Answer: 2
Step by step: I start with a long-division set-up
Looking only at the leading terms, I divide 3x3 by 3x to get x2. This is what I put on top:
x^2 up on top
I multiply this x2 by the 3x + 1 to get 3x3 + 1x2, which I put underneath:
3x^3 + 3x put down underneath the dividend
Then I change the signs, add down, and remember to carry down the "+10x – 3" from the original dividend, giving me a new bottom line of –6x2 + 10x – 3:
(3x^3 – 5x^2 + 10x – 3) – (3x^3 + 1x^2) = –6x^2 + 10x – 3
Dividing the new leading term, –6x2, by the divisor's leading term, 3x, I get –2x, so I put this on top:
(–6x^2) ÷ (3x) = –2x, which goes on top
Then I multiply –2x by 3x + 1 to get –6x2 – 2x, which I put underneath. I change signs, add down, and remember to carry down the "–3 from the dividend:
(–6x^2 + 10x –3) – (–6x^2 – 2x) = 12x – 3, which is my new last line
My new last line is "12x – 3. Dividing the new leading term of 12x by the divisor's leading term of 3x, I get +4, which I put on top. I multiply 4 by 3x + 1 to get 12x + 4. I switch signs and add down. I end up with a remainder of –7:
(12x)/(3x) = 4, 4(3x + 1) = 12x + 4, (12x – 3) – (12x + 4) = –7
This division did not come out even. What am I supposed to do with the remainder?
Think back to when you did long division with plain numbers. Sometimes there would be a remainder; for instance, if you divide 132 by 5:
132 ÷ 5: 2 × 5 = 10; put 2 on top and 10 underneath; 13 – 10 = 3; new divisor is 32; 6 × 5 = 30; put 6 on top and 30 underneath; 32 – 30 = 2; answer is 26 with remainder 2
...there is a remainder of 2. Remember how you handled that? You made a fraction, putting the remainder on top of the divisor, and wrote the answer as "twenty-six and two-fifths":
\dfrac{132}{5} = 26\,\dfrac{2}{5} = 26 + \dfrac{2}{5}
5
132
=26
5
2
=26+
5
2
The first form, without the "plus" in the middle, is how "mixed numbers" are written, but the meaning of the mixed number is actually the form with the addition.
We do the same thing with polynomial division. Since the remainder in this case is –7 and since the divisor is 3x + 1, then I'll turn the remainder into a fraction (the remainder divided by the original divisor), and add this fraction to the polynomial across the top of the division symbol. Then my answer is this:
\mathbf{\color{purple}{\mathit{x}^2 - 2\mathit{x} + 4 + \dfrac{-7}{3\mathit{x} + 1}}}x
2
−2x+4+
3x+1
−7
Find the area of each triangle. Round your answer to the nearest tenth.
Answer:44 is closest to the nearest tenth if not try 35
Step-by-step explanation:35 Heather farm so it just needs five and it will get to 10 because it goes 30 31 32 33 34 35
EASY POINTS
-
What are the values of a positive attitude?
Answer:
Self-confidence: When you develop a positive attitude, you will start feeling better about yourself. You will treat yourself with more respect and love, and this in turn will boost your confidence levels and inner strength. You will take on new challenges and come out of your self-limiting beliefs
hi please figure this out me and my sister are so confused
Answer:
y = - 7
Step-by-step explanation:
Since the solution is always the same for y, y equals that solution and does not depend on x.
Solve the following quadratic equations using the quadratic formula and select the correct solution set.
5x2+2x-4=0
Thank you!
Answer:
x1= -(1-√(21))/5
x2= -(1-√(21))/5
Step-by-step explanation:
5x²+2x-4=0
D=2^2-4*(-4)*5=4+80=84
x1,2 = (-2±√(84))/10
x1= (-2+√(84))/10 = (-2+√(4*21))/10 = (-2+2√(21))/10 = (-2(1-√(21))/10 = -(1-√(21))/5
x2=(-2-2√(21))/10 = -2(1+√(21)/10=-(1+√(21))/5
Answer: x1= -(1-√(21))/5,
x2= -(1-√(21))/5,
What percentage of the apples are green?
Answer:
6 of the 30 apples are green
6 / 30 = .2
So 20% of the apples are green.
Percentage of the apples are green is 20%
What is a percentage?
"A Percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol %".
According to the question
Total Apples = 30
Red Apples = 24
Green Apples = 6
Percentage of the apples are green = [tex]\frac{6}{30}[/tex]×[tex]100[/tex]
= [tex]20[/tex] % or [tex]0.2[/tex]
∴ Percentage of the apples are green is 20%.
Learn more about percentage here
https://brainly.com/question/16797504
#SPJ2
martin works in a furniture store. he earns a base salary of $1,800 per month, plus a 15% commission on the amount of furniture sales he makes during the month. if martin needs to earn at least 3,000 each month to pay his expenses, what is the minimum amount of furniture sales he must make each month?
Answer:
$8000
Step-by-step explanation:
With the provided values you get the equation
1800+.15x=3000
with x being the amount of sales he needs
1. 3000-1800=1200
gives 1200=.15x
2. 1200/.15 = 8000
so x = 8000
find the slope of the line,
Please Help i am confused
Answer:
Slope = -1
Step-by-step explanation:
We will use 2 points from the graph.\
(0 , 2) and (2 , 0)
formula for slope = y2 - y1/x2 - x1
0 - 2/2 - 0
=-2/2
=-1
write the equation of the line?
Answer: Yellow option
Step-by-step explanation:
The points noted are (0,-2) and (3,-1)
So the slope is (-2--1)/(0-3) = -1/-3 = 1/3
So options blue, green and red are out.
So the only option is yellow
A rectangular prism has a length of 8 meters, a width of 6 meters, and a height of 3 meters.
Which equations could be used to determine the volume, V, of the prism?
Select each correct answer.
(A) V = 8 × 6 × 6
(B) V = 8 × 6 × 3
(C) V = 8 × 9
(D) V = 48 × 3
Answer:
(B) V = 8 x 6 x 3
Step-by-step explanation:
The formula to find the volume of a rectangular prism is, V = Length x Width x Height cubic units.
V = 8 x 6 x 3 cm 3.
V = 192 cm 3.
Brainliest?!
help me with geometry please
Answer:
80°
Step-by-step explanation:
the triangles are symmetrical. therefore their angles will be equal.
interior angles of a triangle = 180°
180° - 30° - 70° = m<D
80° = m<D
Simon used these steps to solve an equation:
Step 1: -6(x + 7) = 2(x − 11)
Step 2: -6x − 42 = 2x − 22
Step 3: -8x − 42 = -22
Step 4: -8x = 20
___% of $10 = $2
Please help me I can not figure it out
I need it please
Answer:
20%.Step-by-step explanation:
Sentence should be:
2 is what percent of 10.How we get the %:
To get it, we need to find the fraction of 20% (0.2) (2/10)So, we simply do this:2/10.We then get 20%.2 is 20% of 10.
20% of 10 is 2.
what is 29/8 into a improper fraction (Convert mixed number).
Answer:
3 5/8
Step-by-step explanation:
divide 29 by 8,
8 times 3 is 24
29-24, remainder is 5
Which value, when divided by 5/16, results in a quotient of 1?
Answer:
0.666777
Step-by-step explanation:
not sure not my grade level
the sum of a number squared and five
Answer:
(x+5^3 is the answer of this question
I NEED HELP WITH THIS MATH I DONT GET IT!!!!!
Answer:
It's 5
Step-by-step explanation:
-4x+5=-15 (subtract 5)
-4x=-20 (divide by -4)
x=5
Step-by-step explanation:
Work backwards. First, create a function:
f(x) = x
First, instead of adding 5, subtract it:
f(x) = x - 5
Then, divide by -4:
f(x) = (x - 5) ÷ -4
Then plug in -15:
f(-15) = (-15 - 5) ÷ 4
= -20 ÷ -4
= 20 ÷ 4
= 5
Simplify this expression
-4 - 10x
Is it possible to have a polygon with an exterior angle of 14 degrees
Answer:
No, a polygon cannot have a decimal number of sides.
Explanation:
exterior angle of a polygon = 360 ÷ number of sidesusing the formula:
14 = 360 ÷ number of sides
1/number of sides = 14/360
number of sides = 360/14
number of sides = 25.71428571
Answer:
all polygons have exterior angles that totL to 360 degrees from triangles to 20-gons. so 360 divided by 14 is 25.71 sides which is not possible because what would .71 of a side look like....now this is assuming that you were referring to regular polygon with all sides the same. I suppose you could gave a polygon with a whole number of sides but the relationship between the exterior angles could be such that not all of the angles have the same degree measure. I would say that an exterior angle for any polygon would need to be greater than 0 but less than 360. so my answer is yes it could be possible le
The points (2, 5) and (6,-3) fall on a particular line. What is its equation in slope-intercept form?
y = -2
x+ ?
Answer:
y = -2x + 9
Step-by-step explanation:
slope intercept form : y = mx + b
where m = slope and b = y intercept
first let's find the slope
slope formula :
[tex]m = ( \frac{y2 - y1}{x2 - x1} )[/tex]
where the x and y values are derived from the given points
here we are given (2,5) and (6,-3)
(x1,y1) = (2,5) so x1 = 2 and y1 = 5
(x2,y2) = (6,-3) so x2 = 6 and y2 = -3
we now plug these values into the formula
recall formula
[tex]m= ( \frac{y2 - y1}{x2 - x1} )[/tex]
plug in x1 = 2, y1 = 5, x2 = 6 and y2 = -3
m = (-3 - 5) / ( 6 - 2 )
m = (-8)/(4)
m = -2
the slope is -2
now to find the y intercept we plug in the slope and the x and y value of a given point into slope intercept form and solve for b
y = mx + b
given point : (2,5) x = 2 , y = 5, m = -2
5 = -2(2) + b
5 = -4 + b
9 = b
so the equation would be y = -2x + 9
find the area of a square of the side 8cm
Answer:
64cm squared
All squares side lengths are the same. 8*8=64.Answer:
64cm²
Step-by-step explanation:
8cm x 8cm = (8cm)²
8 x 8 = 64
cm x cm = cm²
=64cm²
what is the hypotenuse?
225cm
55°
390cm
165cm
165cm
please help meeeee i neeeed it quickkkk with the calculations
Answer:
390cm
Step-by-step explanation:
find the inverse
f(x)=(2x-3)^2 -1
Question 6 of 10
What is the most logical first step in solving the equation x2 +6x+9 - 10?
A Factor the left side of the equation
B. Subtract 10 from both sides of the equation
C. Take the square root of both sides of the equation
D. Subtract 9 from both sides of the equation
SUBMIT
Answer:
A.factor the left side of the equation
sorry but to tell u the answer, I need to know this
is there an equal sign between 9 and 10 or it's just a minus sign?
I mean if it is a minus sign the first thing to do to solve the equation is 9-10 which gives you -1. but if there is an equal sign the first step is to subtract 10 from both sides of the equation which means your answer will be option B.
You are arranging 60 pictures on a poster board. the board can fit up to 4 rows of pictures and each row can have up to 20 pictures. you want each row to have the same numbers of pictures. how many different ways can you arrange the pictures?
Answer:
2 different ways
Step-by-step explanation:
You are looking at the factors of 60.
1×60 does not work, too many pictures in a row.
2×30 does not work, too many pictures in a row.
3×20 THIS WORKS!
4×15 THIS ALSO WORKS!
5×12 Nope, too many rows
6×10, no, too many rows
So there's just two ways to arrange the pictures.
Find the area of the shaded area. Round your answer to the nearest tenth
Answer:
45π
Step-by-step explanation:
To find the area of a circle the formula is πr².
To find the shaded region we will subtract the area of the small circle from the area of the big circle.
Area(big circle)=π9²=81π
Area(small circle)=π6²=36π
81π-36π= 45π
A.(-2, -1) is a solution to the linear system B.(-2, -1)is not a solution to the linear system
Answer:
A. (-2, -1) is the solution to the linear system
Step-by-step explanation:
Substitute for x and y and see if the equations are true.
-1 = 3(-2) +5 . . . . true
-2 +(-1) = -3 . . . . .true
(-2, -1) is the solution to the linear system.
en una bolsa hay menos de 30 semillas. podemos hacer grupos de 4 semillas sin que sobre ninguna. si hacemos grupos de 5 semillas tampoco sobra ninguna. ¿Cuántas semillas hay en la bolsa?
What is the slope of the line?
3(y - 1) = 2x + 2
Rewrite the equation in slope- intercept form.
3(y-1) = 2x + 2
Use the distributive property
3y-3 = 2x + 2
Add 3 to both sides
3y = 2x + 5
Divide both sides by 3
Y = 2/3x + 5/3
Slope = 2/3
A scale drawing of a rectangular park is 7 inches wide and 9 inches long. The actual park
is 392 yards long. What is the area of the actual park, in square yards?
PLEASE HELP ME
Answer:
56000 square yards
Step-by-step explanation:
I hope it helps you!!!
Find the product. Write your answer as a mixed number in simplest form 3 x 4 7/9
Answer:
14 1/3
Step-by-step explanation:
3 × 4 7/9
=3 × 43/9
= 43/3
= 14 1/3
Answer:
43/3
Simply 14⅓
Step-by-step explanation:
4 7/9 can also be expressed as (4x9+7)/9 = 43/9
3x43/9 = 43/3
After simplifying = 14⅓