Answers
Answer:
see below
Step-by-step explanation:
Addition and subtraction are both closed under polynomials.
That means that when we add and subtract polynomials, we will end up with a polynomial
f(x) + g(x) will = always be a polynomial when we start with polynomials
f(x) - g(x) will = always be a polynomial when we start with polynomials
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
A polynomial is an expression consisting of variables and coefficients.
[tex]f(x)[/tex] and [tex]g(x)[/tex] are polynomial functions.
Adding polynomials and subtracting polynomials is essentially combining like terms of polynomial expressions.
[tex]f(x)+g(x)[/tex] is always a polynomial
[tex]f(x)-g(x)[/tex] is always a polynomial
If you add, subtract or multiply any two polynomials then the result will be always a polynomial.
Related Questions
For the following data set, you are interested to determine the "spread" of the data. Would you employ calculations for the sample standard deviation, or population standard deviation for this data set: You are interested in the heights of students at a particular middle school. Your data set represents the heights of all students in the middle school with 600 students.
Answers
Answer: Use calculations for population standard deviation.
Step-by-step explanation:
The population standard deviation is defined as
a parameter which is a fixed valueevaluated by considering individual in the population.A sample standard deviation is defined as
a statistic ( whose value is not fixed ). Evaluated from a subset (sample) of population.Since, data set represents the heights of all students in the middle school with 600 students which is population here.
So, we do calculations to find population standard deviation.
The amount of flow through a solenoid valve in an automobile's pollution-control system is an important characteristic. An experiment was carried out to study how flow rate depended on three factors: armature length, spring load, and bobbin depth. Four different levels (low, fair, moderate, and high) of each factor were chosen, and a single observation on flow was made for each combination of levels.A) The resulting data set consisted of how many observations?
B) Is this an enumerative or analytic study? Explain.
Answers
Answer:
A) 64 observations
B) analytic study
Step-by-step explanation:
Given:
There are 3 number of factors i.e. armature length, spring load, and bobbin depth.
There are 4 levels i.e. low, fair, moderate, and high
There is a single i.e. 1 observation on flow made for each combination of levels.
A)
To find:
Number of observations.
There are 4 levels so these 4 levels are to be considered for each factor.
Number of observations = 4.4.4 = 64
For example if we represent low fair moderate and high as L,F,M,H
and factors armature length, spring load, and bobbin depth as a,s,b
Then one of the observations can be [tex]L_{a} F_{s} H_{b}[/tex]
So resulting data set has 64 observations.
B)
This is analytic study.
The study basically "analyses" the amount of flow through a solenoid valve in an automobiles pollution control system. This study is conducted in order to obtain information from this existing process/experiment and this study focuses on improvement of the process, which created the results being analysed. So the goal is to improve amount of flow through a solenoid valve practice in the future. Also you can see that there is no sampling frame here so if the study was enumerative that it should focus on collecting data specific items in the frame so it shows that its not enumerative but it is analytic study.
Simplify (4x)². Rewrite the expression in the form k ⋅ xⁿ
Answers
Answer:
16x²
Step-by-step explanation:
(4x)²4² *x²16*x² 16x²? Question
A slingshot launches a water balloon into the air. Function f models the height of the balloon, where x is the horizontal
distance in feet:
f(x) = -0.05x2 +0.8x + 4.
From what height did the slingshot launch the balloon, and what was the balloon's maximum height? How far from the
slingshot did the balloon land?
The balloon's maximum height was____
The slingshot
launched the balloon from a height of _____
The balloon landed_____
from the slingshot.
Answers
Answer:
4 ft
7.2 ft
20 ft
Step-by-step explanation:
When the balloon is shot, x = 0.
y = -0.05(0)² + 0.8(0) + 4
y = 4
The balloon reaches the highest point at the vertex of the parabola.
x = -b / 2a
x = -0.8 / (2 × -0.05)
x = 8
y = -0.05(8)² + 0.8(8) + 4
y = 7.2
When the balloon lands, y = 0.
0 = -0.05x² + 0.8x + 4
0 = x² − 16x − 80
0 = (x + 4) (x − 20)
x = -4 or 20
Since x > 0, x = 20.
The slingshot launched the ballon from a height of 4 feet. The balloon's maximum height was 72 feet. The balloon landed 20 feet from the slingshot.
To determine the height from which the slingshot launched the balloon, we need to evaluate the function f(0) because when x is zero, it represents the starting point of the balloon's trajectory.
f(x) = -0.05x² + 0.8x + 4
f(0) = -0.05(0)² + 0.8(0) + 4
f(0) = 4
Therefore, the slingshot launched the balloon from a height of 4 feet.
To find the maximum height of the balloon, we can observe that the maximum point of the parabolic function occurs at the vertex.
The x-coordinate of the vertex can be calculated using the formula x = -b / (2a).
In our case, a = -0.05 and b = 0.8.
Let's calculate the x-coordinate of the vertex:
x = -0.8 / (2×(-0.05))
x = -0.8 / (-0.1)
x = 8
Now, substitute this x-coordinate into the function to find the maximum height:
f(x) = -0.05x² + 0.8x + 4
f(8) = -0.05(8)² + 0.8(8) + 4
f(8) = -0.05(64) + 6.4 + 4
f(8) = -3.2 + 6.4 + 4
f(8) = 7.2
Therefore, the balloon reached a maximum height of 7.2 feet.
To determine how far from the slingshot the balloon landed, we need to find the x-intercepts of the quadratic function.
These represent the points where the height is zero, indicating the balloon has landed.
Setting f(x) = 0, we can solve the quadratic equation:
-0.05x² + 0.8x + 4 = 0
x² - 16x - 80= 0
x=-4 or x=20
We take the positive value, so the balloon landed 20 feet from the slingshot.
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Find the values of x and y for both questions.
Answers
Answer:
16. x=48 y=70
17. x=45 y=5
Step-by-step explanation:
16. This is an isosceles triangle meaning that the two angles are the same. Meaning that (x+7)=55.
55-7=48
(48+7)=55 x=48
There are 180 degrees in a triangle, so 55+55=110
180-110=70. y=70
17. This is a right angled triangle meaning that the squared part is 90 degrees. And it is also an isosceles triangle meaning that x=97.
There are 180 degrees in a triangle, and 90 is already taken, meaning that there is 90 degrees more left.
90/2=45
x=45
9✖️5=45 y=5
Hope this helps, BRAINLIEST would really help me!
How to calculate a circumference of a circle?
Answers
Answer: Pi multiplied by the diameter of the circle
Step-by-step explanation:
Answer:
The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].
if a b and c are three different numbers which of the following equations has infinitely many solutions
a. ax=bx+c
b. ax+b=ax+c
c. ax+b=ax+b
Answers
Answer:
c. ax+b=ax+b
Step-by-step explanation:
To know what equation has infinite solutions, you first try to simplify the equations:
a.
[tex]ax=bx+c\\\\(a-b)x=c\\\\x=\frac{c}{a-b}[/tex]
In this case you have that a must be different of b, but there is no restriction to the value of c, then c can be equal to a or b.
b.
[tex]ax+b=ax+c\\\\b=c[/tex]
Here you obtain that b = c. But the statement of the question says that a, b and c are three different numbers.
c.
[tex]ax+b=ax+b\\\\0=0[/tex]
In this case you have that whichever values of a, b and are available solutions of the equation. Furthermore, when you obtain 0=0, there are infinite solutions to the equation.
Then, the answer is:
c. ax+b=ax+b
Answer:
ax + b = ax + b
Step-by-step explanation:
i just answered it
Enter the coordinates of the point on the unit circle at the given angle. 150 degrees. please help!
Answers
Answer:
[tex]\boxed{(-\frac{\sqrt{3}}{2}, \frac{1}{2})}[/tex]
Step-by-step explanation:
Method 1: Using a calculator instead of the unit circle
The unit circle gives coordinates pairs for the cos and sin values at a certain angle. Therefore, if an angle is given, use a calculator to evaluate the functions at cos(angle) and sin(angle).
Method 2: Using the unit circle
Use the unit circle to locate the angle measure of 150° (or 5π/6 radians) and use the coordinate pair listed by the value.
This coordinate pair is (-√3/2, 1/2).
Answer: This coordinate pair is (-√3/2, 1/2).
Step-by-step explanation:
Use the unit circle to locate the angle measure of 150° (or 5π/6 radians) and use the coordinate pair listed by the value.
What is the slope of the line passing through the points (6,7) and (1,5)
Answers
Answer:
2/5
Step-by-step explanation:
(7-5)/(6-1)
Determine which of the sets of vectors is linearly independent. A: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t B: The set where p1(t) = t, p2(t) = t2, p3(t) = 2t + 3t2 C: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t + t2
Answers
Answer:
The set of vectors A and C are linearly independent.
Step-by-step explanation:
A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:
[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)= t^{2}[/tex] and [tex]p_{3}(t) = 3 + 3\cdot t[/tex]:
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0[/tex]
[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1} + 3\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2} = 0[/tex]
[tex]\alpha_{3} = 0[/tex]
Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.
[tex]p_{1}(t) = t[/tex], [tex]p_{2}(t) = t^{2}[/tex] and [tex]p_{3}(t) = 2\cdot t + 3\cdot t^{2}[/tex]
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0[/tex]
[tex](\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1}+2\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2}+3\cdot \alpha_{3} = 0[/tex]
Since the number of variables is greater than the number of equations, let suppose that [tex]\alpha_{3} = k[/tex], where [tex]k\in\mathbb{R}[/tex]. Then, the following relationships are consequently found:
[tex]\alpha_{1} = -2\cdot \alpha_{3}[/tex]
[tex]\alpha_{1} = -2\cdot k[/tex]
[tex]\alpha_{2}= -2\cdot \alpha_{3}[/tex]
[tex]\alpha_{2} = -3\cdot k[/tex]
It is evident that [tex]\alpha_{1}[/tex] and [tex]\alpha_{2}[/tex] are multiples of [tex]\alpha_{3}[/tex], which means that the set of vector are linearly dependent.
[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)=t^{2}[/tex] and [tex]p_{3}(t) = 3+3\cdot t +t^{2}[/tex]
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0[/tex]
[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1}+3\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2} + \alpha_{3} = 0[/tex]
[tex]3\cdot \alpha_{3} = 0[/tex]
Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.
The set of vectors A and C are linearly independent.
The daily revenue at a university snack bar has been recorded for the past five years. Records indicate that the mean daily revenue is $2700 and the standard deviation is $400. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days are randomly selected and the average daily revenue computed. According to the Central Limit Theorem, which of the following describes the sampling distribution of the sample mean?
a. Normally distributed with a mean of $2700 and a standard deviation of $40
b. Normally distributed with a mean of $2700 and a standard deviation of $400
c. Skewed to the right with a mean of $2700 and a standard deviation of $400
d. Skewed to the right with a mean of $2700 and a standard deviation of $40
Answers
Answer:
a. Normally distributed with a mean of $2700 and a standard deviation of $40
Step-by-step explanation:
Given that:
the mean daily revenue is $2700
the standard deviation is $400
sample size n is 100
According to the Central Limit Theorem, the sampling distribution of the sample mean can be computed as follows:
[tex]\mathbf{standard \ deviation =\dfrac{ \sigma}{\sqrt{n}}}[/tex]
standard deviation = [tex]\dfrac{400}{\sqrt{100}}[/tex]
standard deviation = [tex]\dfrac{400}{10}}[/tex]
standard deviation = 40
This is because the sample size n is large ( i,e n > 30) as a result of that the sampling distribution is normally distributed.
Therefore;
the statement that describes the sampling distribution of the sample mean is : option A.
a. Normally distributed with a mean of $2700 and a standard deviation of $40
(SAT Prep) In the given figure, find x+y. A. 95° B. 205° C. 185° D. 180°
Answers
Answer:
I hope it will help you...
The value of [tex]x+y[/tex] will be equal to 185 degrees.
From figure it is observed that,
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
[tex]y=45+60=105[/tex]
We know that, By triangle property sum of all three angles in a triangle must be equal to 180 degrees.
So that, [tex]x+55+45=180[/tex]
[tex]x=180-100=80[/tex]
Thus, [tex]x+y=105+80=185[/tex] degree
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Which of the following is the graph of the function shown above? See file
Answers
Answer:
what we have to tell
Step-by-step explanation:
please send the correct information
Answer:
The answer on PLATO is Graph Z.
Step-by-step explanation:
I just had this question and got it right!!!
Hope this Helps!!!
Please answer this correctly without making mistakes
Answers
Answer:
41.1 miles
Step-by-step explanation:
84 - 42.9 = 41.1
whats the steps when solving 40-:8+3^(2)+(15-7)*2
Answers
Answer:
Step-by-step explanation:
Assuming the colon between 40 and 8 is a mistype...
PEMDAS(Parenthesis, Exponents, Multiplication + Division, Addition + Subtraction)
[tex]40-8+3^2+(15-7)*2\\\\Parenthesis\\\\40-8+3^2+8*2\\\\Exponents\\\\40-8+9+8*2\\\\Multiplication\\\\40-8+9+16\\\\Subtraction\\\\32+9+16\\\\Addition\\\\41+16\\\\Addition\\\\57[/tex]
Hope it helps <3
━━━━━━━☆☆━━━━━━━
▹ Answer
57
▹ Step-by-Step Explanation
You need to follow PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
40 - 8 + 3² + (15 - 7)* 2
40 - 8 + 9 + (15 - 7) * 2
40 - 8 + 9 + 8 * 2
40 - 8 + 9 + 16
= 57
Hope this helps!
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Brainliest is greatly appreciated!
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What is the measure of < x
Answers
Answer:
78
Step-by-step explanation:
The measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.
x = 31 + 47
x = 78
For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve.
(a) A circle with radius 3 and center at (1, 2).
(b) A circle centered at the origin with radius 2.
Answers
It is a well-known fact that Dr. Barnes rides a skateboard, sometimes even on campus. Suppose that Dr. Barnes selects a skateboard by first picking one of two skateboard shops at random and selecting a skateboard from that shop at random. The first shop contains two "rad" skateboards and three "gnarly" skateboards, and the second shop contains four "rad" skateboards and one "gnarly" skateboard. What is the probability that Dr. Barnes picked a skateboard from the first shop if he has selected a "gnarly" skateboard?
Answers
Answer:
75%.
Step-by-step explanation:
In total, there are 3 gnarly boards in the first shop and 1 gnarly board in the second. We know that he has selected one gnarly board out of the 3 + 1 = 4 existing boards.
The probability the board came from the first shop is 3 / 4 = 0.75 = 75%.
Hope this helps!
In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find the energy consumption level for the 45th percentile. Group of answer choices
Answers
Answer: 1022.75 kWh.
Step-by-step explanation:
Given: In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh.
i.e. [tex]\mu=1050\ kWh[/tex] and [tex]\sigma=218\ kWh[/tex]
Let X denote energy consumption levels for random single-family homes and x be the energy consumption level for the 45th percentile.
Then, [tex]P(X<x)=0.45[/tex]
From z-table, [tex]P(z<-0.125)=0.45[/tex]
Also, [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]\Rightarrow\ -0.125=\dfrac{x-1050}{218}\\\\\Rightarrow\ x=-0.125\times218+1050=1022.75[/tex]
Hence, the energy consumption level for the 45th percentile is 1022.75 kWh.
Determine the domain of the function. f as a function of x is equal to the square root of x plus three divided by x plus eight times x minus two.
All real numbers except -8, -3, and 2
x ≥ 0
All real numbers
x ≥ -3, x ≠ 2
Answers
Answer:
[tex]\huge \boxed{{x\geq -3, \ x \neq 2}}[/tex]
Step-by-step explanation:
The function is given,
[tex]\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}[/tex]
The domain of a function are all possible values of x.
There are restrictions for the value of x.
The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.
[tex]x+8\neq 0[/tex]
Subtract 8 from both parts.
[tex]x\neq -8[/tex]
[tex]x-2\neq 0[/tex]
Add 2 on both parts.
[tex]x\neq 2[/tex]
The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.
[tex]x+3\geq 0[/tex]
Subtract 3 from both parts.
[tex]x\geq -3[/tex]
The domain of the function is [tex]x\geq -3[/tex], [tex]x\neq 2[/tex].
The domain of the given function will be x ≥ -3 and x ≠ 2.
What is the domain of a function?The entire range of independent input variables that can exist is referred to as a function's domain or,
The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.
As per the data given in the question,
The given expression of function is,
f(x) = [tex]\sqrt{\frac{x+3}{(x-8)(x-2)} }[/tex]
The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.
x + 8 ≠ 0
x ≠ -8
And, x - 2 ≠ 0
x ≠ 2
Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.
So,
x + 3 ≥ 0
x ≥ -3
So, the domain of the function will be x ≥ -3 and x ≠ 2.
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A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function: Ŷ = 7 - 3x1 + 5x2 For this model, SSR = 3500, SSE = 1500, and the sample size is 18. If we want to test for the significance of the regression model, the critical value of F at the 5% level of significance is a. 3.29. b. 3.24. c. 3.68. d. 4.54.
Answers
Answer: C. 3.68
Step-by-step explanation:
Given that;
Sample size n = 18
degree of freedom for numerator k = 2
degree of freedom for denominator = n - k - 1 = (18-2-1) = 15
level of significance = 5% = 5/100 = 0.05
From the table values,
the critical value of F at 0.05 significance level with (2, 18) degrees of freedom is 3.68
Therefore option C. 3.68 is the correct answer
Probability of landing on even # on a spinner; probability of rolling an odd # on a die
Answers
Answer:
Spinner: 50%
Die: 50%
Step-by-step explanation:
Well for the spinner it depends on the amount of numbers it has,
in this case we’ll use 6.
So The probability of landing on the even numbers in a 6 numbered spinner.
2, 4, 6
3/6
50%
Your average die has 6 sides so the odd numbers are,
1, 3, 5
3/6
50%
8/7=x/5 what is the value of x round to the nearest tenth
Answers
Answer:
x = 5.7Step-by-step explanation:
[tex] \frac{8}{7} = \frac{x}{5} [/tex]
To find x first cross multiply
We have
7x = 8 × 5
7x = 40
Divide both sides by 7
That's
[tex] \frac{7x}{7} = \frac{40}{7} [/tex]
[tex]x = \frac{40}{7} [/tex]
x = 5.7142
We have the final answer as
x = 5.7 to the nearest tenthHope this helps you
Answer:
[tex]\boxed{\sf x = 5.7}[/tex]
Step-by-step explanation:
[tex]\sf \frac{8}{7} = \frac{x}{5} \\=> 1.142 = \frac{x}{5}\\ Multiplying \ both \ sides \ by \ 5\\1.142 * 5 = x\\5.7 = x\\OR\\x = 5.7[/tex]
1. Identify the focus and the directrix for 36(y+9) = (x - 5)^2 2. Identify the focus and the directrix for 20(x-8) = (y + 3)^2
Answers
Problem 1
Focus: (5, 0)
Directrix: y = -18
------------------
Explanation:
The given equation can be written as 4*9(y-(-9)) = (x-5)^2
Then compare this to the form 4p(y-k) = (x-h)^2
We see that p = 9. This is the focal distance. It is the distance from the vertex to the focus along the axis of symmetry. The vertex here is (h,k) = (5,-9)
We'll start at the vertex (5,-9) and move upward 9 units to get to (5,0) which is where the focus is situated. Why did we move up? Because the original equation can be written into the form y = a(x-h)^2 + k, and it turns out that a = 1/36 in this case, which is a positive value. When 'a' is positive, the focus is above the vertex (to allow the parabola to open upward)
The directrix is the horizontal line perpendicular to the axis of symmetry. We will start at (5,-9) and move 9 units down (opposite direction as before) to arrive at y = -18 as the directrix. Note how the point (5,-18) is on this horizontal line.
================================================
Problem 2
Focus: (13,-3)
Directrix: x = 3
------------------
Explanation:
We'll use a similar idea as in problem 1. However, this time the parabola opens to the right (rather than up) because we are squaring the y term this time.
20(x-8) = (y+3)^2 is the same as 4*5(x-8) = (y-(-3))^2
It is in the form 4p(x-h) = (y-k)^2
vertex = (h,k) = (8,-3)
focal length = p = 5
Start at the vertex and move 5 units to the right to arrive at (13,-3). This is the location of the focus.
Go back to the focus and move 5 units to the left to arrive at (3,-3). Then draw a vertical line through this point to generate the directrix line x = 3
A stained-glass window is shaped like a right triangle. The hypotenuse is 15feet. The length of one leg is three more than the other. Find the lengths of the legs.
Answers
let us build equation for unknown legs
If we keep the length pf one leg as x
the other leg would be x +3
so we can build a relationship using pythagoras theorem
x^2 + (x+3)^2 = 15^2
x^2 + x^2 + 6x + 9 = 225
2x^2 + 6x + 9 = 225
2x^2 + 6x+ 9-225 = 0
2x^2 + 6x - 216 = 0
x^2 + 3x - 108 = 0 dividing whole equation by 2
x^2 + 12x - 9x - 108 = 0
x ( x + 12 ) - 9 (x + 12) = 0
(x -9) ( x +12) = 0
solutions for x are
x = 9 or x = -12
as lengths cannot be negative
one side length is 9cm
and other which is( x + 3)
9 + 3
12cm
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:
Hypotenuse² = First Leg² + Second leg²
Let x represent the length of one leg. The other leg is three more = x + 3, hypotenuse = 15 ft. Hence:
15² = x² + (x + 3)²
x² + 6x + 9 + x² = 225
2x² + 6x - 216 = 0
x² + 3x - 108 = 0
x = - 12 or x = 9
Since the length cant the negative hence x= 9, x + 3 = 12
The lengths of the legs of the right angled triangle is 9 feet and 12 feet.
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The function f is defined as follows.
f(x) =4x²+6
If the graph of f is translated vertically upward by 4 units, It becomes the graph of a function g.
Find the expression for g(x).
G(x)=
Answers
Answer:
[tex]g(x)=4x^{2} +10[/tex]
Step-by-step explanation:
If we perform a vertical translation of a function, the graph will move from one point to another certain point in the direction of the y-axis, in another words: up or down.
Let:
[tex]a>0,\hspace{10}a\in R[/tex]
For:
y = f (x) + a: The graph shifts a units up.y = f (x) - a, The graph shifts a units down.If:
[tex]f(x)=4x^{2} +6[/tex]
and is translated vertically upward by 4 units, this means:
[tex]a=4[/tex]
and:
[tex]g(x)=f(x)+a=(4x^{2} +6)+4=4x^{2} +10[/tex]
Therefore:
[tex]g(x)=4x^{2} +10[/tex]
I attached you the graphs, so you can verify the result easily.
help plsssssssssssss
Answers
Answer:
[tex]z = \frac{x}{y} [/tex]
Step-by-step explanation:
Let x be the price of carton of ice cream
Let y be the number of grams in carton
Let z be price per gram.
[tex]z = \frac{x}{y} [/tex]
Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.
Hope this helps ;) ❤❤❤
The formula for centripetal acceleration, a, is given below, where v is the velocity of the object and r is the object's distance from the center of the circular path.
Answers
Answer:2/3-4
Step-by-step explanation:
Hi,
The correct answer is √ra = v or v = √ra.
The original equation is a = v^2/r.
Then we multiply r to get ra = v^2
After that we √ra = √v^2
Our final answer is then √ra = v
XD
Families USA, a monthly magazine that discusses issues related to health and health costs, survey 19 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,800. The standard deviation of the sample was $1095.
A. Based on the sample information, develop a 99% confidence interval for the population mean yearly premium
B. How large a sample is needed to find the population mean within $225 at 90% confidence? (Round up your answer to the next whole number.)
Answers
Answer:
a
$10,151 [tex]< \mu <[/tex] $11448.12
b
[tex]n = 158[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 19
The sample mean is [tex]\= x =[/tex]$10,800
The standard deviation is [tex]\sigma =[/tex]$1095
The population mean is [tex]\mu =[/tex]$225
Given that the confidence level is 99% the level of significance is mathematically represented as
[tex]\alpha = 100 -99[/tex]
[tex]\alpha = 1[/tex]%
=> [tex]\alpha = 0.01[/tex]
Now the critical values of [tex]\alpha = Z_{\frac{\alpha }{2} }[/tex] is obtained from the normal distribution table as
[tex]Z_{\frac{0.01}{2} } = 2.58[/tex]
The reason we are obtaining values for [tex]\frac{\alpha }{2}[/tex] is because [tex]\alpha[/tex] is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while [tex]\frac{\alpha }{2}[/tex] is the area under the normal distribution curve for just one tail and we need the value for one tail in order to calculate the confidence interval
Now the margin of error is obtained as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58* \frac{1095 }{\sqrt{19} }[/tex]
[tex]MOE = 648.12[/tex]
The 99% confidence interval for the population mean yearly premium is mathematically represented as
[tex]\= x -MOE < \mu < \= x +MOE[/tex]
substituting values
[tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]
[tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]
$10,151 [tex]< \mu <[/tex] $11448.12
The largest sample needed is mathematically evaluated as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{\mu} ][/tex]
substituting values
[tex]n = [ \frac{ 2.58 * 1095}{225} ]^2[/tex]
[tex]n = 158[/tex]
Find a solution to the linear equation 9x+4y=−36 by filling in the boxes with a valid value of x and y.
Answers
Answer:
Please look at the picture below!
Step-by-step explanation:
Hope this helps!
If you have any question, please feel free to ask any time.