10. What is the exact equation for the quadratic modeled in the table below?
X
-4
-2
2
4
y
24
12
0
0
0
4
6
4
Answers
The quadratic equation is y = 1/2x^2 - 3x + 4
How to determine the equation?A quadratic equation is represented as:
y = ax^2 +bx + c
Using the values on the table, we have:
a(0)^2 + b(0) + c = 4 ---- when x = 0
a(2)^2 + b(2) + c = 0 ---- when x = 2
a(4)^2 + b(4) + c = 0 ---- when x = 4
Evaluate these equations
c = 4
4a + 2b + c = 0
16a + 4b + c = 0
Substitute c = 4
4a + 2b + 4 = 0
16a + 4b + 4 = 0
Divide through by 2 and 4
2a + b + 2 = 0
4a + b + 1 = 0
Subtract both equations
2a -1 = 0
Solve for a
a= 1/2
Substitute a= 1/2 in 4a + b + 1 = 0
4 * 1/2 + b + 1 = 0
Evaluate
2 + b + 1 = 0
Solve for b
b = -3
So, we have:
y = ax^2 +bx + c
This gives
y = 1/2x^2 - 3x + 4
Hence, the quadratic equation is y = 1/2x^2 - 3x + 4
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Related Questions
please help me!!!!!!!!!!!!!!
20 POINTS
Answers
Answer:
The Area of the Grass is 18 square meters.
Step-by-step explanation:
Find the area of the grass and sand (5*6). The area of the grass and sand is 30.
Next, find the area of just the sand (3*4). The area of the sand is 12.
Subtract the area of the sand (12) from the area of the grass and sand (30).
30-12 = 18
if an equilaterl triangle is inscribed in a circle of a radius 8cm.then what is the area of the triangle?
Answers
The area of the triangle is 83.14 square centimeters.
How to get the area of the triangle?If an equilateral triangle is inscribed in a circle of radius R, each side of the triangle measures:
S = R*√3
In this case R = 8cm.
And we know that the area of an equilateral triangle of side length S is:
[tex]A = \frac{\sqrt{3} }{4} *S^2[/tex]
Replacing what we know in the area formula:
[tex]A = \frac{\sqrt{3} }{4} *(\sqrt{3}*8cm)^2 = 83.14 cm^2[/tex]
The area of the triangle is 83.14 square centimeters.
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Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable. How should Mr. Johns handle this situation
Answers
Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explaining that one component of math is understanding reasonable answers.
Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable.
Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explain that one component of math is understanding reasonable answers.
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The value of a car depreciates at a rate of 15% per year. When brand new the car is worth £42000 How much will it be worth 2 years later?
Answers
Answer:
£ 30 345.
Step-by-step explanation:
15 % off means that 85% is left
42 000 * .85 * .85 = 42 000 (.85)^2 = 30 345
Analyze the graph of the function f(x) to complete the statement.
On a coordinate plane, a curved line, labeled f of x, with a minimum value of (0, negative 3) and a maximum value of (negative 2.4, 17), crosses the x-axis at (negative 3, 0), (negative 1.1, 0), and (0.9, 0), and crosses the y-axis at (0, negative 3).
f(x)<0 over and what other interval?
Answers
The function f(x) is less than 0 at x < -1.8
How to analyze the graph?The missing graph is added as an attachment
The interval where f(x) < 0 are the intervals where the y value of the function is less than 0.
This in other words, represent the negative y-axis
From the attached graph, the function f(x) is less than 0 at x < -1.8.
This extends till x = infinity
Hence, the function f(x) is less than 0 at x < -1.8
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69. REAL-WORLD APPLICATIONS
A gym membership with two personal training sessions costs $125, while gym membership with five personal training sessions costs $260. What is cost per session?
Answers
Answer:
Cost of per session the average rate is $45.
Step-by-step explanation:
It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.
It is required to find what is the cost per session.
Step 1 of 1
It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.
To find the cost of per session calculate the average rate.
Now let $f(x)$ be the cost per session use the for the average rate of change, and the input value is the number of personal traings x.
[tex]$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$$[/tex]
Now substitute, $125 for [tex]$f\left(x_{2}\right)[/tex], 260 for [tex]$f\left(x_{1}\right), 2$[/tex] for [tex]$x_{1}$[/tex] and 5 for [tex]$x_{2}$[/tex] then,
[tex]$m=\frac{260-125}{5-2}$\$$\begin{aligned}&=\frac{135}{3} \\&=45\end{aligned}$$[/tex]
Cost of per session the average rate is $45.
Describe a relationship modeled by the function [tex]f(x) = 4x^3 - 72x^2 + 320x[/tex], and explain how the function models the relationship.
Then, identify and interpret the key features of the function in the context of the situation described in part A.
(Describe a relationship that could be modeled by the given function. There is no single correct answer: any scenario that fits the function type is correct.)
Answers
The relationship modeled that has the function of f(x) = 4x³ - 72x² + 320x is known to be the volume of a right prism that has its dimensions to be : 4 times of its desired length, 10 units lower that its desired length, and 8 units lower than its desired length.
What is the volume of the prism about?For us to know the relationship modeled by the above function, the best way to do it is for one to factor it.
The function is: f(x) = 4x³ - 72x² + 320x
First. we factor it so as to extract the common factor 4x:
Secondly, we factor the quadratic trinomial.
This is often done by writing it as a product of two binomials where the two constant terms are said to be sum up - 18 and its product is said to be 80.
The above terms are known to be -10 and - 8; so the two factors are said to be (x - 10) and (x - 8).
Therefore The relationship modeled that has the function of f(x) = 4x³ - 72x² + 320x is known to be the volume of a right prism that has its dimensions to be : 4 times of its desired length, 10 units lower that its desired length, and 8 units lower than its desired length.
Where it has :
x = the desired length,
4x = 4 times its desired length,
x - 10 = 10 lower than its desired length,
x - 8 = 8 lower than its desired length,
We can therefore say that the volume of the prism is said to be the product of the three factors which are:
V = (4x)(x-10)(x-8)
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hi I have no idea how to do this question :)
Answers
Answer:
A. 36
Step-by-step explanation:
Because the two angles at the bottom of both the triangles are congruent, the two triangles are similar. Therefore, the corresponding side lengths of the triangles must be proportional to each other
if the area of a triangle is hb/2,
(with h=length of height, b=length of base)
the height of the first triangle is:
25 = 10h/2
50 = 10h
h=5
you can write ratios representing the proportions of the two triangles:
5/x = 10/12 (with x=height of second triangle)
x=6
then find the area of the second triangle with the height (6) and base (12)
(6*12)/2 = 36
GEOMETRY QUESTION HELP ASAP THANK YOU)
(The question is on the picture below)
Answers
Answer:
The ANSWER is Option A ( 151° ).
.
.
Mark BRAINLIEST!
Please.. Given the image below, DY,EY ,FY are perpendicular bisectors of △ABC. So, 30.11=
a) FY
b) YE
c) EB
d) DY
e) cannot be determined
Answers
Answer:
e) cannot be determined
Step-by-step explanation:
hope this helps!!
anyone know how to answer this?
Answers
Find all the possible values of tan^-1 1
Answers
The possible values of tan^-1(1) are (3π + 4n)/4
How to determine the possible values?The expression is given as:
tan^-1(1)
To determine the possible values, we plot the graphs of
y = tan(x) and y = 1
From the graph, we have the following values
tan^-1(1) = (3π + 4n)/4 when n = ±{0,1,2....}
Hence, the possible values of tan^-1(1) are (3π + 4n)/4
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A una excursion van 40 niños acopmañados por 30 adultos.Pasaran la noche en cabañas iguale,pero lod niños y los adultos deben dormir separados.Cuantas menos cabañas ocupen,menos pagaran ¿cuantas cabañas deben ocupar para pagar lo menos posible?¿cuantos dormiran en cada cabaña?
Answers
The factor computed illustrates that the number of cabins that should be occupied will be 20 cabins.
How to calculate the cabins?From the information given, there are 40 children and 30 adults. In this case, the common factors are 1, 2, 3, 5, and 10. The highest common factor is 10.
The question depicts that they will have same cabins. Therefore, the total number of cabins will be:
= 10 × 2
= 20 cabins
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Calcular el area de un pentagono regular de 10 centimetros de lado
Answers
el área del pentágono es de 172 centímetros cuadrado.
¿Qué es Área?El área es el espacio ocupado por un objeto bidimensional.
Se calcula en unidades cuadradas.
Se da que , El lado del pentágono mide 10 centímetros
El área del pentágono está dada por
[tex]\rm A = \dfrac{1}{4} \sqrt {5 ( 5 +2\sqrt{5})} \; a^2[/tex]
aquí A es el área
l es la longitud del lado del pentágono
Sustituyendo los valores
[tex]\rm A = \dfrac{1}{4} \sqrt {5 ( 5 +2\sqrt{5})} \; 10^2[/tex]
A = 1.72 * 100
A = 172 centímetro cuadrado
Por lo tanto, el área del pentágono es de 172 centímetros cuadrado.
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Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?
Answers
The quadratic function is A(x) = 2(405 + 36x – x²). Then the maximum potential area of this year's resized garden will be 1458.
What is the maximum and minimum value of the function?The condition for the maximum will be
f(x)'' < 0
The condition for the minimum will be
f(x)'' > 0
Every summer, Richard plants a garden on a rectangular plot of land.
Last summer, Richard's garden measured 45 feet in length and 18 feet in width.
This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction.
The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced.
Length = (45 – x)
Width = (18 + 2x)
Then the maximum potential area of this year's resized garden will be
A(x) = (45 – x)(18 + 2x)
A(x) = 810 + 72x – 2x²
A(x) = 2(405 + 36x – x²)
For maximum potential, A'(x) = 0
A'(x) = 0
36 - 2x = 0
2x = 36
x = 18
Then the maximum potential area will be
A(x) = 2(405 + 36 × 18 – 18²)
A(x) = 1458
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5284 Ib = _______ tn_______ the answer is 2 tn and 1284 Ib how to convert.
Answers
The value of 5284 Ib is expressed as 2000 tons 642 lbs
Conversion of pounds to tonsGiven the following parameters
2000lb = 1 ton
5284 Ib = 5284lb/2000 = 2.642 tons
2.642 tons = 2000 tons 642 lbs
Hence the value of 5284 Ib is expressed as 2000 tons 642 lbs
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Simplify : i) (〖6x〗^2+x-7)/(12x^2+14x)
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of the given expression can be done as,
[tex]\dfrac{(6x)^2+x-7}{12x^2+14x}\\\\\\=\dfrac{36x^2+x-7}{12x^2+14x}\\\\\\=\dfrac{(6x)^2+x-7}{2(6x^2+7x)}[/tex]
Hence, the simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].
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What is the length of BC?
Answers
Answer:
24
Step-by-step explanation:
3x - 15 = x + 33 [sides opposite congruent angles in a triangle are congruent]2x - 15 = 33 [subtract x from both sides]2x = 48 [add 15 to both sides]x = 24 [divide both sides by 2]BC = 24 [BC = x]What is the unit rate in 187pounds of food for 1447.38
Answers
The unit rate of 187pounds of food for 1447.38 is 7.74 per pound
Unit rateQuantity of food = 187 poundsTotal cost of food = 1447.38Unit rate = Total cost of food ÷ Quantity of food
= 1447.38 ÷ 187
= 7.74 per pound
Therefore, the unit rate of 187pounds of food for 1447.38 is 7.74 per pound
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5x + 2 = 8x + 5 Help me before I die quick math is so hardddddd
Answers
Answer:
x = -1
Step-by-step explanation:
Note: when you send a number across it can change it sign. If it is positive it will turn negative.
5x + 2 = 8x + 5
Send 8x across
5x + 2 - 8x = 5
send 2 across
5x - 8x = 5 - 2
- 3x = 3
Divide both sides by - 3
- 3x/- 3 = 3/- 3
- 3 cancel out - 3
x = 3/ - 3
3 divided by - 3 is - 1
x = -1
Step 1: List it as it is so that we can get it correct!
5x + 2 = 8x + 5
Step 2: Subtract 2 from both sides.
2 - 2 = 0
5 - 2 = 3
Step 3: Simplify.
5x = 8x + 3
Subtract 8x from both sides.
5x - 8x = -3x
8x - 8x = 0
Step 4: Simplify.
-3x = 3
Step 5: Divide by -3.
-3 / -3 = 1
3 / (-3) = -1
x = -1
If you need help, let me know and I will gladly assist you!
Which expressions are equivalent to 22c + 33d
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are A, C, and E.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
To know the expressions that are equivalent to 22c+33d, all the expressions in the options are needed to be simplified.
Let simplify each of the given opion,
A.) (−2c−3d)(−11) = 22c + 33d
B.) 2(11c− 33/2) d = 22c - 33d
C.) (66c+99d)⋅1/3 = 22c + 33d
D.) −1×(−22−33d) = 22 + 33d
E.) 11⋅(2c+3d) = 22c + 33d
Hence, the correct options are A, C, and E.
The complete question is:
Which expressions are equivalent to 22c + 33d?
A. (−2c−3d)(−11)
B. 2(11c− 33/2 d
C. (66c+99d)⋅1/3
D. −1×(−22−33d)
E. 11⋅(2c+3d)
choose 3 answers
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Which scatterplot shows no correlation?
A graph with both axes unnumbered. A scattered line increases from left to right.
A graph with both axes unnumbered. A scattered line decreases from left to right.
A graph with both axes unnumbered. A short scattered line increases from left to right.
A graph with both axes unnumbered. A line zig zags up and down the graph.
Answers
Answer:
The graph has random dots all over
Step-by-step explanation:
i need help on question 32 for algebra
Answers
Answer:
d. 40 feet
Step-by-step explanation:
Perimeter = 140 ft
Width = L + 10
P = 2w + 2L
140 = 2(L + 10) + 2L
140 = 2L + 20 + 2L
120 = 4L
L = 30
w = L + 10
w = 30 + 10
w = 40
Find the equation of a circle whose center is at (-3, 7) and radius is 9 units.
Answers
Answer:
(x + 3)² + (y - 7)² = 81
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius
here (h, k ) = (- 3, 7 ) and r = 9 , then
(x - (- 3) )² + (y - 7)² = 9² , that is
(x + 3)² + (y - 7)² = 81
Answer:
[tex]x^2+y^2+6x-14y-23=0[/tex]
Step-by-step explanation:
[tex](x-(-3))^2+(y-7)^2=9^2\\x^2+6x+9+y^2-14y+49=81\\x^2+y^2+6x-14y-23=0[/tex]
Sam opened a savings account with $400. He earns $1,640 a
month at his job and will deposit 3% of his monthly pay every
month into his new savings account. Assuming he doesn't
withdraw money from his savings account, which equation shows
the balance y of his savings account x months after he opened it?
y = 12x + 400
y = 400x + 1640
y = 49.2x + 400
y = 0.03x + 400
Answers
Answer:
y = 49.2x+400
Step-by-step explanation:
He deposits 3% of his monthly pay = 0.03*1640 = $49.2 every month = 49.2x
He put $400 when he opened the account so that needs to be added in = 49.2x+400
P=(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} ) : \frac{4x}{(x-1)^{2} }
Answers
The solution to the division of the given surd is: [tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]
Division of Surds.The division of surds follows a systemic approach whereby we divide the whole numbers separately and the root(s) are being divided by each other.
Given that:
[tex]\mathbf{P=(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} ) : \frac{4x}{(x-1)^{2} }}[/tex]
i.e.
[tex]\mathbf{=\dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )}{ \frac{4x}{(x-1)^{2} }} }[/tex]
Using the fraction rule:
[tex]\mathbf{\dfrac{a}{\dfrac{b}{c}}= \dfrac{a\times c}{b}}[/tex]
[tex]\mathbf{\implies \dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )(x-1)^{2}}{4x}} }[/tex]
By simplification, we have:
[tex]\mathbf{ =\dfrac{\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{2} }{4x} }[/tex]
[tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]
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Find the area of a circle with radius, r = 5.64m.
Give your answer rounded to 2 DP.
r
The diagram is not drawn to scale.
Answers
Answer:
99.93 [tex]m^{2}[/tex]
Step-by-step explanation:
1. The area of a circle is defined by the equation: A = [tex]\pi r^{2}[/tex]
2. We can plug in the radius and solve the equation: A = [tex]\pi *5.64^{2}[/tex]
3. A = π * 31.8096
4. A = 99.932
5. A = 99.93
help me please 10 points
Answers
Answer:
150 square feet
Step-by-step explanation:
Method 1: The area of a trapezoid is
A = (8 + 17) / 2 x 12 = 150 square feet
Method 2: You can also split it into a rectangle and a triangle.
12 x 8 + 12 x (17 - 8)/2 = 150 square feet
go 5
U
12 x 9
18
11
17
how do I solve this
Answers
Answer:
6/17
Step-by-step explanation:
12/18 * 9/17
use 9 to divide 18 u'll be left with
12/2 * 1/17
use 2 to divide 12 u'll be left with
6/1 * 1/17
now u'll multiply leaving you with
6/17 as the final answer or u can also convert to decimal your answer will be
0.352 by approximation.
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Given: The
measure of angle B = 27 degrees, measure of angle C
= 82 degrees, and b = 12. Then a =to the
nearest tenth.
Answers
Answer:
25
Step-by-step explanation:
We can calculate for a using sine rule.
For angle A,
A + 27° + 82° = 180 ( sum of angles in a triangle).
A + 109 = 180
A = 180 - 109 = 71°
Therefore,
A = 71°
calculating for side a
[tex] \frac{sin \: 27}{12} = \frac{sin71}{a} \\ a = \frac{12 \times sin71}{sin27} \\ a \: = \frac{11.346}{0.454} \\ a = 25[/tex]