Hello, please consider the following.
[tex](\forall x \in \mathbb{R}) \\ \\ x=(f^{-1}of)(x)\\\\=(fof^{-1})(x)\\\\=f(f^{-1}(x))\\\\=6\left( f^{-1}(x) \right) ^3-8 = x\\\\\text{We need to express }f^{-1}(x) \text{ in function of x.}\\\\\text{Let's do it!}[/tex]
[tex]6\left( f^{-1}(x) \right) ^3-8 = x\\\\\left( f^{-1}(x) \right) ^3 =\dfrac{x+8}{6}\\\\\Large \boxed{\sf \bf \ \ f^{-1}(x)=\sqrt[3]{\dfrac{x+8}{6}}\ \ }[/tex]
Thank you
Find the value of “a”
Answer:
The correct answer is a = 8.
Step-by-step explanation:
To solve this problem, we must remember the formula for slope, which is:
slope = m = (y2 - y1)/(x2 - x1)
Now, we can plug in the values that we are given into the slope formula:
-3/2 = (-3-6)/(a-2)
Now, we should begin to simplify the equation.
-3(a-2) = 2(-9)
We can use the distributive property to eliminate the parentheses on each side of the equation:
-3a + 6 = -18
Then, we can subtract 6 from both sides of the equation to get the variable term alone on the left side of the equation:
-3a = -24
Finally, we should divide both sides by -3 to completely isolate the variable on the left side of the equation:
a = 8
Therefore, the correct answer is a= 8.
Hope this helps!
Round 467 to the nearest 10
Answer:
470.
Step-by-step explanation:
The units digit 7.
As this is greater than 4 we add 1 to the tens digit. ( 6 + 1 = 7), and the units digit becomes 0.
PLEASE HELP ASAP WILL MARK BRAINLIEST
Answer:
A (the marked answer is correct)
Step-by-step explanation:
The result of a single refection will look like the reverse of the letter Z, so the only possibilities are choices A and C.
Since the horizontal lines are still horizontal, the reflection must be across a horizontal or vertical line. If the reflection is across a horizontal line, the image will be vertically aligned with the preimage. If the reflection is across a vertical line, the image will be horizontally aligned with the preimage.
Choice A is horizontally aligned with the preimage. Choice C is not aligned either way. (It is a "glide reflection.")
Image A is the result of reflection across the y-axis.
The data below represent the weight losses for people on three different exercise programs.
Exercise A Exercise B Exercise C
2.5 5.8 4.3
8.8 4.9 6.2
7.3 1.1 5.8
9.8 7.8 8.1
5.1 1.2 7.9
If we want to test the claim that the three size categories have the same means, why don't we use three separate hypothesis tests for μ1 = μ2, μ2 = μ3, and μ1 = μ3?
A. The risk of type l error increases and becomes too high.
B. Actually, we do want to use three separate hypothesis tests.
C. The risk of type ll error increases and becomes too high.
D. A hypothesis test for comparing two means does not exist.
Answer:
A. The risk of type l error increases and becomes too high.
Step-by-step explanation:
The overall level of significance increases as the number of t- tests ( used for comparing two, three or four means separately ) increases. This in turn increases the risk of type I error.
We might be tempted to apply the two sample t- test to all possible pairwise comparisons of means. This type of running t- test to several means comparison has the risk of increasing overall level of significance
Alastair drives 18.2 miles in 14 minutes.
He passes a sign which gives the speed limit as 50 mph.
By how much, in mph, did Alastair's average speed exceed the speed limit?
Answer:
28 mph
Step-by-step explanation:
Distance
18.2 milesTime
14 min = 14/60 hrAverage speed
d/t = 18.2 ÷ 14/60 = 182/10 × 60/14 = 78 mphThe difference with allowed speed
78 - 50 = 28 mphAnswer:
28mph
Step-by-step explanation:
What is the value of t?
Answer:
[tex]t=22[/tex]
Step-by-step explanation:
First, note that the entire thing is a square. This is because since two of the opposite angles are right angles, the remaining two must also be right angles.
In a square, all four sides are equivalent.
Therefore, the sides PS an RS are equal to each other. Thus:
[tex]PS=RS\\t+22=2t\\22=t\\t=22[/tex]
If you get this, you are a critical thinker.
I enter the bedroom.
There are 34 people. You kill 30. How many people are in the bedroom?
Good Luck!
If you get it correct your answer will be deleted and I’ll message you to continue the game. Don’t bother playing if you’re not going to continue, party poopers!
Answer:
The correct answer is 34 people
Step-by-step explanation:
Killing 3 people does not change the number of people in the bedroom, it only means that there are 30 dead people and 4 living people, but overall, here are 34 people in the room.
There are 35 people in the room.
Killing 30 people does not exclude them from the room.
Similarly I entered the room when there were 34 people adding 1 more to 34 gives 35 people.
35= 34+1
There are 35 people in the room.
https://brainly.com/question/20700704
Assume that you have paired values consisting of heights (in inches) and weights (in lb) from 40 randomly selected men. The linear correlation coefficient r is 0.464. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide?
A.) The coefficient of determination is 0.215. 78.5% of the variation is explained by the linear correlation, and 21.5% is explained by other factors.
B.) The coefficient of determination is 0.785. 21.5% of the variation is explained by the linear correlation, and 78.5% is explained by other factors.
C.) The coefficient of determination is 0.215. 21.5% of the variation is explained by the linear correlation, and 78.5% is explained by other factors.
D.) The coefficient of determination is 0.785. 78.5% of the variation is explained by the linear correlation, and 21.5% is explained by other factors.
Answer: C.) The coefficient of determination is 0.215. 21.5% of the variation is explained by the linear correlation, and 78.5% is explained by other factors.
Step-by-step explanation:
Given that :
Number of observations = 40
Linear Correlation Coefficient (R) = 0.464
The Coefficient of determination ( R^2) =?
The Coefficient of determination (R^2) is the squared value of the linear correlation Coefficient value (R) . The value value ranges from 0 to 1 and depicts the proportion of the variation in the dependent variable that can be accounted for by the independent variable.
For the scenario given above,
The Coefficient of determination (R^2) = 0.464^2 = 0.215296 = (0.215296 * 100%) = 21.5%
This means that 21.5% of the variation can be explained by the relationship between both variables while (100% - 21.5% = 78.5%) can be explained by other factors.
Evaluate the expression if x=12, y=8, and z=3 4x-yz
Answer:
[tex]\huge \boxed{24}[/tex]
Step-by-step explanation:
Let if x=12, y=8, and z=3.
[tex]4(12)-(8)(3)[/tex]
Evaluate.
[tex]48-24[/tex]
[tex]=24[/tex]
Start by substituting the appropriate numbers in for
your variables, using parenthses as you go.
You'll get 4(12) - (8)(3).
Now think about your order of operations.
Multiplication comes before subtraction.
So first multiply 4(12) to get 48.
So we have 48 - (8)(3).
Now multiply (8)(3) to get 24.
So we have 48 - 24 which is 24.
Sandra calculated the height of a cylinder that has a volume of 576 pi cubic centimeters and a radius of 8 centimeters. Her work is shown below. V = B h Step 1: 576 pi = pi 8 squared h Step 2: 576 pi = 64 pi h Step 3: StartFraction 576 pi Over 64 pi EndFraction = StartFraction 64 pi Over 64 pi EndFraction h Step 4: h = 9 pi cm What error did Sandra make when calculating the height of the cylinder? In step 1, she substituted into the volume formula incorrectly. In step 2, she calculated 8 squared incorrectly. It should be 16 rather than 64. In step 4, the pi should have canceled, making the correct answer 9 cm. Sandra calculated the height of the cylinder correctly.
Answer:
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
Step-by-step explanation:
Volume=576π cubic centimeters
Radius=8 cm
h=?
Her work:
Volume of a cyclinder=πr^2h
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h=9π cm
Correct workings:
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h= 9 centimeters
Her error is in step 4
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
Answer:
the error was made in step 4, should have also been cancelled making the correct answer as 9 cm.
Step-by-step explanation:
Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function. 5e^(-x)^2 cos(4x)
Answer:
The first three nonzero terms in the Maclaurin series is
[tex]\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }[/tex]
Step-by-step explanation:
GIven that:
[tex]f(x) = 5e^{-x^2} cos (4x)[/tex]
The Maclaurin series of cos x can be expressed as :
[tex]\mathtt{cos \ x = \sum \limits ^{\infty}_{n =0} (-1)^n \dfrac{x^{2n}}{2!} = 1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}+... \ \ \ (1)}[/tex]
[tex]\mathtt{e^{-2^x} = \sum \limits^{\infty}_{n=0} \ \dfrac{(-x^2)^n}{n!} = \sum \limits ^{\infty}_{n=0} (-1)^n \ \dfrac{x^{2n} }{x!} = 1 -x^2+ \dfrac{x^4}{2!} -\dfrac{x^6}{3!}+... \ \ \ (2)}[/tex]
From equation(1), substituting x with (4x), Then:
[tex]\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}- \dfrac{(4x)^6}{6!}+...}[/tex]
The first three terms of cos (4x) is:
[tex]\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}-...}[/tex]
[tex]\mathtt{cos (4x) = 1 - \dfrac{16x^2}{2}+ \dfrac{256x^4}{24}-...}[/tex]
[tex]\mathtt{cos (4x) = 1 - 8x^2+ \dfrac{32x^4}{3}-... \ \ \ (3)}[/tex]
Multiplying equation (2) with (3); we have :
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1- x^2 + \dfrac{x^4}{2!} ) \times ( 1 - 8x^2 + \dfrac{32 \ x^4}{3} ) }[/tex]
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1+ (-8-1)x^2 + (\dfrac{32}{3} + \dfrac{1}{2}+8)x^4 + ...) }[/tex]
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + (\dfrac{64+3+48}{6})x^4+ ...) }[/tex]
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }[/tex]
Finally , multiplying 5 with [tex]\mathtt{ e^{-x^2} cos (4x) }[/tex] ; we have:
The first three nonzero terms in the Maclaurin series is
[tex]\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }[/tex]
Evaluate r(x)=2x −1 over the domain {0,1,2,3}. What is the range of r(x)? Separate values with a comma.
Answer:
The range of r(x) is [tex]\{-1,1,3,5\}[/tex].
Step-by-step explanation:
The range of a function is the set of images associated with a given domains. As domain is a discrete set, the range can be determined by evaluating the function at each element in domain:
x = 0
[tex]r(0) = 2\cdot (0)-1[/tex]
[tex]r(0) = -1[/tex]
x = 1
[tex]r(1) = 2\cdot (1) - 1[/tex]
[tex]r(1) = 1[/tex]
x = 2
[tex]r(2) = 2\cdot (2) -1[/tex]
[tex]r(2) = 3[/tex]
x = 3
[tex]r(3) = 2\cdot (3) -1[/tex]
[tex]r(3) = 5[/tex]
The range of r(x) is [tex]\{-1,1,3,5\}[/tex].
Sarah orders 34 shirts that cost $7 each. She can sell each shirt for $15. She stole 27 shirt to customers she had to return 7 shirts and pay a $2 charge for each returned shirt. FIND SARAH’S PROFIT.
Answer:
$153
Step-by-step explanation:
She orders 34 shirts for $7 each.
34 × 7 = $238 - total cost for the shirts
She sells 27 shirts for $15 each.
27 × 15 = $405 - profit from selling shirts
Subtract the profit from the amount paid.
$405 - $238 = $167
Sarah has a profit of $167. But, she had to return 7 shirts and pay $2 each.
$7 × 2 = $14 - charge for returning shirts
Subtract this from the profit made to get the final profit.
$167 - $14 = $153
Sarah's profit is $153 from buying and selling the shirts.
Hope that helps.
The value 346.7812 rounded to the nearest hundredth is
346.7800
QQI 300
346.781
346.78
Answer:
346.78
Step-by-step explanation:
Rounding a number to hundredth means approximating or making the number after the second position of the decimal to either a 10 or zero.
Thanks for the number after the second is greater or equal to 5, it is rounded up to ten where the 1 is added to the second position if not it turns 0.
So 346.7812 to hundredth
= 346.78
i need help with this
Answer:
1a. either AC ≅ DF or AB ≅ DE
1b. <A ≅ <D
2a. B
2b. D
Step-by-step explanation:
Find the standard equation of the parabola that satisfies the given conditions. Also, find the length of the latus rectum of each parabola.
focus: (-3,0), directrix: x = 6
Choose the correct standard equation below.
OA.
y2 = - 18(x-3)
OB. x2 = 12(y + 3)
Ос.
x2 =
= -18
OD. y2 = 12(x+3)
Find the length of the latus rectum.
(Simplify your answer.)
Answer:
The standard parabola
y² = -18 x +27
Length of Latus rectum = 4 a = 18
Step-by-step explanation:
Explanation:-
Given focus : (-3 ,0) ,directrix : x=6
Let P(x₁ , y₁) be the point on parabola
PM perpendicular to the the directrix L
SP² = PM²
(x₁ +3)²+(y₁-0)² = [tex](\frac{x_{1}-6 }{\sqrt{1} } )^{2}[/tex]
x₁²+6 x₁ +9 + y₁² = x₁²-12 x₁ +36
y₁² = -18 x₁ +36 -9
y₁² = -18 x₁ +27
The standard parabola
y² = -18 x +27
Length of Latus rectum = 4 a = 4 (18/4) = 18
Evacuation and emergency procedures should be displayed in the classroom lab/office. * 4 points True False
Answer:
The answer is true. I hope this helps
Answer:
yes. If there will be Evacuation and emergency procedures then the students can learn about that and can use that when there is an emergency case.
Solve: X/4=6 Can you please assist?
Answer:
x = 24
Step-by-step explanation:
In order to solve for x, you need to isolate it on one side of the equal sign. So in this case you need to multiply both sides by 4, in order to cancel the dividing factor 4 that appears in the denominator :
[tex]\frac{x}{4} =6\\4\,*\,\frac{x}{4} =6\,*\,4\\x = 24[/tex]
Answer:
X = 24
Step-by-step explanation:
[tex]\frac{X}{4}=6\\\\\mathrm{Multiply\:both\:sides\:by\:}4\\\frac{4X}{4}=6\times\:4\\\\\mathrm{Simplify}\\X=24[/tex]
A car travels 50 mph for 10 minutes. How many miles per minute is the car travoling? Round to the
nearest tenth
To the nearest tenth of a mile, how far doos the car travel in 1 minuto?
0 0.12 miles per minute
o 0.83 miles per minute
1.2 miles per minute
8.3 miles per minute
Answer:
8.3
Step-by-step explanation:
10 minutes is 1/6th of an hour so divide 50 by 6 to find the answer.
50/6= 8.3333333 so rounded to the nearest tenth is 8.3
Where do the lines y=2x+1 and y=-5x-6 intersect?
Answer:
(-1, -1)
Step-by-step explanation:
To find where two lines in slope-intercept form intersect, set them equal to each other.
2x + 1 = -5x - 6
7x = -7
x = -1
Knowing they intersect at x = -1, substitute -1 into either of the two equations to find the y-value of their intersection.
y = 2(-1) + 1
y = -2 + 1
y = -1
So the intersection point of the two lines is (-1, -1).
what is LCM of 2 4 8
Answer:
the LCM would be 8 based on the following set of multiples: Multiples of 2: 2, 4, 6, 8, 10, 12, 14, ... Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
Step-by-step explanation:
A tire manufacturing company has fixed cost of $20,000 and production cost of $60 per tire. If the tires are sold at $100 each, find the following: Profit Loss or Gain if 300 tires are produced
Answer:
A loss of 8,000
Step-by-step explanation:
If each tire is sold at $100 and 300 tires are sold then the amount gained is 30,000.
Cost of production for the tires is 18,000, so now we must subtract 18,000 from 30,000 to get 12,000.
Finally, we take away the fixed cost (20,000) from 12,000 to get -8,000.
The manufacturing company will be in a loss of $8000 after selling 300 tires produced.
What is production cost?Production costs are the expenses incurred by a firm when it manufactures a product or provides a service that generates income.
What is selling cost?The selling cost is defined as the cost at which a particular item is sold.
No. of Tires produced = 300
Production cost of each tire = $60
Total Production cost = 60 * 300 = $18000
No. of Tires sold = 300
Selling cost of each tire = $100
Total selling cost = 300 * 100 = $30000
Total profit in selling 300 tires = $12000.
Fixed cost of the company = $20000
Loss = $20000 - $12000 = $8000
Hence Loss suffered by the company is $8000.
Learn more about profit and loss:
https://brainly.com/question/1112605
#SPJ2
Linda Roy received a $200,000 inheritance after taxes from her parents. She invested it at 4% interest compounded quarterly for 3 years. A year later, she sold one of her rental properties for $210,000 and invested that money at 3% compounded semiannually for 2 years. Both of the investments have matured. She is hoping to have at least $500,000 in 7 years compounded annually at 2% interest so she can move to Hawaii. Will she meet her goal?
Answer:
Step-by-step explanation:
Matured amount of $200000 at 4% compounded quarterly after 3 years
= $200000 x ( FVIF , 1 , 12 )
= $200000 X 1. 1268
= $225360 .
Matured amount of $210000 at 3% compounded semiannually after 2 years
= $210000 x ( FVIF , 1.5 , 4 )
= $210000 X 1. 1268
= $225360 x 1.0614
= $239197
Total amount after maturity
= $225360 + $239197
= $464557
Matured amount of $464557 at 2% compounded annually after 7 years
= $464557 x ( FVIF , 2 , 7 )
= $464557 x 1.1487
= $533636.6
This amount is more than his target amount of 500000.00 So she meets the goal .
Help!!!!!! What is the absolute value of Point A labelled on the number line? Drag and drop the answer into the box to match the correct statement.
Answer:
see below (I hope this helps!)
Step-by-step explanation:
We can see that every 3 tick marks on the line is 1, therefore, the space between 2 tick marks is 1/3. Using this information, we can see that A = [tex]-3\frac{1}{3}[/tex]. The absolute value of a negative number is simply the additive inverse of the number, therefore, our answer is [tex]-(-3\frac{1}{3}) = 3\frac{1}{3}[/tex].
The director of student health decides to test every student on campus for tuberculosis. If there are 3000 students out of which only 50 have tuberculosis and the probability of a false positive on the test is 0.008 and a false negative is 0.15, what is the probability that a person who tested positive actually has TB?
Answer: the probability that a person who tested positive actually has TB is 0.64
Step-by-step explanation:
lets say
T : has tuberculosis
+ : test results +ve
- : test result is -ve
so given that
P(+ITc) = 0.008
P(-ITc) = 0.15
P(T) = 50/3000 = 1/60
P(Tc) = 1 - P(T) = 1 - 1/60 = 59/60
Now required probability
= P(TI+)
P(T∩+) / P(+)
= P(T) × P(+IT) / [[P(T) × P(+IT)] + [(P(Tc) × P(+ITc)]
= P(T) × {1-P(-IT)] / [[P(T) × [1-P(-IT)] + [(P(Tc) × P(+ITc)]
WE SUBSTITUTE
= { 1/60 × (1-0.15) } / [1/60 × (1 - 0.15)] + [(59/60) × 0.008]
= (0.0167 × 0.85) / [(0.0167 × 0.85) + (0.9833 × 0.008)]
= 0.01417 / 0.02206
= 0.6423 ≈ 0.64
∴ the probability that a person who tested positive actually has TB is 0.64
The first term in the sequence is 1, and each other term is 5 more than three times the previous term.
[tex]a_1=1, a_n=a_{n-1}+5[/tex] ([tex]n>1[/tex]).
Hope this helps.
A group of students conducted several trials of an experiment to study Newton’s second law of motion. They concluded that tripling the mass required tripling the net force applied. What quantity were the students holding constant?
net force
acceleration <-- MY ANSWER
number of trials
mass
Answer:
Acceleration
Step-by-step explanation:
The Newton's second law of motion can be expressed as;
F = ma
Where F is the force acting on an object, m is the mass of the object and a is the acceleration of the object.
For an object of mass 2kg and acceleration of 5 m/[tex]s^{2}[/tex], we have;
[tex]F_{1}[/tex] = 2 × 5 = 10 N
If we triple the mass,
m = 2 × 3 = 6 kg
Therefore,
[tex]F_{2}[/tex] = 6 × 5 = 30 N
Thus, at constant acceleration, [tex]F_{2}[/tex] = 3 × [tex]F_{1}[/tex]
someone please help me with this question
Answer:
3rd and 4th option
Answer: Option 3. [tex]\sqrt[c]{a^b}[/tex] Option 4. [tex](\sqrt[c]{a} )^b[/tex]
Step-by-step explanation:
concept to know: when the exponent is a fraction, the numerator will be the real exponent with the base (i.e 7^5), while the denominator will be the root
----------------------------------
[tex]a^{\frac{b}{c}[/tex]
b is the numerator which means it will result in [tex]a^b[/tex]
c is the denominator which means it will result in [tex]\sqrt[c]{a}[/tex]
The combination of this two will be [tex]\sqrt[c]{a^b}[/tex]
This will also be presented as [tex](\sqrt[c]{a} )^b[/tex]
Hope this helps!! :)
Please let me know if you have any question
Was it evaluated correctly?
explain your reasoning.
Answer:
It's not evaluated correctly
Step-by-step explanation:
in the problem 6 × 5 + 30 ÷ 30 we first need to multiply 6 and 5 then divide the 30 by 10 and finally add them up
6×5 = 30
30 ÷ 10 = 3
30 + 3 = 33
(-w^3+8w^2-3w)-(4w^2+5w-7)
Answer:
[tex] \boxed{ \bold{ { \boxed{ \sf{ - {w}^{3} + 4 {w}^{2} - 8w + 7}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{( - {w}^{3} + 8 {w}^{2} - 3w) - (4 {w}^{2} + 5w - 7)}[/tex]
Remove the unnecessary Parentheses
⇒[tex] \sf{ - {w}^{3} + 8 {w}^{2} - 3w - (4 {w}^{2} + 5w - 7)}[/tex]
When there is a ( - ) in front of a parentheses, change the signs of each term in the expression
⇒[tex] \sf{ - {w}^{3} + 8 {w}^{2} - 3w - 4 {w}^{2} - 5w + 7}[/tex]
Collect like terms
⇒[tex] \sf{ - {w}^{3} + 8 {w}^{2} - 4 {w}^{2} - 3w - 5w + 7}[/tex]
⇒[tex] \sf{ - {w}^{3 } + 4 {w}^{2} - 8w + 7 }[/tex]
Hope I helped!
Best regards!!
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\boxed{-w^3 + 4w^2 + -8w + 7}[/tex]
Let's simplify step-by-step.
[tex](-w^3+8w^2-3w)-(4w^2+5w-7)[/tex]
Distribute the Negative Sign:
[tex]= -w^3 + 8w^2 - 3w + -1( 4w^2 + 5w - 7 ) \\= - w^3 + 8w^2 + 3w + -1(4w^2) + -1 (5w)+(-1 )(-7)\\= -w^3 + 8w^2 + -3w + -4w^2 + 5w + 7[/tex]
Combine Like Terms:
[tex]= -w^3 + 8w^2 + -3w + -4w^2 + -5w + 7 \\= (-w^3) + ( 8w^3 + -3w + -4w^2) + ( -3w + -5w) + 7 \\= -w^3 + 4w^2 + -8w + 7[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀