Answer:
1. 14 divided by 7 equals 0.5
2.24 divided by 12
3. 35 divided by 5
What is the domain of the rational function f of x is equal to 2 x over the quantity 2 x cubed minus 5 x squared minus 12 x end quantity
x is an element of all real numbers such that x is not equal to 0
x is an element of all real numbers such that x is not equal to negative three halves comma 4
x is an element of all real numbers such that x is not equal to 0 comma negative three halves comma 4
x is an element of all real numbers such that x is not equal to 0 comma three halves comma negative 4
Using the domain concept, it is found that the domain of the function is: x is an element of all real numbers such that [tex]x \neq (-\frac{3}{2}, 4)[/tex], second option.
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The domain of a function is all possible values that the input value x can assume.The domain of a fraction is all real values of x except the zeros of the denominator.----------------------
The function is:
[tex]f(x) = \frac{2x}{2x^3 - 5x^2 - 12x} = \frac{2x}{x(2x^2 - 5x - 12)} = \frac{2}{2x^2 - 5x - 12}[/tex]
The points outside the domain are the zeros of [tex]2x^2 - 5x - 12[/tex], which we find solving a quadratic equation.
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Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
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[tex]2x^2 - 5x - 12[/tex] is a quadratic equation with [tex]a = 2, b = -5, c = -12[/tex].
[tex]\Delta = b^{2} - 4ac = (-5)^2 - 4(2)(-12) = 121[/tex]
[tex]x_{1} = \frac{-(-5) + \sqrt{121}}{2(2)} = 4[/tex]
[tex]x_{2} = \frac{-(-5) - \sqrt{121}}{2(2)} = -\frac{6}{4} = -\frac{3}{2}[/tex]
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The domain is: x is an element of all real numbers such that [tex]x \neq (-\frac{3}{2}, 4)[/tex], second option.
A similar problem is given at https://brainly.com/question/13136492
Answer:
Step-by-step explanation:
Using the domain concept, it is found that the domain of the function is: x is an element of all real numbers such that , second option.
----------------------
The domain of a function is all possible values that the input value x can assume.
The domain of a fraction is all real values of x except the zeros of the denominator.
----------------------
The function is:
The points outside the domain are the zeros of , which we find solving a quadratic equation.
----------------------
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots such that , given by the following formulas:
----------------------
is a quadratic equation with .
----------------------
The domain is: x is an element of all real numbers such that , second option.
A similar problem is given at brainly.com/question/13136492
In a birthday party, a cake was cut into 30 equal sizes pieces. At the end of the party, 8 pieces were left. What was the percentage of cake consumped?
Answer:
73 1/3 %
Step-by-step explanation:
8 pieces were left
30-8 = 22 so 22 were consumed
22/30 is the percent consumed
.7333333
73.333333%
We know .333333333 is 1/3
73 1/3 %
A rectangular rug has the perimeter of 36 feet. The length of the rug is twice the width. What is the length
Answer:
12 ft
Step-by-step explanation:
l = 2w
P = 2(l+w)
36 = 2(2w+w)
36 = 2(3w)
36 = 6w
Divide each side by 6
36/6 = 6w/6
6 =w
l = 2w
l = 2(6)
l = 12
Find the measure of FG.
Answer:
8
Step-by-step explanation:
By power of a point, (x-2)(x+13) = (x-3)(x+16). Solving, we find that x=11, so FG= 11-3 = 8
find the sum of 56, the product of 18 and - 3 and the positive difference between 52 and 29.... PLEASE
Answer:
25
Step-by-step explanation:
product of 18 and -3=18*-3= -54
positive difference=52-29=23
(18x-3)+56+(52-29)
= -54 + 56 + 23
=25
PLEASE ANSWER ASAP
Write an inequality and show on a number line all numbers: greater than (-3) but less than or equal to 3
Answer:
The inequality is -3<x<3
Step-by-step explanation:
(-3,3)
Express this to single logarithm
[tex] \frac{1}{2} log_{2}(m) - 3 log_{2}(n) + 2 log(q) [/tex]
Answer: [tex]\log_{2}\left(\frac{q^2\sqrt{m}}{n^3}\right)[/tex]
We have something in the form log(x/y) where x = q^2*sqrt(m) and y = n^3. The log is base 2.
===========================================================
Explanation:
It seems strange how the first two logs you wrote are base 2, but the third one is not. I'll assume that you meant to say it's also base 2. Because base 2 is fundamental to computing, logs of this nature are often referred to as binary logarithms.
I'm going to use these three log rules, which apply to any base.
log(A) + log(B) = log(A*B)log(A) - log(B) = log(A/B)B*log(A) = log(A^B)From there, we can then say the following:
[tex]\frac{1}{2}\log_{2}\left(m\right)-3\log_{2}\left(n\right)+2\log_{2}\left(q\right)\\\\\log_{2}\left(m^{1/2}\right)-\log_{2}\left(n^3\right)+\log_{2}\left(q^2\right) \ \text{ .... use log rule 3}\\\\\log_{2}\left(\sqrt{m}\right)+\log_{2}\left(q^2\right)-\log_{2}\left(n^3\right)\\\\\log_{2}\left(\sqrt{m}*q^2\right)-\log_{2}\left(n^3\right) \ \text{ .... use log rule 1}\\\\\log_{2}\left(\frac{q^2\sqrt{m}}{n^3}\right) \ \text{ .... use log rule 2}[/tex]
intergrate x×(x²-3)³
Answer: [tex]\large \boldsymbol{\dfrac{1}{8 } (x^2-3)^4+c}[/tex]
Step-by-step explanation:
[tex]\displaystyle \large \boldsymbol{} \int\limits {x(x^2-3)^2 } \, dx =\int\limits \frac{1}{2} {} \, (x^2-3)' (x^2-3)^3 dx =\frac{1}{8} (x^2-3)^4+c[/tex]
PLEASE HELP ME ASAP!!!
Answer:
5.30
Step-by-step explanation:
Total cost = flat fee + cost per mile * number of miles
c(m) = 3.50 + .60m
Let m=3
c(3) = 3.50 + .60(3)
= 3.50 + 1.80
=5.30
Answer:
B: $5.30
Step-by-step explanation:
Each mile is $0.6, to get the result for 3 miles we would need to multiply $0.6 by 3. $0.60 * 3 = $1.8. Finally we would need to add the 3.50 to $1.8 resulting in $5.30
Look at this cube,,,,,,,
write two properties of right angled triangle
Answer:
The properties of right angle triangle are as follows
the hypotenuse is the longest sideone angle is 90 degree then other angle will be also 90 degree.ASAP!! Photo attached
Answer:
FG = 120 cm
Step-by-step explanation:
The explanation is in the picture!
Bobby think that 5^2 = 10. What is wrong with this answer
Answer:
see below
Step-by-step explanation:
5^2 means 5*5 not 5*2
5^2 = 5*5 = 25 not 10
Answer:
5*5 = 25
bobby mistake is doing 5*2 = 10
Step-by-step explanation:
on
9
emaining:
Point-Slope
out of
question
Instructions: Write the equation of the line in Point-Slope Form given the information below.
Slope =-1/5 y-intercept =-3
Answer:
y = -1/5x - 3
Step-by-step explanation:
A right triangle has a 6cm base and an 8cm height. What is the length of the hypotenuse, in centimeters?
Answer:
the answer is 10 or 6^2+8^2=100
√100=10
The equation T squared = A cubed shows the relationship between a planet's orbital period, T, and the planet's mean distance from the sun, A, in astronomical units, AU. If planet Y is k times the mean distance from the sun as planet X, by what factor is the orbital period increased? k Superscript one-third k Superscript one-half k Superscript two-thirds k Superscript three-halves
Answer:
Ty = √k * Tx
The orbital period of Y has to be be multiplied by √k . or . k∧1/2
Step-by-step explanation:
The general equation:
T² = A³
is for the case of planet X
Tₓ² = Aₓ³
In the case of planet Y
Ty² = k * Aₓ³ . and Aₓ³ = Tₓ²
By substitution:
Ty² = k *Tₓ²
Ty = √k * Tx
Answer:
D: K^3/2
Step-by-step explanation:
Just took the test and this is right
SOMEONE PLEASE HELP ME OUT ON THIS. PLEASE!
n= 1. then a1= 7+3(1)
How to solve it.
Answer:
I think this is right for the 2nd problem
Step-by-step explanation:
a1=7+(3)(1)
Step 1: Simplify both sides of the equation.
a1=7+(3)(1)
a=7+3
a=(7+3)(Combine Like Terms)
a=10
a=10
Answer:
a=10
Each coffee pot hold 6 cups of coffee we sell 10 cups of coffee every fifteen minutes how many pots of coffee do I need to make in an hour?
Answer:
7 pots of coffee (If you want to be precise its 6 2/3)
Step-by-step explanation:
So basically you need 10 cups of coffe in fifteen minutes, so 60/15=4 then time 10. so 40 is how much coffee you need in a hour, but we are solving the pot so 40/6= 6 2/3. but it says how many pots so we round it up so its 7. (Unless you wanna be precise)
Audrey Baker bought 4 new tires for her
car. The cost of each tire was $75. The
Federal Excise tax was $5.10 per tire, and
the state sales tax was 7% of the cost of the
tires, excluding the excise tax. Find the
total cost of the tires.
Please show work
Answer:
the cost of the tire=341.4$
Write a simplified polynomial expression in standard form to represent the area of the rectangle below:
(See photo)
A. 2x^2 + 3x - 20
B. 2x^2 + 13x - 1
C. 2x^2 + 13x - 20
D. 2x^2 + 3x - 1
Answer:
A
Step-by-step explanation:
The area (A) of a rectangle is calculated as
A = length × breadth
= (2x - 5)(x + 4) ← expand using FOIL
= 2x² + 8x - 5x - 20
= 2x² + 3x - 20 → A
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
15x — бу = 48
Answer:
Step-by-step explanation:
15x-6y=48
-6y=48-15x
y=-8+(15/6)x
y=(5/2)x-8
Add.
(-2+6x3 – 3x_) + (4x3 – 5 + x²)
Express the answer in standard form.
Enter your answer in the box.
Explain how to solve the equation
.
b – 7 = 12
Answer:
19
Step-by-step explanation:
Add 7 onto 12 to find answer.
Answer:
b = 19
Step-by-step explanation:
b = 12 + 7
Simplify 12+7 to 19.
which choice is equivalent to the expression below?
6√7 - 5x√7 - x√7
[tex]6 \sqrt{7} (1 - x)[/tex]
solve for y.
y + 5.74 = 9.62
Answer:
3.88
Step-by-step explanation:
1. Subtract 5.74 from both sides of the equation
9.62-5.74=3.88
The distance between Kuala Pilah and Bangi is x km. A bus travelled from Kuala Pilah to Bangi at an average speed of 80 km/h. On the return journey from Bangi to Kuala Pilah, the bus travelled at an average speed of 100 km/h and it took 15 minutes less than the previous one. Calculate the value of x.
A. 80 km
B. 100 km
C. 120 km
D. 160 km
Answer:
100km
Step-by-step explanation:
Time taken to travel to Bangi:
x/80 hours
15min = 1/4hrs
Time taken to travel back:
x/80 - 1/4
x= x/(x/80-1/4)
x^2-100x=0
x(x-100)=0
x=0 (rejected) or x=100
Answer:
B. 100km
Step-by-step explanation:
Brainliest please
Look at the figure. Which step should be taken next to construct a line through point R that is perpendicular to ST ?
Answer:
where is the figure without figure how to find out
i will mark brainliest!!!
Other answers: C. y=25x
D. y=25x+8.34
Answer:
Omg why are you soo beautiful? I love it
Find the common ratio of the geometric sequence 17, -51, 153, ...
Answer:
an = 17 ( − 3 ) n − 1
Step-by-step explanation:
Use the formula an = a 1 r n − 1 to identify the geometric sequence.
break up the denominator and write the product of two fractions see image belows
9514 1404 393
Answer:
1/sec(x) · 1/tan(x)
Step-by-step explanation:
The breakup can be accomplished any of several ways.
[tex]\dfrac{1}{\sec(x)\tan(x)}=\dfrac{1}{\sec(x)}\times\dfrac{1}{\tan(x)}=\dfrac{\cos(x)}{1}\times\dfrac{\cos(x)}{\sin(x)}[/tex]
