Your class is selling boxes of flower seeds as a fundraiser. The total profit p depends on the amount x that your class charges for each box of seeds. The equation p = -0.5x^2 + 36x -113 models the profit of the fundraiser. What's the smallest amount, in dollars, that you can charge and make a profit of at least $409?
The smallest amount that can be charged per box of seeds to make a profit of $409 is $20.125
What is a profit?A profit is the financial gain from a business transaction when the revenue from the transaction exceeds the expenses and taxes.
The function for the profit from the fund raiser is; p = -0.5·x² + 36·x - 113
When the profit is $409, we have;
p = 409 = -0.5·x² + 36·x - 113
-0.5·x² + 36·x - 113 = 409
-0.5·x² + 36·x - 522 = 0
The solutions of the above quadratic function, found using the quadratic formula are as follows;
x = (-36 ± √(36² - 4×(-0.5)×(-522)))/(2×(-0.5))
From which we have;
x = (-36 + √(36² - 4×(-0.5)×(-522)))/(2×(-0.5)) ≈ 20.125
x = (-36 - √(36² - 4×(-0.5)×(-522)))/(2×(-0.5)) ≈ 51.875
Therefore, when the profit is $409, the amount charged are x ≈ 51.875 or x ≈ 20.125
The smallest amount charged when the profit is $409 is therefore;
x ≈ $20.125
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how do find 1/4 in a number line
Answer:move one part on the right-side of zero
Step-by-step explanation:
-7x + 6y = -4
14x-12y = 8
Answer:
Step-by-step explanation:
If f(x) = 3x -121, find the sum of values when f(x) = 4.
Write your answers for x as simplified fractions.
I
and x =
The sum of the values when f(x) = 4 is
The required value of the function x is 41.6
What is a function ?This relationship is typically represented as y = f(x), or "f of x," where y and x are coupled such that for each value of x, there is a specific value of y. This means that f(x) can only have one value for a given x. In set theory jargon, a function connects an element x to an element f(x) in another set.
Given : f (x ) = 3x - 121
to find ; value of f ( x ) when f (x) = 4
Since two values of f(x ) are given
we can simply equate these two values
and the answer which we will get is the final answer
thus we get
3x - 121 = 4
3x = 121 + 4
3x = 125
x = 125/ 3
x = 41.6
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Determine which set of side measurements could be used to form a right triangle. square root of 19 comma square root of 35 comma 54 square root of 15 comma 6 comma square root of 51 5, 8, 30 5, 6, 7
As per the concept of right angled triangle, the set of side measurements that could be used to form a right triangle is √15, 6, and √51
Right-angle triangle:
Right angle triangle means a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
Given,
√19, √35, 54
√15, 6, √51
5, 8, 30
5, 6, 7
Now, we have to determine which set of side measurements could be used to form a right triangle.
Here we know that, according to the Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
So, by using Pythagoras' theorem:
Option (2) √15, 6, √51
Makes the right angle triangle,
Because when we verify these by using the Pythagoras theorem,
(√15)² + (6)² = (√51)²
15 + 36 = 51
51 = 51
Therefore, the set of side measurements that could be used to form a right triangle is √15, 6, and √51 option (2) is correct.
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What is the equation of the line that is parallel to the line y=2/3x−4/5 and passes through the point (−3,2)?
A. 2x−3y=−12
B. 3x+2y=4
C. 2x−3y=−6
D. 3x+2y=8
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x-\cfrac{4}{5}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 2/3 and that it passes through (-3 , 2) in standard form
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{(-3)}) \implies y -2= \cfrac{2}{3} (x +3)[/tex]
[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-2)=3\left( \cfrac{2}{3} (x +3) \right)}\implies 3y-6=2(x+3)\implies 3y-6=2x+6 \\\\\\ 3y=2x+12\implies -2x+3y=12\implies {\Large \begin{array}{llll} 2x-3y=-12 \end{array}}[/tex]
I really need help on this one like asap so if someone can help me i'll be very happy. the question is Determine which equation is false, based on the solution set S:{2}.
7 = 6p − 5
4t = 8
3(3c + 1) = 21
5m + 8 = 16
3(3c + 1) = 21 is false
Answer:
3(3c + 1) = 21 is false.
Step-by-step explanation:
PLEASE HELP ASAP FOR 30 POINTS! !!!! Two Pony Express riders each rode part of a 336-mile trip. Each rider rode the same number of miles. They changed horses every 12 miles. How many horses did each rider use?
Answer:
28 horses
Step-by-step explanation:
336/12=28
because every 12 miles they change the horse.
new york i even degree warmer than pari. if it i -8°c in pari, what i the temperature in new york ?
Answer:
-1°C
Step-by-step explanation:
-8+7=-1
Is your s key broken?
please help i have a test tomorrow and i dont know how to do this
Answer:
90 - 2x
Step-by-step explanation:
Angle A and B are both equal as both connect to the middle of the circle
ABO = [tex]x[/tex]
BAO = [tex]x[/tex]
Look at the diagram I attached
Angle ABC is = [tex]x+90[/tex]
Angle BAC = [tex]x[/tex]
Total Angle in a Triangle = 180
[tex]x + 90 + x + ACB = 180[/tex]
[tex]180 - 90 - 2x = ACB[/tex]
[tex]ACB = 90 - 2x[/tex]
A bag contains 5 blue balls 4 red balls 3 orange balls. if a ball is picked from the bag at random, what is the probability that it is a blue ball. Answers have been rounded to the tenth place
The probability that it is a blue ball is 5/12 ≈ 0.416.
Given:
A bag contains 5 blue balls 4 red balls 3 orange balls.
Total balls = 5 + 4 + 3
= 12
Number of possible outcomes = 12
Number of favorable outcomes = number of blue balls = 5
Probability = Number of favorable outcomes / Number of possible outcomes.
= 5/12.
= 0.416
Therefore the probability that it is a blue ball is 5/12 ≈ 0.416.
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The original price of the flowers was $80, but with discount she paid $60. What percent of the flowers she did NOT pay?
The percentage of flowers she did not pay for is 25% (option A)
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
For instance, 25% means 25/100. This means that 25% of a 50mangoes is 25/100× 50 =12.5mangoes
Similarly, the discount when she paid $60 instead of $80 is $80-$60= $20
therefore %discount = 20/80 ×100= 2000/80= 25%
therefore the percentage she did not pay for is 25%
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PLEASE HELP ME!
Show that quadrilateral ABCD is a parallelogram. A(-3,-2) B(-1,2) C(1,1) D(-1,-3)
Answer:
Step-by-step explanation:
With corners as
A
(
−
2
,
−
1
)
,
B
(
1
,
2
)
,
C
(
5
,
2
)
and
D
(
2
,
−
1
)
, let us find slopes of each side of the parallelogram
A
B
C
D
.
Slope of
A
B
is
2
−
(
−
1
)
1
−
(
−
2
)
=
3
3
=
1
Slope of
B
C
is
2
−
2
5
−
1
=
0
4
=
0
Slope of
C
D
is
(
−
1
−
2
2
−
5
=
−
3
−
3
=
1
Slope of
D
A
is
−
1
−
(
−
1
)
2
−
(
−
2
)
=
0
4
=
0
As slopes of alternate sides of quadrilateral are equal, alternate sides are parallel to each other
and
A
B
C
D
is a parallelogram.
Which function has x-intercepts at 4 and -6?
Function for which x -intercepts is at 4 and -6 is given by
y = k (x - 4)( x + 6).
As given in the question,
Let us consider f(x) be the required function.
y = f(x)
Standard form of a function whose x- intercepts is defined as x = a and
x = b is given by ;
f(x) = k (x - a ) ( x -b)
⇒ y = k (x - a ) ( x -b)
Where 'k' is constant which can be evaluate when quadratic function passes through point ( x₁ , y₁).
Here x - intercept is at 4 and -6
a = 4 and b = -6
Function for which x -intercepts is at 4 and -6 is given by :
y = k (x - 4) ( x -(-6))
⇒ y = k ( x - 4 ) ( x+ 6 )
Therefore, function for which x -intercepts is at 4 and -6 is given by
y = k (x - 4)( x + 6).
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Let f and g be differentiable functions. If g and f are inverses of each other,
g(-4)= 7, and f'(7) = 2, then g'(-4) =
Select one answer
A -2
B -1/2
C 1/2
D 2
Answer:
C 1/2
Step-by-step explanation:
You have differentiable functions f and g that are inverses of each other with ...
f(7) = -4f'(7) = 2g(-4) = 7and you want to know g'(-4).
SolutionConsider the composition ...
f(g(x)) = x . . . . . . the functions are inverses of each other.
Differentiating with respect to x, we get ...
f'(g(x))·g'(x) = 1
g'(x) = 1/f'(g(x)) . . . . . . divide by the coefficient of g'(x)
For x = -4, this is ...
g'(-4) = 1/f'(g(-4)) = 1/f'(7) . . . . . use the given values
g'(-4) = 1/2
__
Additional comment
In the attachment, you can consider the red line to be the tangent to f(x) at x=7, and the blue line to be tangent to g(x) at x=-4. The slope of the tangent, g'(-4), is 1/2, the reciprocal of the slope at f(7)=-4.
A function and its inverse are reflections of each other in the line y=x. That line is shown as dashed orange, and the points of interest are marked: (7, -4) and its inverse, (-4, 7).
Please solve the question below
Answer:
be chill bro but which subject is this
bro someone help me i dont understand anything
Answer:
pretty sure its the 2nd, 3rd, and 5th one
(Sorry if im wrong)
Step-by-step explanation:
The table below shows results of a survey about who uses the World Wide Web.
User Percent
Business 34%
Education and Government 12%
Home 54%
If 600 people were surveyed, how many people used the World Wide Web for Business?
Read the following statements:
Statement 1: If it is a square, then it has more than four sides.
Statement 2: If it has less than four sides, then it is a square.
Are the two statements logically equivalent?
A.) Yes, both statements are true.
B.) Yes, both statements are false.
C.) No, only one statement is true.
D.) No, both statements are false.
Answer: No, both statements are false.
Step-by-step explanation: it's logical a square has to have 4 sides no more and no less.
The statements are not logically equivalent because D.) No, both statements are false.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means it has four equal sides and four equal angles. It can also be defined as a rectangle with two adjacent sides of equal length.
A square is a regular polygon with four equal sides and four equal angles of 90° each. A square is a closed two-dimensional shape with four equal sides and four vertices. Its opposing sides are perpendicular to each other. A square can also be thought of as a rectangle with equal length and width.
In this case, a square has four sides. Therefore, the information given about the square is wrong. The correct option is D.
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HELP PLEASE SOLVE ITS SLOPE!
Step-by-step explanation:
1. gradient=y2-y1/x2-x1
=21-9/-7-(-12)
=21-9/-7+12
=12/5
2.consider any two coordinates:
(13,32),(7,33)
gradient:
=33-32/7-13
=1/-5
if the same number is added to both numerator and denominator of the fraction 3/5. the result is 2/3 what is the number?
Answer:
2
Step-by-step explanation:
For each value of X, determine wether it is a solution to
The solutions of -1 + 3x ≥ 14 are 5 and 8.
Linear Inequality:A linear inequality is a Mathematical expression that represents that both sides are not equal. In simple words, we can say that If the relationship makes a non-equal comparison between any two numbers or expressions, then it is known as Linear inequality.
Here we have
-1 + 3x ≥ 14
To determine the solutions of a given linear inequality substitute each value of x and check if the value satisfies the given expression
At x = 5 ⇒ -1 + 3(5) ≥ 14
⇒ -1 + 15 ≥ 14
⇒ 14 ≥ 14
∴ x = 5 is a solution to -1 + 3x ≥ 14
At x = 8 ⇒ -1 + 3(8) ≥ 14
⇒ -1 + 24 ≥ 14
⇒ 23 ≥ 14
∴ x = 8 is a solution to -1 + 3x ≥ 14
At x = -4 ⇒ -1 + 3(-4) ≥ 14
⇒ -1 - 12 ≥ 14
⇒ - 13 ≥ 14 [ which is not true ]
∴ x = - 4 is not a solution to -1 + 3x ≥ 14
At x = 2 ⇒ -1 + 3(2) ≥ 14
⇒ -1 + 6 ≥ 14
⇒ 5 ≥ 14 [ which is not true ]
∴ x = 2 is a solution to -1 + 3x ≥ 14
Therefore,
The solutions of -1 + 3x ≥ 14 are 5 and 8
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can someone help me pretty pls:)
Answer: Choice B
Step-by-step explanation:
A doesn’t contain any variables
B is literal because you can solve for X
C doesn’t contain any numbers
D is an expression
- Your Welcome
Answer:
C.
Step-by-step explanation:
A literal equation consists of mainly variables.
A. has no variables
B. only has one variable
D. Is not an equation
1.
What are the rational zeros of the function
f(x) = 5x² - 35x - 300?
A -12,5
B-12, -5,5
-5, 12
D-5, 5, 12
For the given function f(x) = 5x² - 35x -300 the rational zeroes of the given function are 12 and -5.
As given in the question,
Given function is equal to:
f(x) = 5x² - 35x -300
Simplify the given function f(x) = 5x² - 35x -300 to get the rational zeros of the function,
f(x) = 0
⇒ 5x² - 35x -300 = 0
⇒ 5( x² - 7x - 60) = 0
As 5≠ 0 ,
⇒ x² - 7x - 60 = 0
⇒ x² - 12x + 5x- 60 = 0
⇒(x-12) (x+ 5) = 0
⇒ x = 12 or -5
Therefore, for the given function f(x) = 5x² - 35x -300 the rational zeroes of the given function are 12 and -5.
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-14 feet and 23 feet use absolute value
Answer:
-14 + 23 = 9
Step-by-step explanation:
if you borrow 14 dollars and pay23 dollars you have a change of 9 dollars
with explanation if possible .
part a and b.
The coordinates on the x-axis (the x-intercepts) and y-axis (the y-intercepts) are;
(a) (i) The point, A = (6, 0)
(ii) The point B = (0, 6)
(b) The point A = (4, 0)
The point B = (0, 3)
What are the x and y-intercepts of a graph?The x and y-intercepts are the points at which the graph intersects the x-axis and the y-axis respectively. The coordinates of the points are (x, 0) and (0, y) respectively.
(a) (i) The equation of the line of the graph is; x + y = 6
The x-intercept of the line is at point A
The y-intercept of the line is at point B
At the x-intercept, the y-coordinate is 0, from the equation, x + y = 6, when y = 0, we get;
x + y = 6
x + 0 = 6
x = 6
The coordinate of the x-intercept, A = (6, 0)
(ii) The y-coordinate of the y-intercept is the value c of the equation of the line y = m·x + c
The x-coordinate at the y-intercept is 0
Rearranging the equation, x + y = 6, we get;
y = -x + 6
The y-coordinate at the y-intercept is therefore, c = 6
The point B is therefore; (0, 6)
(b) (i) The equation of the line is 4·y + 3·x = 12
The equation can be rearranged so that we get;
4·y + 3·x = 12
4·y = 12 - 3·x
y = (12 - 3·x) ÷ 4 = 3 - (3/4)·x
y = 3 - (3/4)·x
At the x-intercept, the value of y is 0. Plugging in y = 0 in the equation, y = 3 - (3/4)·x, we get;
0 = 3 - (3/4)·x
3 = (3/4)·x
x = 3 ÷ (3/4) = 4
x = 4,
y = 0 and x = 4, therefore the coordinate of the point A is (4, 0)
(ii) The y-intercept is point B
The x-value at the y-intercept is 0
Plugging the value x = 0 in the equation y = 3 - (3/4)·x, we get;
y = 3 - (3/4)× 0 = 3
x = 0 and y = 3
The coordinate of the point B is (0, 3)
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Square LMNO has vertices L(-2, 2) M(2, 2) N(2, -2) O(-2, -2). Find the coordinate of the image after a 180 degree rotation around (0,0) for point L.
Check the picture below, assuming counter-clockwise rotation.
If a fair die is rolled 6 times what is the probability rounded to the nearest thousandth of getting at least 5 fours?
To get 1 four, probability is 1/6
To get 2 fours, probability is (1/6)^2
So
To get 5 fours, probability is (1/6)^5 = 0.0001286
Three-eights of the seven grade students were taking advanced math at the beginning of the year, but seven dropped out by the end of the year. If there were 140140 students taking advanced math at the end of the year, how many total 7th grade students are there?
Answer:
147 * 3/8
1176/3 = 392
Examine the triangles, which are similar.
12 mm
18 mm
y
?
12 mm
© 2017 StrongMind. Created using GeoGebra.
How many millimeters long is the missing side?
Note: The triangles may not be drawn to scale.
The missing side of the first triangle is 8 millimeters long.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inversely proportional, can be built to find the desired measures in the problem.
We have been given that;
The first triangle has a side length of 12 millimeters, which corresponds to the second triangle's side of 18 millimeters.
The missing side of the first triangle corresponds to a side of 12 millimeters on the second triangle.
Therefore, The relationship between them is;
12/ n = 18/12
n = 12 x 12/18
n = 144 /18
n = 8
Therefore, the missing side of the first triangle is 8 millimeters long.
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