Turn over into vertex form
y=-30t²+450t-790y=-30(t²-15x+79/3)Solving
y=-30[(t-15/2)²-359/12]Open brackets
y=-30(t-15/2)²+1795/2Accurating
y=-30(t-7.5)²+897..5Compare to Vertex form y=a(x-h)²+k
Vertex
(h,k)=7.5,897.5Max profit is $897.5
ticket price should be $7.5Answer:
$7.50
Step-by-step explanation:
Completing the square formula
[tex]\begin{aligned}y & =ax^2+bx+c\\& =a\left(x^2+\dfrac{b}{a}x\right)+c\\\\& =a\left(x^2+\dfrac{b}{a}x+\left(\dfrac{b}{2a}\right)^2\right)+c-a\left(\dfrac{b}{2a}\right)^2\\\\& =a\left(x-\left(-\dfrac{b}{2a}\right)\right)^2+c-\dfrac{b^2}{4a}\end{aligned}[/tex]
[tex]\begin{aligned}P & =-30t^2+450t-790\\& =-30\left(t^2+\dfrac{450}{-30}t\right)-790\\\\& =-30\left(t^2+\dfrac{450}{-30}t+\left(\dfrac{450}{2(-30)}\right)^2\right)-790-(-30)\left(\dfrac{450}{2(-30)}\right)^2\\\\& =-30\left(t-\left(-\dfrac{450}{2(-30)}\right)\right)^2-790-\dfrac{450^2}{4(-30)}\\\\& =-30(t-7.5)^2+897.5\end{aligned}[/tex]
Therefore, the vertex is (7.5, 897.5)
So the ticket price that maximizes daily profit is the x-value of the vertex: $7.50
Determine whether points are parallel perpendicular or neither
Answer: paralell
Step-by-step explanation: addion
Answer:
a) neither because both of the lines dont have the same slope. there isnt a line is equal to x= (some value)
1-3/1--1= -1
2--3/2-1= 5
b) parallel
8-2/-4--6= 3
2--4/2-0= 3
What is the exact value of sin 11pi/6 radians?
Answer:
-0.5.
Step-by-step explanation:
2pi - 11pi/6 = pi/6
so the angle is in the fourth quadrant where the sine is negative.
pi/6 = 30 degrees and we know form the 30-60-90 triangle that sin 30 = 0.5,
therefore sin pi/6 = 0.5
and sin 11pi/6 = -0.5
The exact value of sin(11π/6) radians is -1/2 by using unit circle
To find the exact value of sin(11π/6) radians, we can use the unit circle and trigonometric identities.
The angle 11π/6 radians is in the third quadrant of the unit circle.
In the third quadrant, the sine function is negative.
We can find the reference angle by subtracting 2π (or 12π/6) from the given angle:
11π/6 - 12π/6 = -π/6
The reference angle is -π/6 radians.
In the unit circle, the coordinates for the angle -π/6 are (√3/2, -1/2). The y-coordinate represents the value of sine.
Therefore, the exact value of sin(11π/6) radians is -1/2.
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All trapezoids are also_____________________. a. squares c. rectangles b. parallelograms d. quadrilaterals
Answer:
The answer is D. quadrilaterals
Step-by-step explanation:
All trapezoids are squares. If a shape is a square, then it is also a rectangle and a rhombus. A trapezoid is a quadrilateral with exactly one set of parallel sidesWhat is the solution of the system below?
x + 2y = 4
y=-2x - 1
Answer:Point form is (-2,3)
Equation form is x=-2y=3
Step-by-step explanation:
Which is the length of side AD?
A.1 unit
B.4 units
C.5 units
D.6 units
х
-4
-2
2
4
А
B
-2
-4
D
с
Answer:
C. 5 units
Step-by-step explanation:
Find the slope and the y-intercept of the line.
5x + 8y = 31
Step-by-step explanation:
1.) Move the 5 to the other side of the equation
8y = -5x + 31
2.)
Divide by 8
y= .625x + 3.8
Answer:
5x + 8y = 31
8y = -5x + 31
y = -0,625x + 3,875
y = mx + b
m = slope
b = intercept
y = -0,625x + 3,875
slope = -0,625
intercept = 3,875
frank bought 6 pens and 3 highlighters in the school store and paid 21$ for the whole purchase. his friend andy paid 19$ for 2 pens and 4 highlighters. if all pens cost the same and all highlighters cost the same what is the price of one pen?
HELP ASAP
The price of one pen is $1.50.
What are the linear equations?6p + 3h = 21 equation 1
2p + 4h = 19 equation 2
Where:
p = number of pens h = number of highlightersWhat is the price of one pen?In order to determine the price of one pen, take the following steps:
Multiply equation 1 by 4 and equation 2 by 3
24p + 12h = 84 equation 3
6p + 12h = 57 equation 4
Subtract equation 4 from 3
27 = 18p
p = $1.50
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If a rectangle has a length of 10 units and an area of 50 units?, what is its perimeter?
60 units
15 units
30 units
Answer- The perimeter should be 30 units
Answer:
30 units
Step-by-step explanation:
a = bh
h = a/b
h = 50/10
h = 5
5(2) + 10(2)
10 + 20
30
Find the length of side a in simplest radical form with a rational denominator.
Answer:
x = 5.5
Step-by-step explanation:
Using a trig ratio, you can use sin, which is opposite over hypotenuse. [tex]sin(30)\textdegree=\frac{x}{11}[/tex]
Now, multiply both sides by 11
[tex]11\cdot sin(30)\textdegree=x[/tex]
this simplifies to x = [tex]\frac{11}{2}[/tex] or 5.5.
Since sin30 is [tex]\frac{\pi}{6}[/tex] radians, it can be written as [tex]\frac{11\pi}{6}[/tex].
when is buying a house better than ranting
Answer:
Buying a home allows you to build wealth over time.
Step-by-step explanation:
no other asset can build your wealth more consistently. When you rent, you are building your landlord's wealth, and not your own. Combined with leverage, real estate appreciation can offer big returns
The radius of a cylindrical gift box is (3x + 2) inches. The height of the gift box is twice the radius. What is the surface area of the cylinder?
The radius of a cylindrical gift box is (3x+2) inches. The height of the gift box is twice the radius. The surface area of the cylinder is 54πx² + 84πx + 32π square inches.
What is the surface area of a cylinder?The surface area of a cylinder is given as:
2πr(r + h)
The radius of a cylindrical gift box is (3x+2) inches. The height of the gift box is twice the radius.
We need to find the surface area of the cylinder.
The radius of a cylindrical gift box is (3x+2) inches.
The height of the gift box is twice the radius = 2(3x + 2) inches
= 6x + 4 inches
The surface area of the cylinder is:
= 2 × π × (3x + 2)( 3x + 2 + 6x + 4) square inches
= 2 × π × (3x + 2)(9x + 8) square inches
= 6πx + 4π( 9x + 8) square inches
= 6πx (9x + 8) + 4π( 9x + 8) square inches
= 54πx² + 48πx + 36πx + 32π square inches
= 54πx² + 84πx + 32π square inches
Hence, The surface area of the cylinder is 54πx² + 84πx + 32π square inches.
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Which classification best describes figure ABCD below?
A. rhombus
B. quadrilateral
C. trapezoid
D. parallelogram
Answer:
Parralelogram
Step-by-step:
Both of the shapes sides are parrallel to the shapes opposite sides, if you need you can look at images of a parralelogram
please give brainliest (:
Answer: D. Parallelogram
Step-by-step explanation:
Both pairs of opposite sides are parallel.
Both pairs of opposite sides are congruent.
Both pairs of opposite angles are congruent.
Diagonals bisect each other.
One angle is supplementary to both consecutive angles (same-side interior)
Evan saves 7 dollars each week. let d represents the total amount of money in dollars Evan saves after w weeks.
What is the definition of a narrator?
A. The person who reads the story
B. The person who says all the dialogue
C. The person who writes the story
D. The person who tells the story
Answer:
D. The person who tells the story
Step-by-step explanation:
The narrator is the person telling the story, or the voice that an author takes on to tell a story.
The person who reads the story is simply a reader. They aren't narrating.
Someone who says all of the dialouge isn't a narrator either, because only saying the dialouge excludes the rest of the story. It's not telling the story.
The person who writes the story is the author, not the narrator.
Therefore, option D makes the most sense.
hope this helps!
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Answer:
52
Step-by-step explanation:
180-128
Answer:
the answer is 28 degrees
Step-by-step explanation:
all you do is subtract 180-128 since this is a supplementary angle and not a complimentary one.
find the distance between (5,5) and (8,1)
Answer:
5
Step-by-step explanation:
Imagine a triangle with two of the corner points being the points (5,5) and (8,1)
The length and width would be 3 and 4 to find the hypotenuse (distance) do
3^2+4^2=x^2
9+16=x^2
25=x^2
x=5
[tex]here \: is \: your \: answer...[/tex]
Step-by-step explanation:
Let (x1,y1) = (5,5) and (x2,y2) = (8,1)
By using distance formula,
[tex]d \: = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
[tex]d = \sqrt{ {(8 - 5)}^{2} + {(1 - 5)}^{2} } [/tex]
[tex]d = \sqrt{ {(3)}^{2} + {( - 4)}^{2} } [/tex]
[tex]d = \sqrt{9 + 16} [/tex]
[tex]d = \sqrt{25} [/tex]
[tex]d = 5 \: units[/tex]
Therefore, the distance between (5,5) and (8,1) is 5 units
A long distance race begins with 28 runners from Team A and 28 runners from Team B. 4 runners from Team A and 12 runners from Team B do not finish the race. What percentage of the runners who finish the race are from Team B?
The percentage of the runner from team B that finishes the race is 21.4%
How to find the percentage that finish the race from team B?
Team A and Team ran a race. Team A had 28 runners and Team B also had 28 runners.
4 runners from team A finishes the race while 12 runners from team B finishes the race.
Therefore, the percentage from team B that finishes the race can be calculated as follows.
percentage from team B that finishes = 12 / 56 × 100
percentage from team B that finishes = 1200 / 56
percentage from team B that finishes = 21.4285714286
percentage from team B that finishes = 21.4%
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DO Tuesday Write 1,003,498 in each form. Word: Expanded: need help really please
word form: one million, three thousand, four hundred ninety eight
number form : 1,003,498
expaned form 1000000 + 30000 + 400 + 90 + 8
i would so base form but i cant
The rectangle has an area 125 square inches find the length and width
Answer:
1 and 125, 5 and 25
Step-by-step explanation:
Any two numbers that multiply to 125 could be considered as the length and width. Because the formula is: A=wl.
What is the fifteenth term of the sequence
5,-10,20,-40,80,...?
1)-163 840
2)-81.920
3)81,920
4)327.680
Answer:
81920.
Step-by-step explanation:
1) the ration of the given sequence is -2=-10/5=20/(-10)...
2) the 15th term can be calculated according to the formula:
a₁₅=a₁*(ratio)¹⁴, then
a₁₅=5*(-2)¹⁴=-5*1024*16=81920.
20. Which of the following shows the inverse of {0, 4), (5,-2), (-1,8), (2,5)}?
O {(0,-4), (-5, 2), (1,-8)(-2,-5)}
O {0,4), (-5, -2), (1,8), (-2,5)}
O {(4,0), (-2,5), (8,-1), (5, 2)}
O {(0,-4), (5,2), (-1,-8), (2,-5)}
Answer:
4,0), (-2,5), (8,-1), (5, 2)}
Help me please
Use the Distributive Property. Fill in each blank to complete the expansion
(x + y)(x - y)= _____2-_____+______-________^2 =______^2 - 2
Round your answer to the nearest hundredth.
Answer:
38.6598 ° or 38.66 °
Step-by-step explanation:
Sides:
a = 4 cm
b = 6.40312 cm
c = 5 cm
Angles:
A = 38.6598 °
B = 90 °
C = 51.3402 °
Other:
P = 15.4031 cm
s = 7.70156 cm
K = 10 cm2
r = 1.29844 cm
R = 3.20156 cm
Agenda:
A = angle A
B = angle B
C = angle C
a = side a
b = side b
c = side c
P = perimeter
s = semi-perimeter
K = area
r = radius of inscribed circle
R = radius of circumscribed circle
Find f(-3) for the function: f(x)= -2x^2+5x+7 show steps
Answer:
f(-3) = -26
Step-by-step explanation:
To find the answer plug -3 in for every x in the equation. Like this:
[tex]-2(-3)^{2} +5(-3)+7[/tex]
Now, simplify:
-2(9) - 15 + 7 Square -3.
-18 - 15 + 7 Multiply -2 by 9.
-26 Simplify.
So, f(-3) = -26.
Hope this helps! If you have any questions feel free to leave them in the comments!
Answer:
Step-by-step explanation:
f(-3)= -2(-3)^2 + 5(-3) + 7
-2(9) - 15 + 7
-18 - 15 + 7
-33 + 7 = -26
What is the answer to this question ?
Answer:
[tex]10x^{3}+x^{2} -1[/tex]
Step-by-step explanation:
Standard form means firstly you will combine like terms (which the problem has already done) and then rewrite the polynomial from greatest power to least power.
We have three separate parts to this polynomial:
-1 [tex]10x^{3}[/tex][tex]x^{2}[/tex]The part that has the greatest power is [tex]10x^{3}[/tex]. This is because the x is multiplied by a power of 3, which is the largest power given. Next up would be [tex]x^{2}[/tex]. Finally, -1 would come last.
Thus, the rewritten equation should look like this:
[tex]10x^{3}+x^{2} -1[/tex]
I hope this helps! If you have any questions about my work feel free to ask down in the comments!
A bag contains 4 red balls, 2 green balls, 3 yellow balls, and 5 blue balls. Find each probability for randomly removing balls with
replacement.
Removing a yellow, a red, a green, and a blue ball =
Removing a blue, a green, a green, and a yellow ball =
Removing a red, a red, a yellow, and a yellow ball =
Removing a green, a yellow, a yellow, and a red ball =
Answer:
[tex]\frac{15}{4802}[/tex], [tex]\frac{15}{9604}[/tex], [tex]\frac{9}{2401}[/tex], [tex]\frac{9}{4802}[/tex]
Step-by-step explanation:
The bag has a total of (4+2+3+5) = 14 balls. Set up the proportions:
Red: [tex]\frac{4}{14}[/tex]
green: [tex]\frac{2}{14}[/tex]
yellow: [tex]\frac{3}{14}[/tex]
blue: [tex]\frac{5}{14}[/tex]
Now solve!
Removing 1 yellow, 1 red, 1 green, and 1 blue = [tex]\frac{3}{14} \cdot \frac{4}{14} \cdot \frac{2}{14} \cdot \frac{5}{14} =\frac{15}{4802}[/tex]
Removing 1 blue, 1 green, 1 green, and 1 yellow = [tex]\frac{5}{14} \cdot \frac{2}{14} \cdot \frac{2}{14} \cdot \frac{3}{14} =\frac{15}{9604}[/tex]
Removing 1 red, 1 red, 1 yellow, and 1 yellow = [tex]\frac{4}{14} \cdot \frac{4}{14} \cdot \frac{3}{14} \cdot \frac{3}{14} =\frac{9}{2401}[/tex]
Removing 1 green, 1 yellow, 1 yellow, and 1 red = [tex]\frac{2}{14} \cdot \frac{3}{14} \cdot \frac{3}{14} \cdot \frac{4}{14} =\frac{9}{4802}[/tex]
The tree diagram represents an
experiment consisting of two trials.
P(D) = [? ]
Answer:
9 over 11 plus 8 over 12 = 2.7
What is 163.28 + 75.459 =
The expression 163.28 + 75.459 is a sum expression, and the result of 163.28 + 75.459 is 238.739
How to solve the expression?The expression is given as:
163.28 + 75.459
The expression is best solved using a calculator.
However, in the absence of a calculator, the following steps can be applied.
Expand each term
163.28 + 75.459 = 163 + 0.28 + 75 + 0.459
Reorder the terms
163.28 + 75.459 = 163 + 75+ 0.28 + 0.459
Add the decimals and integers
163.28 + 75.459 = 238.739
Hence, the result of 163.28 + 75.459 is 238.739
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i need to know what 8 divided by 1 4/5
Congruent yes or no
Congruent? _______
If so, what property? ________
Answer:
Step-by-step explanation:
Congruent by SSS ( three sides are equal in length).