12. The table of values below describes a quadratic relation. Find the missing value and include calculations that demonstrate that this is the correct value.
Answers
Answer:
The quadratic equation is;
y = 3x^2-7x + 5
when x = 4, y = 25
Step-by-step explanation:
Mathematically, the general form of a quadratic equation is;
y = ax^2 + bx + c
From the first point, we have that x = 0
Thus;
5 = a(0)^2 + b(0) +c
c = 5
Now, in a case when x is 2
3 = a(2)^2 + b(2) + 5
3 = 4a + 2b + 5
4a + 2b = -2 ••••••(i)
when x = 6
71 = a(6)^2 + b(6) + 5
66 = 36a + 6b ••••••(ii)
From equation i,
2b = -2-4a ••••(iii)
we can rewrite equation ii as
66 = 36a + 3(2b)
Substitute iii into ii
66 = 36a + 3(-2-4a)
66 = 36a - 6 - 12a
66 + 6 = 36a -12a
24a = 72
a = 72/24
a = 3
Recall;
2b = -2-4a
2b = -2-4(3)
2b = -2-12
2b = -14
b = -14/2
b = -7
So the quadratic equation would be;
y = 3x^2 -7x + 5
Now let us test;
when x = 10, y = 235
That would be:
y = 3(10)^2 -7(10) + 5
y = 300 - 70 + 5
y = 235
This shows that the derived quadratic equation is correct
Now, when x = 4; we have it that;
y = 3(4)^2 -7(4) + 5
y = 48 -28 + 5
y = 20 + 5 = 25
Related Questions
Question 5 (1 point)
Find the volume of the figure below. Leave in terms of TT for answers that contain T. Round your answer to the nearest hundrednth if
necessary
7 ft
8 ft
10 ft
Оа
214.21 ft3
Ob
186.67 ft?
Ос
115.78 ft?
Od
560 ft3
Answers
Answer:
The volume of the shape is 560 ft^3
Step-by-step explanation:
To find the volume of the figure, we need to multiply the base area by the height of the figure
mathematically, we have the base area as a rectangular shape and its area is the product of its side lengths
We have this as 8 ft * 10 ft = 80 ft^2
So multiplying this by the height which is 7 ft, we have this as;
7 ft * 80 ft^2 = 560 ft^3
Can someone please help me
Answers
Answer:
11^2*pi= 121pi
Step-by-step explanation:
3.14x121=121pi
3 Anthony has
$5 to buy breakfast in the
cafeteria a few times this week. Each
breakfast costs $1.25. Which inequality
represents the relationship between the
number of breakfasts, b, he can buy and
the amount of money he has?
F 5 1.25 + b
G5 < 1.25 + b
H 5 > 1.25b
J 5 < 1.25b
Answers
Answer:
The answer would be letter J
The inequality for total expenditure & number of breakfasts is 5 > 1.25b
Formulation of inequality equation for expenditure & breakfasts
Assumed : Number of breakfasts = b
Number of breakfast meals x Price per breakfast meal = Total Expenditure
Total expenditure should be less or than equal to $1.25
So, 1.25b < 5
It implies that inequality : 5 > 1.25b
To learn more about Inequality, refer https://brainly.com/question/19491153?referrer=searchResults
Create an equivalent ratio to 30:40 by dividing both sides by 10. What is the equivalent ratio?
Answers
Answer:
3:4
Step-by-step explanation:
Se prestan 45 000 € y al cabo de un año, 4 meses y 20 días se reciben 52 500 €. Calcular la tasa de interés
Answers
Answer:
the rate of interest is 11.7453%
Step-by-step explanation:
Given that
The present value is € 45,000
The Future value is €52,500
Time period 1 year, 4 months and 20 days i.e. 1.38809 years
We need to find out the interest rate
Here we apply the RATE formula in the spreadsheet
The formula is
= RATE(NPER;PMT;-PV;FV;TYPE)
The PMT would be zero
After applying the above formula, the rate of interest is 11.7453%
31% of what number is 25?
Answers
Uhh, I think it is 80.65
Hope this helped （￣︶￣）↗
Answer: 7.75
PLEASE HELP I NEED IT TO PASS THIS CLASS
Answers
Answer:
Angle 5 = 37°
Angle 8 = 143°
Step-by-step explanation:
Angle 2 = Angle 8
Reason : Alternate exterior angles are equal.
Therefore,
Angle 8 = 143°
Angle 5 + Angle 8 = 180°
Reason : Angle 5 & 8 are in a linear pair.
Angle 5 + 143° = 180°
Angle 5 = ( 180 - 143 )°
Angle 5 = 37°
Write an exponential function and then find the value when t=7 initial value2000 annual rate:9.2%growth
Answers
Answer:
Step-by-step explanation:
Write an exponential function and then find the value when t=7 initial value2000 annual rate:9.2%growth
Exponential growth function
= y = a(1 + r)^t
Solving for y
y = 200(1 + 0.092)⁷
In AWXY, w = 6.7 inches, x = 7.4 inches and ZY=71°. Find the area of AWXY, to the
nearest 10th of a square inch.
Answers
Answer:
23.4
Step-by-step explanation:
The area of the triangle is 23.55 in².
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
ΔWXY
w = 6.7 inches
x = 7.4 inches
∠Y = 71°
Now,
The area of the triangle.
= 1/2 (wx) siny
= 1/2 x (6.7 x 7.4) x sin 71
= 1/2 x 49.58 x 0.95
= 23.55
Thus,
The area of the triangle is 23.55 in².
Learn more about triangles here:
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(WILL GIVE BRAINLIEST)
Vanessa has a vase shaped like the triangular prism shown.
She wants to paint the vase's sides, but not the top and
bottom. What is the closest to how many square
centimeters of paint will she need?
ANSWER CHOICES:
27.2 cm^2
31.2 cm^2
17.6 cm^2
44.8 cm^2
Answers
Answer:
C.
Step-by-step explanation:
4 x 2.8 x 2 x 2 = 44.8
PLEASE HELP ! giving a lot of points!
Answers
Answer:
458 g144 gStep-by-step explanation:
As per equation, the initial amount is:
A(0) = 458*(1/2)^(0/30) = 458*1 = 458 gSample amount left after 50 years:
A(50) = 458*(1/2)^(50/30) = 144 g (rounded)Find the value of x- helppp
Answers
Answer:
60º
Step-by-step explanation:
A triangle is 180º so you do (180-60)/2 and you get that x=60.
Hope that helps :)
Answer:
Hey love! x = 60
Step-by-step explanation:
Because a triangle adds up to 180 so
180 - 60 = 120 and sense both angles will be the same measure I divide 120 by 2 and get 60 so
x =60 Hope that helps!
Problem PageQuestion A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 lower than in the first. The tax in the first city was 10%, and the tax in the second city was 8%. The total hotel tax paid for the two cities was $825. How much was the hotel charge in each city before tax?
Answers
Answer:
the hotel charge in the first city is $5250 while the hotel charge in the second city is $3750
Step-by-step explanation:
Let a represent the charge in the first city before tax and b represent the charge in the second city before tax.
Therefore tax in first city = 10% of a = 0.1a
Tax in second city = 8% of b = 0.08b
From the total tax as $825, hence:
0.1a + 0.08b = 825 (1)
The hotel charge before tax in the second city was $1500 lower than in the first. This gives the equation:
b = a - 1500
a - b = 1500 (2)
To find a and b, solve equation 1 and 2 simultaneously. Multiply equation 2 by 0.1 and subtract from equation 1:
0.18b = 675
b = $3750
a = b + 1500 = 3750 + 1500 = 5250
a = $5250
Therefore, the hotel charge in the first city is $5250 while the hotel charge in the second city is $3750
what is the value of [(-3)^3]^2+2^4?
Answers
Hope this helped :)
Which is a direct variation equation?
1. Y=x+5
2. Y=-5/x
3. Y=-5x
4. Y=x-5
Help
Answers
Answer:
3. y = -5x
Step-by-step explanation:
In a direct variation equation, the constant of proportionality (k) is a direct coefficient of the variable x.
Y will be set equal to x multiplied by this coefficient.
Since y = -5x directly relates x to y, with the constant of proportionality, it is a direct variation equation.
So, 3. y = -5x is the correct answer.
Multiply and find the value of x
Answers
Answer:
X=15
Step-by-step explanation:
i only need a little guidance on this, please.
Answers
Answer:
Use the following identities:
sin²θ + cos²θ = 1Since sinθ = -1
cos²θ = 1 - sin²θcosθ = √1 - sin²θ = √1 - (-1)² = √0 = 0Tangent:
tanθ = sinθ / cosθtanθ = -1 / 0 = undefined in any interval where sinθ = -1sinØ=-1
cosØ
√1-sin²Ø√1-10tanØ
sinØ/cosØ1/0undefinedHELP PLEASE I NEED IT LIKE NOW ILL GIVE BRAINLEST
Answers
Answer:
42
Step-by-step explanation:
Since the scale factor is , we know that the bigger shape went to the smaller shape.
If we know that the smaller shape's side, 12, is of the bigger one, we can make the equation
.
To solve for x, we can divide both sides by .
We can multiply by the reciprocal:
Hope this helped!
The first 4 terms of a sequence are 5,-3,-11,-19 which of the following is an equation for the nth term of the sequence?
Answers
Answer:
Step-by-step explanation:
Option D is the correct answer
The next term is - 27
Find the volume of the figure. Use 3.14 for pi
Answers
Answer:
13
Step-by-step explanation:
Suppose the depth of the tide in a certain harbor can be modeled by y = 23 - 5 cos (6.), where y is the water depth in fect
and t is the time in hours. Consider a day in which t= 0 represents 12:00 midnight. For that day, when are high tide and
low tide and what is the depth of each?
a. high tide at 6:00 a.m. and 6:00 p.m., depth 28 ft
low tide at 12:00 noon and 12:00 midnight, depth 18 ft
b. high tide at 6:00 a.m. and 6:00 p.m., depth 23 ft
low tide at 12:00 noon and 12:00 midnight, depth 5 ft
c. high tide at 12:00 noon and 12:00 midnight, depth 28 ft
low tide at 6:00 a.m. and 6:00p.m., depth 18 ft
d. high tide at 12:00 noon, depth 23 ft
low tide at 6:00 a.m., depth 5 ft
Answers
High tide at 6:00 a.m. and 6:00 p.m., depth 23 ft low tide at 12:00 noon and 12:00 midnight, depth 5 ft. Therefore, option B is the correct answer.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given trigonometric function is y=23-5cos(πt/6).
The given equation is y=23-5cos(πt/6), where y is the water depth in feet and t is the time in hours.
To find the high and low tide depths, we need to find the maximum and minimum values of y.
The maximum value of y is obtained when cos(πt/6) = -1, which gives y = 23 - 5(-1) = 28 ft.
The minimum value of y is obtained when cos(πt/6) = 1, which gives y = 23 - 5(1) = 18 ft.
To find the time when high and low tide occur, we need to find the values of t when cos(πt/6) equals -1 and 1 respectively.
When cos(πt/6) = -1, we get πt/6 = 3π/2, which gives t = 12 hours.
When cos(πt/6) = 1, we get πt/6 = 0, which gives t = 0 hours.
Since t = 0 represents 12:00 midnight, we can conclude that high tide will occur at 6:00 a.m. and 6:00 p.m., with a depth of 28 ft, and low tide will occur at 12:00 noon and 12:00 midnight, with a depth of 18 ft.
Therefore, option B is the correct answer.
To learn more about the function visit:
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Find the hypotenuse of the triangle, the
distance between points (4, 4) and (-2,-2).
[?]
(4.4)
Enter the number that
6 goes beneath the radical
symbol
(-2,-2)
6
Answers
Find the inverse of the following function.
f(x) = + 12
OA (1) = x
= 1 – 12
OB. (v) = 12 - Foto
oc. 5- (6) = x3 – 12
OD. 1-() =
= 1 + 12
Answers
Answer:
c
Step-by-step explanation:
exchange y and x
then find y
Can someone plz help me with this one problem!!!
Answers
Answer:
Step-by-step explanation:
Answer:
v = 9 m
Step-by-step explanation:
the formula for the perimeter is P = 2W + 2L.
Here the perimeter is 42 m = 2(12 m) + 2v. Solving for 2v, we get:
42 m - 24 m = 2v, or
v = 21 m - 12 m, or
v = 9 m
A tree grew 92 4/5 feet in 19 1/3 years. What was the average yearly growth rate of the tree
Answers
26912/15
Decimal Form:
1794.13
Mixed Number Form:
1794 2/15
Answer:
4 247/290 or 4.85 ft/year
Step-by-step explanation:
93 4/5 ÷ 19 1/3 = 469/5 ÷ 58/3 = 469/5 x 3/58 = 1407/290 = 4 247/290
Find the 5th term of the arithmetic sequence −5x−6, -x-10,3x−14,.
Answers
I think this is going to help you understand the concept and hope that the answer is correct. Thanks for understanding.
Which graph best represents the
solution to the following pair of
equations?
y = -X - 5
y = 2x + 4
Answers
Answer: The first graph
Step-by-step explanation: I used a graphing calculator
Which ordered pair is a solution to the equation y= 4x - 8?
(2, 1)
(3, 5)
(4, 8)
(5, 10)
(Please help me ASAP I will give u 30 points and brainliest.
Answers
Answer:
(4,8)
Step-by-step explanation:
1=8-8 no
5=12-8 no
8=16-8 YES
10=20-8 no
Answer:
I have that same problem!
Step-by-step explanation:
HELP!!!!!!!!
5. chords AB and CD intersect, forming segments with the measurements shown. What is the value of x?
Answers
Answer:
I don't know if this is correct but I'm pretty sure its C:
explanation: CD is in total 10 in length, The first part of AB is 3 before the lines intersect, AB is larger than CD because of its position, Again i wouldn't totally trust this answer but I think I'm correct
There are 18 students participating in a spelling bee. How many ways can the students who go first, second, third, and fourth be chosen? a. 73,440 ways c. 4,896 ways b. 1,028,160 ways d. 13,366,080 ways
Answers
Answer:
the answer is: A
18 * 17 * 16 * 15 = 73,440