous.
Categorical data – what is it?Categorical variables represent different sorts of data that may be categorized. Race, sex, age group, and educational level are some examples of categorical variables.
Data types that may be kept and recognized based on the names or labels assigned to them are referred to as categorical data. Numerical data refers to the data that is in the form of numbers, and not in any language or descriptive form. Also known as qualitative data as it qualifies data before classifying it.
Over here we have the data for the average time spent reading per day for students in an 8th grade class.
Average Time is a numerical data
Bivariate data deals with two variables
univariate data, which is one variable data
we have numerical data and one variables so its
Numerical and univariate
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Please help with 17-20.
Answer:
17. VN ll OP
18. VN perp. TR
19. Yes because the both a straight line (m 180) and are not crossing at any point.
20. Yes because there crossing at an right angle.
Hope this helps!
Identity the slope and y intercept of the graph then write the equation in slope intercept form
Answer:
m = -4
b =1
y = -4x+1
Step-by-step explanation:
We want to find the slope and y intercept
Given the two points ( -1,5) and ( 1,-3), we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -3 -5)/( 1 - -1)
= -8/( 1+1)
= -8/2
= -4
The y intercept is where it crosses the y axis
It crosses at 1
The slope intercept form of the line is
y = mx+b
y = -4x+1
i have no idea how to do this can anyone help
The end behavior of the functions is obtained considering the limits of the functions as the input variable x goes to infinity.
For limits when x goes to infinity, only the term with the highest exponent of each of the numerator and of the denominator is considered, hence the functions are written as follows:
f(x) = x²/x³.g(x) = x³/x³.h(x) = x^4/x³.Applying the exponent properties, the equivalent expressions are given as the base x elevated to the subtraction of the exponents 2 and 3, hence:
f(x) = 1/x.g(x) = 1.h(x) = x.Which is how the functions behave as x goes to infinity.
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The lengths of the legs of an isosceles right triangle are x and [tex]\sqrt{6x+16}[/tex]
a. Find the length of the hypotenuse, in terms of x, in simplest radical form
b. Find the length of all three sides of the triangle, in simplest radical form.
Check the picture below. Let's recall is an isosceles, so it has twin sides and is a right-triangle.
[tex]x^2+(\sqrt{6x+16})^2\implies \sqrt{x^2+6x+16}\qquad \impliedby hypotenuse \\\\[-0.35em] ~\dotfill\\\\ x~~ = ~~\sqrt{6x+16}\implies \stackrel{\textit{squaring both sides}}{x^2=6x+16}\implies x^2-6x-16=0 \\\\\\ (x-8)(x+2)=0\implies x= \begin{cases} 8 ~~ \textit{\LARGE \checkmark}\\\\ -2 ~~ \bigotimes \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underset{\textit{length of each side}}{\stackrel{\sqrt{(8)^2 + 6(8) + 16}}{{\Large \begin{array}{llll} 8\sqrt{2} \end{array}}}\hspace{5em}\stackrel{x}{\text{\Large 8}}\hspace{5em}\stackrel{\sqrt{6(8) - 16}}{\text{\Large 8}}}[/tex]
now, let's notice, the negative value is a legitimate value, however for this case is invalid since the lengths of the triangle can't be negative.
Bill jumps off a diving board that is 12 feet above the surface of a swimming pool. Jumping upward and outward, he reaches a maximum height of 18 feet above the surface of the water when he has jumped outward 4 feet. Find f(x) an equation for his parabolic path and when he hits the water, how far out has he reached, to to the nearest tenth of a foot.
The f(x) = -ax²+18 function equation for his parabolic path. x=√8 is he reached, to the nearest tenth of a foot.
What does "function equation" actually mean?A function is an equation that has just one answer for y for every possible value of x. When utilizing a function, each input of a certain type receives exactly one output.
Briefing:f(x) = -ax² + 18
f(2)= -a(2)²+18 = 12
-4a = 12-18
-4a = -6
a = -6/-4
a = 3/2
f(x) = (-3/2) x² + 12
f(0) = (-3/2) x² + 12
(3/2) x² = 12
x² = 8
x = √8
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