A quadratic function has its vertex at the point (6,10). The function passes through the point (7, – 4).
Find the quadratic and linear coefficients and the constant term of the function.
The quadratic coefficient:
The linear coefficient is:
The constant term is:
I’m confused
Answer:
Quadratic coefficient = -14, linear coefficient = 168, constant term = -494
Step-by-step explanation:
Its easiest to first start out with a vertex form equation because it can then be converted to a standard quadratic.
given a vertex at (6,10) , and point of intersection at (7,-4), the equation can be set up like this:
y = a(x-6)^2+10, because we know h and k from the vertex.
We also know y and x from the given point of intersection so a can be solved.
-4 = a(7-6)^2+10
-4 = a + 10
-4-10 = a
a = -14 which is also known as the quadratic coefficient because it is part of a second degree quantity and a Trionomial as a whole(quadratic).
since all the variables are known, you can
expand the equation and set it to standard form
y = -14(x-6)^2+10
y = -14(x^2-12x+36)+10
y = -14x^2+168x-504+10
y = -14x^2+168x-494
For reference, the standard form equation is ax^2+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.
In this instance, -14x^2+168x-494 = ax^2+bx+c
An iceberg weighs 450,000 pounds. If it loses 0.2% of its weight during the day, what is its new weight at the end of the day?
Answer:
449,100 pounds
Step-by-step explanation:
0.2% in decimal form is 0.002
0.002 (percent lost) * 450,000 (weight) = 900 (pounds lost)
450,000 - 900 = 449,100 pounds
Members of the theater club sold tickets for the spring
musical. On Friday night, they made $125 in presales a
sold 120 tickets at the door. For the Saturday night sho
they earned $180 in presales and sold 110 tickets at the
door, If the theater club earned the same amount each
night, what is t, the cost per ticket?
Answer:
C. 125 + 120x = 180 + 110x
t = $5.5
Step-by-step explanation:
A.125t + 120 = 180t + 110
B. 120t + 110t = 125 + 180
C. 125 + 120t = 180 + 110t
D. 125 - 120t = 180 - 110t
Friday
$125 + 120t
Saturday
110t + 180
equate Friday and Saturday
125 + 120t = 110t + 180
Collect like terms
125 - 180 = 110t - 120t
-55 = -10t
Divide both sides by -10
t = -55 / -10
= 5.5
t = $5.5
What is the solution, if any, to the inequality |3x|2O?
Answer:
No solutions
Step-by-step explanation:
A triangle has sides with lengths of 21m, 28m, and 49m. Is it a right triangle?
Answer:
To find : If 21m, 28m and 49m form a right angle or not.
Logic : To find if this triangle is a right angle, we can use the Pythagoras Theorem, which states that the square if the longest side should be equal to the square of the sum of the other two sides.
The name of the longest side is called the hypotenuse, while the others are called legs or one is the perpendicular and the other the base.
Proof : [tex]h^{2} = p^{2} + b^{2}[/tex]
=> [tex]49^{2} = 28^{2} + 21^{2}[/tex]
=> 2401 = 784 + 441
=> 2401 ≠ 1225
Therefore these side lengths cannot be the lengths of a right angled triangle.
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Tracey is looking at two different travel agencies to plan her vacation. ABC Travel offers a plane ticket for $295 and a rental car for $39 per day. M & N Travel offers a plane ticket for $350 and a rental car for $33 per day. What is the minimum number of days that Shirley’s vacation should be for M & N Travel to have the better deal?
Answer:
10 days.
Step-by-step explanation:
Let d represent number of days.
We have been given that ABC Travel offers a plane ticket for $295 and a rental car for $39 per day. The total cost of travelling x days using ABC travel company would be .
We have been given that M and N Travel offers a plane ticket for $350 and a rental car for $33 per day. The total cost of travelling x days using M and N travel company would be .
To make M and N travel the better deal, we will set an inequality, where total cost of x days using ABC travels is greater than M and N travels as:
Since the closest integer to 9.1677 is 10, therefore, for a vacation of 10 days using M and N travels will be the better deal.
Which of the following represent the distance formula? Select all that apply.
A. d=(x1−x2)2+(y1−y2)2−−−−−−−−−−−−−−−−−−−−−−−−−√
B. d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−−−−−−−−√
C. d=(x2+x1)2+(y2+y1)2−−−−−−−−−−−−−−−−−−−−−−−−−√
D. d=|x2−x1|2+|y2−y1|2−−−−−−−−−−−−−−−−−−−−−−−√
The distance formular is represented as :
d = √(x2 - x1)² + (y2 - y1)²
Let d = distance
The vertical and horizontal coordinates as x and y respectively ;
The square root of the sum of square of the difference between the x and y coordinates ;
Distance = √(x2 - x1)² + (y2 - y1)²
Hence, d = √(x2 - x1)² + (y2 - y1)²
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NEED YOU GUYS HELP ONCE AGAIN!!
Answer:50
Step-by-step explanation:
help me do this question
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Which table represents a function?
Answer: D
Step-by-step explanation:
For every input there can be only one output. D is the only answer that has one output per input.
Which of the following equations represents a line with a positive slope and a negative y-intercept?
HELP PLEASE!!!!!!!
The y-intercept is the value in the equation without the x and the slope is the value in the equation with the x, it would respond to y = 7.5 - 2
What is the Equation of a Line?A line's equation is a unified representation of all of the line's points. Any point on a line will satisfy the equation in its general version, which is of the type ax + by + c = 0. The slope of the line and a point on the line are the two essential elements needed to create the equation of a line.
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
The y-intercept is the value in the equation without the x and the slope is the value in the equation with the x, it would respond to y = 7.5 - 2
Therefore, the correct answer is option C) y= 7.5x-2.
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1/2 of a number is three more than 1/5 of the same number. What is the number?
PLEASE HELP MEEEEE???????!!!!!!!
Answer:
3
Step-by-step explanation:
18 divided by 6 is 3
Answer:1.333
Step-by-step explanation:
PLEASE HELP ILL GIVE YOU EXTRA POINTS AND MARK YOU AS SOMETHING!!
WHAT IS 144 + 19 PLEASE HELP!!
Answer:
144+19= 163
Step-by-step explanation:
hope this helps! Have a great day!
Answer:
163
Step-by-step explanation:
ADD
can someone help me with the following question in the picture please
Answer:
its a straight origin
Step-by-step explanation:
I'm smart
on Monday the price of gas decrease 6 cent on Tuesday in increased 9 cent what was the overall decrease or increase of the price of gas by the of the day on Tuesday
Answer:
The increase would be 3 cents
Step-by-step explanation:
Find the domain of the graphed function.
What is the positive solution to (x+7)(x−4)=0?
The positive solution would be 4
math question plz help
Answer:
1.8z^2
2.6p^5
3.Yes
Step-by-step explanation:
1.You have to use the Quotient Rule and subtract the exponents but sense they do not have the same base number you would divide the bases 24/3=8 and 4-2=2 and leave the variable the same
2.You would multiply 3*2 giving you six and then you would add the exponents together giving you 5 leaving 6p^5 as your final answer
3.When solving an equation like this you have to use The Product Rule meaning exponents with the same base number you would add the exponents which in this case results in 3+7=10 therefore leaving you with a^10
HOPE THIS HELPS!!!
A box of candy includes 36 pieces. If 2/5 of the candy are peppermints and the remaining candy is chocolates. How many pieces are chocolates?
Answer:
about 22 chocolate pieces
Step-by-step explanation:
total candy - peppermints = chocolate
5/5 - 2/5 = 3/5 chocolates
x/36 = 3/5
cross multiply
x × 5 = 36 × 3
5x = 108
divide both sides by 5
x = 21.6
x is an integer Write down all the solutions of inequality 3<2x +1 < 13
Answer:
1<x<6
Step-by-step explanation:
subtract 1 from every side: 2<2x<12
divide 2 every side: 1<x<6
Answer:1
Step-by-step explanation:
The scatterplot below shows the average yearly consumption of bottled water by people in the United States starting in 1990. Using the trend line, predict the average consumption of bottled water in the year 2000.
5 & 6 ? Explain please
Answer:
5. Rational
6. 4.27 Rational, 0.375 Rational,
0.232342345 Rational, √62 Not rational, 13/1 Rational
Step-by-step explanation:
A rational number is an integer, fraction, terminating decimal, or repeating decimal.
An irrational number is a number that cannot be expressed as the ratio of two integers.
Hope this helps :)
how do you solve a system of linear equations by graphing
Answer:
It depends on the equation/coordinates
Step-by-step explanation:
When solving a linear function, you just have to have a straight line in the coordinate plane.
(11x-3) (4x+39) find x
Answer:
x=6
Step-by-step explanation:
find the x intercept x-y=-1
for every 5 hours that he works, andre is paid $60.20. use this information to complete the table.
Answer:
i hope u understand this
Step-by-step explanation:
i have not even tried it before
but i am sure is excellent
attached is my problem
Answer:
f(x) = 3x - 3
Step-by-step explanation:
First, the slope of the line has to be the same for it to be parallel, so the slope(coefficient of x) of the equation is 3.
Next, to make it pass through that specific point, we need to add/subtract a number to make the equation cross that point.
f(x) = 3x at x = 2 evaluates as 6, but the equation needs to pass through the point (2, 3), so we subtract 3 from the equation, leaving us with f(x) = 3x-3.
help im stupid plzzzzz
Answer:
the third option: x + 2(2x - 4) = 10
Step-by-step explanation:
the question tells you that y = 2x - 4.
so, instead of writing y in the equation, just replace it with 2x - 4.
x - 2y = 10
becomes
x - 2(2x-4) = 10
