Answers
For the given graph of parabola the equation is \(y = x^2 + 6x + 8\).
What is parabola?
A parabola is a symmetrical U-shaped curve that can be formed by intersecting a cone with a plane parallel to its side. In mathematics, it is the graph of a quadratic function, which is a second-degree polynomial equation in the form of \(y = ax^2 + bx + c\), where a, b, and c are constants.
The given set of points form a unique parabola. We can find the equation of the parabola by solving the system of equations formed by substituting the coordinates into the standard form equation of a parabola, which is:
\(y = a(x - h)^2 + k\)
where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.
Substituting the given coordinates, we get the following system of equations:
8 = a\((0 - h)^2\) + k
3 = a\((-1 - h)^2\) + k
0 = a\((-2 - h)^2\) + k
0 = a\((-4 - h)^2\) + k
3 = a\((-5 - h)^2\) + k
8 = a\((-6 - h)^2\) + k
-1 = a\((-3 - h)^2\) + k
Simplifying each equation, we get:
8 = a\(h^2\) + k
3 = a\((h + 1)^2\) + k
0 = a\((h + 2)^2\) + k
0 = a\((h + 4)^2\) + k
3 = a\((h + 5)^2\) + k
8 = a\((h + 6)^2\) + k
-1 = a\((h + 3)^2\) + k
We can solve this system of equations to find "a", "h", and "k". One way to do this is by using a matrix equation:
| \(h^2\)1 | | a | = | 8 |
| \((h+1)^2\) 1 | | k | = | 3 |
| \((h+2)^2\) 1 | | 0 |
| \((h+4)^2\) 1 | | 0 |
| \((h+5)^2\) 1 | | 3 |
| \((h+6)^2\) 1 | | 8 |
| \((h+3)^2\) 1 | | -1 |
We can use a tool like a matrix calculator to solve this system of equations. Solving the matrix equation gives us:
a = 1
h = -3
k = 8
Therefore, the equation of the parabola is:
\(y = x^2 + 6x + 8\)
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Related Questions
Help me please I need help
Answers
Answer:
x = 180
∠DBC = 23
∠ABC = 157
Step-by-step explanation:
A straight line is always 180 degrees
A to D line = 180
6x + 19 + x = 180
7x + 19 = 180
-19 -19
7x = 161
/ 7 / 7
161 /7 = 23
x = 23
Then plug it in
6x + 19
6 ( 23 ) + 19 = 157
x
x = 23
Hope this helps !
evaluate the expression 6x + 4 9/10 when x = 2/3.
Answers
x=2/3
6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10
Answer:
2x-1=y,2y+3=x
Step-by-step explanation:
no explanation
Factor the equation and show your work.
x^2 + 14x + 49
Answers
Answer: (x+7)(x+7), 7 plus 7 is 14 and 7 times 7 is 49
Plz show work if ya can so I can understand this thanks
Answers
Answer:
area = 57√3 cm²
Step-by-step explanation:
lower polygon:
14-8 = 6, 6/2 = 3
3 is the base of the lower left triangle
cos 60° = 3/hypotenuse
hypotenuse = 6
height of triangle² = 6² - 3² = 45
height of triangle² = 36 - 9 = 27
height of triangle = √27 = √(9 x 3) = 3√3
area of lower polygon = 1/2(8+14)(3√3) = 33√3 cm²
upper parallelogram:
area = 8(3√3) = 24√3 cm²
total area = 24√3 + 33√3 = 57√3 cm²
= f(x)= 4 -x, for what input is the output 7
Answers
Answer:
-3
Step-by-step explanation:
Rewrite as follows and solve for x:
7 = 4 - x
Add x to both sides to get positive x
x + 7 = 4
Subtract 7 from both sides to get x by itself
x = -3
A spinner is spun twice with 4 equal sections colored red, orange, green, and blue. What is the P(spinning two Reds)?
1 over 2
1 over 4
1 over 8
1 over 16
Answers
The probability of the spinner landing on 2 reds is P ( 2 Reds ) = 1/8
Given data ,
To find the probability of spinning two reds, we need to calculate the probability of spinning a red on the first spin and then multiply it by the probability of spinning a red on the second spin.
The probability of spinning a red on the first spin is 1/4 since there is one red section out of four equal sections.
Now , the value of P ( R ) = 1/4
when the spinner is spun twice ,
P ( A ) = P ( R ) P ( R )
P ( A ) = 1/4 ( 1/4 )
On simplifying , we get
P ( A ) = 1/8
Hence , the probability is P ( A ) = 1/8.
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Scott owns his house completely subject to his mortgage. Which term describes Scott's interest? A. A Secured party B. Fee Simple C. A License D. An Easement
Answers
Option(B), Scott's interest in his house is a Fee Simple. This means that he has full ownership and control over the property, including the right to sell, lease, or transfer it to others.
Scott's interest in his house is a Fee Simple. This means that he has full ownership and control over the property, including the right to sell, lease, or transfer it to others. The mortgage that he owes is simply a lien on the property, which gives the lender the right to foreclose if he fails to make payments. However, this does not affect Scott's ownership rights or his ability to use and enjoy the property as he sees fit. In contrast, a secured party would be someone who has a security interest in the property, such as a lender or creditor who holds a lien or mortgage. A license would be a limited right to use the property, while an easement would be a right to use a specific portion of the property for a particular purpose.
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A regular pentagon is centere about the orgin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?.
Answers
A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.
The number of sides (n) of the pentagon is:
n =5
The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).
To draw the pentagon onto itself, the pentagon has to be rotated.
The angle of rotation is:
θ \(= \frac{360}{n}\)
θ \(=\frac{360}{5} = 72\)
Other possible angles of rotation must be multiple of 72. i.e.
θ= 72, 144, 216, 288...
Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.
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The complete question is:
A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?
a. A reflection across line m
b. A reflection across the x-axis
c) A clockwise rotation of 144 degrees about the origin
At Sunday’s Best Ice Cream in New Orleans, the price of Ice Cream was $4.00 for a large sundae. Due to the holidays, they are decreasing their price by 12%. What is the new price for the large sundae?
Answers
the answer is $3.88
Step-by-step explanation:
because the ice cream was $4.00 and they subtracted it by 12% which would be $4.00 minus .12 which would give you $3.88
The diameter of a circle is 25 m. Find its area to the nearest whole number.
Answers
Answer:
Answer down below
Step-by-step explanation:
Multiply the following. Show your work to illustrate your understanding of the standard:
a) 3x (7x+8)
b) (x-7) (x+4)
c) (x - 6)²
Answers
Help with this problem please
Answers
The function of u that takes the input u and gives output as v is g(u) = - (8v -2)/ 12.
What are functions?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given that the equation that takes the input and output value to give the function is:
-12u + 3 = 8v + 1
Isolate the value of u.
Subtract 3 from both sides of the equation:
-12u + 3 - 3= 8v + 1 -3
-12u = 8v -2
Divide both sides of the equation with -12.
-12u / -12 = 8v - 2/ -12
u = - (8v -2)/ 12
Hence, the function of u that takes the input u and gives output as v is g(u) = - (8v -2)/ 12.
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Find the slope of the line that passes through the two points below
(-6,5) and (-3,4)
Answers
-1/3
The slope is -3
Slope = -3x
Hope this helps
- Zayn Malik
Solve for x in the equation x squared 14 x 17 = negative 96.
Answers
The value of x in the given quadratic equation is determined as -7 ± 8i.
Solution of the quadratic equationThe solutiion to the linear equation is determined as follows;
x² + 14x + 17 = -96
x² + 14x + 17 + 96 = 0
x² + 14x + 113 = 0
solve the equation using formula method;
a = 1, b = 14, c = 113
\(x = \frac{-b \ \ \pm\sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{- 14\ \ \pm\sqrt{(14)^2 - 4(1\times 113)} }{2(1)} \\\\x = \frac{- 14\ \ \pm\sqrt{-256} }{2}\\\\x = \frac{- 14\ \ \pm\sqrt{256} \times \sqrt{-1} }{2}\\\\x = \frac{-14 \ \ \pm 16 \times i}{2} \\\\x = -7 \pm 8i\)
Thus, the value of x in the given quadratic equation is determined as -7 ± 8i.
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Answer:
-7 ± 8i.
Step-by-step explanation:
I took the test
Let theta be an acute angle of a right triangle. Find the values of the other five trigonometric functions of theta.
Answers
The exact values of the remaining trigonometric functions are listed below:
Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4
Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11
Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3
Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2
How to find the exact values of trigonometric functions
In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:
sin θ = y / √(x² + y²)
cos θ = x / √(x² + y²)
tan θ = y / x
cot θ = x / y
sec θ = √(x² + y²) / x
csc θ = √(x² + y²) / y
Now we proceed to determine the exact values of the trigonometric functions:
Case 3: y = 4, √(x² + y²) = 5
x = √(5² - 4²)
x = 3
cos θ = 3 / 5
tan θ = 4 / 3
cot θ = 3 / 4
sec θ = 5 / 3
csc θ = 5 / 4
Case 4: x = 5, √(x² + y²) = 6
y = √(6² - 5²)
y = √11
sin θ = √11 / 6
tan θ = √11 / 5
cot θ = 5√11 / 5
sec θ = 6 / 5
csc θ = 6√11 / 11
Case 5: x = 8, √(x² + y²) = √73
y = √(73 - 8²)
y = 3
cos θ = 8√73 / 73
sin θ = 3√73 / 73
tan θ = 3 / 8
cot θ = 8 / 3
csc θ = √73 / 3
Case 6: x = √3, y = 1
sin θ = 1 / 2
cos θ = √3 / 2
tan θ = √3 / 3
sec θ = 2√3 / 3
csc θ = 2
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6. You have $1.95 in quarters and dimes. You have 12 total coins. How many of each denomination
do you have? IS
Answers
Step-by-step explanation:
d+q =12
.25q + .10d = 1.95
d = 12-q
substitute
.25q + .10(12 -q) =1.95
.25q + 1.2 - .1q = 1.95
.15q = .75
q = 5. quarters
d + 5 = 12
d = 7 dimes
Answer:
5 quarters and 7 dimes
Step-by-step explanation:
5 quarters = $1.25
7 dimes = $0.70
7 + 5 = 12
$1.25 + 0.70 = $1.95!!
I hope this helped :)
Also, this answer was calculated by g00gle.
The formula for the surface area of a cylinder is s = 2707 + 270 h.
myra is painting a solid cylindrical pillar. the radius of the pillar
is 2 cm, and the height is 15 cm. myra will paint the entire
pillar, including the top and bottom. how many square
centimeters will be painted? use 3.14 for a
Answers
Myra will paint approximately 213.52 square
centimeters
on the cylindrical pillar.
To determine how many square centimeters will be painted on the cylindrical pillar, we need to calculate the
surface area
of the cylinder. The formula for the surface area of a cylinder is given by:
S = 2πrh + 2πr^2
where S is the surface area, r is the
radius
, and h is the
height
.
In this case, the radius of the pillar is 2 cm and the height is 15 cm. We can substitute these values into the formula to find the surface area:
S = 2 * 3.14 * 2 * 15 + 2 * 3.14 * 2^2
Simplifying the expression:
S = 6.28 * 2 * 15 + 12.56 * 4
S = 188.4 + 50.24
S = 238.64 square centimeters
It's important to note that the
formula
for the surface area of a cylinder includes the areas of both the curved surface (2πrh) and the top and bottom circles (2πr^2). Since Myra is painting the entire pillar, including the top and bottom, we need to consider both of these areas in our calculation.
Using the value of π as 3.14, we have found that the surface area of the cylindrical pillar to be painted is approximately 238.64 square centimeters.
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i’ll give brainliest
Answers
Answer: The line is dotted and shaded above
Can someone help me on this ASAP it’s very tricky
Answers
Well the two equations are in y=mx+b form, also known as slope-intercept form.
The slope for the first equation is 5/6. The slope for the second is -4/3. Its very simple. We say that x is 0 for example...
When X = 0...
First equation: Y=7
Second Equation: Y=-6
On the graph you plot (x,y) (0,7) on the graph. so on the Y axis, put a dot at 7. This is for the first equation. We can say x is 6 also, and then the answer is -1.
So the second point is (6,-1).
FIRST EQUATION ONLY: Plot (0,7), (6,-1)
For the second I wont be elaborate as much but its (0,-6), (3,-10)
Brainiest/Heart if helpful!
Answer:
(-6, 2)
Step-by-step explanation:
When you graph \(y=\frac{5}{6} x+7\), you get the red line.
When you graph \(y=-\frac{4}{3} x-6\), you get the blue line.
The answer is the point they intersect, or cross. That would be (-6, 2).
I hope this helps!
pls ❤ and mark brainliest pls!
What the equation would be
Answers
Answer:
4 and 2 respectfully
Step-by-step explanation:
¿Cuántos enteros divisibles por 9 hay entre 95 y 450?
Answers
Answer:
s so you're going to divide when you going to divide 95 why you take it to the other side it will become 95 * 450 equals to 42750 / 9 when we divide 42750 / 9 to give you 4750 that is your answe
The graph of the function, f(x) = x2 - 5x - 7 opens
and has a
value.
Answers
The two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14).
What is a general equation of a quadratic equation?The general equation of a quadratic equation is -
y = ax² + bx + c
It has two possible roots. It has a degree of 2.
Given is the graph of the function, f(x) = x² - 5x - 7.
We have the following -
f(x) = x² - 5x - 7.
We will draw the graph of this function.
Now, the graph cuts the [x] axis at (-1.14) and (6.14).
Therefore, the two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14). The graph opens upwards.
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Which operation would be last when solving the inequality -5x + 9 < -6
Answers
Answer: divding both sides by -5
Step-by-step explanation:
Subtract 9 from both sides.
−5x+9−9<−6−9
−5x<−15
Step 2: Divide both sides by -5.
−5x/−5<−15/−5
x>3
Brian is solving an equation where both sides are quadratic expressions. He sets the expressions equal to y. Then he graphs the system finding that the two graphs share a common vertex, but one graph opens upward and the other opens downward. How should Brian interpret this outcome?Then he graphs the system finding that the two graphs share a common vertex, but one graph opens upward and the other opens downward. How should Brian interpret this outcome?
Answers
Brian interprets this outcome because There is exactly one intersection point.
What is a Quadratic equation?ax2+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given, Both sides of the problem Brian is solving have quadratic expressions. He sets y as the value for the expressions. The system is then graphed, and he discovers that the two graphs have a similar vertex but that they have opposite opening directions.
The parabola expands upward if the leading coefficient is larger than zero and downward if the leading coefficient is less than zero.
A route that starts and finishes at the same vertex is called a circuit. A cycle is a circuit that doesn't repeat its vertices. If a path connects any two of a graph's vertices, the graph is said to be linked.
Therefore, Brian interprets this outcome because There is exactly one intersection point.
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37 of the 998 digital video recorders (dvrs) in an inventory are known to be defective. what is the probability that a randomly selected item is defective?
Answers
The probability that a randomly selection of 998 digital video recorders in a inventory one of them is defective is 3.71%
To solve this exercise the formula and the procedure that we have to use for probability is:
% probability= (achieving success / possible outcomes) * 100
Information about the problem:
Achieving success = 37Possible outcomes = 998Applying the formula to calculate the probability we get:
% probability= (achieving success / possible outcomes) * 100
% probability= (37/ 998) * 100
% probability= (0.0371) * 100
% probability= 3.71%
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
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Determine the equation of a line that passes through the point (3,-2) and is PERPENDICULAR to the equation
y= 3x - 1
Answers
If the line is perpendicular, it means the slope is negative reciprocal of 3, which is -1/3.
Equation where b (y-intercept) is unknown:
y= -1/3x + b
Replace x with 3 and y with -2 since the line passes through those points.
-2= -1/3(3) + b
-2= -3 + b
Add 3 to both sides of the equation:
1=b, the y-intercept is 1.
The full equation:
y = -1/3x + 1
A bus company is doing research to determine if it can save money by switching from gasoline-powered buses to electric-powered buses. The company randomly selects records of gasoline usage from 30 days and calculates that the buses use a mean 22 gallons of gas each day with a standard deviation of 1.8 gallons. The gas station the buses use charges $2.95 for a gallon of gas. The company also knows it would cost $62 to charge the buses enough to be able to run for one day.
Use a 95% confidence interval to recommend a strategic decision for the bus company.
A. The bus company should switch to the electric buses because 22 gallons of gas costs more than $62.
B. The bus company should switch to the electric buses because the least amount of mean gas per day in the confidence interval costs more than $62.
C. The bus company should not switch to the electric buses because the least amount of mean gas per day in the confidence interval costs less than $62.
D. The bus company should not switch to the electric buses because the greatest amount of mean gas per day in the confidence interval costs less than $62.
Answers
Answer: B.
Step-by-step explanation:
D. C. B.
100%
solve the equation using the properties of equality: what is the answer
Answers
Answer:
x = 535
Step-by-step explanation:
x/30 - 1/6 = 18
6x - 30/180 = 18
6x - 30 = 18 × 180
6x = 3240 - 30
6x = 3210
x = 3210/6
x = 535
Answer:
x=545
Step-by-step explanation:
Find in slope intercept form the equation of the line parallel to y + 5x = 2 and passing through the point (-1, 4)
Answers
Step-by-step explanation:
The slope of the line is - 5, the equation will be y=-5x-1.
y+5x=-1
help me its an algebra 2 question 2. John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours. How long will it take them to mow their lawn if they work together?
A. 1 hour 12 minutes
B. 1 hour 15 minutes
C. 1 hour 20 minutes
D. 1 hour 30 minutes
E. 1 hour 35 minutes
Answers
Answer:
A
Step-by-step explanation:
John can mow the same lawn in 3 hours.
In 1 hour he can mow 1/3rd of the lawn.
In 1 hour they can together mow (1/2+1/3)=5/6th of the lawn.
Together they can mow the lawn in 6/5 hours=1.2 hours.
I hope this helped, please mark Brainliest, thank you!!
Time taken to mow the lawn together is 6/5 hours i.e., 1.2 hours.
The correct option is (C).
What is a algebra ?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Given:
John can mow his lawn in 3 hours.
Julie can mow same lawn in 2 hours.
In 1 hour = 1/3rd of the lawn.
In 1 hour, together they can mow
= (1/2+1/3)
=5/6th of the lawn.
Hence, time taken to mow the lawn together is 6/5 hours i.e., 1.2 hours.
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