The remainder obtained when x⁴ +15x³ +6x² - 12x + 3 is divided by (x+2) is____.
Answer:
-53
Step-by-step explanation:
(x+2)
x^4 = -2^4 = 16
15x^3 = 15* (-2)^3 = -120
6x^2 = 6(-2^2) = 24
12x = 12*(-2) = -24
substitute into equation:
x^4 + 15x^3 + 6x^2 - 12x + 3 = 16+ (-120) + 24 - (-24) + 3 = -53
Given Polynomial is x^4 +15x^3 +6x^2 - 12x +3
Divisor = x+2
We know that
Remainder Theorem:
Let P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is another linear polynomial,If P(x) is divided by (x-a) then remainder is P(a).
So, P(x) is divided by (x+2) then the remainder is P(-2).
P(-2) =
⇛(-2)^4+15(-2)^3+6(-2)^2-12(-6)+3
⇛ 16+15(-8)+6(4)+72+3
⇛16-120+24+72+3
⇛ 67-120
⇛ -53
P(-2) = -53
Answer:- The remainder is -53.
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Draw a square and its diagonals. Guess the measures of these angles.
Answer:
Each angle measures 45° with diagonals
Step-by-step explanation:
What is the opposite of 3√ ?
13√
−3√
−32
3²
Answer:
D or B
Step-by-step explanation:
Dakota earned $12.50 in interest in Account A and $11.25 in interest in Account B after 15 months.
If the simple interest rate is 4% for Account A and 3% for Account B, which account has the greater
principal? Explain.
Answer:
You haven't explained the time for account A - we will assume 12 months or the answer is obvious:
for Acct(A) : I = 12.5 = A1 * .04 A1 = $312.50
for Acct(B) I = 11.25 = A2 * .03 * 5/4 = 300
Note that annual interest in B is .03 or I = .03 + .03 * 1/4 = .0375 for 15 mos.
11.25 = .0375 * A2 A2 = 300
Account A will have the greater principal
NEED HELP NOW thanks
Answer:
13 uvugugugugycycycycycycy
Step-by-step explanation:
cycle yvy
Step-by-step explanation:
it's somehow confusing because there's no coordinates for line k
GIVING BRAINLIEST!!!!!!!!
[tex]\red{\bold{Answer:}}[/tex]
The Inverse variation of the total stopping distance and the force of the pavement to determine the speed the car travelling.
#BrainlyFast
#CarryOnLearning
(≡^∇^≡)
What is the value of x?
Answer:
x = 21
Step-by-step explanation:
The angles are supplementary
therefor
(3x + 2) + (5x + 10) = 180
Combine like terms
8x + 12 = 180
subtract 12 from both sides
8x = 168
Divide both sides by 8
x = 21
Answer:
x = 21
Step-by-step explanation:
The angle adjacent to 3x + 2 corresponds to 5x + 10 and are congruent.
The 2 adjacent angles then lie on a straight line and sum to 180° , then
5x + 10 + 3x + 2 = 180
8x + 12 = 180 ( subtract 12 from both sides )
8x = 168 ( divide both sides by 8 )
x = 21
In 10 minutes a heart can beat 700 times.At this rate in how many minutes will a heart beat 140 times? AT what rate can a heart beat
Answer:
2 minutes
Step-by-step explanation:
700/10 = 70
1 minute = 70 times
140/70 = 2 minutes
Answer:
2 minutes
Step-by-step explanation:
The heart beats 70 times per minute so 70+70=140.
solving systems of equations in three variables
Answer:
Option B: (x= -8, y=10, z=-6)
Step-by-step explanation:
2x + 4y + 3z = 6 ... eq.(1)
5x + 8y + 6z = 4 ... eq.(2)
4x + 5y + 2z = 6 ... eq.(3)
From eq.(1),
2x= 6 - 4y - 3z
x= (6-4y-3z)/2 ... eq.(4)
Putting x as (6-4y-3z)/2 in both eq.(2) and eq.(3)
In eq.(2),
5[(6-4y-3z)/2] +8y +6z =4
Multiplying through by 2
5(6-4y-3z) + 16y + 12z = 8
30-20y-15z+16y+12z = 8
22= 4y + 3z ... eq(5)
In eq.(3),
4[(6-4y-3z)/2] +5y +2z = 6
2(6-4y-3z) +5y + 2z =6
12-8y-6z + 5y +2z = 6
6= 3y + 4z ... eq.(6)
Multiplying eq.(5) and eq.(6) by 3 & 4 respectively
66=12y + 9z ... eq(8)
24=12y + 16z ... eq(9)
Subtracting eq(8) from eq(9)
42= -7z
z= -42/7
z = -6
Putting z as -6 in eq.(5)
22= 4y + 3(-6)
22= 4y -18
4y = 40
y = 40/4
y = 10
Putting y as 10 and z as -6 in eq(4)
x = [6 - 4(10) - 3(-6)]/2
x = (6 - 40 - 18)/2
x = -16/2
x = -8
x= -8, y= 10 , z= -6
Solve for the variable in the following proportion.
1/4 is to 1 1/4 as 2 is to b
B =
Can someone give an explanation?
Answer: b = 10
Step-by-step explanation:
We want a ratio of b/2 that is equal to the ratio of 1/4 to 1 1/4 (or 5/4).
Ratio of (1/4)/(5/4):
(1/4)/(5/4) = (1/4)*(4/5) = 4/20 = 1/5 or 0.2
We want 2/b = 1/5 or 0.20
2/b = 0.20
b = 2/0.20
b = 10
--
Check: Does 10/2 = (1/4)/(5/4)?
Yes
b is 10
pls answer 4th and 5th question . i do not understand
Step-by-step explanation:
4) total length of the journey is
1st hr = 74km 224m = 74224m
2nd hr = 74km 224m = 74224m
3rd hr = 58km 56m = 58056m
4th hr = 62km 8m = 62008 m
total distance (adding all) = 268512m = 268km 512m .
5) total weight = 22kg 200g = 22200g
mangoes weight = 14kg 750g = 14750g
apples weight = 5kg 80g = 5080g
total weight - fruits weight
(22200-14750-5080)g
= 2370g
= 2kg 370g.
hope this helps you.
write 13/19 as a decimal rounded to the nearest hundred
Determine the range of the following graph:
Answer:
5,_5,5,
_8,_3,5,
Step-by-step explanation:
from 5 u get _8,from _5 you get _3 and so on
Simplify each expression.
1.) 50 1/2 + (-12.3)
2.) -50 1/2 + (-12.3)
3.) -50 1/2 + 12.3
Please and thanks! (I'm horrible at my math)
Answer:
1.) 38.2
2.) -62.8
4.) -38.2
solve pls brainliest
Answer:
0.2% as a decimal is 0.002, 3.71 as a percentage is 371%
A 2-lb block of cheese us cut into 8 pieces of equal mass. What is the mass of each piece? (In oz)
Answer:
4 ounces each
Step-by-step explanation:
16 ounces = 1 pound
16x2=32
32/8=4
a hockey team earns 2 points for a win,1 point for a tie, and 0 points for a loss. the number of points earned can be calculated using this formula
P = 2x + y where P = number of points
x = number of wins
y = number of ties
How many points would a team earn if they played 52 games, won 24 and lost 19?
Answer: 57
Step-by-step explanation: First add the won and lost games then subtract the sum from the total games played to determine how many games were tied. Then take the won games and multiply them by 2, take the tied games, and add them together to get your answer: 57.
The prices of items in a shop were reduced by 10% during reduction sales. if a costumer buys an electric fan at $810.00. What was the original price?
Answer:
See below:
Step-by-step explanation:
Hello! I hope you are having a nice day.
We can solve the problem in 2 steps, one being Solving, and the second being Comprehending. I'll start with comprehending.
Comprehending
We can start by analyzing the problem and creating an equation to then begin solving.
So, we know that a number, which we will call [tex]x[/tex] has a discount of 10% to get the current price of $810. We know that when there is a discount, we need to find what the 10 percent is then add it to the current price;$810.
We can create a formula and steps by doing the following:
[tex]x*0.9=810[/tex]
We have 0.9 as there is a 10% discount (0.1) and we subtract 1.00 by 0.1 to get 0.9. (Which is 90%).
This states that 90% of a number is equal to 810.
Now that we have an equation, we can begin solving.
Solving
We can solve the problem by using basic algebra.
[tex]x*0.9=810\\x*\frac{9}{10}=810\\x=(810*10)\div 9\\x=8100 \div 9\\x=900[/tex]
On step 1, we convert the decimal to a fraction for easy simplification/solving.
On step 2, we split the fraction into two and since we're dividing, we can flip the fraction and multiply by 10 and divide by 9.
On step 3, we use basic algebra and after step 4 we get our answer.
We can double check out answer by doing the following:
[tex]900-(900*0.10)=810?\\900-90=810?\\810=810[/tex]
We have checked our answer and gotten our answer of $900.
Cheers!
Which component is missing from the researcher’s process?
A.
B.
C.
D.
Answer:
It is B I believe, if not it's you're fault for not putting the choices...
Find the equation of a line that passes through the point (3,4) and has a gradient of 4.
Leave your answer in the form
y=mx+c
Answer:
The equation of a line in the slope-intercept form is:
y = 5x - 18
The slope-intercept form of the line equation
where
m is the slope
b is the y-intercept
In our case, we are given
m = 5
Point (4, 2)
now substituting m = 5 and (4, 2) in the slope-intercept form of the line equation to determine the y-intercept
y = mx + b
2 = 5(4) + b
20 + b = 2
subtract 20 from both side
20 + b - 20 = 2 - 20
b = -18
now substituting b = -18 and m = 5 in the slope-intercept form of the line equation
y = mx + b
y = 5x + (-18)
y = 5x - 18
Therefore, the equation of a line in the slope-intercept form is:
y = 5x - 18
Pls mark me as brainliest thank you
Answer:
Step-by-step explanation:
m = 4
y = mx +c
y= 4x + c
Plugin x = 3 and y= 4 in the above equation
4 = 4*3 + c
4 = 12 +c
4 - 12 = c
c = -8
Equation of the line :
y = 4x - 8
A book of 20 stamps costs $10.20. What is the cost of one postage stamp? A stamp costs cents.
Answer:
1 stamp = $0.51
Step-by-step explanation:
20 stamps = $10.20
=> 1 stamp = 10.20/20
=> 1 stamp = $0.51
Hoped this helped.
The formula to find the volume of a sphere is = 4 3, where is the radius of the 3
sphere. What is the formula in terms of ?
Answer:
d.
took the test
Step-by-step explanation:
I desperately need this answer. Thank You so much and have a great day
Answer: D.25
Step-by-step explanation:
Since they gave you P(10) You'll have to substitue 10 wherever you see the variable 10.
2(10)+5
2(10)=20
20+5+25
Answer:
25
Step-by-step explanation:
Since they're asking you to find the value of p(10) when t is 10, you would substitute t out for 10 in the function and then solve.
p(10)=2(10)+5
p(10)=20+5
p(10)=25
help me plz hey the answer questions
Answer:
The area of the triangle is 30The triangle is a scalene triangleStep-by-step explanation:
To solve the first question write an equation of
[tex]a=\frac{1}{2} (12)(5)[/tex]
[tex]a=\frac{1}{2} 60[/tex]
[tex]a=30[/tex]
To find the answer to the second question we need to know how to classify the different triangles
Equilateral Triangle- 3 equal sides and 3 equal angles (angles always are 60)
Isosceles Triangle- 2 equal sides and 2 equal angles
Scalene Triangle- No equal sides and no equal angles
So this triangle has no equal sides or angles meaning that it is a scalene triangle
Answer: The area of the triangle is 30
The triangle is a scalene triangle
Step-by-step explanation:
PLS HELP ME 86 points
Answer:is easy
Step-by-step explanation:
your answers are:
A. 76
B. 35
C. 48
D. 62
E. 77
F. 78
G. 87
H. 67
I. 32
J. 63
K. 72
L. 78
Is this relation a function? Justify your answer. a 10 av DOO 4 3 - NA 1 2 3 4 5 6 7 8 9 10 A. Yes, because every x- and y value is positive. B. Yes, because the number of x-values is the same as the number of y values. C. No, because two points with the same x-value have different y values. D. No, because two points with the same y-value have different x- values.
Answer:
The answer is C
Step-by-step explanation:
Write the equation of the line from the graph.
Answer: y = 4x + 2
Step-by-step explanation:
A linear equation is usually in y= mx + b form, where m is the slope and b is the y-intercept.
In order to calculate the slope, we choose two-point from the graph. (-1 ,-2) and (0, 2).
slope = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
= (2 - (-2)) / (0 - (-1))
= (2 + 2) / (0 + 1)
= 4 / 1
= 4
y-intercept means the y value when x is 0, according to the graph, the y value when x at 0 was 2. So the y-intercept is 2.
Plug both slope and y-intercept in, we get the equation:
y = 4x + 2
Answer: y = 4x + 2
Step-by-step explanation:
if motorist drove a distance of 90km at constant speed for the first 40km and then drove 30 km/hr faster for the rest of the journey if the journey took him one hour, his average speed for the first 40 km is
Answer:
Step-by-step explanation:
The motorist drove at a distance of 90km at a constant speed for the first 40km, and then 20 km/hr faster for the rest of the journey.
The whole journey took him 1hr.
Let S denotes the average speed (in km/hr) for the first 40 km.
Hence we get the following relation,
40/S + (90 - 40)/(S + 20) = 1
or 50/(S + 20) = 1 - 40/S = (S - 40)/S
or (S + 20)(S - 40) = 50S or S^2 - 70S - 800 = 0 or (S - 80)(S + 10) = 0
or S = 80 (km/hr) [Ans]
[S cannot be negative value]
a(5+b) HELPPPP btw use distribitive
Answer:
a(5+b)
5a+ab
Step-by-step explanation:
Answer:
5a + ab
Step-by-step explanation:
a(5 + b)
Times a by 5 and by b
5a + ab
Find the perimeter.simplify your answer.
Answer:
proly
Step-by-step explanation:
2 * (2z-9) + 2 * (10z)
4z-18 + 20z
24z - 18
Answer:
22z
Step-by-step explanation:
10+10+2z-9+2z-9= 22z