Answer:
a = 5, b = - 13
Step-by-step explanation:
The Remainder theorem states that the remainder when f(x) is divided by (x - a) is equal to f(a)
Thus the remainder for division by (x + 2) is zero , then by substituting x = - 2 into the expression.
2(- 2)³ + a(- 2)² + b(- 2) - 30 = 0
2(- 8) + 4a - 2b - 30 = 0
- 16 + 4a - 2b - 30 = 0
- 46 + 4a - 2b = 0 ( add 46 to both sides )
4a - 2b = 46 → (1)
----------------------------------------------------
Similarly when f(x) is divided by (cx - a) the remainder is f([tex]\frac{c}{a}[/tex] )
The remainder on dividing by (2x - 1) is - 35, then by substituting x = [tex]\frac{1}{2}[/tex]
2([tex]\frac{1}{2}[/tex] )³ + a([tex]\frac{1}{2}[/tex] )² + [tex]\frac{1}{2}[/tex] b - 30 = - 35
2([tex]\frac{1}{8}[/tex] ) + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b - 30 = - 35 ( add 30 to both sides )
[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b = - 5 ( multiply through by 4 to clear the fractions )
1 + a + 2b = - 20 ( subtract 1 from both sides )
a + 2b = - 21 → (2)
Solve (1) and (2) simultaneously )
Add (1) and (2) term by term to eliminate b
5a = 25 ( divide both sides by 5 )
a = 5
Substitute a = 5 into (2)
5 + 2b = - 21 ( subtract 5 from both sides )
2b = - 26 ( divide both sides by 2 )
b = - 13
According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). The value of a and b are 5 and -13, respectively.
What is the Remainder theorem?According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.
Using the remainder theorem we can write,
f(x) = 2x³+ ax² + bx - 30
f(-2) = 2(-2)³ + a(-2)² + b(-2) - 30 = 0
-16 + 4a - 2b - 30 = 0
4a - 2b = 46 ........ equation 1
f(x) = 2x³+ ax² + bx - 30
f(1/2) = 2(1/2)³ + a(1/2)² + b(1/2) - 30 = -35
(1/4) + a(1/4) + b(1/2) = -35 + 30
(1+a+2b)/4 = -5
1 + a + 2b = -5 × 4
a + 2b = -21 .......... equation 2
Adding the two equations,
4a + 2b + a - 2b = 46 - 21
5a = 25
a = 25/5
a = 5
Substitute the value of a in any one of the equation,
a + 2b = -21
5 + 2b = -21
2b = -21 - 5
2b = -26
b = -26/2
b = -13
Hence, the value of a and b are 5 and -13, respectively.
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Help plz due in 20 min
Answer:
its either the 3rd one or the 5th one
sorry hope this helps a little bit
Step-by-step explanation:
Answer:
49½+5½
Step-by-step explanation:
Because here, we have 7√5, which we can place the two numbers in index form, 7 is equal to√49 which is 49½ and √5 is equal to 5½. So the answer is 49½•5½
The surface area of a cone with radius r units and slant height s units is shown below: Surface area = 3.14(rs + 2) Part A: Ifr= 6 units and s = 4 units, write an expression that can be used to calculate the surface area of the cone. (4 points) Part B: What is the surface area of the cone? Show your work. (6 points)
Answer:
188.4 units²
Step-by-step explanation:
Hi there!
Part A
Surface area of a cone = [tex]3.14(rs+r^2)[/tex] where r is the radius of the base and s is the slant height
⇒ r = 6
Replace r with 6
[tex]3.14(6s+6^2)[/tex]
⇒ s = 4
Replace s with 4
[tex]3.14(6*4+6^2)[/tex]
Part B
Evaluate the expression found in Part A:
[tex]3.14(6*4+6^2)[/tex]
Find 6²:
[tex]=3.14(6*4+36)[/tex]
Find 6*4:
[tex]=3.14(24+36)[/tex]
Find 24+36:
[tex]=3.14(60)\\=188.4[/tex]
Therefore, the surface area of the cone is 188.4 units².
I hope this helps!
4/10 divided by 5/8
Answer:
16/25
Step-by-step explanation:
keep the first fraction the same, make the second fraction 8/5, and then multiply the two fractions across.
Helppp me pleaseee!!!!!!!!!!
Answer:
A
Step-by-step explanation:
-4.5+4.4= -0.1
-0.1 + x = 0
So the answer needs to be equal to 0.1.
-6.7+6.8= 0.1
-4.5+4.4 -6.7+6.8 =0
What is an equation of the line that passes through the point (-1, 4) and is perpendicular to the line x-6у = 12?
Answer:
y=-6x-2
Step-by-step explanation:
x-6y=12
y=x/6-2
y=mx+c
since theyre perpendicular, 1/6 * m = - 1
m = -6
y=-6x+c
sub x=-1,y=4
4=-6(-1)+c
c = -2
y=-6x-2
if 6 pipes fill a tank in 120 minutes, then 5 pipes can fill it in how many minutes
Answer:
It'll take 144 minutes for 5 pipes.
Step-by-step explanation:
[tex]{ \sf{6 \: pipes = 120 \: mins}} \\ { \sf{5 \: pipes = ( \frac{6}{5} \times 120) \: mins}} \\ \\ = { \sf{144 \: mins}}[/tex]
but practically, it seems to be abnormal. if 6 pipes take 120 mins, 5 pipes must takes a time greater than 120 mins cause amount of water flowing to the tank is decreasing.
But there is a possibility that pressure of water was increased for the case of five pipes, that's why it takes a time less than 120 mins. (t < 120)
Answer:
144 minutes
Step-by-step explanation:
here we use inverse proportion because the more pipes there are the less time is needed
the formula for inverse proportion is y = k/x
first we need to find k which is the constant
if y is the number of minutes and x is the number of pipes we can substitute these into the formula like so: 120 = k/6
to find k rearrange the formula to get k = 6 * 120 = 720
now that we have k we can substitute 720 (k) and 5 (x) into y = k/x
y = 720 / 5
y = 144
(y is the number of minutes in this case so the answer is 144 minutes)
1. Write the following numbers in the expanded form:
(i) 20.03
(ii) 200.03
(iii) 2.034
Answer:
(I). 20.03:
[tex] = 2.003 \times {10}^{1} [/tex]
(ii). 200.03
[tex] = 2.0003 \times {10}^{2} [/tex]
(iii). 2.034
[tex] = 2.034 \times {10}^{0} [/tex]
What does this symbol mean ~=
Answer:
It means that it is approximately equal to or about/around.
Jonathan drinks four and three sixths cups of water in the morning and three and two sixths in the evening. How much did Jonathan drink in all?
Answer:
2 cups
Step-by-step explanation:
3 + 3 = 6 (one cup)
4 + 2 = 6 (two cups)
A wire 24 inches long is to be cut into four pieces to form a rectangle with one side of length x. Write the area A of the rectangle as a function of x.
Answer:
If the function is the Area, then Area = length*width = x*(12-x) = 12x - x^2Domain is x>0, since you can't have a rectangle with negative length.
0 < x<6, If x is 7 then width would be 5, but x must be shorter
Step-by-step explanation:
Slope-Intercept Form
Directions: Re-write the equation of
the line in slope-intercept form.
Slope must be in simplest/fraction
form. Do NOT put any spaces in
your answer.
Standard Form
2x+y=8
3x-y=7
5x+2y=8
4x+3y=9
X-y=0
x+4y=16
4x-3y=6
x+2y=-10
x+y=3
3x-2y=9
(Please vote me Brainliest if this helps!):
y = -2x + 8y = 3x - 7y = [tex]-\frac{5}{2}x[/tex] + 4y = [tex]-\frac{4}{3}x[/tex] + 3y = x + 0y = [tex]-\frac{1}{4}x[/tex] + 4y = [tex]\frac{4}{3}x[/tex] - 2y = [tex]-\frac{1}{2}x[/tex] - 5y = -x + 3y = [tex]\frac{3}{2}x - \frac{9}{2}[/tex]
What’s the answer ASAP
Answer:
none
Step-by-step explanation:
38×2=76
43×2=86
45×2=90
twice a number added to the product of 14 and 2 is 30. find the number
Answer:
1
Step-by-step explanation:
2x + (14 • 2) = 30
2x + 28 = 30
2x = 30 - 28
2x = 2
x = 2/2
x = 1
Hope this helps you. Do mark me as brainliest.
Define terminating and non terminating decimals.
Answer:
terminating decimals has an end digit and has a finite number of digits.
Non-terminating has no end term and has an infinite number of terms.
YA'LL ARE SMART!! PLEASE HELP!!
Answer:
Its C
Step-by-step explanation:
Substitute in 3 for x and check. The equation doesn't work.
Substitute 2 in for y. The equation still doesn't work.
So its right.
lol are u using edguenity
rip
616÷2=308. I got 38 instead of 308 when solved with long division
Answer:
U forgot to add zero while dividing
Solve for X: 2^3x + 1 = 2^10
please look at photo and give detailed steps!! thank you
Step-by-step explanation:
since the bases are the same all you have to do is just get the powers of both bases which is 3x + 1 and 10
you're then going to equate 3 x + 1 to 10 and then you have to make +1 cross to the other side making it become -1
you then can subtract 1 from 10 leaving you with 9
and at the LHS we have 3x
we are gonna get rid of the three by dividing it into itself and the 9 at the RHS then X = 3
14.127 divided by 5.1 show work please
The quotient of 14.127 divided by 5.1 is 2.77
14.127 ÷ 5.1
To make the calculation easier without the use of a calculator :
Multiply both sides such that bith the dividend and divisor are integer values :
Multiply both by 1000
14.127 × 1000 = 14127
14127 51 × 1000 = 5100
Hence,
14127 ÷ 5100 = 14127 / 5100 = 2.77
Hence, 14.127 ÷ 5.1 = 2.77
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4. Write the equation of the line that
passes through (9,4) (0-5)
Answer:
Equation of line is y = x - 5
Step-by-step explanation:
general equation of a line:
[tex]y = mx + c[/tex]
m » slope
c » y-intercept
for the slope, m :
[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1} } [/tex]
substitute in accordance of the points:
[tex]slope = \frac{ - 5 - 4}{0 - 9} = \frac{ - 9}{ - 9} \\ \\ m= 1[/tex]
for y-intercept :
[ consider point (0, -5) ]
[tex]y = mx + c \\ - 5 = (0 \times 1) + c \\ c = - 5[/tex]
Therefore, equation of line is
[tex]{ \boxed{y = x - 5}}[/tex]
The graph represents a function.
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
O (0,0)
0 (-3,1)
0 (1,3)
O (31)
If we consider the ordered pair (0,0) then only the graph still represents a function.
How to define a graph represent a function?
In a function, there can not be two different values of x corresponding to the same value of y.
Here, the points on the graph are (0,0), (-3,1), (1,3) and (3, 1).
If we consider point (-3,1) then there will be two points corresponding to the same y value i.e. (-3,1) and (3, 1).
The values of x for a single value of y.
i.e. y = 1.
So, if we consider the ordered pair (0,0) then only the graph still represents a function. Therefore, the correct answer is option (a) (0,0).
To learn more about the graph
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4.) Which equations below have no solution? Select all that apply, and justify your response with work. a.) x - 9 = 2(x - 3) + 12 b.) 5(-2x + 7) + 3 = -10x + 38 1 c.) (6x - 4) = 3(x - 2) 1 d.) 0.01x + 0.001 = (x + 10) 100 e.) 3(x + 2) + 1 = x + 2(4 + x)
Answer: Equations (b) and (e) do not have solutions
Step-by-step explanation: b) The x cancels out (-10x + 35) = -10x + 318; 35 = 318???? NO. e) 3(x + 2) + 1 = x + 2(4 + x); 3x + 7 = 3x + 8. The x cancels out again.
The other s can be solved for x.
Hi! I'm happy to help!
To solve this, we need to simplify all of the equations. There are 3 ways equations like this can go, infinitely many solutions, 1 solution, or no solution. Infinitely many is something like 6=6, that could mean infinite solutions because 6 always equal 6, and would apply in infinitely many ways. (in the equation) One solution refers to something like x=6. This tells your exactly what x is, and that is your only solution. (for the equation) And no solution is something like 5=6, 5 will never equal 6, so that is no solution. (to the equation)
Now, let's start out with our first equation. To find if our equations have solutions or not, we need to simplify them. We do this by singling out x to see what the solution is (if there is one).
x-9=2(x-3)+12
We can multiply 2, by x and -3 inside of the parenthesis, to simplify:
x-9=2x-6+12
Since we have at least one x on both sides, we can subtract it to isolate it:
x-9=2x-6+12
-x -x
-9=x-6+12
Combine -6 and twelve:
-9=x-6+12
-9=x+6
Now, we subtract 6 to fully isolate x:
-9=x+6
-6 -6
-15=x
We see we have 1 solution, so you should not pick option 1.
Second equation:
5(-2x + 7) + 3 = -10x + 38
We should first multiply the parenthesis:
-10x+35+3=-10x+38
Since we want to simplify, let's add 10x on both sides
-10x+35+3=-10x+38
+10 +10x
35+3=38
Add 35 and 3:
38=38
Since 38 will always equal 38, there are infinite solutions, and you should not pick option 2.
Third equation:
(6x - 4) = 3(x - 2)
Since there is nothing outside of the parenthesis (right side), we don't need them:
6x-4=3(x-2)
From here, multiply the parenthesis:
6x-4=3x-6
Subtract 3x from both sides:
6x-4=3x-6
-3x -3x
3x-4=-6
Add 4 to both sides to isolate x:
3x=-2
Divide both sides by 3, to fully isolate x:
x=-[tex]\frac{2}{3}[/tex]
Since there is only 1 solution, you should not pick option 3.
Fourth equation: (not sure if the 100 is supposed to be there)
0.01x + 0.001 = (x + 10)
First, let's subtract 0.01x from both sides:
0.001=9.99x+10
Then, we subtract 10 from both sides to start isolating x:
-9.999=9.99x
Then, we divide both sides by 9.99:
______
1.000900900=x
Kind of a weird number, but regardless, you should not pick option 4, because it has 1 solution.
Fifth equation:
3(x + 2) + 1 = x + 2(4 + x)
First, let's multiply the parenthesis on both sides:
3x+6+1=x+8+2x
Combine like terms:
3x+7=3x+8
Subtract 3x from both sides:
7=8
7 will never equal 8, there will be no solution, and you should pick option 5.
You should pick option e, because it has no solution.
I hope this was helpful, keep learning! :D
HELP BRAINIEST TO WHOEVER RIGHT
Answer:
180 degrees
Step-by-step explanation:
Two angles are called supplementary when their measures add up to 180 degrees.
I don’t understand this
Answer:
Yes
Step-by-step explanation:
Statement 1: If JK and LM bisect each other then, they divide each other in 2 equal parts.
So,
JP = PK [Because of statement 1]
MP = PL [Because of statement 1]
∠JPM = ∠LPK [Because they are vertically opposite angles]
So, ΔJPM ≅ to ΔKPL [By SAS congruence criteria of triangle]
look at the image bellow<3
Answer:
1770000, 1800000
Step-by-step explanation:
1770000
Answer:
1,770,000 & 1,780,000
Step-by-step explanation:
Rounding, I suppose
Use the similar shape concept of geometry to find the missing value (x). Round your answer to the nearest tenth if necessary.
7 in
3 in
x in
4 in
Step-by-step explanation:
7:3
4:x
-cross multiply
7x = 12
x = 12÷7
x = 1.7
Help!! Truth Table
Thank you!!
Answer:
Step-by-step explanation:
[tex]\begin{array}{c|c|c|c|c}p&q&r&p \vee q&(p \vee q)\ =>\ r\\---&---&---&---&------\\T&T&T&T&T\\T&T&F&T&F\\T&F&T&T&T\\T&F&F&T&F\\F&T&T&T&T\\F&T&F&T&F\\F&F&T&F&T\\F&F&F&F&T\\---&---&---&---&------\\\end{array}[/tex]
what is the length of an arc subtended by an angle of 1.25 radians in a circle with a diameter of 24 cm?
Answer:
15 cm.
Step-by-step explanation:
Recall that the arc-length of a circle is given by the formula:
[tex]\displaystyle s = r\theta[/tex]
Where r is the radius and θ is the measure of the central angle in radians.
The circle has a diameter of 24 cm, so its radius is 12 cm.
And its central angle is 1.25 radians. Hence, the arc-length will be:
[tex]\displaystyle s = \left(12\right)\left(1.25\right) = 15\text{ cm}[/tex]
In conclusion, the arc-length for a circle with a diameter of 24 cm subtended by a central angle of 1.25 radians is 15 cm.
Rony earns 17 dollars less than half of what John earns. If John earns p dollars, how much does Rony earn in dollars?
a. p - 1/2
b. 1/2 + p
c. (p/2) - 17
d. 17 + (p/2)
Answer:
The correct choice is option c. (p/2) - 17
help me to solve this question
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Addition, subtraction, and multiplication by a scalar all work on a term-by-term basis. For example the upper left term of A+2B is (2) +2[2] = 6, where (2) is the upper left term of A, and [2] is the upper left term of B.
It is convenient to let your graphing calculator or a spreadsheet do the repetitive arithmetic for you. Attached is the result of using the free Go.ogle Sheets spreadsheet.
Simplify this algebraic expression with the steps