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.
What’s 5 divided by 6.2
Answer:
8
Step-by-step explanation:
Because you need to round 0.8064516129 to the nearest tenth
NEED HELP!! ILL MARK YOURE ANSWER BRAINLIST.
1) In 2005 the number of seniors at Falcon decreased by 63 students over the 9 month school year. If the decrease was the same over the entire 9 months, write the monthly decrease as a quotient of integers and find the monthly decrease. please show you're work.
Answer
9
Step-by-step explanation:
Divide 63 by 9 months
7 students per month
63 / 9 = 7
Evaluate the expression for x=5, y=-3 and z=7 *
7 – 3y – 3z
Answer:
-5
Step-by-step explanation:
i tried my best but this is the result
HELP pleaseee i’m beggingggg
Answer:
35 1/3°54 2/3°Step-by-step explanation:
Angle AOB and BOC create a complementary angle. This means when two angles sum up to 90°. We can write an equation for this problem;
(x + 8) + 2x = 90
~Remove parenthesis
x + 8 + 2x = 90
~Combine like terms
3x + 8 = 90
~Subtract 8 to both sides
3x = 82
~Divide 3 to both sides
x = 82/3 or x = 27 1/3
Use what have for x to solve for the angle measures.
Angle AOB:
x + 8
(27 1/3) + 8
35 1/3°
Angle BOC:
2x
2(27 1/3)
54 2/3°
Check.
35 1/3 + 54 2/3 = 90°
Best of Luck!
Examine the diagram. It is not drawn to scale.
In the diagram shown, mZ1 = 30° and m25 = 120°.
What is the sum of the measures of 24, 25, and 26?
4
1
2
5
on
degrees
Identify the following angle measures.
m22= v degrees
m24 =
v degrees
3
3
m26 =
v degrees
6
Answer:
Examine the diagram. It is not drawn to scale.
A triangle has angles 1, 2, 3. The exterior angle to angle 1 is 4, to angle 2 is 5, to angle 3 is 6.
In the diagram shown, m∠1 = 30° and m∠5 = 120°.
What is the sum of the measures of ∠4, ∠5, and ∠6?
✔ 360
degrees
Identify the following angle measures.
m∠2 =
✔ 60
degrees
m∠4 =
✔ 150
degrees
m∠6 =
✔ 90
degrees
Step-by-step explanation:
Examine the diagram. It is not drawn to scale.
In the diagram shown, mZ1 = 30° and m25 = 120°.
What is the sum of the measures of 24, 25, and 26?
4
1
2
5
on
degrees
Identify the following angle measures.
m22= v degrees
m24 =
v degrees
3
3
m26 =
v degrees
6
I HOPE YOU GET IT RIGHT IK ITS THE ANSWERS I ALWAYS DO IT!!!!!!❤
The values of m∠2, m∠4 and m∠6 are 60°, 150° and 90° respectively.
What is an angle?An angle is formed from the intersection of two or more lines. Angles less than 90 degrees are called acute angles, angles greater than 90° are called obtuse angles while angles with a measure of 90° are called right angles.
From the diagram:
m∠1 + m∠4 = 180° (sum of angles in a straight line)
30 + m∠4 = 180°
m∠4 = 150°
m∠2 + m∠5 = 180° (sum of angles in a straight line)
120 + m∠2 = 180°
m∠2 = 60°
m∠1 + m∠2 + m∠3 = 180° (sum of angles in a triangle)
30 + 60 + m∠3 = 180°
m∠3 = 90
m∠3 + m∠6 = 180° (sum of angles in a straight line)
90 + m∠6 = 180°
m∠6 = 90°
The values of m∠2, m∠4 and m∠6 are 60°, 150° and 90° respectively.
Find out more on angle at: https://brainly.com/question/25770607
Numbers like 10, 100, 1,000, and so on are
called?
Factor the expression
x^2 − 14x + 45 completely.
Answer:
(x+5) (x+9)
Step-by-step explanation:
In order to the trinomial
x
2
+
14
x
+
45
Begin by finding the factors for the first term
x
2
=
x
⋅
x
Place those factors as the first term in each parenthesis
(
x
_
)
(
x
_
)
Since both signs of the trinomial are positive you will be adding the factors and both signs will be positive.
(
x
+
_
)
(
x
+
_
)
Now determine the factors of the third term
45
=
1
⋅
45
,
3
⋅
15
,
5
⋅
9
We need the factors that will add up to the middle term
14
=
5
+
9
Place these factors as the second term in each of the parenthesis.
(
x
+
5
)
(
x
+
9
)
(x-5)(x-9) is the factored form of the expression x²-14x+45
The given expression is x²-14x+45
x is the variable in the expression
x square minus forteen times of x plus forty five
Plus and minus are operators in the expression
x²-9x-5x+45
Now let factor out the expression
x(x-9)-5(x-9)
(x-5)(x-9)
Hence, the factored form of the expression is (x-5)(x-9)
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ6
Solve for x.
–2(x - 1) - x + 3 = -1
Anyone wanna help?
Answer:
-2(x-1) - x + 3 = -1
First if all, we operate the parenthesis knowing that [tex]a(b+c) = ab + ac[/tex]:
-2(x-1) - x + 3 = -1 ---->.-2x -2*(-1) - x + 3 = -1
Now, we operate:
.-2x -2*(-1) - x + 3 = -1 ----> -2x + 2 - x + 3 = -1
Now we operate another time to put all the x together and the independent terms too:
-2x + 2 - x + 3 = -1 ----> -3x + 5 = -1
We substract 5 at both sides to have only the x at one side:
-3x + 5 = -1 ----> -3x + 5 - 5 = -1 - 5 ----> -3x = -6
As both sides have a minus (-) we can eliminate it:
-3x = -6 ----> 3x = 6
We divide both sides by 3 to have only a x:
3x = 6 ----> 3x/3 = 6/3 ----> x = 2
Now, we know that x=2. We can also verify it by replacing it on the first equation:
-2(x-1) - x + 3 = -1 ---> -2(2-1) - 3 + 3 = -1 ---> -2(1) - 2 + 3 = -1 ---> -2 - 2 + 3 = -1
Now we know it's true, as we have replaced it and we got he answer.
HELP!! please explain how you got the answer too.
Determine whether cach point lies on the graph of the line y = 4.6x -7.
H(0, -7)
Answer:
Point H does lie on the graph y = 4.6x - 7
Step-by-step explanation:
Step 1: Define
y = 4.6x - 7
H(0, -7)
Step 2: Substitute, Evaluate, and Check
-7 = 4.6(0) - 7
-7 = 0 - 7
-7 = -7
Answer:
H(0,-7) does lie on the graph of line y = 4.6x - 7
Step-by-step explanation:
All you have to do is simply plug in the x and y values.
From the point H (0,-7) we can say that
x = 0
y = -7
Now just plug it into the equation.
y = 4.6x - 7
(-7) = 4.6(0) - 7
-7 = -7
Since -7 does equal -7, the point H is on the line of y = 4.6x - 7.
Please help! I’ll give brainliest to anybody who answers correctly!
1.(02.01)
Solve -4(x + 1) – 3 = -3(x – 4). (1 point)
O
-19
19
2.
Answer:
x = -19
Step-by-step explanation:
hope this help :)
Answer:
[tex]\boxed {x = -19}[/tex]
Step-by-step explanation:
Solve for the value of [tex]x[/tex]:
[tex]-4(x + 1) - 3 = -3(x - 4)[/tex]
-Use Distributive Property to both sides of the equation:
[tex]-4(x + 1) - 3 = -3(x - 4)[/tex]
[tex]-4x - 4 - 3 = -3x + 12[/tex]
-Combine like terms:
[tex]-4x - 4 - 3 = -3x + 12[/tex]
[tex]-4x - 7 = -3x + 12[/tex]
-Take [tex]-3x[/tex] and add it to [tex]-4x[/tex]:
[tex]-4x - 7 + 3x = -3x + 3x + 12[/tex]
[tex]-x - 7 = 12[/tex]
-Add both sides by [tex]7[/tex]:
[tex]-x - 7 + 7 = 12 + 7[/tex]
[tex]-x = 19[/tex]
-To make the variable [tex]x[/tex] positive, divide both sides by [tex]-1[/tex]:
[tex]\frac{-x}{-1} = \frac{19}{-1}[/tex]
[tex]\boxed {x = -19}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]-19[/tex].
Find the value of x so that the function has the given value
f(3) = 3x + 2
f(3) = 8
x=
Answer:
f(3) =3(2)+2
Step-by-step explanation:
Therefore, x = 2
Find the distance from P(6,-9) to the origin.
Please helppp
Answer:
10 units
Step-by-step explanation:
Distance from P(6, -9) to O ( 0, 0 ) PO
Let
X1 = 6 X2 = 0
Y1 = -9 Y2 = 0
Formula of Distance
[tex]\sqrt{(x2 - x 1) + (y2 - y1)}[/tex]
[tex]\sqrt{6^{2} +(-9^{2}) }[/tex]
[tex]\sqrt{100}[/tex]
10 units
Helpppppp I don’t understand
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION RQ!
Answer:
33.5
Step-by-step explanation:
40 % of 33.5 is 13.4
33.5/x = 40/100
13.4
Answer:
33.5
Step-by-step explanation:
A pack of 8 pairs costs 9:80. What is the cost of one pair of socks?
Answer:
1 1/2
Step-by-step explanation:
Answer:
$1.26
Step-by-step explanation:
9.80/8 = 1.22500
1.22500 rounded up = 1.26
Fill in the blanks by creating the line perpendicular to y=1/3x-3 that goes through (-1, -4) in slope intercept form.
Answer:
y = -3x - 7
Step-by-step explanation:
To find the slope of this perpendicular line, you'll have to keep in mind that a perpendicular line will have an opposite reciprocal of the slope of the line you are given. Here's what I mean:
Given Line: y = 1/3x - 3
Slope of Perpendicular Line: m = -3/1 = -3
Now, you'll have to find the y-intercept. But, to make sure your line passes through the given points, (-1, -4), you'll have to plug in the x and y values:
y = mx + b
-4 = (-3) (-1) + b
-4 = 3 + b
b = -7
Now just plug in your y-intercept and slope into the slope-intercept formula:
y = -3x - 7
can someone help me solve this system. thanks
2y = 6
3(x + y) = 12
Answer
y=3 x=1
Step-by-step explanation:
3(x+3)=12
3x+9=12
subtract 9 from both sides to get...
3x=3
divide 3 from both sides to get...
x=1
Step-by-step explanation:
this is very easy
2y=6
y=2/6=3
so ,
3(x+y)=12
3x+3y=12
3x+3+3=12
3x+9=12
3x=12-9
3x=3
x=3/3
x=1
Ryan shaded 70 squares on his hundredths grid. Sarah shaded 80 squares on her hundredths grid Part A Which value is greater than Ryan's decimal and less than Sarah's decimal A.70/100+4/100 B. 60/100+5/100 C. 80/100 D. 80/100+15/100
Answer:
A
Step-by-step explanation:
Here, we want to select which of the options is greater than Ryan’s decimal but less than Sarah’s
Ryan shades 70 out of 100 so his decimal will be 70/100 = 0.7
Sarah shades 80 out of 100, so his decimal will be 80/100 = 0.8
So we want a decimal greater than Ryan’s but less than Sarah’s
Let’s take a look at the options
The first option would be 70/100 = 0.7 + 4/100 = 0.7 + 0.04 = 0.74
We can see that this is greater than 0.7 but less than 0.8
So, this is our answer
=-09i8u9yh8guvyh bcnvjhulygtfrdsezawDFxcghjiuhygtfyhvbjkliouyggvbjhkio;uytfrderswaqwszedrtfyguhiiio
Which expressions are equivalent to 9+h+ (j+k)? Check all that apply.
9+(n+}) +
(9+1) +jk
(9+h) +j+k
9+(hj)+k
gh+jk
g(h+)
9+h[j+k)
Answer:According to the associative property of equality: (a + b) + c = a + (b + c) we can see that the parenthesis do not mean anything when we are only doing addition.
So answers 1. and 3. are correct
Answer:
1,3
Step-by-step explanation:
Which is the simplified form of 7+5-12?
O
1
7912
O-/7-912
17
o
لے
N
$12
1
+
1
312
[tex] \green {\boxed{Answer}}[/tex]
[tex] {r}^{ - 7} + {s}^{ - 12} [/tex][tex] \frac{1}{ {r}^{7} } + \frac{1}{ {s}^{12} } [/tex]#IfWrongPleaseReport
#StudyTogetherWithMe
#ILoveMath
Find the x and y intercepts of the graph of the linear equation -x + 8y = 4
Answer: x-int: (-4, 0), y-int: (0, 1/2)
Step-by-step explanation:
x-int: when y = 0
-x + 8*0 = 4
-x = 4
x = -4
(-4, 0)
y-int: when x = 0
0 + 8y = 4
8y = 4
y = 1/2
(0, 1/2)
A local clothing store sells t-shirts for $8 each, sweaters for $12 each, jeans for $15 each. Let x represent the number of t-shirts sold, y represents the number of sweaters sold, and z represent the number of jeans sold. Write an expression to represent the total amount of sales from t-shirts, sweaters, and jeans
Answer:
8x + 12y + 15z
Step-by-step explanation:
Given the sales rate of three items: 8$ for t-shirts, 12$ for sweaters, and 15$ for jeans. It also states that these rates are represented by the corresponding variables being x for t-shirts, y for sweaters, and z for jeans.
To complete the expression, just combine the rate with the corresponding variables. i.e 8$ for t-shirts, and x for shirts = 8x, 12$ for sweaters and y for sweaters = 12y, 15$ for jeans, and z for jeans = 15z. Finally, sum them together.
8x + 12y + 15z
(5x10₃) x (9x10₇)
answered in standard form
Answer:
5x9x10^10
Step-by-step explanation:
your question is incomplete
Find the distance between the pair of points, round to the nearest tenth if necessary.
Step-by-step explanation:
distance between the two points is given by formula
d=
[tex] \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } = \sqrt{( - 2 - 4)^{2} + {( - 3 - 0)}^{2} } = \sqrt{( - 6)^{2} + ( - 3)^{2} } = \sqrt{36 + 9} = \sqrt{45} = \sqrt{9 \times 5} = 3 \sqrt{5} [/tex]
Costumers can pick their own blueberries at Blueberry Hill. They pay $5 to enter the patch and $4 per pound for the blueberries they pick. Write an equation to model the total cost, y, fo x pounds of blueberries.
Answer:
c. y = 4x + 5
Step-by-step explanation:
you are paying a one time fee of $5 to get in and $4per x number of pounds.
Answer:
B
Step-by-step explanation:
Firstly you pay 4 dollars to enter BH
If x is the number of pounds of blueberries, then the amount spent is going to be 5x as each pound is 5 dollars. Then you add the costs together, so it would be 5x+4 which is B
How many 9-inch ribbons can be cut from 112yards of ribbon? show work
Answer:
448 ribbons
Step-by-step explanation:
in order to find this, you need to convert the yards into inches. there are 36 inches is a yard (a yard is 3 feet and one foot is 12 inches ) so you would multiply 112 and 36 to find the total number of inches it woulde be. 112x36=4,032. Now that you know the total number of inches, divide it by 9 to find the total number of ribbions you can make.
4,032/9= 448
so you could make a total of 448 ribbons
Answer:
12.4
Step-by-step explanation:
Do 112 divided by 9
4 The scale drawing represents the aerial view of a building. The actual building has
a perimeter of 48 m. Draw another scale drawing of the building using the scale
2 m to 1 unit length from the building to the drawing,
Answer:
Step-by-step explanation:
Evaluate the function for x = 3 * f(x) = x2 – 2x + 6 O x=9 O x = 6 O x=21 O x = 4
Answer:
When you input values for x, you can determine a single output for y. ... f(x)= 4x + 1 is written in function notation and is read “f of x equals 4x plus 1. ... perimeter, P = 4s, as the function p(x) = 4x, and the formula for area, A = x2, as a(x) = x2. ... in both cases, you substitute 2 for x, multiply it by 4 and add 1, simplifying to get 9
Step-by-step explanation:
got it off of google
helppp (picture below)
Answer:
Rate me 1 star if wrong but its answer A
Step-by-step explanation: