Which function matches this graph?
f(x)=x2−3f ( x ) = x 2 − 3
f(x)=x2+9f x = x 2 + 9
f(x)=x2−6x+9f ( x ) = x 2 − 6 x + 9
f(x)=x2+6x+9f ( x ) = x 2 + 6 x + 9
Answers
Answer:
[tex]\large\boxed{\sf f(x) = x^2-6x+9}[/tex]
Step-by-step explanation:
We are here given a graph of a equation and we are interested in finding the equation .
From the given graph we can see that it cuts the x axis at point (3,0) . This graph represents a quadratic function and its two zeroes are 3,3 . We can write the equation using the two zeroes .
Say if the zeroes of the quadratic equation are p and q , then the quadratic equation can be written as ,
[tex]\longrightarrow (x-p)(x-q)=0 [/tex]
And the quadratic function can be written as ,
[tex]\longrightarrow f(x)= k[ (x-p)(x-q)][/tex]
where k is a constant .In this case k = 1 . So we can write the function as ,
[tex]\longrightarrow f(x) = (x-3)(x-3)[/tex]
Distribute ,
[tex]\longrightarrow f(x)= x (x-3)-3(x-3)[/tex]
Simplify by opening the brackets,
[tex]\longrightarrow f(x) = x^2-3x -3x +9 [/tex]
Add like terms,
[tex]\longrightarrow \underline{\underline{f(x) = x^2-6x+9}}[/tex]
And we are done!
Related Questions
what is the slope of the line that passes through the points (3,5) and (1-5)
Answers
Answer:
the slope is 5
Step-by-step explanation:
7d+3/4=6 prove that d=3
Answers
7d+3/4(4)=6(4)
7d+3=24
7d=24-3
7d/7 =21/7
d=3
At the gas station, each liter of gas costs $ 3 $3dollar sign, 3, but there's a promotion that for every beverage you purchase you save $ 0.20 $0.20dollar sign, 0, point, 20 on gas. Is your total savings on gas proportional to the number of beverages you purchase? Choose 1 answer:
Answers
Answer:
Yes! Our total savings on gas proportional to the number of beverages you purchase.
Step-by-step explanation:
Here, each liter of gas costs $3.
Every beverage you purchase you save $0.20.
So, if you purchase for $9, you will save 3*$0.20 = $0.60
So, this is proportional because when increase in purchase, there is proportional increase in savings.
PLEASE ANSWER AND SHOW WORK
1.5 kg of rice for $9
the unit rate:????
A town grows by 350 people over 7 years
unit rate:????
PLEASE HELP URGENTLY AND ANSWER
Answers
9514 1404 393
Answer:
$6/kg50 people/yearStep-by-step explanation:
A unit rate is a ratio. When dollars are involved, we usually want dollars in the numerator. When time is involved, we usually want time in the denominator.
__
rice: $9/(1.5 kg) = (9/1.5) $/kg = $6/kg
__
growth: (350 people)/(7 years) = (350/7) people/year = 50 people/year
Line segments AB and CD are
congruent. Their coordinates
are A(-11, -3), B(-2,5), C(7, 1)
and D(x, 9). Find the value of x.
Answers
Answer:
x = 16 or -2
Step-by-step explanation:
If both lines are congruent, their magnitudes are equal.
To find the magnitude of a line, the equation to use is;
D = √(x2-x1)^2 + (y2-y1)^2
So for AB, we have
D = √(-2 + 11)^2 + (5 + 3)^2
D = √81 + 64 = √145
For the second line
The distance would be;
D = √x-7)^2 + (9-1)^2
D = √(x-7)^2 + 8^2
Equate both magnitude
√145 = √(x-7)^2 + 64)
Simply remove the square roots on both sides
145 = 64 + (x - 7)^2
145 -64 = (x -7)^2
81 = (x-7)^2
Thaw the square root of both sides
x - 7 = 9
or x -7 = -9
x = 9 + 7 or x = -9 + 7
x = 16 or -2
Daisy keeps her stamp collection in a box that is 12 inches long, 10 inches wide, and 4 inches tall.
1. What is the volume of her box?
2. Daisy's friend Quinn keeps his stamp collection in a box that has the same volume as Daisy's box but different dimensions. What could be the dimensions of Quinn's box
Answers
Answer:
1. 480 inches^3
2. 6 inches tall, 8 inches wide, and 10 inches ong
Step-by-step explanation:
3/12 + 5/6 Convert the Improper fraction to a mixed number
Answers
- What transformation is described by the
notation (x, y) = (x-3, y)?
A translation left 3 units
B translation down 3 units
C translation right 3 units
Answers
AC = BC, <ACB = 40°, <AMN = 25° <CPM = ?
Answers
Answer:
∠ CPM = 135°
Step-by-step explanation:
given AC = BC , then Δ ABC is isosceles with base angles congruent , then
∠ ABC = [tex]\frac{180-40}{2}[/tex] = [tex]\frac{140}{2}[/tex] = 70°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, then
∠ AMN + ∠ BPM = ∠ ABC , that is
25° + ∠ BPM = 70° ( subtract 25° from both sides )
∠ BPM = 45°
∠ CPM and ∠ BPM are adjacent angles on a straight line and sum to 180°
∠ CPM + 45° = 180° ( subtract 45° from both sides )
∠ CPM = 135°
what’s -4-3+x-3x simplified?
Answers
-4 - 3 + x - 3x
-7 + x - 3x
-7 - 2x
advice: just combine like terms
Answer:
-7 -2x
Step-by-step explanation:
-4-3+x-3x
Combine like terms
-4-3 +x-3x
-7 -2x
Can someone help me with this?
Find the product. Write your answer in factored form.
Answers
write at least 3 different expressions that are eqivalent to -1/2 (-12x + 30)
Answers
Answer:
6x-15 3(x-5) 3/2(2x-10)
Step-by-step explanation:
simplify
-1/2(-12x+30)
6x-15
factor in different ways
3(x-5)
3/2(2x-10)
The area of a trapezoid is given by A=1/2(B+b) where A is the height B is the big base and b is the small base. We are going to plant a trapezoid shaped flower garden. What would the height of the garden be if the area was 27 ft squared and the big base was 10 and the small base was 8? Include units
Answers
Answer:
The height of the garden will be 3 ft.
Step-by-step explanation:
Given;
area of trapezoid, A = 1/2(B+b)h
Where;
A is the area
h is the height
B is the big base
b is the small base
If; A = 27 ft²
B = 10 ft
b = 8 ft
h = ?
[tex]A= \frac{1}{2} (B+b)h\\\\27= \frac{1}{2} (10+8)h\\\\27*2 = 18h\\\\54 = 18h\\\\h = \frac{54}{18}\\\\ h = 3 \ ft[/tex]
Therefore, the height of the garden will be 3 ft.
Add another set of points that are 8 units below points A, B, C, and D. This time, you'll need to rotate the lines into a different orientation. Connect
the points you created to form another polygon that is congruent to ABCD. When you're done, you'll have translated polygon ABCD down by 8
units.
Measure the slopes of the line segments (i.e., construction paths) you created. Record the measurements in the table.
Answers
Yupppppppppppppppppppppppppppppp
Answer:
Lines segments:I Slope:
AI I Undefined
BJ I Undefined
CK I Undefined
DL I Undefined
Step-by-step explanation: ye
is 4,3,2,1 arithmetic or geometric
Answers
Answer:
Arithmetic
Step-by-step explanation:
A sequence is a set of numbers, called terms, arranged in some particular order. An arithmetic sequence is a sequence with the difference between two consecutive terms constant
what is an right angle and obtuse angle?
Answers
Answer:
Right angle is an angle of 90°
Obtuse angles is an angle greater than 90°
Answer:
A right angle is an angle of 90°
An Obtuse angles is an angle greater than 90°
The right rectangular prism is made up of 12 cubes. Each cube has an edge length of
12 cubic inches.
Answers
Hey there!
Option answer: [tex]1 \frac{1}{2} \: \: cubic \: inches[/tex]
According to the title,
Volume = 12 × (1/2)[tex] {}^{3} [/tex]
=> 12 × 1/8
=> [tex] \frac{12}{8} [/tex]
=> [tex] \frac{3}{2} [/tex]
=> [tex]1 \frac{1}{2} [/tex]
Answer:
d
Step-by-step explanation:
first i do my formula which is length x width x height
the length is 3 the width is 2 and the height is 2 so 3x2x2 is 12
so the answer is d
Using the slope equation m = y2−y1x2−x1 and given the points (0, 4) and (2, 1), find the slope.
Answers
Answer:
[tex] - \frac{3}{2} [/tex]
Step-by-step explanation:
[tex]\textcolor{steelblue}{\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }}[/tex]
where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate
Slope
[tex] = \frac{4 - 1}{0 - 2} [/tex]
[tex] = \frac{3}{ - 2} [/tex]
[tex] = \bf{- \frac{3}{2} }[/tex]
a manufacturer has determined that if his company sells x items per day then their profit is given by P=-x^2+ 700 x-10000 euros. . How many items must be sold each day in order to make a profit
Answers
Answer:
15
Step-by-step explanation:
To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula
[tex]x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}; x= \frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]x= \frac{-700+\sqrt{700^{2}-4(a)(-10000) } }{2(1)}; x= \frac{-700-\sqrt{700^{2}-4(a)(-10000) } }{2(1)}[/tex]
[tex]x= \frac{-700+\sqrt{530000} }{2}; x= \frac{-700-\sqrt{530000} }{2}[/tex]
[tex]x=\frac{-700+100\sqrt{53} }{2}; x=\frac{-700-100\sqrt{53} }{2};[/tex]
[tex]x=-350 + 50\sqrt53 = 14.005; x = -350 - 50\sqrt53 = -714.005[/tex]
In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.
[tex](-714.005)^2+700(-714.005)-10000=-0.360[/tex]
Furthermore, we must round to the nearest whole number, as you cannot make part of an item.
Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:
[tex](14)^2+700(14)-10000=-4\\\\(15)^2+700(15)-10000=725[/tex]
The area of the triangle below is 28.8 square centimeters. What is the length of the
base?
7.2 cm
Answers
Answer:
8
Step-by-step explanation:
The length of the base of the triangle is, 8 cm.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
The area of the triangle is 28.8 square centimeters.
The height of the triangle = 7.2 cm
We know that;
⇒ Area of triangle = 1/2 ( Height × Base)
Substitute all the values, we get;
⇒ Area of triangle = 1/2 ( Height × Base)
⇒ 28.8 = 1/2 ( 7.2 × Base)
⇒ 28.8 × 2 = 7.2 × Base
⇒ 57.6 = 7.2 × Base
⇒ Base = 57.6 / 7.2
⇒ Base = 8 cm
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Guys, I’m giving you at least 100 points for you to answer to my last 2 weeks of my Number Sense and Numeracy: The Order of The Operations word problem homework package So guys, please listen up and pay attention to me without ignoring my last 2 weeks of my Number Sense and Numeracy: The Order of The Operations word problem homework package for no reason! :D
The question #6 is by how much is the sum of –8 and 6 more than –4?
The question #7 is how much less is the sum of –8 and –4 than the product of 4 and –2?
The question #11 is by how much is (–3 + 5)^2 more than –(–3 + 5)^2?
Please answer to my math word problem questions as soon as possible with the best efforts and the best step-by-step explanations in order to get the Brainliest award of all the time! :D
Well anyways, guys, good luck on answering 3 math word problem questions of my last 2 weeks of my Number Sense and Numeracy: The Order of The Operations word problem homework package in order to get the best Brainliest award of all of the time, and I will check the answers to see if it’s appropriate for me. :)
Answers
Answer:
ok i am here to explain :)
Step-by-step explanation:
So, for #6, all we do is -8+6, since it said sum, so we add, and we get -2. this is 2 more than -4, and to check, all we would have to do is -4+2, which equals -2.
for #7, all we have to do is -8+(-6), since again it says sum so we add. the sum of these values are -14. for the second part, because it says "product" this means we multiply! and when we multiply -2 by 4, we get -8. this would lead us to believe that the sum is 4 less than. we can check it by subtracting positive 4 from the negative 8, or -8-4, which would give us -12.
for #11, all i really did was plug it into a calculator, and for the first one, i got 4, and for the second one i got -4. this would give us a difference of 8, and to check all we would have to do is add the 8 to the negative 4, or -4+8=4.
Hope this helps, please mark as brainlest.
Answer:
6: -2
7: 14
11: -4
Step-by-step explanation:
6:
-8 + 6 = -2
-2 is bigger than -4 because it is closer to 0. If it was regular numbers, like 2 and 4, 4 would be larger! :)
7:
-8 - 4 = -12
4 - 2 = 2
The correct answer is 14 because there are 14 numbers between 4 and -12 :)
11:
(–3 + 5)^2
2^2
4
–(–3 + 5)^2
-2^2
-4
The correct answer is 4 because it is a positive number and positive numbers are ALWAYS bigger than negative numbers :)
Have a great day!!
Please rate and mark brainliest!!
hello people ~
factorise: y² - 2y - 15
Answers
Answer:
[tex](y+3)(y-5)[/tex]
Step-by-step explanation:
Given the following equation:
[tex]y^2-2y-15[/tex]
To factor any equation, we must first break the equation into different groups and then factor out common terms in till we reach our solution.
[tex]y^2-2y-15[/tex]
[tex](y^2+3y)+(-5y-15)[/tex]
[tex]y^2=yy=y(y+3)[/tex]
[tex]y(y+3)+(-5y-15)[/tex]
[tex](-5y-15)=-5(y-15)[/tex]
[tex]y(y+3)+-5(y-15)[/tex]
[tex]15\div5=3[/tex]
[tex]y\left(y+3\right)-5\left(y+3\right)[/tex]
[tex]y\left(y+3\right)-5\left(y+3\right)=(y+3)(y-5)[/tex]
[tex]=(y+3)(y-5)[/tex]
Your answer is "(y + 3)(y - 5)."
Hope this helps.
Answer:
[tex](y-5)(y+3)[/tex]
Step-by-step explanation:
To factorize [tex]y^2-2y-15[/tex]
[tex]\textsf{for} \ ax^2+bx+c \ \textsf{find} \ v, w \ \textsf{such that} \ v \cdot w=a \cdot c \ \textsf{and} \ v+w=b\\ \textsf{ and group into} \ (ax^2+vx)+(wx+c)[/tex]
[tex]a \cdot c=1 \cdot -15=-15[/tex]
[tex]b=-2[/tex]
Therefore, the 2 numbers that multiply together to give -15 and add together to give -2 are: -5 and 3
[tex]\implies y^2-5y+3y-15[/tex]
[tex]\implies (y^2-5y)+(3y-15)[/tex]
Factor the parentheses:
[tex]\implies y(y-5)+3(y-5)[/tex]
Factor out the common term [tex](y-5)[/tex]:
[tex]\implies (y-5)(y+3)[/tex]
Part D You can solve the problem in part Cusing a different method. To set up this method, first find the total number of strands required to make a pair of pom-poms.
Answers
Answer:(Actual answer they provide) There are two pom-poms in a pair. The total number of strands required to make pom-poms is 80 x 2 = 160
Step-by-step explanation:
can someone help me please and thank you :)
Answers
Answer:
the answer is 4328
Step-by-step explanation:
may God bless you and your family during spring break
Please help! Parallel lines Pythagorean theorem
Answers
Answer:
m∠A = 150°
m∠B = 30°
m∠E = 110°
Step-by-step explanation:
Linear pair:
⇒ m∠A + 30° = 180°
⇒ m∠A = 150°
Alternate interior angles:
⇒ m∠B = 30°
Sum of interior angles of a triangle is 180°:
⇒ m∠C + 30° + 40° = 180°
⇒ m∠C = 110°
Linear pair:
⇒ m∠C + m∠D = 180°
⇒ 110° + m∠D = 180°
⇒ m∠D = 70°
Alternate interior angles:
⇒ m∠E = m∠C
⇒ m∠E = 110°
3/5 divided by 1 1/4
Answers
Answer:
[tex]\frac{12}{55}[/tex]
Step-by-step explanation:
To divide fractions, here are your steps:
1) Invert the fraction you are dividing by.
2) Multiply the numerators and denominators.
3) Simplify if necessary.
1)
[tex]\frac{3}{5}[/tex] / [tex]\frac{4}{11}[/tex]
2)
[tex]\frac{3 * 4}{5 * 11}[/tex] = [tex]\frac{12}{55}[/tex]
3)
Cannot be further simplified.
Answer:
12/55
Step-by-step explanation:
caculator
Is this angle supplementary or congruent?
Answers
Answer:
Congruent
Step-by-step explanation:
An angle is congruent if its corresponding angle is the same degrees.
It is supplementary if there are two angles that add up to 180°.
College Alisha is putting cheese cubes and crackers onto small plates. She has 24 cubes of cheese and 40 crackers. She want both cheese and crackers on each plate and each plate must have the same number of cheese cubes and the same number of crackers. What is the greatest number of plates she can make using all the cheese and crackers.
Answers
Answer:
there will be 8 plates each having 3 cubes of Cheese and 5 crackers
Step-by-step explanation:
To determine the greatest number of plates she can make using all the cheese and crackers, find the highest common factor of 24 and 40
24 = 2, 3, 4, 6, 8, 12, 24
40 = 2, 4, 5, 8, 10, 20, 40
Highest common factor of 24 and 40 is 8
24 cubes of cheese / 8 plates = 3 cubes of cheese per plate
40 crackers / 8 plates = 5 crackers per plate
So, there will be 8 plates each having 3 cubes of Cheese and 5 crackers
The sum of a number and fourteen is less than or equal to three times the number.
Answers
Answer:
x=7
Step-by-step explanation:
x+14=3x
shift x to the other side
14=3x-x
14=2x
2x=14
x=14/2
x=7
Checking:
x+14=3x
7+14=3(7)
21=21
The sum of a number and fourteen is less than or equal to three times the number x + 14 = 3x, x = 7.
Given Information:
The sum of a number and fourteen is less than or equal to three times the number.
Let' consider the number is x, then w get this equation,
x + 14 = 3x
shift x to the other side
14 = 3x - x
14 = 2x
2x = 14
Divide 2 on both side,
x = 14/2
x = 7
For checking this value,
x + 14 = 3x
7 + 14 = 3(7)
21 = 21
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If m 2 BOC = 27 and m ZAOC = 61, what is the measure of ZAOB?