Answer:
[tex](2\, x^{3} - 3\, x^{2} - 18\, x - 8) / (x - 4) = (2\, x^{2} + 5\, x + 2)[/tex].
Step-by-step explanation:
The leading term of a one-variable polynomial refers to the term with the highest power of the variable. For example, in the polynomial [tex](2\, x^{3} - 3\, x^{2} - 18\, x - 8)[/tex], [tex]x[/tex] is the variable, and [tex]2\, x^{3}[/tex] is the leading term. The power of the leading term [tex]2\, x^{3}\![/tex] is [tex]3[/tex].
The numerator is [tex](2\, x^{3} - 3\, x^{2} - 18\, x - 8)[/tex] while the denominator is [tex](x - 4)[/tex].
Leading term of the numerator: [tex]2\, x^{3}[/tex].Leading term of the denominator: [tex]x[/tex].Divide the leading term of the numerator by the leading term of the denominator to find the next term of the quotient. In this case, [tex](2\, x^{3}) / (x) = 2\, x^{2}[/tex].
Multiply the denominator by the quotient that was just found. In this case, [tex]2\, x^{2}\, (x - 4) = 2\, x^{3} - 8\, x^{2}[/tex]. Subtract this product from the current numerator to find the next numerator:
[tex]\begin{aligned} & (2\, x^{3} - 3\, x^{2} - 18\, x - 8) - (2\, x^{3} - 8\, x^{2}) \\ =\; & 2\, x^{3} - 3\, x^{2} - 18\, x - 8 - 2\, x^{3} + 8\, x^{2}\\=\; & 5\, x^{2} - 18\, x - 8\end{aligned}[/tex].
Thus, the next numerator would be [tex](5\, x^{2} - 18\, x - 8)[/tex]. The denominator stays
the same.
Repeat the steps above until the power of the numerator is less than that of the denominator.
The numerator is [tex](5\, x^{2} - 18\, x - 8)[/tex] while the denominator is still [tex](x - 4)[/tex].
Leading term of the numerator: [tex]5\, x^{2}[/tex].Leading term of the denominator: [tex]x[/tex].Next term of the quotient: [tex](5\, x^{2}) / (x) = 5\, x[/tex]. Add that term to the quotient. The quotient is now [tex](2\, x^{2} + 5\, x)[/tex].
The next numerator should be:
[tex]\begin{aligned} & (5\, x^{2} - 18\, x - 8) - 5\, x \, (x - 4) \\ =\; & (5\, x^{2} - 18\, x - 8) - (5\, x^{2} - 20) \\ =\; & 2\, x - 8\end{aligned}[/tex].
The numerator is now [tex](2\, x - 8)[/tex] while the denominator continues to be the same.
Leading term of the numerator: [tex]2\, x[/tex].Leading term of the denominator: [tex]x[/tex].Next term of the quotient: [tex](2\, x) / (x) = 2[/tex]. Add that term to the quotient to get [tex](2\, x^{2} + 5\, x + 2)[/tex].
The next numerator should be:
[tex]\begin{aligned} & (2\, x - 8) - 2\, (x - 4) \\ =\; & (2\, x - 8) - (2\, x - 8) \\ =\; & 0 \end{aligned}[/tex].
The numerator is now a constant. The power of [tex]x[/tex] is the current numerator would be [tex]0[/tex]. The power of [tex]x\![/tex] in the denominator continues to be [tex]1[/tex]. Thus, the power of the numerator is now less than that of the denominator.
The quotient is now the required quotient, with the "numerator" being the remainder of the division. That is:
[tex](2\, x^{3} - 3\, x^{2} - 18\, x - 8) = (2\, x^{2} + 5\, x + 2)\, (x - 4) + 0[/tex].
[tex](2\, x^{3} - 3\, x^{2} - 18\, x - 8) = (2\, x^{2} + 5\, x + 2)\, (x - 4)[/tex].
Equivalently:
[tex](2\, x^{3} - 3\, x^{2} - 18\, x - 8) / (x - 4) = (2\, x^{2} + 5\, x + 2)[/tex].
Write 15 as a product of primes.
Answer:
15 is a composite number. 15 = 1 x 15 or 3 x 5. Factors of 15: 1, 3, 5, 15. Prime factorization: 15 = 3 x 5
Step-by-step explanation:
Answer:
15= 3 x 5
Step-by-step explanation:
15
/ /
5 x 3
3 and 5 both multiply together to make 15
how do you do this??????????
Step-by-step explanation:
these are all isoceles triangles (2 sides are equal). that also means that the 2 angles at the end of the equal sides are equal.
so, the angle at F and H are both 65°.
the angle at J = 2×65 = 130°.
the angle at G = 2×(180 - 65 - 65) = 2×50 = 100°.
remember, the sum of all angles in a triangle is always 180°.
so many ways now to get y.
let's use the triangle GH and crossing point of diagonals (there is a right angle).
y = 180 - G/2 - 90 = 180 - 50 - 90 = 40°
-x+3y=0
x+3y=12
System of linear equation by elimination
Answer:
x=6
y=2
Step-by-step explanation:
-x+3y=0 (1)
x+3y=12 (2)
(1)+(2)<=> 6y=12
The weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g. Is the distribution a standard normal distribution? Why or why not?Is the distribution a standard normal distribution? Why or why not? Choose the correct answer.
The distribution is not a standard normal distribution.
We know that the variable (X) usually obeys and follows a standard normal distribution provided that the summation of (X) is zero and the variance of the random variable V(X) = 1.
Mathematically:
E(X) = 0 and V(X) = 1
Given that;
the mean which follows a normal distribution (X) = 4.5338 g, and the standard deviation SD(X) = 0.1039 gAs such, the distribution is not a standard normal distribution.
Therefore, we can conclude that the distribution is not a standard normal distribution.
Learn more about standard normal distribution here:
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What is the average length fingernails will grow in 12 months? Pls I need help I have school tomorrow
Answer:
3.47 millimeters (mm) per month
Step-by-step explanation:
The angles in a quadrilateral ABCD are A(3x+10), B(3x+4), C(x+50) and D(5x+8). Find the angles of the quadrilateral ABCD
please answer it fast..thank u
Answer:
A 8º
B 76º
C 74º
D 128º
Step-by-step explanation:
The sum of the angles is 360
(3x + 10) + (3x + 4) + (x + 50) + (5x + 8) = 360
Combine like terms
12x + 72 = 360
Subtract 72 from both sides
12x = 288
Divide both sides by 12
x = 24
--------------
A (3x+10) = 3*24 + 10 = 82
B (3x+4) = 3*24 + 4 = 76
C (x+50) = 24 + 50 = 74
D (5x+8) = 5*24 + 8 = 128
How to Solve 3x = 18?
Step-by-step explanation:
devide both sides on 3 and x=6
as u can see 3*6=18
u have to find a number hat when its multiplied on 3 equals 18
so x(the number were searching for) is 6
Answer:
x = 6
Step-by-step explanation:
1. Divide Both Sides By The Coefficient
18/3 = 3x/3
6 = x
2. Move the variable to the Left
x = 6
Topic: Mathematics 8, Pre-Algebraic Skills
Aliza plays basketball every Tuesday and
Thursday. She practices piano every other
day. If June started on a Monday, and if
Aliza played piano that day, on how many
days did she both play basketball and practice piano in June (which has 30 days)?
A. 2 days
B. 4 days
C. 5 days
D. 7 days
Answer:
4 days
Step-by-step explanation:
June starts on Monday
for 30days we have 4 weeks starting from Monday to Sunday and extra 2 days which are Monday and Tuesday
so we have 5 mondays and tuesdays
4 wed, thu, fri, sat, sun
Aliza played piano on june1 monday
So aliza played basketball on 5 tues + 4 thurs = 9 days
for calculating both basketball and paino
piano day should be on tuesday or thursday
from the below picture u can see pink dots are piano days
and yellow circles are both piano and basketball days
so on alternate weeks they are coinciding
so there are 4 days
0.5 was rounded to 1 significant figure
What is the upper bound?
Step-by-step explanation:
Find the value of X- triangle measurments
Answer:
its a triangle you neeed to seee and to solve this
Step-by-step explanation:
y = x + 3
y=-x+ 5
A. (4, -1)
B. (-1,4)
C. (1,4)
D. (4,1)
It's an equilateral traingle
All angles measure 60°[tex]\\ \sf\longmapsto 4x-20=60[/tex]
[tex]\\ \sf\longmapsto 4x=80[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
3. Four subway cars can safely hold 264 people. How many people can fit in one subway car ?
Answer:
66 people
Step-by-step explanation:
There are 264 in 4 subway cars, we can use proportions to solve this question so 264 people/4 cars = 4 cars/4 cars which equals 66 people = 1 car
someone help now! urgent!
Answer:
5√8, √170, 5/8, 0.62
Step-by-step explanation:
5√8 = 14.1
√170 = 13.03
5/8 = 0.625
0.62 = 0.62
Answer:
5sqrt(8), sqrt(170), 5/8, 0.62
Step-by-step explanation:
Solve any equations and put them in decimal form to make it easier to list them from biggest to smallest.
Ex: sqrt(170) = 13.04
5sqrt(8) = 14.14
5/8 = .625
Can someone answer these for me???!!!
1: Angles 2 & 6 + angles 3 & 7
- Angles that are on the inside of the parallel lines and on opposite sides of the transversal
2: Angle 1
- Angles in the same position but the other line
3: Alternate exterior angles
- Angles that are on the outside of the parallel lines and opposite sides of the transversal
4: Same side interior angles
- They are on the same side of the transversal and inside the parallel lines
5: Angle 2
- It is supplementary and on the inside of the parallel lines
6: Angle 4
- It is supplementary and on the outside of the parallel lines
7: 146°
- They are corresponding angles, so they are the same measurement
8: 128°
- They are supplementary angles, so 180 - 52 = 128
For 9 & 10:
- They are supplementary, so adding them together will result in 180 degrees
- (8x + 63) + (5x) = 180 -> 8x + 5x + 63 = 180 -> 13x = 117 -> x = 9
- Now we will plug it in to find the individual measurements:
9: 135°
- 8x + 63 -> 8(9) + 63 -> 72 + 63 = 135
10: 45°
- 5x -> 5 (9) = 45
I hope this helps, have a nice day! :D
The first three terms of a geometric sequence are
-2, 8 ,-32
Find the next two terms of this sequence.
Answer:
a4 = 128
a5 = -512
Step-by-step explanation:
a1= -2
q= (-1)^(n+1) × 4
a4 = a1q³ = (-2) (-4)³ = -2 × -64 = +128
a5 = a1q⁴ = (-2) (-4)⁴ = -2 × 256 = -512
Define "risk".
1. A mutual fund fee used to pay brokers for steering clients to the fund.
2. What a job will pay you.
3. Unemployment due to job switching.
4. The potential for loss.
14. The supervisors of a rural county are interested in the proportion of property owners who
support the construction of a new high school for the area. Rather than contact all 7,000 of
the owners, the supervisors decide to take a random sample of 300.
(a) During each interview, the supervisor's representative asks, “Do you support the building
of a new high school for the area?” For this sample, 58% of the respondents said yes. If
the representative took a second random sample of 300 property owners, would this
second sample proportion of those who support building a new high school be exactly the
same as that found in the first sample?
(b) If the representative has increased the sample size to 600 owners, what effect would this
have on the estimated proportion of owners who would support building the high school?
question 9, literally almost done
Answer:
A 4
Step-by-step explanation:
2(3)=6-2=4
Answer:
D. 8
Step-by-step explanation:
f(3) = 2·3 - 2 = 4
2·f(3) = 2·4 = 8
Last person got it wrong so, give it a try? At the beginning of the year, Sam weighs 57 pounds. During the year, he loses 4 pounds and then gains 9 pounds. What is Sam's weight now? Also, its not 64 so, dont tell me 64 thx
Answer:
62 Pounds
Step-by-step explanation:
Sam weighs 57 pounds
he loses 4 pounds So he has 53 pounds now
then gains 9 pounds
53 + 9 = 62
Therefore Sam weighs 62 pounds
Need to know the slope and the y intercept
Answer: Slope (M) = 7.5
Y-intercept (B) = 0
Step-by-step explanation:
For the slope, the first step is to find your "pretty points" (spots on the slope that hit the corner perfectly, like (0, 0) or (2, 15).
Now, make a triangle with the two points. Count the amount of squares on both. This will give you 3 and 4, but when taking the units into consideration, 15 and 2. The last step is to divide 15 and 2 which gives you 7.5. I would recommend writing both 15/2 and 7.5 but it's up to you.
The Y-intercept is just the spot where the Y is 0, or where the line touches the Y-axis. This is at the origin, where both X and Y are 0, so your Y-intercept is 0.
I'm kinda bad at explaining things in words, so sorry if this makes no sense, but I hope this helps!
I think of a number ÷ 4 and add 11 result is 19 find the number
Answer:
32
Step-by-step explanation:
work backwards, 19-11=8 then x 4 makes 32.
Answer:
32
Step-by-step explanation:
Let the number be 'x'
[tex]\dfrac{x}{4}+11=19[/tex]
Subtract 11 from both sides
[tex]\dfrac{x}{4}=19 - 11\\\\\dfrac{x}{4}=8\\[/tex]
Multiply both sides by 4
x = 8*4
x = 32
whats the answer for this oneeeeeeee
Answer:
2/3
Step-by-step explanation:
the top has 2 on top and bottem has 3 or i am just du mb
Answer:
y = - [tex]\frac{4}{3}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line
m = [tex]\frac{-2-2}{3-0}[/tex] = [tex]\frac{-4}{3}[/tex] = - [tex]\frac{4}{3}[/tex]
The line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = - [tex]\frac{4}{3}[/tex] x + 2 ← equation of line
The perimeter of the aqua rectangle is 72 feet. What is the measure of the rectangle’s longest side?
If you do not know the answer please don't plagiarize, post answers unrelated answers, or post incorrect answers.
Answer:
53
Step-by-step explanation:
72 = x + 3x - 4
72 = 4x - 4
72 + 4 = 4x - 4 + 4
76 = 4x
76/4 = 4x/4
x = 19
3(19) - 4 = 53
Hope this helps!
Describe the order of operations you would use to
evaluate 8 +
4(32)
"The first step is to…then..finally
11) A map of North Carolina is scaled so that 3 inches represents 93 miles. How far apart are Raleigh
and Charlotte if they are 1.8 inches apart on the map. Do not use a proportion.
please help
Answer:
Step-by-step explanation:
please help
Two friends collect boxes of cereal for charity. One friend collects 22 bins with 36 boxes each, and the other collects 18 bins with 24 boxes each.
How many boxes did they collect altogether?
Answer:
1224 boxes altogether
Step-by-step explanation:
Form two products and add the products together, as follows:
(22 bins)(36 boxes) + (18 bins)(24 boxes) = 1224 boxes altogether
Analyze the diagram below.
Which statements regarding the diagram are correct? Check all that apply.
ST ≅ ST by the reflexive property.
∠RWS ≅ ∠UWT because they are vertical angles.
△RWS ≅ △UWT by AAS.
△RST ≅ △UST by SAS.
∠WTU ≅ ∠WSR because CPCTC
Answer:
the answer to your question : Which statements regarding the diagram are correct? Check all that apply.
✔ST ≅ ST by the reflexive property.
✔∠RWS ≅ ∠UWT because they are vertical angles.
✔△RWS ≅ △UWT by AAS.
△RST ≅ △UST by SAS.
✔∠WTU ≅ ∠WSR because CPCTC
is provided in the picture below have a good day :)
Answer:
A, B, C, E
Step-by-step explanation:
There are 84 fish to be spread out in three fish
tanks that have two sections each divided into
two parts. How many fish should be put in each
part of the fish tank for each part to have the
same number of fish?
23
Answer:
14
Step-by-step explanation:
Divide
84 ÷ 3
= 28
28 ÷ 2
= 14
Therefore, there has to be 14.
The first four terms of a sequence are 5,-3,-11,-19. Which of the following is an equation for the nth term of the sequence?
an=8n−3A sub n is equal to 8 n minus 3
an=n−4A sub n is equal to n minus 4
an=−8n+13A sub n is equal to negative 8 n plus 13
an=−8n−8
Answer:
Step-by-step explanation:
-3-5=-8
-11-(-3)=-11+3=-8
-19-(-11)=-19+11=-8
it is an A.P. and c.d.=-8
so nth term is
an=a1+(n-1)d
an=5-(n-1)(-8)
an=5+8n-8
an=8n-3
Suppose the matrix R represents a railroad map between cities 1, 2, 3, 4, and 5.
How many different ways can you travel from city 1 to city 3 with exactly 1 connection
How many different ways can you travel from city 2 to city 5 with exactly one
connection?
Observing the given matrix we can say that:
1) The value is 4.
2) The value is 2.
So analyzing the different paths that can connect city 1 to city 3: The value is 4. It represents the number of one-stop routes between City 1 and City 3 that pass through City 2.
For the second statement we will have the value is 2. It is the number of direct routes from City 2 to City 5.
Learn more: brainly.com/question/16823190
How much would it cost to build 10 houses if it costs 7 500 000 per house.
Answer:
75 000 000
Step-by-step explanation:
7 500 000 times 10 = 75 000 000
