The equation of the quadratic function represented by given table is f(x) = -0.25x² -x + 3.
Given table is:
x y
-3 3.75
-2 4
-1 3.75
0 3
1 1.75
Let us say the quadratic function is:
f(x) = ax² +bx + c
What is a quadratic function?
A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are non-zero.
When, x=0, f(x) =3
So, 3 = c
So, f(x) = ax² +bx +3
When, x=1, f(x) =1.75
1.75 = a+b+3
a+b = -1.25........(1)
When, x=-1, f(x) =3.75
3.75 = a-b+3
a-b = 0.75........(2)
Solving equations (1) and (2)
a = -0.25
b = -1
So quadratic function will be:
f(x) = -0.25x² -x + 3
Therefore, the equation of the quadratic function represented by given table is f(x) = -0.25x² -x + 3.
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5/12 x 2/5???
CAN SOMEONE PLEASE ANSWER
20 Point Reward!!!!
Answer:
1/6
Multiply 5/12 x 2/5 then cross cancel 12 and 2 and get 6 then cross cancel 5 and 5 to get 1.
Final answer:
1/6
Need Help! 50 points!!
Answer:
see below
Step-by-step explanation:
eq.1 2a - b + 2c = -8
eq.2 5b - 3c = 21
eq.3 -7a -10c = -2
3 equations, 3 unknown.
first step is to eliminate b using eq1 and eq2
2a - b + 2c = -8 (5)
5b - 3c = 21
10a - 5b + 10c = -40
5b - 3c = 21
10a + 7c = -21 ------------eq. A
lets solve a using eq. A
10a + 7c = -21
a = (-7c - 21) / 10
now substitute a into eq.3
-7a -10c = -2
-7(-7c - 21) -10c = -2 distribute
10
4.9c + 14.7 - 10c = -2 add similar terms
-5.1c = -2 - 14.7 simplify
c = -16.7 / -5.1
c ≈ 3
solve b using eq. 2 and substitute c.
5b - 3c = 21
5b = 21 + 3c
5b = 21 + 3(3.2)
b = 30.825 / 5
b ≈ 6
solve a using eq. A
10a + 7c = -21
10a + 7(3.2) = -21
10a = -21 - 22.4
a = -43.4 / 10
a ≈ -4
therefore, the statement (-4, 6, 3) is correct.Answer:
a
Step-by-step explanation:
(17.7) x (11.4)
Show the work that helped you solve it please
abc is isosceles triangle above is ac=20 and bc=3x-7 what is x
Answer:
x = 9
Step-by-step explanation:
Isosceles means that the two sides equal each other
As such, to find the value of x we must equal the two expressions together and isolate the variable
20 = 3x - 7
add 7 to both sides
27 = 3x
divide both sides by 3
9 = x
Answer:
The variable x equals 9.
Step-by-step explanation:
3x - 7 = 20
3x = 27
X = 9
Helppppp meeeeee question 2 pleaseeee !!
What is below the question is what I mean.
PLS HELP ME DUE TODAY
Answer:
Domain: (-∞, -5) (-1, ∞)
Step-by-step explanation:
Note:
For f(x) > 0: See the points of x for which the graph of f(x) lies above the x-axis.
For f(x) < 0: See the points of x for which the graph of f(x) lies below the x-axis.
We need to find the domain of f(x) for which f(x) < 0
From the graph, we can tell:
f(x) < 0 on (-∞, -5) ∪ (-1, ∞)
Therefore: The domain on which the given graph f(x) is negative, is (-∞, -5) ∪ (-1, ∞)
recursive formula for 0.15, 0.17, 0.19, 0.21, 0.23
Answer:
An = a1 + (n-1) d
Step-by-step explanation:
plsssss help no one is helping me
Answer:
x=-3
Step-by-step explanation:
there are three x's and five one's so the equation is 3x+5
on the other side there are 2 negative x's and 10 negative one's so the equation is -2x-10
set them equal to each other
3x+5=-2x-10
5x=-15
x=-3
Answer:
hey how old are you
Step-by-step explanation:
jnedjed
Find the common difference of the
arithmetic sequence -6, -13, -20, ...
Answer:
-7
Step-by-step explanation:
What is the simplified version of [tex]\frac{x^5x^6}{y^6}[/tex]
16(2x + 3) (3x + 5) ÷ 8 (2x + 3)
Answer:
2(3x+5) OR (6x+10)
Step-by-step explanation:
16 (2x+3) (3x+5)8 (2x+3)
16 (3x+5)8
2 (3x+5) = 6x+5 ThxWhich shows the correct placement of the decimal point in the product?
52.1
× 3.4
1771.4
177.14
17.714
1.7714
i will crown to correct answer pls and ty
Answer:
b.177.14
Step-by-step explanation:
because 52.1x 3.4 = 177.14
Please help!!!!!! Hurry i only have 10 mins ill give brainy
Which operation should be used to solve LaTeX: \frac{x}{3} = 15x3=15 ?
Group of answer choices
+ 3
÷ 3
x 3
– 3
Carlos and Diya perform the same transformations on the same pre-image, but in reverse order.
Carlos translates, then dilates.
Diya dilates, then translates.
Carlos claims the resulting images will always be the same. Diya disagrees.
Who is right? and why
Answer:Diya
Step-by-step explanation: she’s right because she is black and all black peoples is always right
Which of the following is equal to -11?
0-6-(-5)
0-5+-6
0-5+6
Find the distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9
a.6.7
b.6.73
c.6.71
d.6.72
The distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9 is 7.71 units.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The distance between the two straight parallel lines can be found by finding the difference between the y-intercept of the two lines. Therefore, for the two of the given equation, the value of the y-intercept can be written as,
Y-intercept of -4x + 7y + 9 = 0
-4x + 7y + 9 = 0
7y = 4x - 9
y = (4x - 9)/7
y = 4x/7 - 9/7
y-intercept = -9/7
Y-intercept of y = 4/7x - 9
y = 4/7x - 9
y-intercept = -9
Now, the difference distance between the two lines will be,
Distance = Difference between the y-intercept
= -9 - (-9/7)
= -9 + 1.2857
= 7.71
Hence, the distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9 is 7.71 units.
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In the diagram, AC is a diameter of the circle with center O. If m_ACB = 50°, what is m_BAC?
Answer: Your answer 40°
Step-by-step explanation:
Hope this helped!
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A train travels at a rate of (4x + 5) miles per hour. How many miles can it travel at that rate in
(x - 1) hours? Express your answer as a polynomial.
(4x+5) miles..........1 hour
x miles .........(x-1) hour
(4x+5) * (x-1) = 1 * x
in (x - 1)h = x / (4x+5) miles
You earn $1500 a month and 1/4 of your money goes to pay rent. What expression represents the money you have after you pay rent?
Answer:
x-375
Step-by-step explanation:
First, we find a fourth of $1500.
1/4*1500=375
Then we know that you need to pay $375. We will represent the money right before you pay as x, or any variable you choose.
= x-375
hellpppppppppppppppp 43points
Answer:
a) 4x
b) 2 + 4y
Step-by-step explanation:
a) 7x - 6x + 3x
To do this, we just need to collect the terms together. They are all coefficients of x, so all we need to do is add the number together.
7 - 6 + 3 = 4
7x - 6x + 3x = 4x
b) 2(1 + 2y)
Here we need to expand the brackets. 2 is shown to be multiplied by 1 +2y:
2(1 + 2y)
= 2*1 + 2*2y
= 2 + 4y
I hope this helps :)
∠ R and∠ S are complementary. If m ∠ R = 12x - 3 and m ∠ S = 7x - 2, find m ∠ R.
m ∠ R = (blank)degrees
Step-by-step explanation:
Sum of two complementary angle is 90°so. <R+<S =90°12x-3+7x-2=90°19x-5=90°19x=95°X= 5<R= 60-3=57°if 11 is subratecet from 4 times a number the result is 89 find the number
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
4x-11=89
4x=89+11
4x=100
x= 25
I hope this will help
What do you call the point where a perpendicular bisector crosses another line?
Answer:
If AB crosses at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types. For obvious reasons, the point F is called the midpoint of the line PQ. See also Angle bisector.
what is the answer to this equation using the quadratic formula? 3x^2+2x+4x=0
Answer: No real number solutions
The complex number solutions are [tex]x = \frac{-1+ i\sqrt{11}}{3} \ \text{ or } \ x = \frac{-1- i\sqrt{11}}{3}\\\\[/tex]
where [tex]i = \sqrt{-1}[/tex]
=======================================================
Explanation:
The given equation 3x^2+2x+4 = 0 is in the form ax^2 + bx + c = 0
We have
a = 3b = 2c = 4Let's compute the discriminant.
d = b^2 - 4ac
d = (2)^2-4(3)(4)
d = -44
The result is negative, so there are no real number solutions.
----------------
If you wanted to find the complex valued solutions, then we apply the quadratic formula.
Plug in a = 3, b = 2, c = 4
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(3)(4)}}{2(3)}\\\\x = \frac{-2\pm\sqrt{-44}}{6}\\\\x = \frac{-2\pm\sqrt{-1*4*11}}{6}\\\\x = \frac{-2\pm\sqrt{-1}*\sqrt{4}*\sqrt{11}}{6}\\\\[/tex]
[tex]x = \frac{-2\pm i*2*\sqrt{11}}{6}\\\\x = \frac{-2\pm2i\sqrt{11}}{6}\\\\x = \frac{2(-1\pm i\sqrt{11})}{6}\\\\x = \frac{-1\pm i\sqrt{11}}{3}\\\\x = \frac{-1+ i\sqrt{11}}{3} \ \text{ or } \ x = \frac{-1- i\sqrt{11}}{3}\\\\[/tex]
Notice in step 3 we have -44 under the square root. The negative value in the square root leads directly to the imaginary number [tex]i = \sqrt{-1}[/tex]
Though the term "imaginary" is a bit unfair and misleading because numbers like -22 are just as imaginary and made up by humans. It just depends on context in which imaginary numbers are useful (eg: with physics or engineering).
write the equation in slope-intercept form.
Answer:
y = 2x - 3Step-by-step explanation:
Given line:
y = - 1/2x - 1We need to find a line that is perpendicular to the given line and passes through the pint (6, 9)
We know perpendicular lines have opposite-reciprocal slopes.
The slope of the line is:
(-1) / (- 1/2) = 1 *2 = 2Use point-slope form to find the line:
y - 9 = 2(x - 6)Convert the equation into slope-intercept form:
y - 9 = 2x - 12y = 2x - 12 + 9y = 2x - 3 How many is this
2( 9 - 7r ) + 8r
solving steps:
2( 9 - 7r ) + 8r
2(9) - 2(7r) + 8r
18 - 14r + 8r
18 - 6r
Answer:
18 - 6r
Step-by-step explanation:
2(9 - 7r) + 8r
Expand the brackets:
⇒ 2 · 9 - 2 · 7r + 8r
⇒ 18 - 14r + 8r
Combine like terms:
⇒ 18 - 6r
Please help (explain pls)
Answer:
C
Step-by-step explanation:
The reason it is C is mainly because it is the only line with a negative slope. A negative slope this direct \. It is not A because that is a positive slope (/). It is not B because that line is undefined which means it would look like this x = 2. And D is wrong because that is a zero slope line which looks like this y = 5. So it is C.
Here is a helpful website for problems like this Desmos. com
Which fruit has the lowest unit price?
A.
2.5 pounds of grapes for $4.19
B.
4 pounds of apples for $5.49
C.
5 pounds of oranges for $6.99
D.
6.5 pounds of strawberries for $9.59
Answer:
A unit is a measure of ratio between two quantities. In this instance, the unit is a pound. The ratio you need to take is the price of each fruit and divide it by the number of pounds each fruit has to get a price per pound. See below for solution.
Step-by-step explanation:
A. 4.19 dollars / 2.5 pounds = 1.676 dollars / pound
B. 5.49 dollars / 4 pounds = 1.3725 dollars / pound
C. 6.99 dollars / 5 pounds = 1.398 dollars / pound
D. 9.59 dollars / 6.5 pounds = 1.475 dollars / pound
The lowest is B, the apples.
2
Think: A student attempted to solve the equation below by Pair/Share: Do you agree or
completing the square.
disagree with the steps taken so
far? Explain.
x²- 2x-1=2
+1+1
because ...
x ²-2x=3
XP-2x +1 = 3+1
*²-2x + 1 = 4
(X+1}=4
b = 2
half:-1
Square: 1
Answer:
Step-by-step explanation:
Here is how to solve it using factoring:
x^2 - 2x - 1 = 2
x^2 - 2x - 3 = 0
(x + 1)(x - 3) = 0
x = -1, 3.
Answer:
your process is not correct
(x^2-2x+1 = 3+1)
you were wrong here
Step-by-step explanation:
I am not good in english so it is hard for me to explain...
Carla is a waitress at Daybreak Diner, and she earns $5 for each hour she works. Last week, she
out earned $148 total, including $68 in tips. How many hours did Carla work last week?
Answer:
16 hours
Step-by-step explanation:
148 - 68 = 80
80 / 5 = 16