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
Expand and simplify 3(2x-y)-2(4x-2y)
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A=144pi^2 ft. Find the radius
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1. Find the area of each circle. Use 3.14 for A. Round to the nearest tenth.
5cm
RE
Answers
Answer:
78.5 cm²Step-by-step explanation:
Area of circle:
A = πr²A = 3.14*5² = 78.5 cm²
I need Help please!!
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bakit mahalagang matutunan ang mga angkop na pahayag sa panimula gitna at wakas mg isang akda
Answers
Answer:
i understand your statement my good sir but, what is the question?
Step-by-step explanation:
Antoinette Applied for a $6000 loan, which she will start paying back after the interest has accumulated. She had a initial offer for a simple annual interest rate of 6% for three years, but decided to consider other options. Which of the following options of all the crease the interest she pays the most?
F. $5500 loan, simple interest, annual rate of 6%, term of three years
G. $6000 loan, simple interest, annual rate of 5.75%, term of three years
H. $6000 loan, simple interest, annual rate of 6%, term of 2.8 years
J. $5500 loan, compound interest, annual rate of 6%, term of three years
Please Help
Answers
J. $5500 loan, compound interest, annual rate of 6%, term of three years
Need help on this one last question
Answers
Answer:
available
Step-by-step explanation:
if its available if available comment
Find the circumference
Answers
C=D x 3.14
Answer:
37.7 cm
Step-by-step explanation:
C = 2πr
diameter = 12cm
radius(r) = diameter ÷ 2radius(r) = 12 ÷ 2radius(r) = 6cmC = 2πr= 2 × 22/7 × 6Circumference = 37.7 cmevaluate 5^28·5^-32·5^-4
A. 17,920
B. 0.017920
C. 0.000256
D. 0.00000256
Answers
Answer:
D 0.00000256
Step-by-step explanation:
[tex]5^{28} *5^{-32}*5^{-4}=5^{28-32-4}=5^{-8}=\frac{1}{5^{8}} =0.00000256[/tex]
Answer:
B. 0.000256
Step-by-step explanation:
5^28 . 5^- 32 . 5^ -4
= 5^( 28 - 32 - 4 )
= 5^( 28 - 36 )
= 5^- 8
= 1 / 5^8
= 1 / 390625
= 0.000256
please help
if your gonna scam just leave i really need help
Answers
Answer:
x = 23
Step-by-step explanation:
The measures of the angles in a triangle add up to equal 180
That being said we can create an equation to solve for x
180 = 2x + 3x + 1 + 3x - 5
Now we solve for x using basic algebra
step 1 combine like terms
2x + 3x + 3x = 8x
1 - 5 = -4
now we have 180 = 8x - 4
step 2 add 4 to each side
-4 + 4 cancels out
180 + 4 = 184
now we have 184 = 8x
step 3 divide each side by 8
8x/8=x
184/8=23
we're left with x = 23
help
What is the domain and range of the exponential graphed below?
A.Domain: All real numbers
Range: y > -4
B.Domain: All real numbers
Range: All real numbers
C.Domain: x > 0
Range: y < -6
D. Domain: All real numbers
Range: y > 0
Answers
Answer:
B
Step-by-step explanation:
I just did the test
The range and domain of the function exists on all real values
Domain and Range of functionsDomain of a function is the value of the input of graph for which the function exists.
The range of a function is the value of the output of graph for which the function exists.
The given graph denotes an exponential function showing the arrow pointing infinitely in both directions. Hence the range and domain of the function exists on all real values
Learn more on range and domain here: https://brainly.com/question/2264373
Find the discriminant of the following quadratic equation then state the number of rational, irrational, and imaginary solutions.
Equation: −6x2−6=−7x−9
Discriminant: Answer
Solutions:
Answers
Answer:
-6x² - 6 = -7x - 9-6x² + 7x - 6 + 9 = 0-6x² + 7x + 3 = 06x² - 7x - 3 = 0Discriminant:
D = (-7)² - 4*6*(-3) = 49 + 72 = 121Since D > 0, there are 2 real solutions:
x = (- (-7) ±√121 )/12x = (7 ± 11)/12x = 1.5, x = -1/3what inequality is equivalent to 2/3x - 5 <11 ?
Answers
An 80–calorie apple is 4% of jeremy’s daily caloric intake. What is Jeremy’s daily caloric intake?
Answers
Answer:
3.2 calories
Step-by-step explanation:
4% is .04
so
80 x .04 = 3.20
Select the correct answer
Answers
Answer:
x = 95°
y = 147°
z = 128°
Step-by-step explanation:
z = 180 - 52 = 128°
x: first find the remaining angle in the big triangle, 180 - (45 + 50) = 85°
x = 180 - 85 = 95°
y: first find the remaining angle in the small triangle, 180 - (95 + 52) = 33°
y = 180 - 33 = 147°
A rectangular garden has an area of 84 square feet and a length of 7 feet. What is the width of the garden?
Answers
Answer:
12 ft
Step-by-step explanation:
Given data
Area= 84 ft^2
Length= 7ft
The expression for the area is
Area= L*W
substitute
84=7*W
W= 84/7
W= 12ft
Hence the width is 12 ft
Answer:12ft
Step-by-step explanation:
What is the measure of the missing angle?
Answers
Answer:
42
Step-by-step explanation:
A cylinder has a height of 17 inches and a radius of 8 inches what is the use π = 3.14 and round your answer to the nearest hundredth
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Answer:
3418.05
Step-by-step explanation:
What is the probability of landing on a 9 and then landing on a 7?
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Answer:
what are we landing on? D 10s D20s?...
Step-by-step explanation:
:/
3. A circle with center (0,0) has a y-intercept at (3,0).
Find the equation of the circle.
Answers
Answer:
x^2 + y^2 = 9
Step-by-step explanation:
The standard equation of a circle with center at (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2. Here h = 0, k = 0, x = 3 and y = 0:
(3 - 0)^2 + (0 - 0)^2 = r^2, or
9 = r^2. Thus, the radius is 3.
The equation of this circle is (x - 0)^2 + (y - 0)^2 = 9, or
x^2 + y^2 = 9
What is the median of the data set? History Test Scores 5 0 8 6 5 6 8 9 7 0 3 5 8 8 0 6 7 7 7 9 0 1 3 5 6 8 9 9 5 0 = 50 points
Answers
Answer:
The median is 6
Step-by-step explanation:
What is the solution to follow system of equations?
x-3y=7
2x-6y=12
Answers
Last month a bakery sold a total of 3,500 cookies and cupcakes. They sold cookies for $0.75 each and cupcakes for $2 each. If the total sales last month was $4,500, how many cookies and how many cupcakes did the bakery sell?
Answers
Answer:
Number of cookies sold is 2000 and number of cupcakes sold is 1500
Step-by-step explanation:
Let number of cookies be [tex]x[/tex]
and number of cupcakes be [tex]y[/tex] so
[tex]x+y=3500[/tex]
Cost of one cookie is $0.75
Cost of one cupcake is $2
[tex]0.75x+2y=4500[/tex]
[tex]x+y=3500[/tex] [tex]\times 2[/tex]
[tex]2x+2y=7000[/tex]
[tex]-1.25x=-2500\\\Rightarrow x=\dfrac{2500}{1.25}\\\Rightarrow x=2000[/tex]
[tex]y=3500-x=3500-2000\\\Rightarrow y=1500[/tex]
Number of cookies sold is 2000 and number of cupcakes sold is 1500.
At a glass vase factory, 2 out of the last 20 vases produced were chipped. Considering this data, how many of the next 10 vases would you expect to be chipped?
Answers
2 out of 20 = 2/20 which reduces to 1/10 which means 1 out of every 10.
I would expect 1 out of the next 10 to be chipped.
Answer:
1
Step-by-step explanation:
The ages of six boys are given as 12years 3 months,18years 10months,18years 8months,13years 4months,17years 11month and 15years respectively, what is their average age?
Answers
12+0.25+18+0.83+13+0.333+17+0.916+15=77.326
77.326/11=7.029 which rounds to 7
20 points help i dont get my brothes school work LOL
Answers
Answer:
1/12 a mile
Step-by-step explanation:
Answer:
B. 1/12 is the right answer because you have to times the fraction by the reciprocal because you can't divide a fraction. So, you do 1/3 *1/4 = 1/12
Step-by-step explanation:
have a good day/night
may i please have a branlliest
Idil has a smart phone data plan that costs $25 per month that includes 10 GB of
data, but will charge an extra $20 per GB over the included amount. How much
would Idil have to pay in a month where she used 4 GB over the limit? How much
would Idil have to pay in a month where she used went over by x GB?
Answers
Girrls and boys plsss i need help like frl:)
Answers
D- Most babysit because it pays more per-hour.
The reason this is the correct answer is because the question said which is NOT a valid response. This one is not because it didnt tell you how much they get paid per-hour so its incorrect.
Hope this helps!
Have a great day!
- Hailey
11. A rectangle has a diagonal of length 10 units and one side of length 6 units.
How many units long is the perimeter of the rectangle?
Answers
10 + 10 + 6 + 6 = 32
The required perimeter of the rectangle is 28 units.
What is a rectangle?
The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
Here,
Let's denote the length of the rectangle as L and the width as W. We know that the diagonal of the rectangle has a length of 10 units, and we can use the Pythagorean theorem to relate the length, width, and diagonal,
L² + W² = diagonal² [= 10² = 100]
We also know that one side of the rectangle has a length of 6 units, which we can assume is the width W. Therefore, we can solve for the length L,
L² + 6² = 100
L² = 100 - 36
L² = 64
L = 8
So the length of the rectangle is 8 units.
To find the perimeter of the rectangle, we can use the formula P = 2L + 2W, where L is the length and W is the width:
P = 2(8) + 2(6)
P = 16 + 12
P = 28
Therefore, the perimeter of the rectangle is 28 units.
Learn more about rectangles here:
brainly.com/question/15019502
#SPJ2
A right triangle has an area of 98 square inches. If the triangle is not an Isosceles triangle, what are the all possible lengths of the legs?
Answers
Answer:
The possible length of the triangle =
1) (1inches, 196inches)
2) (2incheq, 98inches)
3) (4inches , 49 inches)
4) (7 inches , 28 inches)
Step-by-step explanation:
We are told the above Triangle is not an Isosceles Triangle
Hence, we assume it is a right angle triangle
The area of a triangle is = 1/2 × Base × Height
= let us represent Base and Height = x
Hence:
1/2 × x × x = 98
x² /2 = 98
Cross Multiply
x² = 98 × 2
x² = 196
Step 2
We find the factors of 196
1× 196 = 196 (1, 196)
2 × 98 = 196 (2, 98)
4 ×49 = 196 (4, 49)
7 × 28 = 196 (7, 28)
Therefore, all the possible length of the triangle =
1) (1inches, 196inches)
2) (2incheq, 98inches)
3) (4inches , 49 inches)
4) (7 inches , 28 inches)
