The quotient of dividing (3x⁴ - 2x³ + 7x² - 4) by (x - 3) is 3x³ + 7x² + 28x + 84 and the remainder is 248
How to determine the quotient and the remainder?The division expression is given as:
(3x⁴ - 2x³ + 7x² - 4) / (x - 3)
Set the divisor to 0
x - 3 = 0
Solve for x
x = 3
Substitute x = 3 in 3x⁴ - 2x³ + 7x² - 4
3x⁴ - 2x³ + 7x² - 4 = 3(3)⁴ - 2(3)³ + 7(3)² - 4
Evaluate
3x⁴ - 2x³ + 7x² - 4 = 248
This means that the remainder is 248
Recall that:
Dividend = Divisor * Quotient + Remainder
So, we have:
3x⁴ - 2x³ + 7x² - 4 = x - 3 * Q + 248
Subtract 248 from both sides
3x⁴ - 2x³ + 7x² - 252 = x - 3 * Q
Divide both sides by x - 3
Q = (3x⁴ - 2x³ + 7x² - 252)/(x - 3)
Factorize the numerator
Q = (x - 3)(3x³ + 7x² + 28x + 84)/(x - 3)
Cancel out the common factors
Q = 3x³ + 7x² + 28x + 84
Hence, the quotient is 3x³ + 7x² + 28x + 84 and the remainder is 248
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Whoever helps me get the right answer gets 20 points
A triangle has side lengths 3.4 cm, 4 cm, and 5.2 cm. The angle measures are 40°, 50°, and 90°.
What type of triangle is this triangle?
acute isosceles
acute scalene
right isosceles
right scalene
Answer:
right scalene
Consider the questions below:
Are the line parallel or perpendicular?
[tex]\Large\textsc{Answer\::}[/tex]
ParallelPerpendicular[tex]\Large\textsc{\textbf{Calculations\::}}[/tex]
First , notice that the equation of the second line , 6x=3y+5 , is not written in the same form as y=2x , so determining the slope is hard .
To determine the slope , we need to convert the first equation into slope intercept form .
Subtract 6x on both sides :
0 = 3y+5-6x
Now , subtract 3y on both sides :
-3y=-6x+5
Divide by -3 on both sides :
y=-6/-3x+5/-3
Which simplifies to :
y=2x-5/3 (remember , a negative divided by a negative results in a positive)
Put both equations together :
y=2x and y=2x-5/3
Notice that the slopes are the same . This indicates that the lines are parallel .
Now let's focus on the second maths problem :
Consider the equations below .
x=-4 and y=-2
Are the lines parallel or perpendicular?
The slope of the first line is undefined , and the slope of the second line is zero .
Lines with undefined slopes are vertical , and lines with slopes of zero are horizontal .
Here's something you may have recalled from your Geometry class :
Is a vertical line parallel or perpendicular to a horizontal line ?
The ans is : perpendicular .
Henceforth , the lines x = -4 and y = -2 are perpendicular to each other .[tex]\footnotesize{\texttt{hope helpful~}[/tex]
If a₁ = 2 and an = an-1 +5 then find the value of a5. for recursive sequence
Answer:
[tex]a_{5} = 22[/tex].
Step-by-step explanation:
In this recursive sequence, the value of the first term [tex]a_{1} = 2[/tex] is stated explicitly. The value of every other term of this sequence is given as an expression of the previous term.
For example, the value of the term [tex]a_{2}[/tex] ([tex]n = 2[/tex]) is given in terms of the value of [tex]a_{1}[/tex]:
[tex]\begin{aligned}a_{2} &= a_{(2 - 1)} + 5 \\ &= a_{1} + 5\end{aligned}[/tex].
Likewise, the value of [tex]a_{3}[/tex] ([tex]n = 3[/tex]) would be:
[tex]\begin{aligned}a_{3} &= a_{(3 - 1)} + 5 \\ &= a_{2} + 5 \\ &= (a_{(2-1)}+5) + 5 \\ &= (a_{1} + 5) + 5 \\ &= a_{1} + 2 \times 5 \\ &= a_{1} + (3 - 1) \times 5\end{aligned}[/tex].
In general, the value of [tex]a_{n}[/tex] (for integer [tex]n \ge 1[/tex]) would be:
[tex]\begin{aligned} a_{n} &= a_{1} + (n - 1) \times 5 \\ &= 2 + (n - 1) \times 5\end{aligned}[/tex].
Therefore, the value of [tex]a_{5}[/tex] ([tex]n = 5[/tex]) would be:
[tex]\begin{aligned}a_{5} &= a_{1} + (5 - 1) \times 5 \\ &= 2 + (5 - 1) \times 5 \\ &= 22\end{aligned}[/tex].
Use unit price to decide which pizza deal is the better buy. Explain.
Deal A: 30 slices for $75
OR
Deal B: 18 slices for $48
please explain your answer!!
Answer:
1. 0.4
2. 0.375
Step-by-step explanation:
All you gotta do is find how much does it cost for each slice for example 30/75=0.4 and decide which one is better
Determine the value of x.
is it 20?
Answer:
X = 20
Step-by-step explanation:
The two angles are vertical.
62 = (2 + 3x)
60 = 3x
60/3 =
20
You were correct
ANSWER THIS CORRECTLY FOR BRAINLIEST (ALGEBRA)
Answer:
33.49 cubic inches
Step-by-step explanation:
5th grade pls help
Cy bought a laptop computer, a printer, and a router. Cy used a $35 coupon to make the purchase. He wrote (1,415.00 + 277.50 + 44.95) - 35 to show how he can calculate the final cost, not including sales tax. Write an expression that can be used to find the total price of the items he bought before sales tax and the coupon.
Answer:
1702.45
Step-by-step explanation:
your welcome
1737.45 coupon not included
Vistance Formula
Find the distance between the two points. Show all work!
AY
(5.-10). (-5, 4)
Answer:
2 sqrt 74
Step-by-step explanation:
d^2 = ( x1-x2)^2 + (y1-y2)^2
d^2 = ( 5 - -5 )^2 + ( -10 -4)^2
= 100 + 196
d^2 = 296
d = sqrt 296 = 2 sqrt (74)
A dinner plate has a circumference of 100.48 cm. What is the area of the dinner plate? Use 7 = 3.14.
Circumference = 2914 Area Пr2
A. 1,607,68 cm2
B. 200.96 cm?
C. 803.84 cm?
D. 50.24 cm
Answer:
803.84, or C.
Step-by-step explanation:
If we know the circumference then we can use that to find the radius!
-
(π =pi)
Area of a circle formula: π · r^2
-
Let us plug in the circumference into the formula (not the area formula, the circumference one!)
c=2πr
100.48=2πr - 2*3.14 =6.28
100.48=6.28r
divide both sides by 6.28!
r= 16
Now, we plug that in the area formula.
π · r^2
3.14 * 16^2
3.14 * 256 =
803.84
PLEASE HELP
Describe how the variable h and the variable k of the general formula for a cube root function effects the graph. The general formula is y=a^3sqrt x-h+k
Answer: h = left or right, k = up or down
Step-by-step explanation:
h determines if the function is shifted left or right and k determines if the graph is shifted up or down
Use the drawing tools to form the correct answer on the graph. Plot function f on the graph. f(x)= 3, -9
The equation of the function f with solution 3, -9 is x²+6x-27 and the graph of this equation with the use of drawing tools is attached below.
What is the definition of a Function?A function assigns the value of each element of one set to the other specific element of another set.
A function has to be plot which has the value of f(x) as 3 and -9. Here, 3 and -9 are the solution of the function. Thus,
x=3
x-3=0
The second solution is,
x=-9
x+9=0
Multiply both factor for the function as,
f(x)=(x-3)(x+9)
f(x)=x²+9x-3x-27
f(x)=x²+6x-27
This is the required function. The graph of this function is attached below.
Thus, the equation of the function f with solution 3, -9 is x²+6x-27 and the graph of this equation with the use of drawing tools is attached below.
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Use the ordered pair (2, 4) to find which equation describes the graph below.
Answer:
the answer is b , sub 2for x in each equ then whatever answer you get , use it to check is that what y is on grph
Jo is pouring a driveway and he mixes cement and water in the correct ratio. X represents the cement and y represents the water. The graph includes (54,120) (108, 240) (162, 360) (216, 480). He says (63, 140) is included in the relationship of the graph. Is he correct?
Answer:
Yes.
Step-by-step explanation:
y/x = 2.22..... for all the 4 points given.
The graph is a straight line with slope 2.22....
140/63 = 2.2222... also so this is included in the realtionship
FIND THE DOMAIN AND RANGE
Answer:
B
Step-by-step explanation:
Can any math experts please help me with this thank you so much
[tex]1.~\boxed{\sf0.55555555555}\boxed[/tex]
[tex]2.~\boxed{\sf 0.54545454545}\boxed[/tex]
A rectangular prism and its net are shown below.
(All lengths are in yards.)
If the dimension of the rectangular prism will be 11 by 8 by 4. Then the volume of the rectangular prism will be 352 cubic yards.
What is a rectangular prism?A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.
A rectangular prism and its net are shown below.
Then the volume of the rectangular prism will be
Volume = LWH
where
Width (W) = 8 yd
Length (L) = 11 yd
Height (H) = 4 yd
Then the volume will be
Volume = 11 × 8 × 4
Volume = 352 yd³
Then the volume of the rectangular prism will be 352 cubic yards.
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The cost of downloading a movie from a website is $4.99. Which equation can be used to find c, the cost in dollars of downloading n movies? A. c = 4.99 +n = B. n = 4.990 C. n = 4.99 +c D. c = = 4.99n
Answer:- The answer is letter B, c=1.75n
Step-by-step explanation: Hope this helps.
if lin has already run 19.6 miles of the marathon how many miles does she have left
Answer:
6.6 miles she has to runStep-by-step explanation:
the marathon actual race distance is 26.2 now that Lin has already ran 19.6 miles so now we should subtract this two decimal numbers so that were get 6.6
varies directly with the number of
The doliar amount d that Megan earns
hours h that she works. In her last paycheck, she earned $148.50 working
18 hours.
If her next paycheck is $90.75, how many hours did she work?
Step-by-step explanation:
Let p and h represent pay and hours worked respectively,
p = kh
k = p/h = 148.5/18 = 8.25
p= 8.25h
90.75 = 8.25h
h = 11 hours.
Hope it helps! :)
Javier loves flying kites. He flies his kite for 1 hour on Monday, 2 hours on Tuesday, 4 hours on Wednesday, and 3 hours on Thursday. How many more hours did Javier fly his kite on Wednesday and Thursday than Monday and Tuesday?
Answer:
4 more hours
Step-by-step explanation:
wednesday+thursday=7
monday+tuesday=3
7-3=4
There are 10 girls in an athletics club.
e ratio of girls to boys is 5:3.
w many boys are there?
Answer:
6Step-by-step explanation:
There are 10 girls in an athletics club.
e ratio of girls to boys is 5:3.
w many boys are there?
we can solve with an equation
10 : x = 5 : 3
x = 10 * 3 : 5
x = 30 : 5
x = 6
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What is the absolute value of negative 1/2
Answer:
The absolute value of negative 1/2 is 1/2
Step-by-step explanation:
The absolute value of a number is the positive form of the number
complete this statement: A plolygon with all sides the same length is said to be
Answer:
it is said to be a regular polygon.
Step-by-step explanation:
A regular polygon is a polygon that has all angles of the same measure and all sides of the same length.
a is 25% of b
b is 30% of c.
Write the ratio a:b:c
Give your ratio in its simplest form.
Answer:
40a : 10b : 3c
Step-by-step explanation:
We can write this information more mathematically by saying:
[tex]a = \frac{1}{4} b[/tex]
[tex]b= \frac{3}{10} c[/tex]
This can be written as ratios as well by making them all integers so:
4a : b
10b : 3c
By making the b's in both equations the same, we can link all the ratios together so:
40a : 10b
10b : 3c
So,
40a : 10b : 3c
Please help!!!! (07.05 LC)
How many solutions does the equation 3x + 6 = -1 - 3 + 4x have?
O Two
O None
One
O Infinitely many
Answer:
one
Step-by-step explanation:
3x + 6 = -1 - 3 + 4x
Combine like terms
3x+6 = -4 +4x
Subtract 3x from each side
3x+6-3x = -4+4x-3x
6 = -4+x
Add 4 to each side
4+6 = -4+x+4
10 =x
There is one solution
Only one it's 10
And environmental group would like a representative sample of its members to complete a survey. Which method gives the most representative sample?
a. Survey all the people who attended the month club meeting.
b. Survey every third person from the list of group members.
c. Survey the first five people who joined the club.
d. Survey every other person that went on the weekend nature walk.
Answer:
D.
Step-by-step explanation:
When you survey every 3rd person you will use that as a good sample for the survey. Hope this helps!
Pls help me!!!!!!!!!!’
Answer:
m<6 = 119°
Step-by-step explanation:
Two lines are parallel with each along a line.
m<4 and m<6 are supplementary angles which both angles add up to 180°.
m<4 + m<6 = 180°
61° + m<6 = 180°
m<6 = 180° - 61°
m<6 = 119°
Answer:
Step-by-step explanation:
m<6 + 61 = 180
m<6 = 139
a line passing through the point (−2, −3) with a slope of −6.
y + 3 = −6(x + 2) A
y + 2 = 6(x + 3) B
y − 3 = −6(x − 2) C
y − 2 = 6(x − 3) D
Answer:
A
Step-by-step explanation:
y + 3 = -6(x + 2)
y + 3 = -6x - 12
y + 3 = -6x - 12
y = -6x - 15
How many sets of one eighths are in 3/4
Answer:
6
Divide the fractions.
3 / 1 = 3
4 / 8 = 2
Use the numerator as a multiplicand.
2 × 3 = 6
Find -5B.
Please help
Answer:
[tex]-5B = \begin{bmatrix}-15&10\\ 20&40\end{bmatrix}[/tex]
Step-by-step explanation:
[tex]B=\begin{bmatrix}3&-2\\ -4&-8\end{bmatrix}[/tex]
[tex]\Longrightarrow -5B = -5 \times\begin{bmatrix}3&-2\\ -4&-8\end{bmatrix}[/tex]
[tex]\Longrightarrow -5B = \begin{bmatrix}-5 \times3&-5 \times-2\\ -5 \times-4&-5 \times-8\end{bmatrix}[/tex]
[tex]\Longrightarrow -5B = \begin{bmatrix}-15&10\\ 20&40\end{bmatrix}[/tex]
