The simplest form of [(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)] is 3p/ (p - 3).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given expression is
[(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)]
Now factories p²- 4p -12, p²-9p+18, and 6p + 12:
p²- 4p -12
= p²- (6 - 2)p -12
= p²- 6p + 2p -12
= p(p - 6) + 2(p - 6)
=(p - 6)(p + 2)
p²- 9p + 18
= p²- (6 + 3)p + 18
= p²- 6p -3p + 18
= p(p - 6) -3(p -6)
=(p - 6)(p - 3)
6p + 12
=6(p+2)
Now putting p²- 4p -12 = (p - 6)(p + 2); p²- 9p + 18 = (p - 6)(p - 3); 6p + 12 = 6(p+2) in the given expression:
[ (p - 6)(p + 2)/6(p+2)] × [18p/(p - 6)(p - 3)]
Multiply the denominator with denominator and numerator with numerator:
= 18p (p - 6)(p + 2)/ 6(p+2)(p - 6)(p - 3)
Now cancel out (p+2)(p - 6) from denominator and numerator:
= 18p/ 6(p - 3)
Divide denominator and numerator by 6:
= 3p/ (p - 3)
To learn more about factorization, click on below link:
https://brainly.com/question/15156431
#SPJ1
PLEASE HELP ASAP GIVING BRAINLIEST W/ POINTS PLSS
9514 1404 393
Answer:
108 ft²
Step-by-step explanation:
When x=6, the length is 6+6 = 12 ft, and the width is 6+3 = 9 ft. The area is given by ...
A = LW
A = (12 ft)(9 ft) = 108 ft²
The area of Cameron's garden is 108 ft².
Express as a trinomial.
(3x+1)(2x-1)
Answer:
6x^2-x-1
Step-by-step explanation:
Use the FOIL method.
Write a system of linear equations.Write two-variable equations in slope-intercept form.
Answer:
A linear relation can be written in the slope-intercept form as:
y = a*x + b
Where a is the slope, and b is the y-intercept.
And if a line passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
Now let's look at our lines.
The left one passes through the points (0, -3) and (-2, 0)
Then the slope of this line is:
a = (0 - (-3))/(-2 - 0) = 3/-2 = -(3/2)
Then the line will be something like:
y = -(3/2)*x + b
Knowing that this line passes through the point (0, -3), we know that when x = 0, we must have y = -3
Then:
-3 = (-3/2)*0 + b
-3 = b
So the first linear equation is:
y = -(3/2)*x - 3
Now let's look at the second line, this one passes through the points (0, 2) and (1, 0)
Then the slope of this line is:
a = (0 - 2)/(1 - 0) = -2
And we can write the line as:
y = -2*x + b
Knowing that this line passes through the point (0, 2), we know that when x = 0 we must have y = 0, replacing that we get:
2 = -2*0 + b
2 = b
Then the equation of this line is:
y = -2*x + 2
Now that we know both equations we can write our system as:
y = (-3/2)*x - 3
y = -2*x + 2
To solve it, we need to remember that y = y
then:
(-3/2)*x - 3 = y = -2*x + 2
(-3/2)*x - 3 = -2*x + 2
We can solve this for x.
2*x - (3/2)*x = 2 + 3
(1/2)*x = 5
x = 5((1/2) = 5*2 = 10
And to find the y-value, we need to input this x-value in one of the equations:
y = -2*10 + 2 = -20 + 2 = -18
Then the solution of the system is the point (10, -18)
What is the word form of the number 43.06? A forty-three and six B forty-three and six tenths c forty-three and six hundredths D forty-three and six thousandths
it is C forty-three and six hundredths.
Help! Quick! Find the area of the composite figure
Answer:
60m
Step-by-step explanation:
To find the area of the triangle you multiply the base by height and divide by two, but we don’t know the base of the triangle!
Luckily, the bottom of the triangle is a rectangle. Rectangles are symmetrical, and the other side of the rectangle is 8.
So, the base of the triangle is 8.
Now let’s find the area of the triangle:
8 x 5 = 40
40/2 = 20
20 is the area of the triangle
Now, we must find the area of the rectangle!
The formula for rectangle area is just width x length:
8 x 5 = 40
Add them together:
40 + 20 = 60
Therefore, the area is 60m.
Stacy opens an account with a deposit of $100. She deposits an additional $25 every week after opening the account. Determine how much money will be in her account after 15 weeks.
Answer:
$450
Explanation:
after 15 weeks, stacy would have deposited a total of $25 × (15 - 1) = $350. (remember to subtract 1 from the 15 weeks since she did not deposit $25 during the week she opened the account, but only after that.)
now, we need to add this to the original deposit: $100 + $350 = $450.
therefore, after 15 weeks, there would be $450 in her account.
i hope this helps! :D
pls answer quick Doug makes a parallelogram-shape sign for his shop.
What is the area of this parallelogram?
Round to the nearest hundredth.
5.32 ft²
8.96 ft²
14.28 ft²
17.02 ft²
Answer: 1.9x2.8 + 3.2+2.8 = 14.28
HOPE THIS HELPS
I need help with this lol
Answer:
1350
Step-by-step explanation:
multiply
A sample of a radioactive isotope had an initial mass of 450 mg in the year 2005 and decays exponentially over time. A measurement in the year 2012 found that the sample's mass had decayed to 310 mg. What would be the expected mass of the sample in the year 2017, to the nearest whole number?
Answer: 238
Step-by-step explanation:
blank minus 1/2 equals to 1/6
Answer:
Blank = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
blank = x
[tex]x-\frac{1}{2} =\frac{1}{6} \\\\x=\frac{1}{6} +\frac{1}{2} \\\\x=\frac{1}{6} +\frac{3}{6} \\\\x=\frac{4}{6} \\\\x=\frac{2}{3}[/tex]
Using the graph, determine the equation of the axis of symmetry.
Answer:
One Point I believe
Step-by-step explanation:
I need help this is due today
Answer: the amount of money after the purchase depends on the amount of money before the purchase
Step-by-step explanation:
Tú tienes la mitad de lo que tenías y tendrás el triple de lo que tienes. Si tuvieras lo que tienes, tenías y tendrás, tendrías lo que yo tengo que es 180 dólares más de lo que tú tendrás ¿Cuánto tenías?
Answer:
Step-by-step explanation:
HELP ME PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS URGENTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
9514 1404 393
Answer:
90 m²
Step-by-step explanation:
The given linear dimensions have the ratio ...
red/blue = (6 m)/(4 m) = 3/2
The ratio of areas is the square of the ratio of the linear dimensions:
(red area)/(blue area) = (3/2)²
S = (blue area)(9/4) = (40 m²)(9/4)
S = 90 m²
∠3 and ∠6 are alternate interior angles. If m∠3 = 75, what is the measure of ∠6
a. 15°
b. 75°
c. 105°
d. 180°
Answer:
B. m<3 = m<6 = 75degreesStep-by-step explanation:
First you must understand that in geometry, the alternate interior angles are equal
Hence if ∠3 and ∠6 are alternate interior angles, then <3 = <6
Given that m<3 = 75 degrees
m<6 will also be 75 degrees since both angles are equal
Uncle Howard left his only niece 56% of his assets according to his will. If his totaled assets
totaled
$564,000, when he died, how much will his niece inherit?
Answer:
$315,840.00
Step-by-step explanation:
$564,000 x 0.56 = $315,840.00
Answer:
$315,840
Step-by-step explanation:
56% of 564,000 is this
Pls Help!
Aimee wants to order some DVDs from Amazon. Each DVD costs $8.49 and shipping for the entire order is $5. She has only $70 to spend. How many DVDs can she order?
Answer:
she can buy 13
please brainliest or hear
Answer:
She can order 7 DVDS
Step-by-step explanation:
8.49 x 7 = 59.43
59.43 + 5 = 64.43.
evaluate the expression x-9=3 (solve)
Answer:
x = 12
Step-by-step explanation:
[tex]x - 9 = 3 \\ x = 3 + 9 \\ [/tex]
[tex]\boxed{Answer:{\boxed{\green{x = 12}}}}[/tex]
Vx
Which two figures have the same number of lateral faces?
O sphere and cylinder
O triangular prism and rectangular prism
O rectangular prism and cube
O triangular prism and cylinder
Two hockey teams, the Winnipeg Jets (yay!) and the Toronto Maple Leafs (boo!), miraculously make it to
the Stanley Cup finals. As soon as a team wins 3 games, the championship is over.
The schedule for the playoffs (for home games) is: Jets - Leafs - Jets - Leafs - Jets
If the Jets are playing at home, there is a 60% chance they'll win. If they are playing on the road, there is
a 45% chance they'll win.
Find the probability that the Jets win the Stanley Cup. Round answers to at least 4 decimal places.
Can anyone help me. answer with full explanation. No links please
Answer:
There is a 54% chance that the Jets will win the Stanley Cup.
Step-by-step explanation:
Since two hockey teams, the Winnipeg Jets and the Toronto Maple Leafs, miraculously make it to the Stanley Cup finals, where as soon as a team wins 3 games, the championship is over, and the schedule for the playoffs for home games is: Jets - Leafs - Jets - Leafs - Jets; since if the Jets are playing at home, there is a 60% chance they'll win, while if they are playing on the road, there is a 45% chance they'll win, to find the probability that the Jets win the Stanley Cup the following calculation must be performed:
(0.60 + 0.45 + 0.60 + 0.45 + 0.60) / 5 = X
2.70 / 5 = X
0.54 = X
Thus, there is a 54% chance that the Jets will win the Stanley Cup.
HELPP IM FAILING MATH RN!!
LC is 40°. What is the measure of arc CB?
I hope this helps you
Hi there!
[tex]\large\boxed{100^{o}}[/tex]
∠C = 40° and triangle ABC is isosceles, therefore:
∠C = ∠A = 40°
Angles in a triangle sum up to 180°, so:
180 = 40 + 40 + ∠A
180 = 80 + ∠A
100 = ∠A
Thus, arc CB has a measure of 100°.
∫(cos3x+3sinx)dx integration
Answer:
[tex] I = \dfrac{1}{3}sin(3x) - 3cos(x) + C[/tex]
Step-by-step explanation:
We need to integrate the given expression. Let I be the answer .
[tex]\implies\displaystyle I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]
Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx .Rewrite using du and u .[tex]\implies\displaystyle I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \boxed{\boxed{\displaystyle I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}[/tex]
5= 1 over 3(x+7)
What is your answer
Answer:dddddd
Step-by-step explanation:
Last month we had only five sunny days. There were 30 days in all last month.
What was the ratio of sunny days to the total number of days? What was the ratio
of sunny days to days that were not sunny?
Answer:
6
Step-by-step explanation:
30 ÷ 5 = 6
Answer:
6
Step-by-step explanation:
it is 6
(-55) +____ = -89
Find the missing
The yield of a certain chemical reaction is believed to be related to temperature. A study collected the yield from 15 such reactions selected at random to test the belief and producedthe following results.
Variable Estimate
Intercept 1 15.5 2.96
Temp 1 0.05 0.017
R-sq = 0.73
Which of the following is the appropriate test statistic for the test?
a. t=0.05/0.73
b. t=15.5/0.73
c. t=0.05/15.5
d. t=15.5/0.05
Answer:
t = 0.05 / 0.017
Step-by-step explanation:
Given the table :
Variable ____ Estimate
Intercept 1 ____ 15.5 ____2.96
Temp 1 _______0.05 ___ 0.017
R-sq = 0.73
The test statistic for a regression test :
t = b1 / E
Where ;
b1 = slope ; E = Standard error of the slope
From the result table ;
b1 = 0.05 ;
E = 0.017
The test statistic, t = 0.05 / 0.017
The appropriate test statistic for the test is t = 0.05 / 0.017.
Calculation of the test statistic for the test:Since
Variable ____ Estimate
Intercept 1 ____ 15.5 ____2.96
Temp 1 _______0.05 ___ 0.017
R-sq = 0.73
So here the test statistic should be
t = b1 / E
here,
b1 = slope ;
E = Standard error of the slope
So,
The test statistic, t = 0.05 / 0.017
learn more about random here: https://brainly.com/question/24172316
which two quadrilaterals have 4 congruent sides
Answer:
rhombus and parallelogram .
Step-by-step explanation:
In the figure, Line a is parallel to line b. Name the angles congruent to angle 3.
helppp it’s due today
The graph of a linear function is shown on the coordinate grid.
What is they y-intercept of the graph of the linear function?
Answer:
y=-6
Step-by-step explanation:
just look at the bottom and yahhhh
Kimi buys a box of blueberry, poppy seed, and chocolate-chip muffins. There are 17 blueberry
muffins and 17 chocolate-chip muffins in the box. How many muffins are in the box?
42
50
61
There is not enough information to solve this
problem.
Answer:
we need more info
Step-by-step explanation: