Answer:
Because it helps children and other people understand how the number system works. if you develop number sense you will have a range of different maths strategies like addition subtraction
If f(x)=ax²+bx+c and f(1)=6,f(2)=11,f(3)=18 find the value of a,b,c
f(x) = ax² + bx + c
f(1) = 6
f(2) = 11
f(3) = 18
Find:value of a,b,c
Solution:Substitute x = 1 , 2 , 3 in the given polynomial.
★ f(1) = a(1)² + b(1) + c
⟹ 6 = a + b + c -- equation (1)
Similarly,
★ f(2) = a(2)² + b(2) + c
⟹ 11 = 4a + 2b + c -- equation (2)
★ f(3) = a(3)² + b(3) + c
⟹ 18 = 9a + 3b + c -- equation (3)
Subtract equation (1) from (2).
⟹ 4a + 2b + c - (a + b + c) = 11 - 6
⟹ 4a + 2b + c - a - b - c = 5
⟹ 3a + b = 5 -- equation (4).
From equation (3) ,
⟹ 18 - c = 9a + 3b
⟹ 18 - c = 3(3a + b)
Substitute the value of 3a + b from equation (4).
⟹ 18 - c = 3 * 5
⟹ 18 - 15 = c
⟹ 3 = c
substitute the value of c in equation (1).
⟹ 6 = a + b + 3
⟹ 6 - 3 = a + b
⟹ 3 = a + b -- equation (5)
Subtract equation (5) from equation (4).
⟹ 3a + b - (a + b) = 5 - 3
⟹ 3a + b - a - b = 2
⟹ 2a = 2
⟹ a = 1
Substitute a value in equation (5).
⟹ 1 + b = 3
⟹ b = 3 - 1
⟹ b = 2
Therefore,
a = 1
b = 2
c = 3.
I hope it will help you.
Regards.
The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal. What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years?
Answer:
$80
Step-by-step explanation:
From the question, we are given The simple interest formula as I = Prt,
where l = simple interest on an amount= $40
t= years=5years
at a rate r= 10%
The rate= 10/100= 0.1
Then since we are looking for P, we can make P subject of formula from this expression;
I = Prt
P=I/rt
P= 40/(0.1 ×5)
P= 40/0.5
P= 80
therefore, the amount of money p that is needed is $80
Answer:
the answer would be $80. :)
Step-by-step explanation:
Which equation should you use to solve for x?
40°
60°
16x
O 60 + 16x + 40 = 180
O 60 + 40 = 16x
0 60 + 16x = 40
O 60 + 16x + 40 = 90
Answer:
1st Option
Step-by-step explanation:
All angles in a triangle must add up to 180°.
Step 1: Set up equation
40° + 60° + 16x = 180°
Step 2: Rewrite
60° + 16x + 40° = 180°
Answer:
Option: A.
Step-by-step explanation:
Hey there!
In the given triangle;
60° +16x° + 40° = 180° { Sum of interior angle of a triangle}
100° + 16x= 180°
16x = 180° - 100°
[tex]x = \frac{80}{16} [/tex]
Therefore, X= 5°.
So, Option A (equation) is used for solving the value of"X".
Hope it helps...
ANSWER ASAP PLEASE I WILL GIVE BRAINLIEST TO FIRST ANSWER!!!!
Which one would you choose? Explain your reasoning.
1. A 5-pound jug of honey for $15.35
2. Three 1.5-pound jars of honey for $13.05
Answer:
Three 1.5-pound jars of honey for $13.05
Step-by-step explanation:
15.35/5 = 3.07
3x1.5=4.5
13.05/4.5 = 2.90
Four friends get the lunch special at a restaurant and leave a $3 tip. The total amount paid was $26.00. How much does the lunch special cost?
Answer:
23 dollars
Step-by-step explanation:
26 is the total with tax, so subtract the tax to get the lunch by itself
Answer:
it's 5.75
Step-by-step explanation:
first i subtracted 3$ from 26.00 and got 23.00 then i divide 23.00 by 4 and got 5.75 so that's what they payed
The perimeter of a rectangle is 72 inches. The ratio of the width to the length is 4:5. What is the width of the rectangle?
9514 1404 393
Answer:
16 inches
Step-by-step explanation:
The sum of length and width is half the perimeter, so is 36 inches.
The width is 4/(4+5) = 4/9 of the total of length and width, so is ...
(4/9)(36 inches) = 16 inches
The width of the rectangle is 16 inches.
Please answer real quick
Answer:
use symbolab
Step-by-step explanation:
a= 18 in.
C = 82 in.
What is the length of b?
Answer:
B should equal 80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Use Pythagorean theorem so 18^2 +b^2 =82^2 which is 324 +b^2=6724 then subtract 324 on both sides then square root which is 80
Miguel completed the division problem below. What is Miguel's error? 754 divided by 0.52. 52 StartLongDivisionSymbol 7540 EndLongDivisionSymbol minus 52 = 234. 234 minus 208 = 260. 260 minus 260 = a remainder of 0 and a quotient of 145. He included a 5 in the quotient, which does not belong. He multiplied the divisor by 10 and the dividend by 100. He subtracted 208 from 234 incorrectly. He multiplied the divisor by 100 and the dividend by 10.
Answer:
He multiplied the divisor by 100 and the dividend by 10.
Step-by-step explanation:
Given that
Divisor = 0.52
And, the dividend is 754
It can be written as
Divisor is 52 i.e. (0.52 × 100)
And, the dividend is 7540 i.e. (754 × 10)
Now if we multiplied by 100 and divide by 10 so it gives the same result
Therefore the last option is correct and the same is to be considered
And all the other options are wrong
Answer:
D He multiplied the divisor by 100 and the dividend by 10
Step-by-step explanation:
Hope this helps:)
Help with these math questions grade 12
Answer:
1. 15.1%
2. 8.3%
3. 12%
4. 25%
Step-by-step explanation:
1.
percent change = (new number - old number)/(old number) * 100%
percent change = (21300 - 18500)/(18500) * 100%
percent change = 15.1%
A positive percent change is a percent increase.
Answer: The percent increase is 15.1%.
2.
percent change = (new number - old number)/(old number) * 100%
percent change = (298000 - 325000)/(325000) * 100%
percent change = -8.3%
A negative percent change is a percent decrease.
Answer: The percent decrease is 8.3%.
3.
percent change = (new number - old number)/(old number) * 100%
percent change = (110 - 125)/(125) * 100%
percent change = -12%
A negative percent change is a percent decrease.
Answer: The percent decrease is 12%.
4.
percent change = (new number - old number)/(old number) * 100%
percent change = (1500 - 2000)/(2000) * 100%
percent change = -25%
A negative percent change is a percent decrease.
Answer: The percent decrease is 25%.
What is the factored form of 8x^3 - 27y^3?
A. (2x + 3y)(4x^2 - 6xy + 9y^2)
B. (2x – 3y)(4x^2 + 9xy + 6y^2)
C. (2x – 3y)(4x^2 + 6xy + 9y^2)
D. (2x + 3y)(4x^2 - 9xy + 6y^2)
Once the child in the sample problem reaches the bottom of the hill, she continues sliding along the flat, snow-covered ground until she comes to a stop. If her acceleration during this time is -.392m/s^2 how long does it take her to travel from the bottom of the hill to her stopping point
Sample problem is;
A child slides down a steep, snow covered hill with an acceleration of 2.82 m/s². Her initial speed is 0.0 m/s² and her final speed is 15.5 m/s travelling from top to bottom of the hill.
Answer:
t = 39.54 s
Step-by-step explanation:
We are told that her acceleration is now -0.392 m/s²
Thus; a = -0.392 m/s²
From the sample problem, we have;. Initial velocity = 0 m/s
Final velocity = 15.5 m/s
However, in this question, we want to find the time from the bottom of the hill to her stopping point.
This means her initial velocity will now be; u = 15.5 m/s and final velocity since she will come to rest will be v = 0 m/s
To find the time it takes her to travel from the bottom of the hill to her stopping point, we will use Newton's equation of motion and so, we have;
v = u + at
making t the subject, we have;
t = (v - u)/a
t = (0 - 15.5)/(-0.392)
t = 39.54 s
Raymond uses the Venmo
app to transfer money to
his friends. He had $6.50.
He gave $2.95 to Theresa
and received $1.26 from
Peyton. How much money
does he have now?
Answer:
2.29
Step-by-step explanation:
2.95 plus 1.26 is 4.21, and 6.50 minus 4.21 is 2.29.
Determine whether the given function is even,odd,or neither f(x)=2x^2+x^4
And this one help me with
what is the missing angle?
Answer:
the missing angle is 73
Juan's rock collection consists of 8 quartz, 6 turquoise, 4 mica, and 2 silica. What is the percent for each of the given ratios? quartz turquoise mica silica
Answer:
Step-by-step explanation:i need points sorry
Is the expression |-3|+ 4 equal to |-3 + 4| ? Justify your answer.
Answer:
Yes
Step-by-step explanation:
Absolute value keeps a number positive so, the 2 equations both equal 7.
Zn + 2HCI ZnCI2 + h2
Based on the reaction shown above, which statement best supports the law of conservation of mass?
There are more chlorine atoms in the reactant.
There are more hydrogen atoms in the product
The number of chlorine atoms is unequal in the reactants and products
.
The number of reactant atoms is equal to the number of product atoms.
Answer:
The number of reactant atoms is equal to the number of product atoms.
Step-by-step explanation:
F = 9/5C + 32 solve for C
i'm not sure but this is what i got
c=9/5(f−32)
ayo if you answer youll get brainliest
Solve the following Linear Equation.
3a + 2 (2a - 1) = 33
show work pls
Answer:
[tex] \huge{ \boxed{ \tt{a = 5}}}[/tex]
Step-by-step explanation:
[tex] \text{3a + 2(2a - 1) = 33}[/tex]
Distribute 2 through the parentheses
↦[tex] \text{3a + 4a - 2 = 33}[/tex]
Add the terms : 3a and 4a
↦ [tex] \text{7a - 2 = 33}[/tex]
Move 2 to right hand side and change it's sign
↦ [tex] \text{7a = 33 + 2}[/tex]
Add the numbers : 33 and 2
↦ [tex] \text{7a = 35}[/tex]
Divide both sides by 7
↦[tex] \text{7a\: / \: 7 \: = 35 \: / \: 7}[/tex]
↦ [tex] \text{a = 5}[/tex]
Hope I helped!
Best regards! :D
~[tex] \text{TheAnimeGirl}[/tex]
[tex]
\tt{\huge{ {a = 5}}}
[/tex]
Step-by-step explanation:
[tex]3a + 2(2a - 1) = 33 \\
Distribute \: 2 \: through \: the \: parentheses \: \\ 3a + 4a - 2 = 33 \\ 7a - 2 = 33
\\ 7a = 33 + 2\\ 7a = 35 \\
a = 5.\\ ♨Rage♨
[/tex]
HELP ME ASAP BRO THIS IS DUED BY TONIGHT, LITERALLY ANYONE OUT THERE
SHOW THE WORK BRO PLEASEEEE
What is the value of x?
Answer:
14
Step-by-step explanation:
∠AOB is a straight angle, meaning that it is 180°. Since ∠AOC, ∠COD, and ∠DOB are within ∠AOB, the sum of all of the angles is equal to 180°.
∠AOC + ∠COD + ∠DOB = ∠AOB
(5x) + (3x + 30) + (2x + 10) = 180
5x + 3x + 30 + 2x + 10 = 180
10x + 30 + 10 = 180
10x + 40 = 180
10x + 40 - 40 = 180 - 40
10x = 140
10x/10 = 140/10
x = 14
A multiplication table. In the row labeled 3, the numbers 9, 12, 15, and 18 are highlighted. Consider the highlighted products. The common factor is _____.
Answer: 3 for edgenuit y
Step-by-step explanation:
i need some math help
Answer:
n = 15
Step-by-step explanation:
Step 1: Write equation
n/3 = 5
Step 2: Solve for n
Multiply both sides by 3: n = 15Answer:
n = 15
Step-by-step explanation:
Step 1: Write equation
n/3 = 5
Step 2: Solve for n
Multiply both sides by 3: n = 15
these triangles are congruent by the triangle congruence postulate
Answer: SSS
Step-by-step explanation:
SSS because we see no angles, and we know the triangles are congruent. B and C are eliminated which leaves SSS as the right choice.
If a loaf of bread was priced $1.50 on one day and $1.20 the next, what is the percent decrease
of the price of the loaf of bread?
Answer:
20 percent decrease
Step-by-step explanation:
0.15 cents is 10 percent of 1.50, and that multiplied by 2 is 0.30 cents. 0.30 cents is equal to 20 percent, and the difference between 1.50 and 1.20 is 30 cents.
question attached through picture
Step-by-step explanation:
(1/n)^-2/3
= n^2/3
= 3 root of n^2
solution is 3)
Which statement best describes the intersection of three planes?
A) The planes could form one or two lines.
B) The planes could form one, two, or three lines.
C) The planes will form two lines.
D) The planes could form one, two, or three lines, or they could intersect at exactly one point.
Answer:
D
Step-by-step explanation:
from what I could tell, it sounds like D would be correct
what are the numbers if the GCF of these numbers is 12?
A) 24 and 36
B ) 18 and 24
C)14 and 16
D) 12 and 21
explain please...
Answer:
a...................
the floor of a room is in the shape of a square of side 4.8m. the floor is to be covered with square tiles of perimeter 1.2m. Find the cost of covering the floor if each tile costs rupees 27
Answer:
the room square side is 4.8m
Area of the room is= 4.8=²23.04²m
perimeter of square tiles=4a =1.2
a=1.2/4
or a=o.3m
area of the square tiles =0.3²=0.09m²
numbers of the tiles are rcover floor of the room
23.0.4/0.09=256
each tiles cost Rs 27
the total cost=256*27=6912
the th coalst cover by the th floor is Rs .6912