Find the domain of the function. (Enter your answer using interval notation.) f(x) = 1 /(x2 + 3x − 4)
Answers
Step-by-step explanation:
The domain of a function is the range of x such that the function is defined.
Now we know the function
[tex]f(x) = \frac{1}{ {x}^{2} + 3x - 4 }[/tex]
is only defined when the denominator is not zero, in other words, when
[tex] {x}^{2} +3x - 4 \neq \: 0[/tex]
or
[tex](x + 4)(x - 1) \neq0[/tex]
[tex]x \ne-4 [/tex]
and
[tex]x \neq +1[/tex]
1/(x^2+3x-4)
1/(x+4)(x-1)
{x|x≠1,-4}
Answer:
(negative infinity, -4) U (-4,1) U (1, infinity)
Related Questions
Help!!!!! Pleaseee I don’t understand
Answers
Answer:
Question 22: x = 3Question 23: AB = 10Question 24: BD = 14Question 25: CE = 17Concept:
Here, we need to know the idea of the segment addition postulate.
The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
If you are still confused, you may tell me or refer to the attachment below for a graphical explanation.
Solve:
Question 22. If AC = 16, what is x?
Given information
AC = 16
AB = x + 7
BC = 2x
Given expression deducted from the segment addition postulate
AB + BC = AC
Substitute values into the expression
x + 7 + 2x = 16
Combine like terms
x + 2x + 7 = 16
3x + 7 = 16
Subtract 7 on both sides
3x + 7 - 7 = 16 - 7
3x = 9
Divide 3 on both sides
3x / 3 = 9 / 3
[tex]\boxed {x=3}[/tex]
Question 23. What is AB?
Given information
x = 3
Given expression deducted from the segment addition postulate
AB = x + 7
Substitute values into the expression
AB = (3) + 7
[tex]\boxed {AB=10}[/tex]
Question 24. What is BD?
Given information
BC = 2x
CD = 3x - 1
x = 3
Given expression deducted from the segment addition postulate
BD = BC + CD
Substitute values into the expression
BD = 2x + 3x - 1
BD = 2(3) + 3(3) - 1
BD = 6 + 9 - 1
BD = 15 - 1
[tex]\boxed {BD=14}[/tex]
Question 25. What is CE?
Given information
CD = 3x - 1
DE = 2x + 3
x = 3
Given expression deducted from the segment addition postulate
CE = CD + DE
Substitute values into the expression
CE = 3x - 1 + 2x + 3
CE = 3(3) - 1 + 2(3) + 3
CE = 9 - 1 + 6 + 3
CE = 8 + 6 + 3
CE = 14 + 3
[tex]\boxed {CE=17}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Evaluate:
45
O 256
O 625
0 1024
o I don't know
Answers
Answer:
A. 256
Step-by-step explanation:
4×4×4×4=256
I hope this helps!
pls ❤ and mark brainliest pls!
answer : 1024
100% correct ;)
Which represents a function?
Answers
Answer:
B
Step-by-step explanation:
For a function to be a function, every x value can only equal a single y value. A has two y values for one x value, and so does C and D. This leaves only B.
8. Is it possible to have an object that does not have 360° rotational symmetry? Explain your reasoning.
Answers
Don't forget put heart ♥️
1. Which is an example of an algebraic expression?
Answers
Answer:
3-a
Step-by-step explanation:
it involves variables like x, y, z
in this case a
Add the Following Fractions:
\large \frac{3}{8}+\frac{2}{8}=?
a. 5/16
:b. 5/8
c. 6/8
d. 1/8
Answers
Answer:
B. [tex]\frac{5}{8}[/tex]
Explanation:
Because the denominators (bottom numbers) of both fractions are the same, we simply just add the numerators (top numbers) and keep 8 as the denominator.
Please help and please give explanation
Answers
Answer: -5 i guess i might b wrong i dont know -5
Step-by-step explanation:
Show Work! There are 380 students, teachers, and chaperones going on school buses for a field trip. Each school bus can hold 68 passengers. Everyone will ride on a school bus. How many school buses does this group need?
Answers
Answer:
6 buses
Step-by-step explanation:
i believe you just have to divide 380/68
then it'll give you 5.5 and then have to round to the nearest integer
0.2 kg
2m
9.8g
Pls help quick
Answers
Complete the equation. (x-2)(x^2 + 2x + 4) = ( , )
Answers
Answer:
Step-by-step explanation:
x(x² + 2x + 4)-2((x² + 2x + 4)
x³+2x²+4x -2x²-4x-8
x³-8
9.62 - 3 =
2.57 + 7.706 =
15 - 6.108
Answers
Step-by-step explanation:
[tex]9.62 - 3[/tex]
[tex] = 6.62[/tex]
•♧•♧•♧•♧•♧•♧•
[tex]2.57 + 7.706[/tex]
[tex] = 10.276[/tex]
•◇•◇•◇•◇•◇•◇•
[tex]15 - 6.108[/tex]
[tex] = 9.892[/tex]
Which statement is true regarding the graphed functions?
euf
12
40
B
4
914
2
1 2
3
4.
5
B
X
I f 5 4 3 2 12)
-4
B
be
10
2
141
f(4) = g(4)
f44) = (1-2)
Answers
Maybe upload an image of the choice rather than text since it’s unreadable
Help meeeeeeeeeeeeeeeee
Answers
Answer:
x-3
Step-by-step explanation:
the inverse is x-3
this is the answer
Determine a quadratic equation that has 7 and -4 as solutions.
Answers
Answer:
(x+x1)(x-x2)
let x1=7 and x2=-4
(x+7)(x-(-4))
(x+7)(x+4)
x^2+4x+7x+28
x^2+11x+28
find the distance between each pair of points if necessary round to the nearest tenth.
17. A(6,7),B(-1,7)
18. C(5,-5),D(5,3)
19. E(-1,0),F(12,0)
20. Q(2,-6),T(10,0)
21. H(20,-4),I(-4,3)
22. J(-5,5),K(-3,-2)
I will give brainliest please help and show work
Answers
Step-by-step explanation:
q17
[tex]d = \sqrt{ {(7 - 7)}^{2} + {(6 - ( - 1))}^{2} } = 7[/tex]
q18
[tex]d = \sqrt{ {(5 - 5)}^{2} + {(3 - ( - 5))}^{2} } = 8[/tex]
q19
[tex]d = \sqrt{ {(12 - ( - 1))}^{2} + {(0 - 0)}^{2} } = 12[/tex]
q20
[tex]d = \sqrt{ {(10 - 2)}^{2} + {(0 - ( - 6))}^{2} } = 10[/tex]
q21
[tex]d = \sqrt{ {(3 - ( - 4))}^{2} + {(( - 4) - 20)}^{2} } = 25[/tex]
q22
[tex]d = \sqrt{ {(( - 3) - ( - 5))}^{2} + {(( - 2) - 5)}^{2} } = 7.1[/tex]
What is the equation of a circle with center -4, 7 and radius 6
Answers
Answer:
[tex]( x + 4 )^2 + ( y - 7 )^2 = 36[/tex]
Step-by-step explanation:
Use the circle equation, [tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]
Plug in the center and radius:
[tex]( x + 4 )^2 + ( y - 7 )^2 = 6^2[/tex]
Simplify:
[tex]( x + 4 )^2 + ( y - 7 )^2 = 36[/tex]
So, the equation is [tex]( x + 4 )^2 + ( y - 7 )^2 = 36[/tex]
Emily Bought the Following items for Christmas gifts for her Friends: 5 Hannah Montana calendars, 3 DVDs, 2 books, 1 Monopoly game, 8 CDs, 1 Box of Candy, and 2 gift Cards to Walmart.What is the Ratio of DVDs to the total number of Gifts.
Answers
Answer:
Ig its 22:3
Step-by-step explanation:
First we add all the gifts and put it in the ratio and the other is 3 dvds
One positive number is 2 more than twice another. If their product is 1012, find the numbers.
Answers
Answer:
46 and 22
Step-by-step explanation:
22 x 2 = 44
44 is 2 less than 46
46 x 22 = 1012
|72| ÷ |-12| =
?????????
Answers
Answer:
6
Step-by-step explanation:
|72| ÷ |-12|
Absolute value of 72 = 72
Absolute value of -12 = 12
72 ÷ 12 = 6
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
What is the equation of the line that passes through the point (8,−3) and has an undefined slope?
Answers
Answer:
[tex]x = 8[/tex]
Step-by-step explanation:
Recall that horizontal lines have a slope of zero, while vertical lines have an undefined slope.
Therefore, the line must be vertical.
And since it is vertical, we will only need to consider the x-coordinate of our point.
The x-coordinate of (8, -3) is 8.
Hence, the equation of the line that passes through (8, -3) with an undefined slope is:
[tex]x = 8[/tex]
Answer: x= 8
Step-by-step explanation:
It is a vertical line that passes through point 8 on the x axis.
write and simplify an expression for the area of the triangle
(show step by step)
Answers
Answer:
Step-by-step explanation:
The area of the triangle is
B*h/2
Where B=x+5 and h=x-2 so if we substitute
(x+5)*(x-2)/2 =
(x^2 +3*x -10)/2=
x^2/2 + 3/2 *x -5
Which of the following is a true statement of the figure
Answers
Answer:
The last one
Step-by-step explanation:
Need help!!!!
Will earns $6.50 per hour and time-an-a-half for all hours over 40.
Find his weekly pay if he worked 47 hours.
a. $305.50
b. $328.25
c. $269.75
d. $68.25
Answers
Answer:
b
Step-by-step explanation:
what is 6% of 3125
Answers
Answer:
187.5
Step-by-step explanation:
6% of 3125
=> 6/100 x 3125
=> 18750/100
=> 187.5
You are wrapping a gift box that is 16 inches long,
7 inches wide, and 9 inches tall. Find the amount of
wrapping paper you need to wrap the gift box to the
nearest square inch.
Answers
Answer:
1008 inches
Step-by-step explanation:
1109,1116,1123 what’s next
Answers
Answer:
C. 1130
BRAINLIEST, PLEASE!
Step-by-step explanation:
1109 + 7 = 1116
1116 + 7 = 1123
1123 + 7 = 1130
The value of the missing number is 1130.
Missing numberThe missing number in the series can be determined by finding the common difference or pattern of the numbers.
let the common difference = d
1109 + 7 = 1116
1116 + 7 = 1123
1123 + 7 = 1130
Thus, the value of the missing number is 1130.
Learn more about missing numbers here: https://brainly.com/question/1241542
Which of the following is the best example of kinetic energy?
A book sitting on a bookshelf
A golfer preparing to putt the ball
A race car in position at the start line
A satellite orbiting the Earth
Answers
Answer:
i had this question a little while back and the right answer was
d. a satellite orbiting the Earth.
(:
Simplify
5(x + 8) - 2x = 7(x + 10)
Answers
Answer:
-15/2
Step-by-step explanation:
5(x + 8) - 2x = 7(x + 10)
=> 5x + 40 - 2x = 7x + 70
=> 3x + 40 = 7x + 70
=> 3x - 7x = 30
=> -4x = 30
=> x = -30/4
=> x = -15/2
Explanation : 5(x) + 5(8) = 5x+40, 5x+40-2x= 3x+40 , 7(x)+7(10)=7x+70
3x+40=7x+70
what is the answer to this problem (40+35+2(30+25))/5
Answers
Answer:
37
Step-by-step explanation:
Answ 925
Step-by-step explanation:
Rewrite in simplest terms: 9w-3(-w-8)
Answers
Answer:
[tex]12w+24[/tex]
Step-by-step explanation:
[tex]9w−3(−w−8)[/tex]
[tex]9w+(−3)(−w)+(−3)(−8)[/tex]
[tex]9w+3w+24[/tex]
[tex](9w+3w)+(24)[/tex]
[tex]12w+24[/tex]
Hope it is helpful.....In the simplest form we can write the expression as - 12(w + 2).
We have the following expression -
9w - 3(- w - 8)
We have to write it in simplest form.
Expand the following expression -Δ = (x - α)(x - β)Expanding we get -
Δ = x(x - β) - α(x - β)
Δ = [tex]x^{2}[/tex] - βx - αx + αβ
According to the question, we have -
9w - 3(- w - 8)
Simplifying it, we get -
9w + 3(w + 8)
9w + 3w + 24
12w + 24
12(w + 2)
Hence, in the simplest form we can write the expression as - 12(w + 2).
To solve more questions on Simplifying expressions, visit the link below-
https://brainly.com/question/20456437
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