y= (−1/6)x^2+7x−80 multiply both sides by -6
-6y = x^2 - 42x + 480 subtract 480 from both sides
-6y - 480 = x^2 - 42x take (1/2) of 42 = 21.....square this = 441 and add to both sides
-6y - 480 + 441 = x^2 - 42x + 441 simplify the left, factor the right
-6y - 39 = (x - 21)^2 factor the left side as
-6 (y + 39/6) = ( x - 21)^2 (1)
Using the form
4p (y - k) = ( x - h)^2 we can write (1) as
4 (-3/2)(y - (-39/6) ) = ( x - 21)^2
The vertex = ( h, k) = ( 21, -39/6) and p = -3/2
And the directrix is given by
y = k - p → y = -39/6 - (-3/2) = -39/6 + 3/2 = -39/6 + 9/6 =
-30/6 = - 5-------> y=-5
the answer Part 1) is
y=-5
Part 2) (y+2)^2= 129X-5
What is the equation of the directrix of the parabola?Using the form
4p (x - h) = ( y - k)^2 we can write (1) as
4*(129/4)*(x-5/129)=(y+2)²
The vertex = ( h, k) = ( 5/129, -2) and p = 129/4
And the directrix is given by
x = h - p → x = 5/129 - (129/4) = (20-16641)/516-----> -16621/516
x=-32.21
the answer part 2) is
x=-32.21solve the equation 4(-x+4)=12
A color called “shocking pink” is made by mixing red paint with white paint. The ratio of red to white is 2 to 7. How much red paint should be mixed with 16 fl. oz of white paint?
Answer:
4.5 oz
Step-by-step explanation:
The football team is running a jackpot in which the prize will start at $2500 for the first game, and then increase $500 each game if there is no winner. If there are no winners, find the value of the jackpot at the end of their 16-game season.
The value of the jackpot at the end of the 16-game season will be $10,000.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The jackpot prize starts at $2500 for the first game and increases by $500 for each game if there is no winner.
For the second game,
The prize will be $2500 + $500 = $3000.
For the third game,
The prize will be $3000 + $500 = $3500.
Continuing in this pattern, the prize for the 16th game will be:
$2500 + ($500 × 15)
= $2500 + $7500
= $10000
Therefore,
The value of the jackpot at the end of the 16-game season will be $10,000.
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Rewrite with only sin x and cos x.
sin 2x - cos 2x
Select one:
a. 2 sin2x - 2 sin x cos x + 1
b. 2 sin x
c. 2 sin2x + 2 sin x cos x - 1
Last Monday, Luis's mother gave birth to twins and named them Ashley and Umaima. When they were first born, Ashley weighed 2.82.8 2.8 2, point, 8 kilograms , and Umaima weighed 2.52.5 2.5 2, point, 5 kilograms and was 4949 49 49 centimeters tall. How much did the babies weigh in total?
Air is escaping from a spherical balloon at the rate of 4cc/min. how fast is the surface area of the balloon shrinking when the radius is 24 cm? (a sphere of radius r has volume 4 3 πr3 and surface area 4πr2 .)
which of the following parametric equations are equivalent to the polar equation r=3 cos theta
Answer:
B
Step-by-step explanation:
Factor the trinomial below.
9x2 + 6x + 1
A. (9x + 1)(x – 1)
B. (9x + 1)(x + 1)
C. (3x + 1)(3x + 1)
D. (3x + 1)(3x – 1)
Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. How much will Vivian pay for her surgery if it costs $9600?
2320
2420
2820
after doing the math and writing it out. it has to be one of these three answers but i do beleive that its the second answer but i need reassurance
We have been given that Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. We have been given that her surgery costs $9600 and we need to find how much will Vivian have to pay for her surgery.
Since we know that the insurance company will pay any amount after Vivian has paid $500. Therefore, the remaining amount after Vivian pays $500 as deductibles will be $9600 - $500 = $9100.
Now we know that Vivian's insurance company will pay 80% of this amount, therefore, Vivian will have to pay the 20% of $9100 in addition to the $500 she already paid.
20% of $9100 is [tex]9100\cdot \frac{20}{100} = \$1820[/tex]
Therefore, the total amount that Vivian pays for surgery is $500 + $1820 = $2320.
Therefore, the first choice given is the right answer.
YO!!!!!!WILL GIVE 100 POINTS!!!!!!!!!!!BRAIN!!!!!!!!!!!!
Answer:
Following function:
f (x) = {(x + 2)²} × (x-4) × (x + 1)³
The roots are given by:
{(x + 2)²} × (x-4) × (x + 1)³ = 0
x + 2 = 0
x = -2
x-4 = 0
x = 4
x + 1 = 0
x = -1
Answer:
option A
Step-by-step explanation:
Find the exact values of cos (3pi/4radians) and sin (3pi/4 Radians)
If you are doing on apex the answer is √2/2
Write the quadratic function in vertex form: f(x) = 4x2 + 2x -5
A)f(x) = 4(x + 14)2 - 214B)f(x) = 4(x + 116)2 - 214C)f(x) = 4(x + 14)2 - 194D)f(x) = 4(x + 116)2 - 194
Answer:its B
Step-by-step explanation:
f(x) = -4 (x + 1/4)² - 15/4
True or False: A rectangular equation that is not a function may be a function in the polar coordinate system
The given statement is true.
The given statement is a rectangular equation that is not a function that may be a function in the polar coordinate system.
What is a rectangular equation?A rectangular equation or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane.
Polar equations indeed can describe graphs as functions, even when the equations in the rectangular coordinate system are not one of the functions. Polar equations can be graphed accurately using hands by using the Polar Coordinate System.
Therefore, the given statement is true.
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-9 > -2 -3/4v solve.
for v=4i-8j, find unit vector u in the direction of v
a. u= 1/3i - 2/3j
b. i-j
c. sqrt3/3 i - 2 sqrt3/3 j
d. sqrt5/5 i - 2 sqrt5/5 j
The rectangular prism shown has a volume of 140 m3. This prism is enlarged using a scale factor of 2. What is the volume of the enlarged prism?
exactly 2/5 of the unversity students live off campus. Of those students, 3/10 of them live at home. what fraction of the univesity's students live at home? Reduce your answer to lowest terms
Choose the best answer.
The most expensive type of life insurance is:
term insurance
whole-life insurance
endowment life insurance
limited-payment life insurance
Answer:
Endowment life insurance
Step-by-step explanation:
got it right on odyssey
When darcy's school bus travels at 30 miles per hour, it gets from her home to school in 12 minutes. what is the speed of darcy's bus if it makes the same trip in 18 minutes?
Compare your prediction with the total number of pennies on Row 1. How would you change your estimate? Is the result surprising?
Answer:
a statement that your prediction was less than or greater than the actual count
a statement about how you would change your estimation process
Step-by-step explanation:
Choose any of these two.. There both correct btw
The statements that is true about your prediction of the total pennies on rows 1-4 are statement (b) and (d).
A predictive function is one of mathematical function that helps us to know about future events based on past events. There are many types of functions that can be classified as predictive functions.
The prediction was off by greater than 1,000,000 of the actual total. After seeing the result for rows 1-4, you would indeed change your prediction for the total because it indicates a significant deviation.
Complete question
Check every statement that is true about your prediction of the total pennies on rows 1-4.
a) Your prediction was off by less than or equal to 1,000,000 of the actual total.
b) Your prediction was off by greater than 1,000,000 of the actual total.
c) After seeing the result for rows 1-4, you would change your prediction for the total.
d After seeing the results for rows 1-4, you would not change your prediction for the total.
A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?
What is the perimeter of rectangle that is 92 feet long and 46 feet wide?
The perimeter of a rectangle that is 92 feet long and 46 feet wide is calculated using the formula P = 2l + 2w, resulting in a perimeter of 276 feet.
Explanation:The question asks for the perimeter of a rectangle with specific dimensions. To calculate the perimeter of a rectangle, we use the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. Given that the rectangle is 92 feet long and 46 feet wide, we substitute these values into the formula to get the perimeter: P = 2(92) + 2(46) = 184 + 92 = 276 feet.
Therefore, the perimeter of the rectangle is 276 feet.
Geo: Topic 3- Parallelograms 1pt A rhombus is a parallelogram with all four sides of equal length. One way to determine if a given parallelogram is a rhombus is to test whether its diagonals are perpendicular. The vertices of a parallelogram are M(−1,2), N(9,2), P(3,−6), and Q(−7,−6). Determine whether the parallelogram is a rhombus by checking to see if the diagonals are perpendicular. What is the slope of MP¯¯¯¯¯¯? What is the slope of NQ¯¯¯¯¯¯? Are diagonals MP¯¯¯¯¯¯ and NQ¯¯¯¯¯¯ perpendicular? Is the parallelogram a rhombus?
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)^6 are _____.
Answer:
1, 6, 15, 20, 15, 6, 1
Step-by-step explanation:
A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 miles above sea level. The radius of the Earth is 3959 miles. What is the climber's distance to the horizon?
Factor the polynomial:
–x3 – 3x2 – 4x
A. –x(x2 + 3x + 4)
B. –x(–x2 – 3x – 4)
C. –x(x2 + 3x – 4x)
D. x(x2 + 3x + 4
Answer:
D. [tex]-x(x^2+3x+4)[/tex]
Step-by-step explanation:
[tex]-x^3-3x^2-4x = -(x^3+3x^2+4x)= -x(x^2+3x+4)[/tex]
Find the average value have of the function h on the given interval. h(u) = (15 − 10u)−1, [−1, 1]
The average value have of the function h(u) = (15 − 10u)−1 on the given interval [−1, 1] is -5.
What is average value of the function?The average value of a function is given by the formula:
[tex]fav = \frac{1}{b - a} \int\limits^b_a f({x}) \, dx[/tex]
Now the given function is,
h(u) = (15 − 10u) − 1
or, h(u) = 15 − 10u − 1
or, h(u) = 14 − 10u
So, the average value on the given interval [−1, 1] is given as:
[tex]fav = \frac{1}{1 - (-1)} \int\limits^1_{-1} h({u}) \, du[/tex]
Thus, putting the value of h(u) we get,
[tex]fav = \frac{1}{(1 + 1)} \int\limits^1_{-1} (14 - 10u) \, du[/tex]
Thus integrating we get,
fav = (1/2) { [14u] - [10u²/2]
⇒ fav = (1/2) { [14u] - [5u²]
Applying the limits we get, -1 to 1,
⇒ fav = (1/2) { 14[-1 + 1] - [5{-1² + 1²}]
Solving we get,
⇒ fav = (1/2) { 14[0] - [5{1 + 1}]
⇒ fav = (1/2) {- [5{2}]
⇒ fav = -5
Thus, the average value have of the function h(u) = (15 − 10u)−1 on the given interval [−1, 1] is -5.
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Use the intercept form to find the equation of the line with the given intercepts. the intercept form of the equation of a line with intercepts (a, 0) and (0,
b.is
In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red.
If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?
-1/8
-1/2
-2/3
-3/4
Find the sum of the series