Answers
Answer: C
Step-by-step explanation:
[tex]\frac{3x^{2}-3}{x^{2}+3x}=\frac{3(x^{2}-1)}{x(x+3)}=\frac{3(x-1)(x+1)}{x(x+3)}[/tex]
So, the original fraction is equal to
[tex]\frac{\frac{3(x-1)(x+1)}{x(x+3)}}{\frac{x+1}{x(x+3)}}=\boxed{3(x-1)}[/tex]
Related Questions
T(h) = - A - B * cos((pi*h)/12) Where T is the temperature in degrees Fahrenheit and h is the number of hours from midnight (0 <= h <= 24) . a. The initial temperature at midnight was - 15 degrees * F and at Noon of New Year's Day it was 5 degrees * F Find A and B. b. Find the average temperature for the first 10 hours. C. Find an expression for the rate that the temperature is changing with respect to h.
Answers
The value of A and B is 5 , 10 ;The average temperature for first ten hours is -7.466 degree F ; an expression for the rate that the temperature is changing with respect to h ; dt/dh = +B sin ((pi*h)/12)
What is a Function ?A function is a mathematical statement used to correlate two variables.
The function given is
T(h) = - A - B * cos((pi*h)/12)
T is the temperature in degrees Fahrenheit and
h is the number of hours from midnight (0 <= h <= 24)
a. The initial temperature at midnight was - 15 degrees * F and
at Noon of New Year's Day it was 5 degrees * F
At midnight h = 0
T(h) = -15 degrees F
-15 = -A-B* cos 0
-15 = -A-B
A+B = 15------------------- (1)
At noon , h = 12 , T(h)= 5
- A - B* cos(pi) = 5
-A - B (-1) = 5
B -A = 5 ----------------------- (2)
Solving equation 1 and 2
2B = 20
B = 10
A = 5
The value of A and B is 5 , 10
The average temperature for first ten hours is -7.466 degree F
Find an expression for the rate that the temperature is changing with respect to h
dt/dh = +B sin ((pi*h)/12)
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Find the area of the trapezoid. TOP 11ft, RIGHT4√3ft , BOTTOM 15ft ,LEFT 8ft
Answers
Answer:
[tex]52\sqrt{3} ft^{2}[/tex]
Step-by-step explanation:
Please refer to the attached picture.
First we will find the area of rectangle BCDE.
Area of Rectangle = Length x Breadth = DE x CD
= 11 x [tex]4\sqrt{3}[/tex]
[tex]=44\sqrt{3} ft^{2}[/tex]
Next we will find Area of Triangle ABE.
Area of Triangle = 0.5 x Base x Height
[tex]0.5*4*4\sqrt{3} \\=8\sqrt{3} ft^{2}[/tex]
Area of Trapezoid = Area of Rectangle + Area of Triangle
[tex]=44\sqrt{3} +8\sqrt{3} \\=52\sqrt{3} ft^{2}[/tex]
Answer:
A = 52[tex]\sqrt{3}[/tex] ft² ≈ 90.1 ft²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁ , b₂ the parallel bases
here h = 4[tex]\sqrt{3}[/tex] , b₁ = 15 , b₂ = 11 , then
A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{3}[/tex] × (15 + 11)
= 2[tex]\sqrt{3}[/tex] × 26
= 52[tex]\sqrt{3}[/tex] ft²
≈ 90.1 ft² ( to the nearest tenth )
I need help ASAP please
Which statement is true about whether Z and B are independent events?
A: Z and B are independent events because P(Z | B) =P(Z).
B: Z and B are independent events because P(Z | B) = P(B).
C: Z and B are not independent events because P(Z | B) ≠ P(Z).
D: Z and B are not independent events because P(Z | B) ≠ P(B).
Answers
Explanation:
Independent event means P(Z|B)=P(Z)
P(Z|B)=(Z ∩ B)/B
=(126)/280
=.45
P(Z)=297/660
=.45
Therefore they are independent events, and the answer is A.
four big water bottles can hold 8 gallaons how much can 10 big water gallons hold
Answers
For 10 big bottles = 10 x 2 = 20 gallons.
If you are looking for how many bottles can be filled with 10 gallons, the answer is 5.
If 4=8 then,
10=x
You cross multiply
4x = 10*8
4x /4= 80/4
x = 20
It has been estimated that only about 40% of California residents have adequate earthquake supplies suppose you randomly survey 22 California residents we are interested in the number who have adequate earth quake supplies
Answers
The answers are as follows:
a) X denotes the number of the california residents that have adequate earthquake insurance
b) x = 1 ,2 ,3 ......
c) P( X=x ) = 0.3(1-0.3) ^ (x-1)
d) P( X=1) + P( X=2) + P( X=3) + P( X=4)
e) 0.49
f)0.42
g)0.33
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
The complete question is
It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. a. In words, define the random variable X. b. List the values that Xmay take on. c. Give the distribution of X.X~ _____(_____,_____) d. WhatistheprobabilitythatwemustsurveyjustoneortworesidentsuntilwefindaCaliforniaresidentwhodoes not have adequate earthquake supplies? e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies? f. HowmanyCaliforniaresidentsdoyouexpecttoneedtosurveyuntilyoufindaCaliforniaresidentwhodoesnot have adequate earthquake supplies? g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?
given that 30% of California residents have adequate earthquake supplies.
a) variable X denotes the number of the california residents that have adequate earthquake insurance
b) x = 1 ,2 ,3 ......
c) p=0.3
P( X=x ) = 0.3(1-0.3) ^ (x-1)
d) P( X=1) + P( X=2) + P( X=3) + P( X=4)
= 0.3(1-0.3) ^ 0 + 0.3(1-0.3) ^1 + 0.3(1-0.3)^ 2 +...
e) P( X≥ 3) = 1- P(X<3)
= 1- (P(X=1) + (X=2))
= 1- 0.051
= 0.49.
f) E(X)= 1/P
p is the resident who does not have adequate earthquake supplies
p= 1-0.3
p = 0.7
E(X) = 1/0.7
= 0.42
g) E(X) = 1/q
= 1/0.3
= 3.333
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What are the solutions to the equations y= 4x^2+5x-6
Answers
Answer:
D. x = -2; x = 3/4
Step-by-step explanation:
Read the values of a, b, and c from the quadratic equation: a is the number in front of x^2, b is the number in front of x, c is the number at the end. In our case: a = 4,b = 5,c = −6 The formula for the roots is = [tex]\frac{-b +-\sqrt{b^{2}-4ac } }{2a\\}[/tex]How many pounds of candy that sells for $0.82 per lb must be mixed with candy that sells for $1.36 per lb to obtain 9 lb of a mixture that should sell for $0.91 per lb?
Answers
7.5 pounds of the $0.82 per lb candy must be used in the mixture.
How many pounds of each candy should we use?First, let's define the variables:
x = pounds of the $0.82 candy used.y = pounds of the $1.36 candy used.We want to make 9 lb of mixture, then:
x + y = 9.
And the price of these 9 pounds must be $0.91, then we can write:
x*$0.82 + y*$1.36 = 9*$0.91 = $8.19
Then we have a system of equations:
x + y = 9.
x*$0.82 + y*$1.36 = $8.19
We can isolate y on the first equation so we get:
y = 9 - x
Now we can replace that on the other equation:
x*$0.82 + (9 - x)*$1.36 = $8.19
And now we can solve this for x.
x*($0.82 - $1.36) = $8.19 - 9*$1.36
-x*$0.54 = -$4.05
x = (4.05/0.54) = 7.5
So 7.5 pounds of the $0.82 per lb candy must be used in the mixture.
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One positive number is 8 times another number. Their difference is 70.
Which of the following equations could be used to find the numbers?
Answers
Answer:
X equals 10.
8x - x = 70
Step-by-step explanation:
8 x 10 = 80
80 - 10 = 70
A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?
Answers
Select the correct answer from each drop-down menu.
Consider the function Ax) = 3x+ 1 and the graph of the function g(x) shown below.
Answers
Answer:
write three methods of writing set. Give one example of each methods.
Which of the following terms best fits this definition?
The angle between two sides of a triangle.
Select one:
AAS Theorem
SAS Postulate
Included Side
ASA Postulate
HL Congruence Theorem
Included Angle
SSS Postulate
Answers
Step-by-step explanation:
hope you can understand
Find the value below using your calculator. Round to the nearest hundredth. e³ Find the value below using your calculator . Round to the nearest hundredth . e³
Answers
The value of e³ = 20.079.
What is Euler's number , e ?e is an irrational number , It is a numerical constant used in mathematical constant .
The value of e = 2.718
It is asked in the question to determine the value of e³
Therefore
e³ = ( 2.718)³
e³ = 20.079
Therefore the value of e³ = 20.079.
The image of the calculation is attached with the answer.
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can someone help me asap :)
Answers
Answer:
Option 2 - TU is perpendicular to MN and MN is parallel to PQangle M = angle P ( 90°)
so MN is parallel to pq
MN makes 90° with UT so it is perpendicular
|4x + 7| − 4 = 20
Can anyone help me with this
Answers
Answer:
x = -31/4 or x = 17/4
Step-by-step explanation:
|4x + 7| − 4 = 20
⇔ |4x + 7| − 4 + 4 = 20 + 4
⇔ |4x + 7| = 24
⇔ 4x + 7 = 24 or 4x + 7 = -24
⇔ 4x = 24 - 7 or 4x = -24 - 7
⇔ 4x = 17 or 4x = -31
⇔ x = 17/4 or x = -31/4
Answer:
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
Step-by-step explanation:
| | is notation for absolute value
absolute value - the distance that a number is from 0
> essentially, you can think of absolute value as the "positive version" of whatever is inside of the | |
if we have | x | = 20, we could really have (without the | | ) two versions of x
either | x | = 20 ; or | -x | = 20 {because a negative x inside of the | | has the same value as positive x}
we set this up as two equations:
x = 20 or -x = 20
^ {multiply by -1}
x = 20 or x = -20
now, let's plug our understanding into the equation
|4x + 7| - 4 = 20
first, we should simplify our equation to:
|4x + 7| - 4 = 20
+ 4 + 4
|4x + 7| = 24
now, let's separate this absolute value equation into two separate equations:
4x + 7 = 24:
- 7 - 7 {subtract 7 from both sides to isolate x}
4x = 17
÷4 ÷4 {divide both sides by 4 to get 1x}
x= [tex]\frac{17}{4}[/tex]
or,
4x + 7 = -24:
- 7 -7 {subtract 7 from both sides to isolate x}
4x = -31
÷4 ÷4 {divide both sides by 4 to get 1x}
x = [tex]-\frac{31}{4}[/tex]
so, we know that
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
hope this helps!!
(7 + 7i)(2 − 2i)
(a) Write the trigonometric forms of the complex numbers. (Let
0 ≤ < 2.)
(7 + 7i) =
(2 − 2i) =
(b) Perform the indicated operation using the trigonometric forms. (Let
0 ≤ < 2.)
(c) Perform the indicated operation using the standard forms, and check your result with that of part (b).
Answers
The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number shown in the picture:
-7i(3 + 3i)
= -7i
In trigonometric form:
z = 7 (cos (90) + sin (90) i)
= 3 + 3i
z = 4.2426 (cos (45) + sin (45) i)
[tex]\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)[/tex]
[tex]\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)[/tex]
[tex]\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}[/tex]
[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]
=21-21i
After converting into the exponential form:
[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]
From part (b) and part (c) both results are the same.
Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)
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To purchase 13700 worth of restaurant equipment for her business Maria made a down payment of 1500 and took out a business loan for the rest after 3 years of paying monthly payments of 371.16 she finally paid off the loan
What was the total amount Maria ended up paying for the equipment
How much internet did Maria pay on the loan
Answers
The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
To purchase 13700 worth of restaurant equipment for her business.
Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.
The total amount Maria ended up paying for the equipment will be
Total amount = 371.16 × 3 × 12 + 1500
Total amount = $14,861.76
The interest of Maria on the loan will be
Interset = [(14861.76 – 13700) / 13700] x 100
Interset = 8.48%
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March 8, 2017, one U.S. dollar was worth 66.79 Indian rupees.
a) On that date, how many dollars was 110.66 rupees worth?
Round your answer to the nearest hundredth of a dollar. I need help with this question.
Answers
[tex] \huge \tt \underline {\green{Answer}}[/tex]
If on March 8, 2017 , one U.S. dollar worth 66.79 Indian rupees
ie. $1 = Rs 66.79
$ 1 = 66.79 × 1
$ ? = 110.66
$ = New / old
$ = 110.66 / 66.79
$ = 1.65683485552
or
$1.66 = 110.66
Find an equation for the line that passes through the point P(-5,-3) and is parallel to the line
7x + 4y
10. Use exact values.
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -1.75x - 11.75}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: We need to first solve for y in the equation that was provided so we can determine the slope. Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.
Subtract 7x from both sides
[tex]\textsf{7x - 7x + 4y = 10 - 7x}[/tex][tex]\textsf{4y = 10 - 7x}[/tex]Divide both sides by 4
[tex]\textsf{4y/4 = (10 - 7x)/4}[/tex][tex]\textsf{y = (10 - 7x)/4}[/tex][tex]\textsf{y = 10/4 - 7x/4}[/tex][tex]\textsf{y = 2.5 - 1.75x}[/tex]Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-3) = -1.75(x - (-5))}[/tex]Simplify and distribute
[tex]\textsf{y + 3 = -1.75(x + 5)}[/tex][tex]\textsf{y + 3 = (-1.75 * x) + (-1.75 * 5)}[/tex][tex]\textsf{y + 3 = -1.75x - 8.75}[/tex]Subtract 3 from both sides
[tex]\textsf{y + 3 - 3 = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 11.75}[/tex]Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75
Can someone answer this question for me? Thanks!
Answers
Answer:
The costco basmati rice
Step-by-step explanation:
Under the label it is given that the bag is 18.14 kg
When converted to lbs= 18.14*2.2~39.91
39.91lbs>10lbs, so it has more quantity of rice: Costco Basmati
Answer:
The Costco bag is a better deal as each pound is $0.65 cheaper
Step-by-step explanation:
Let make the weight of each bag in a common unit
18.14kg = about 40 pounds (formula: multiply the mass value by 2.205)
Now find how much it cost per pound for each bag,
Costco: 49.99 / 40 = $1.25 per pound
Bulkmarket: 18.99 / 10 = $1.90 per pound
1.25 < 1.90
What are m and b in the linear equation y=16+6x
Answers
Answer: B=16 and m=6
Step-by-step explanation:
in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.
A sells an article to B at profit of 20% and B sells it to C at a profit of 25%. If C buys it for Rs.225, what did A pay for it?
Answers
Answer:
A pay 120 for itLet the cost price be X
A Sells to B
profit = 20%
= cost price + 20%
= X + 20/100 of X
= 6x/ 5
B sells to C
profit = 25%
= Cost price + + 25%
= cost price + 25%
= 6x/5 + 25/100*6x/5
= 6x/5.+ 3x/10.
= 3x/2
3x/2 = 225.
3x = 450
x = 150.
sp = C. p + profit
S. p - profit = C. p
X - X/5
4x/5
4(150)/5.
120
What is the simplified form of √ 144x36?
Answers
Answer:
12x^18
Step-by-step explanation:
A hyperbola centered at (7, 0) has a focus at (7, 5) and vertex at (7, 4). Which is the equation of the hyperbola in standard form?
quantity x minus 7 end quantity squared over 16 minus y squared over 9 equals 1
quantity x minus 7 end quantity squared over 25 minus y squared over 16 equals 1
y squared over 16 minus quantity x minus 7 end quantity squared over 9 equals 1
y squared over 25 minus quantity x minus 7 end quantity squared over 16 equals 1
Answers
Based on the calculations, the equation of this hyperbola in standard form is: A. [tex]\frac{x\;-\;7}{16} + \frac{y}{9} = 1[/tex].
How to determine the equation of a hyperbola?Mathematically, the equation of a hyperbola in standard form is given by:
[tex]\frac{x\;-\;h}{a^2} + \frac{x\;-\;k}{b^2} = 1[/tex]
Given the following data:
Center (h, k) = (7, 0)
Vertex (h+a, k) = (7, 4)
Focus = (h+c, k) = (7, 5)
Also, we can deduce that the value of a and c are 4 and 5 respectively.
For the value of b, we would apply Pythagorean's theorem:
c² = a² + b²
b² = c² - a²
b² = 5² - 4²
b² = 9.
Substituting the parameters into the standard equation, we have:
[tex]\frac{x\;-\;7}{4^2} + \frac{y\;-\;0}{3^2} = 1\\\\\frac{x\;-\;7}{16} + \frac{y}{9} = 1[/tex]
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \texttt{ \:The absolute maxima of f is f(-8) = 6} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Absolute maxima is the maximum possible value for a given x, of a function.
and here, the maximum value is at -8, and the maximum value is 6.
[tex]\qquad \tt \rightarrow \: maximum - \: \: f( - 8) = 6[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
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Two runners are saving money to attend a marathon.
The first runner has $110 in savings, received a $45 gift
from a friend, and will save $25 each month. The
second runner has $50 in savings and will save $60
each month.
After how many months will both runners have the
same amount of money?
02
O 3
Answers
Answer:
3 months
Step-by-step explanation:
The first runner: $110 + $45 = $155 starting out, plus 25x for $25 each month.
The second runner: $50 starting out, plus 60x for $60 each month.
To find out when both runners have the same amount of money, we will set the expressions equal to each other and solve.
155 + 25x = 60x + 50
105 = 35x
x = 3
Brainliest, please :)
which expression is equivalent to...
Answers
Answer:
B
Step-by-step explanation:
Need help with the following question
Answers
A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one- quarter of the second number and 5. The situation can be represented by using the graph below, where x represents the second number. 16 NO 8 K 3₂ 5 2 4 st 6 8 10 12 14 16 Which equations represent the situation? Hurry
Answers
this is how we do it, jus learn abt it
find the slope of the line that passes through (3,10) and (1,17)
Answers
Answer:
[tex]m=- \frac{7}{2}[/tex]
Step-by-step explanation:
The slope of a line passing through the two points [tex]\displaystyle{\large{{P}={\left({x}_{{1}},{y}_{{1}}\right)}}}[/tex] and[tex]\displaystyle{\large{{Q}={\left({x}_{{2}},{y}_{{2}}\right)}}}[/tex] is given by [tex]\displaystyle{\large{{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}}}[/tex].
We have that [tex]x_1=3[/tex], [tex]y_1=10[/tex], [tex]x_2=1[/tex], [tex]y_2=17[/tex].
Plug the given values into the formula for slope: [tex]m=\frac{\left(17\right)-\left(10\right)}{\left(1\right)-\left(3\right)}=\frac{7}{-2}=- \frac{7}{2}[/tex]
Answer: the slope of the line is [tex]m=- \frac{7}{2}[/tex].
Answer:
slope = - [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{x_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 10 ) and (x₂, y₂ ) = (1, 17 )
m = [tex]\frac{17-10}{1-3}[/tex] = [tex]\frac{7}{-2}[/tex] = - [tex]\frac{7}{2}[/tex]
The Strikers soccer team has 20 members, and 8 of them play offense. What percent of the team members play offense?
Answers
Answer:
40%
Step-by-step explanation:
We already have our first value 20 and the second value 8. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
Step 1 ⇒ Y = 8/20
By multiplying both numerator and denominator by 100 we will get:
Step 2 ⇒ Y = 8/20 × 100/100 = 40/100
Step 3 ⇒ Y = 40
Finally, we have found the value of Y which is 40 and that is our answer.
