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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3.) Find the mean for each data set. ROUND FINAL ANSWERS TO THE TENTHS PLACE.
Answer:
6.4
Step-by-step explanation:
5+7+7+5+7+7+6+7+7 = 58
There are 9 numbers
58 ÷ 9 = 6.444444
To the tenth = 6.4
Cooldown
Tyana swims at a constant speed, 4 meters every 5 seconds. How long does it take her to swim 20
meters? Solve using two different methods
Answer:
25 seconds
Step-by-step explanation:
Two methods:
1) Calculate Tyana's speed in m/sec: 4m/5sec = 0.8 m/sec. Now find the number of seconds, x, needed to travel 20 meters:
x*(0.8 m/sec) = 20 m
x = 20 m/(0.8 m/sec)
x = 25 seconds
2) Do a proportion. If Tyana can swim 4 meters in 5 sec, then she can do 8 meters in 10 seconds. That also then means 16 meters in 20 seconds. Another 5 seconds adds another 4 meters, for a total of 20 meters in 25 seconds.
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
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
can you answer number four please
Answer:
l = 104/3
w = 40/3
Step-by-step explanation:
l = 2*w + 8
P = 2(l + w) = 96
48 = l + w
2w + 8 + w = 48
3w = 40
w = 40/3
l = 2*40/3 + 8
= 80/3 + 8
= 80 + 24 / 3
= 104/3
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
I need help :( I forgot how to do this
Answer:
[tex]A=\frac{1}{2}h(b_{1}+b_{2} ) | *2\\2A=h(b_{1}+b_{2} ) | : (b_{1}+b_{2} )\\\frac{2A}{(b_{1}+b_{2} )} = h[/tex]
I hope it's good.
Take care !
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
1/2 (x + 8) - 15 = - 3
Answer:
x=16
Step-by-step explanation:
Heres the work below
Hope this Helps
What is the answer? I have looked and there is no question that is close to mine.
Answer:
Since there is a right angle, this is a right-angled triangle and we can solve for x using Pythagoras Theorem that goes [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse (longest side of the triangle).
In this case, x would be the c.
Substitute in values of a and b:
[tex]10^2+10^2=c^2[/tex]
[tex]c^2=200[/tex]
[tex]c=\sqrt{200}[/tex]
[tex]c=10\sqrt{2}[/tex] (Option A)
write 13/19 as a decimal rounded to the nearest hundred
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
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:
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
(≡^∇^≡)
Use the vertical-line test to determine whether each graph represents a function.
Answer:
14) Not a function 15) Function 16) Function
Step-by-step explanation:
The vertical line test is when you draw a line on the graph to see if it passes the function. The rule is that you can only have one intersection per line
for number 14, if you draw a line, it intersects the function twice each time
for 15, no matter what kind of vertical line you draw, each line will only intersect the function once and the same for 16 (except 16 is more of a linear function)
Answer:
Well a function can’t be on the same one as each other so thats why the vertical line test is used.
For number 14 if you’d draw a vertical line, you’d see there would be 2 answers So that can’t be a function.
For number 15, if you draw a vertical line, none of the given have 2 questions so number 15 is a function.
Whilst in number 16 if you’d draw a vertical line, there wouldn’t be anything that have 2 answers of that overlap. So it is a function
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.
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
A family reunion has 184 people together at a local hotel. They travel in groups of 13 from the airport by van. How many vans will be needed to take the people to the hotel?
184 people
groups of 13
to find:How many vans needed to take the people to the hotel.
solution:[tex] \frac{184}{13} [/tex]
[tex] = 14.1538461538[/tex]
[tex]nearest \: whole \: number = 14[/tex]
therefore, they'll need 14 vans to take the people to the hotel.
answer= option B
Sorry for the spam, I just really need help.
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
Jeffrey purchased a car for $180 that gives him 20 visits to a new gym and includes a one time fee for unlimited use of the sauna. After five visits, Jeff has $123.75 left on the card, and after 11 visits, he has $74.25 left on the card. Write an equation in point slope form, then determine the cost of each visit in the fee for the sauna use.
Write an equation that represents the line. Use exact numbers
Answer: [tex]y=\frac{2}{3}x+1\frac{1}{3}[/tex]
Step-by-step explanation:
take 2 points and use slope formula to find slope
[tex]\frac{4-2}{4-1}[/tex][tex]=\frac{2}{3}[/tex]
take the slope and a point on the graph and use point slope formula to get equation in point slope intercept form
[tex]y-2=\frac{2}{3}( x-1)[/tex]
[tex]y-2=\frac{2}{3}x-\frac{2}{3}[/tex]
[tex]y=\frac{2}{3}x-\frac{2}{3} + 2[/tex]
[tex]y=\frac{2}{3}x+1\frac{1}{3}[/tex]
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
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
Draw a square and its diagonals. Guess the measures of these angles.
Answer:
Each angle measures 45° with diagonals
Step-by-step explanation:
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:
A house is sold for 8% above its original price. If it was sold for £378000 then calculate its original price
Answer:
$350,000
Step-by-step explanation:
lets say the original price is x, then 378000=1.08x, divide by 1.08 to get 350000
What is the opposite of 3√ ?
13√
−3√
−32
3²
Answer:
D or B
Step-by-step explanation:
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