a
The expression ax²+bx+c is divisible by x-1, has a
remainder of 2 when divided by x+1 and has a remainder of 8 and when divided by x-2 find the values of a, b, and c and
factorise completely.
Answer:
(x - 1)(3x + 2)
Step-by-step explanation:
By the Remainder theorem
Given expression is divisible by x - 1 then f(1) = 0
when divided by (x + 1) then f(- 1) = 2
when divided by x - 2 then f(2) = 8
Substitute x = 1, x = - 1, x = 2 into the expression , that is
a + b + c = 0 → (1)
a - b + c = 2 → (2)
4a + 2b + c = 8 → (3)
Subtract (1) from (2) to eliminate a and c
- 2b = 2 ( divide both sides by - 2 )
b = - 1
Subtract (1) from (3) to eliminate c
3a + b = 8 ← substitute b = - 1
3a - 1 = 8 ( add 1 to both sides )
3a = 9 ( divide both sides by 3 )
a = 3
Substitute a = 3, b = - 1 into (1) and evaluate for c
3 - 1 + c = 0
2 + c = 0 ( subtract 2 from both sides )
c = - 2
Then a = 3, b = - 1, c = - 2
Thus
ax² + bx + c
= 3x² - x - 2
= (x - 1)(3x + 2) ← in factored form
The function h is given by h ( t ) = ( 1 − t ) ( 8 + 16 t ) models the height of a ball in feet, t seconds after it is thrown.
Where are the zeros of the function?
______and______
Are both zeros meaningful and why?
At what height is the ball thrown?
9514 1404 393
Answer:
zeros: t = 1, t = -1/2no: the domain of the function is t ≥ 08 feetStep-by-step explanation:
The zeros are the values of t that make the factors zero.
1 -t = 0 ⇒ t = 1
8 +16t = 0 ⇒ t = -8/16 = -1/2
The equation is used to model height after the ball is thrown. We don't expect it to be a good model before the ball is thrown (t < 0), so the zero in that region is extraneous.
Only the positive zero is in the function's domain, so that is the only one that is meaningful.
__
When t = 0 (at the time the ball is thrown), the function value is ...
h(0) = (1 -0)(8 +0) = 8
The ball is thrown from a height of 8 feet.
Use the Pythagorean Theorem to confirm the three sides of a right triangle.
3. a = 5, b = 12,c = 13
4. a = 4, b = 10,0 = 20
Answer:
3) confirmed right triangle
4) not a right triangle
Step-by-step explanation:
3) 5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
4) 4^2 + 10^2 = 20^2
16 + 100 = 400
116 does not equal 400
Find the value of x.
Answer:
[tex]x + 1 + x + 3 = 180[/tex]
by vertically opposite angle theorem
[tex]x + x + 1 + 3 = 180[/tex]
[tex]2x + 4 = 180[/tex]
[tex]2x = 180 - 4 = 176[/tex]
[tex]x = \frac{176}{2} [/tex]
[tex]x = 88[/tex]
have a nice day
What is the square root of ten rounded to the nearest 100th
Answer:
3.162
Step-by-step explanation:
√10 = 3.162
Answer:
Step-by-step explanation:
I hope I can use a calculator and not use logs or a type of long division!
√10 = 3.16227
The hundredth place is the 6. The next place is a 2 which does not have any effect on the 6.
Answer: 3.16
write the equation in slope intercept form from the information given
slope=2/7 y-intercept=0
Answer:
y = 2/7x
Step-by-step explanation:
What is the solution to the equation below? Round your answer two decimal places. 3^x = 9.2
3x = 9.2 ⇒ x = 2.02000606
Answer:
X=2.02
Step-by-step explanation:
Help me Please I will give brainliest! (please dont answer if you dont know)
Answer:
16.5 feet or
about 17 feet long.
Step-by-step explanation:
A = bh
Squares have equal side lengths all around so with there being 4 sides, you will take 66 and divide by 4.
66 ÷ 4 = 16.5
So it is about 17 feet
Here is an expression: 4•3^x
a. Evaluate the expression when x = 2
b. Evaluate the expression when x = 4.
Answer:
First one is 36 and second one is 324!!!
Which of the following represents a polynomial expression? Select one: A. 2x + 3log(x) + 5 B. 10x−−√ − 2 C. (x + 1)(x - 1) D. 4x + 2(3x + 3)
Answer:
none!
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
Explanation: I searched up "what don't polynomials have"
There are 230 cal in 4 ounces of a type of ice cream how many calories are in 6 ounces of that ice cream
Answer: 345 cal
Step-by-step explanation:
Solution 1:
230/4 = x/6
4x = 6(230) use cross multiply
4x = 1380
x = 345 cal
Solution 2:
Cal in 1 ounces: 230/4 = 57.5cal/ounces
Cal in 6 ounces: 57.5cal/ounces x 6 = 345 cal
Which of these is the quadratic parent function?
f(x) = x2
f(x) = |x|
f(x) = x
f(x) = 2x
Answer:
the first one
f(x) = x²
its making me write more
I have to find the value of x
k so I tried, and honestly I'm not sure what I'm doing wrong but I'm not sure how to solve it. If anyone could help that would be lovely :') thank youu
Answer:
x = 25
Step-by-step explanation:
A quadrilateral is inscribed in a circle, so it is a cyclic Quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
Therefore,
3x + 21y = 180°.....(1)
2x + 26y = 180°.....(2)
From equations (1) & (2)
3x + 21 y = 2x + 26y
3x - 2y = 26y - 21y
x = 5y
y = 1/5 x
Plug y = 1/5 x in equation (1)
3x + 21*1/5x = 180
15x + 21x = 180*5
(Multiplying both sides by 5)
36x = 900
x = 900/36
x = 25
URGENT!!!!
Find Perimeter of the square with the side 15 in.
Use formula P=4s
100 in
60 in
225 in
30 in
Answer:
It's 60 in
Step-by-step explanation:
P = 4s
P = 4 x 15
P = 60 in
9 + 15m
factorisation of algebraic expression that contain common factor
Answer:3(3+5m)
Step-by-step explanation:
Solve 2x + 6 less than 10
2x2=10
Step-by-step explanation:
2x2==2+2=4
4+6=10
Isabel has 6.75 bags of coffee. A full bag weighs 5.2 pounds. How many pounds of coffee does Isabel have? *
11.77
11.95
31.5
35.1
which one ^
Answer:
35.1
Step-by-step explanation:
6.75x5.2=35.1
What's the answer to this questions?
42
40
x
Find the unknown side length, x. Write your answer in simplest radical form.
A. 2.41
B. 429
C. 48
D. 58
Answer:
Your answer is D. 58
Step-by-step explanation:
x= [tex]\sqrt{(42^2+40^2)}[/tex]
how far is 18 from -14 on a number line
Answer:
32
Step-by-step explanation:
add the absolute value of -14 and 18
If you are going 250 miles somewhere and it cost 75 cents per mile how much money is that
Answer:
$187.50
Step-by-step explanation:
Set up an equation
250 m/$x = 1 m/$0.75
Cross multiply
250 miles × $0.75 = 1x
$187.50 = x
Guys Im so confused right now on these questions please stop and help meh
Answer:= 293.09
Step-by-step explanation:
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d)
The size is 22.6 degrees, but how did they get it?
Answer:
Step-by-step explanation:
a). Since, BC is perpendicular to the plane FEDC, measure of angle BCD = 90°
By applying Pythagoras theorem in ΔBCD,
BD² = BC² + CD²
BD² = (10)² + (24)²
BD = √676
BD = 26 cm
B). Surface area of the wedge = Sum of all the surfaces of the wedge
Area of BCD = Area of AEF = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(10)(24)[/tex]
= 120 cm²
Area of CDEF = Length × Width
= ED × CD
= 26 × 24
= 624 cm²
Area of BCFA = 10 × 26 = 260 cm²
Area of ABDE = ED × BD
= 26 × 26
= 676 cm²
Total surface area of the wedge = 2(120) + 624 + 260 + 676
= 1800 cm²
C). Volume of the triangular prism = Area of the triangular base × Height
= (Area of BCD) × DE
= 120 × 26
= 3120 cm³
d). By applying sine rule in the right triangle BCD,
sin(∠BDC) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{BC}{BD}[/tex]
m(∠BDC) = [tex]\text{sin}^{-1}(\frac{10}{26})[/tex]
= 22.6°
Select the word to make the statement true.
Similar polygons are ____ the same size.
A. always
B. sometimes
C. never
Answer:
B.
Hope that helps!
Step-by-step explanation:
Answer:
B. Sometimes
Step-by-step explanation:
Hope this helps!
1/6=n+7/9 what does n equal
Answer:
n=-11/18
Step-by-step explanation:
1/6=n+7/9
Change the sign and move the variable to the left hand side
-n+1/6=7/9
Change its sign and move constant to the right hand side
-n=7/9-1/6
Subtract the fractions
-n=11/18
Change the sign on both sides
n=-11/18
Alex was thinking of a number. Alex doubles it the adds 20 to get answer of 22.7. What was his original number.
Answer:
2.7
Step-by-step explanation:
Let the number alex think be x
Answer = 22.7
According to the question,
x + 20 = 22.7
x = 22.7 - 20
x = 2.7
Therefore, his original number is 2.7
Plz mark me as brainliest
Have a great day
33°
114"
33
A) right scalene
B) acute scalene
C) obtuse isosceles
D) equilateral
Answer:
b acute I think so ok but that was a weird quistoin
The triangle below are similar find the lengths of the missing side.
Answer:
The answer is b =9
Step-by-step explanation:
20:12=15:b
5:3=15:b
cross multiply
5×b=3×15
5b=45
divide both sides by 5
b=45÷5
b=9
how do i find the volume in 3d shapes, please help i need to get better grades
$4000 is compounded annually at a rate of 7% for 7 years.
Answer:
hey i think its $16,819 i'm so sorry if i get it wrong
Step-by-step explanation: