Given :-
f(x) = 2x² - x + k .When f(x) is divided by (x-1) , the remainder is 3 .To Find :-
The value of k .Solution :-
Here we are given that ,
→ f(x) = 2x² - x + k
By Remainder Theorem , if f(x) is divided by x-a , then the remainder is f(a) .Hence here is f(x) is divided by x-1 , then the remainder will be f(1) . On substituting x = 1 , we have ,→ f(x) = 2x² - x + k
→ f(1) = 2(1)² - 1 + k
f(1) = 3 ,→ 3 = 2*1 -1 + k
→ 2 -1 + k = 3
→ k +1 = 3
→ k = 3-1
→ k = 2
Hence the value of k is 2 .
I hope this helps.
Convert the statement into if-then form, "Squares have right angles."
Answer:
If the shape is a square, then it has right angles.
Answer:
If a shape is a square, then it has right angles.
Step-by-step explanation:
Hi there!
The statement 'squares have right angles' tells us that any and all squares have right angles. Therefore, if a shape is a square, then it has right angles.
I hope this helps!
It will be lovely if anyone would help?
Answer:
yes
Step-by-step explanation:
I would help. Just give me the question
Can anybody help me with this
Answer:
c ≈ 9.1 m
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
c² = 4.1² + 8.1² = 16.81 + 65.61 = 82.42 ( take square root of both sides )
c = [tex]\sqrt{82.42 }[/tex] ≈ 9.1 m ( to the nearest tenth )
can you please tell me how to do easy way can you please show me in numbers how to multiply
[tex] \frac{2 }{3} - \frac{1}{9} [/tex]
same as before, we look at the denominators, hmmm do a quick prime factoring.
3 = 3 * 1
9 = 3 * 3 * 1
since 9 already contains 3 and 1, we can us that
[tex]\cfrac{\underline{2}}{3}~~ - ~~\cfrac{1}{9}\implies \cfrac{(2)\underline{2}~~ - ~~(1)1}{\underset{\textit{using this LCD}}{9}}\implies \cfrac{4-1}{9}\implies \cfrac{\stackrel{1}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{3}{~~\begin{matrix} 9 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{1}{3}[/tex]
Average house prices in Hobart are expected to grow by 8%
per year for the next 5 years. What is the expected average
value of a house in Hobart in 5 years time, to the nearest
dollar, if it is currently valued at $370000?
Answer:
518000 if it increases 8% per year
Step-by-step explanation:
8 times 5, because there are 5 years, is 40%
we take 40% out of 370000 and we get 148000 then we add 370000 and 148000 together and we get 518000
Order the numbers from least to greatest. -1.895, -1.95, -1 , a. 15 -1.895, -1.95 b. -1.95, -1.895, -1 . -1.95,-1,-1.89 d. 1.895, -1.95, -1 WOMALOWAS Please select the best answer from the choices provided B c D
Answer:
Step-by-step explanation:
uhhhh O-1.895, -1.95, -1 , a. 15 -1.895, -1.95 b. 1.95-, -1.895, -1 . -1.95,-1,-1.89 d. 1.895, -1.95
The larger the negative number, the lower the value the number actually is.
Answer: b. -1.95, -1.895, -1
If a(x)=5x^2+7x+4 and b(x)=4x^2+3x+2
Then 4a(x) + 2b(x) =
Answer:
[tex]28x^2+34x+20[/tex]
Step-by-step explanation:
figure out 4a(x) and 2b(x) separately by distributing, and then add them together to get your answer.
hope this helps :)
The Amount of sales tax on a new car varies directly to the purchase price of the car. On a 25,000 car, sales tax is 1,750. What's the purchase price of a new car with 3,500 in sales tax?
Please show your work because I still don't understand it and don't know how to do it.
Answer:
50,000
Step-by-step explanation:
1st car had $1,750 tax
2nd car has $3,500 tax
1750(2) = 3500
so your tax doubled so the price must be doubled.
The car is $50,000
Algebraically using direct variation:
t = kp where t=tax, p = purchase price,
and k is constant of variation
1750 = 25000k
k = 1750/25000
k = 0.07
Your equation is: t = 0.07p
3500 = 0.07p
p = 3500/0.07
p = $50,000
1.5 divided by 12
i want an explanation cuz i don't know how to divide a small decimal with a larger number
Step-by-step explanation:
1.5 ÷ 12
1½÷12
³/²÷12
3/2 *1/12
3/24
1/8
4) Shown below is a series of steps to solve the equation 4x + 2(x - 4) = 28.
Given: 4x + 2(x - 4) - 28
Step 1 = 4x + 2x - 8 = 28
Step 2 => 6x - 8 = 28
Step 3 => 6x - 8 + 8 = 28 + 8
Step 4 = 6x = 36
6x36
Step 5
6 6
Step 6 => x = 6
Which THREE statements are correct?
A) Step 1 is justified by the distributive property.
B) Step 2 is justified by the subtraction property of equality
C) Step 3 is justified by the addition property of equality
D) Step 4 is justified by the additive Identity property.
E) Step 5 is justified by the division property of equality
Find the value please and ty
Answer:
-3
Step-by-step explanation:
The value of f(-3) can be found at looking at the x-value of -3, then drawing a vertical line. If you look at the point where the vertical line hits th graph, you get the point (-3,-3)
The y-value is what we are looking for, which is -3.
-Chetan K
6/9×1/2=
please simplify
please and thank you
Answer:
1/3
Step-by-step explanation:
[tex]\frac{6}{9}*\frac{1}{2}[/tex]
[tex]\frac{6*1}{9*2}[/tex]
[tex]=\frac{6}{18}[/tex]
Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(6,18) = 6
[tex]\frac{6/6}{18/6}=\frac{1}{3}[/tex]
Therefore:
[tex]\frac{6}{9}*\frac{1}{2}=\frac{1}{3}[/tex]
[RevyBreeze]
NIE
VIEW
(Score for Question 3: of 5 points)
Admissions to a zoo cost $12 for adults and $8 for children. A group of 34 people attending the zoo paid a
total of $312 in admission fees
(a) Write and solve a system of equations that model the problem. Show all your work,
(b) How many adults went to the zoo?
(c) How many children went to the zoo?
Answer:
Hi!
Please see the attached image for your answer with explanation.
Have a great day!
Need help with this question ASAP for geometry!
Can the triangles be proven similar?
-
Find the 7th term of the arithmetic sequence – 2x – 1, 4x – 5, 10x - 9, ...
Help
How do you solve?
2.5 x 1/4=
here you go, hope this helps
Please help me asap!
Answer:
[tex]-3+2\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{3} -\sqrt{6}}{\sqrt{3} +\sqrt{6}}[/tex]
[tex]=\frac{(\sqrt{3} -\sqrt{6})(\sqrt{3} -\sqrt{6})}{(\sqrt{3} +\sqrt{6})(\sqrt{3} -\sqrt{6})}[/tex]
[tex]=\frac{9-6\sqrt{2} }{-3}[/tex]
[tex]=\frac{3(3-2\sqrt{2} )}{-3}[/tex]
[tex]=-(3-2\sqrt{2})[/tex]
[tex]=-3+2\sqrt{2}[/tex]
Mary sold 50 tickets for the school play Student tickets cost $2 and adult tickets cos $ 5. Mary's sales totaled $ 154.00. How many adult tickets and how many student tickets did Mary sell?
Answer:
the correct answer is that mary sold 18 adult tickets and 32 student tickets
if she sold 18 adult tickets it would be 90 dollars, and if she sold 32 student tickets she would get 64 from that, if we add the amount of people that bought tickets and how much she got it would work out
with 18 adults+32 students being exactly 50
and 90+64 being 154.
I tried different solutions, I did 18 adults and 32 Students, since there are 50 tickets sold, this is the correct answer since if we do this the amount she makes from the adults will be 90 and she will make 64 from the students this will add up to $154
Graph the solution to this inequality on the number line.
−12≥−4p
Answer:
A closed circle on 3 going right.
Step-by-step explanation:
-12 ≥ -4p
/-4 /-4
3 ≤ p which also mean p ≥ 3
This will be a closed circle on 3 going right.
Hope that helps!
64x-16 I need 3 equivalent expressions
Answer:
8 (8x - 2)
(64) x X - 16
4 (16 x- 4)
Step-by-step explanation:
Write an equation for the line in point-slope form and then convert it to standard form. through (2, 3) and (3,5)
Answer:
equation of the line: 2x - y = 1
Step-by-step explanation:
Given coordinates: (2, 3) and (3,5)
find slope of the equation:
[tex]\frac{y2-y1}{x2-x1}[/tex]using the formula:
→ [tex]\frac{5-3}{3-2}[/tex]
→ [tex]2\\[/tex] .............this is slope, also refereed as (m) in short form.
using the equation formula:
y - y1 = m ( x - x1 )using the formula:
→ y - 3 = 2 ( x - 2 )
→ y - 3 = 2x - 4
→ y = 2x -4 +3
→ y = 2x - 1
→ -2x + y = -1
→ (-2x + y)/-1 = -1 /-1 [ divide both sides by -1 ]
→ 2x - y = 1 .......final answer in standard form where ( Ax + By = C ) where "A" should be positive and "C" constant on the right hand side.
HELP ME NOWWW PLS K12
Answer:
2 units
Step-by-step explanation:
for each order, the website applies a 7. 7% sales tax to the price of the cards
Answer:
what's the full question...?
Step-by-step explanation:
What is the radius and diameter of 11cm
Answer: Radius=11cm Diameter=22cm
Step-by-step explanation:
Alexa put $850 into savings account that earns 0.75% annual simple interest. If Alexa doesn’t make any deposits or withdrawals for 18 months, how much money will be in her account?
Principal= 850
rate = 0.75%
period = 18months
interest = 850x0.75%x18
= 850x0.0075x18
= 114.75
amount after 18 months
= 850+114.75 = $964.75
Can someone help me!?
Answer:
A
Step-by-step explanation:
Set equation equal to 0
six tickets were purchased a total cost pf $345. the cost of each ticket includes a $11.25 fee. what was the price of each ticket before the fee was applied?
Answer:
57.50
Step-by-step explanation:
simply divide 345/6 which equals 57.5 which is 57.50
Answer:
price before fee was applied is $46.25
Step-by-step explanation:
$345/6= $57.5
divide total cost by number of tickets bought
$57.5-$11.25= $46.25
subtract the fee applied
If line q bisects EG at point T, and if ET= 1/3 x and TG= x-2, then find EG
please help I have no idea how to do this its geometry problem for my math hw even my parents and siblings who are older than me don't know how to do this
Answer:
EG = 2 units
Step-by-step explanation:
Given that line q bisects EG at T , then
ET = TG ( substitute values )
[tex]\frac{1}{3}[/tex] x = x - 2 ( multiply through by 3 to clear the fraction )
x = 3x - 6 ( subtract x from both sides )
0 = 2x - 6 ( add 6 to both sides )
6 = 2x ( divide both sides by 2 )
3 = x
Then
ET = [tex]\frac{1}{3}[/tex] x = [tex]\frac{1}{3}[/tex] × 3 = 1
TG = x - 2 = 3 - 2 = 1
Thus
EG = ET + TG = 1 + 1 = 2 units
EG = [tex] \frac{4x}{3} - 2[/tex]
Step-by-step explanation:
( First check the attached image for diagram )
[tex]EG=ET+TG[/tex]
Substituting the given values,
[tex]EG = \frac{1}{3}x + (x - 2)[/tex]
Opening the brackets and multiplying,
[tex]EG = \frac{1 \times x}{3} + x - 2 [/tex]
[tex] = > EG = \frac{x}{3} + x - 2[/tex]
Finding LCM,
[tex] = > EG = ( \frac{x}{3} + \frac{x \times 3}{1 \times 3} ) - 2[/tex]
[tex] = > EG = ( \frac{x}{3} + \frac{3x}{3}) - 2[/tex]
Combining them,
[tex]EG =( \frac{x + 3x}{3}) - 2[/tex]
[tex]EG = \frac{4x}{3} - 2[/tex]
Note:- T is midpoint of EG
because ET = TG
Please help me with this math problem!! NO LINKS PLEASE!! I will give brainliest!!
Answer:
z = 7, x = 3, y = 20
Step-by-step explanation
3z + 5 = 26
3z = 21
z = 7
NP = NQ x 2
8x - 4 = 4x + 8
4x = 12
x = 3
y = pq/2
p = y; q = 10
10 x 2 = 20
y = 20
I hope this helps!
aayan gets 48 out of 60 in his music exam. state the result as a percentage
Answer:
It can be set up as: 48/60
But it can also written as 48 divided by 608. When we put a percent sign we always move the decimal to the right two places. The percentage is 80%