Which of the following lines are parallel to 2Y - 3X = 4?
A. Y = 2/3 X + 4
B. Y = 6/4 X
C. 2Y=8-3X
Answers
Answer:
B. Y = 6/4 X
Step-by-step explanation:
Well to find its parallel line we need to put,
2y - 3x = 4 into slope-intercept.
+3x to both sides
2y = 3x + 4
Now we divide everything by 2,
y = 3/2x + 2
So a line that is parallel to the given line will have the same slope but different y intercept, meaning we can cross out choices A and C.
To check look at the image below ↓
Thus,
answer choice B. Y = 6/4 X is correct.
Hope this helps :)
Related Questions
Select the correct answer. Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing diameters of the circle. He labels the ends the diameters A, B, C, D, E, and F, and he uses a straightedge to draw the chords that form a hexagon. Which statement is true? A. Vincent’s construction method produces a hexagon that must be regular. B. Vincent’s construction method produces a hexagon that must be equilateral but may not be equiangular. C. Vincent’s construction method produces a hexagon that must be equiangular but may not be equilateral. D. Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.
Answers
Answer:
B.
Step-by-step explanation:
Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular. The correct option is D.
What is a regular polygon?A regular polygon is a polygon that is equiangular and equilateral. Therefore, the measure of all the internal angles and the measure of all the sides of the polygon are equal to each other.
Given that Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing the diameters of the circle.
Now as it can be seen as the paper is folded as shown in the below image but it does not create a hexagon that is equilateral and equiangular.
Hence, Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.
Learn more about Regular Polygon:
https://brainly.com/question/10885363
#SPJ2
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.
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.
factorize 3x square+5x
Answers
Answer:
x(3x+5)
Step-by-step explanation:
3x^2+5x
take out common factor x
= x(3x+5)
Answer:
[tex]x(3x + 5)[/tex]Step-by-step explanation:
3x² + 5x
Factor out X from the expression
= x ( 3x + 5 )
Hope this helps...
Best regards!!
given sin theta=3/5 and 180°<theta<270°, find the following: a. cos(2theta) b. sin(2theta) c. tan(2theta)
Answers
I hope this will help uh.....
The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v).
Estimate the values of fT(−15, 50) and fv(−15, 50).
V 20 30 40 50 60 70
T
−10 −18 −20 −21 −22 −23 −23
−15 −25 −26 −27 −29 −30 −30
−20 −30 −33 −34 −35 −36 −37
−25 −37 −39 −41 −42 −43 −44
Answers
Answer:
value of Ft(-15,50) = 1.3
Value of Fv(-15,50) = -0.15
Step-by-step explanation:
W = perceived temperature
T = actual temperature
W = f( T,V)
Estimate the values of ft ( -15,50) and fv(-15,50)
calculate the Linear approximation of f at(-15,50)
[tex]f_{t}[/tex] (-15,50) = [tex]\lim_{h \to \o}[/tex] [tex]\frac{f(-15+h,40)-f(-15,40)}{h}[/tex]
from the table take h = 5, -5
[tex]f_{t}(-15,40) = \frac{f(-10,40)-f(-15,40)}{5}[/tex] = [tex]\frac{-21+27}{5} = 1.2[/tex]
[tex]f_{t} = \frac{f(-20,40)-f(-15,40)}{-5}[/tex] = 1.4
therefore the average value of [tex]f_{t} (-15,40) = 1.3[/tex]
This means that when the Temperature is -15⁰c and the 40 km/h the value of Ft (-15,40) = 1.3
calculate the linear approximation of
[tex]f_{v} (-15,40) = \lim_{h \to \o} \frac{f(-15,40+h)-f(-15,40)}{h}[/tex]
from the table take h = 10, -10
[tex]f_{v}(-15,40) = \frac{f(-15,50)-f(-15,40)}{10}[/tex] = [tex]\frac{-29+27}{10} = -0.2[/tex]
[tex]f_{v} (-15,40) = \frac{f(-15,30)-f(-15,40)}{-10}[/tex] = [tex]\frac{-26+27}{-10}[/tex] = -0.1
therefore the average value of [tex]f_{v} (-15,40) = -0.15[/tex]
This means that when the temperature = -15⁰c and the wind speed is 40 km/h the temperature will decrease by 0.15⁰c
w = f(T,v)
= -27 + 1.3(T+15) - 0.15(v-40)
= -27 + 1.3T + 19.5 - 0.15v + 6
= 1.3T - 0.15v -1.5
calculate the linear approximation
[tex]\lim_{v \to \infty}[/tex][tex]\frac{dw}{dv} = \lim_{v \to \infty} \frac{d(1.3T-0.15v-1.5)}{dv}[/tex] = -0.15
PLZ CHECK MY ANSWER. Round your answer to the nearest tenth.
I chose D.
A: 72.56 cm^2
B: 80.29 cm^2
C: 60.66 cm^2
D: 70.32 cm^2
Answers
Answer:
D. [tex]70.34 cm^2[/tex]
Step-by-step explanation:
Area of sector of a circle is given as θ/360*πr²
Where,
r = radius = 12 cm
θ = 56°
Use 3.14 as π
Plug in the values into the formula and solve
[tex] area = \frac{56}{360}*3.14*12^2 [/tex]
[tex] area = 70.34 [/tex]
Area of the sector ABC = [tex] 70.34 cm^2 [/tex]
The answer is D
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.
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].
Simplify (4x)². Rewrite the expression in the form k ⋅ xⁿ
Answers
Answer:
16x²
Step-by-step explanation:
(4x)²4² *x²16*x² 16x²whats 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!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
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.
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!
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 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
Exhibit 3-3Suppose annual salaries for sales associates from Hayley's Heirlooms have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500.The z-score for a sales associate from this store who earns $37,500 is ____
Answers
Answer:
The z-score for a sales associate from this store who earns $37,500 is 2
Step-by-step explanation:
From the given information:
mean [tex]\mu[/tex] = 32500
standard deviation = 2500
Sample mean X = 37500
From the given information;
The value for z can be computed as :
[tex]z= \dfrac{X- \mu}{\sigma}[/tex]
[tex]z= \dfrac{37500- 32500}{2500}[/tex]
[tex]z= \dfrac{5000}{2500}[/tex]
z = 2
The z-score for a sales associate from this store who earns $37,500 is 2
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.
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]
Please answer this correctly without making mistakes
Answers
Answer:
41.1 miles
Step-by-step explanation:
84 - 42.9 = 41.1
verify:
cos(2A)=(cotA-tanA)/cscAsecA
Answers
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
cot A = [tex]\frac{cosA}{sinA}[/tex], tanA = [tex]\frac{sinA}{cosA}[/tex], cscA = [tex]\frac{1}{sinA}[/tex], secA = [tex]\frac{1}{cosA}[/tex]
Consider the right side
[tex]\frac{cotA-tanA}{cscAsecA}[/tex]
= [tex]\frac{\frac{cosA}{sinA}-\frac{sinA}{cosA} }{\frac{1}{sinA}.\frac{1}{cosA} }[/tex]
= [tex]\frac{\frac{cos^2A-sin^2A}{sinAcosA} }{\frac{1}{sinAcosA} }[/tex]
= [tex]\frac{cos^2A-sin^2A}{sinAcosA}[/tex] × sinAcosA ( cancel sinAcosA )
= cos²A - sin²A
= cos2A
= left side ⇒ verified
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.
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
? 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.
To learn more on Quadratic equation click:
https://brainly.com/question/17177510
#SPJ2
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.
To know more about Domain:
https://brainly.com/question/28135761
#SPJ3
A large sample of men, aged 48 was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men 90% were alive at 65%. Is this a sample or population?
Answers
(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
Learn more:
https://brainly.com/question/12230244
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
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.
Find out more at: https://brainly.com/question/10040532
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
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!!!