Final answer:
The vertex of the profit function f(x) = -x^2 + 16x - 60 is (8, 4), meaning the maximum profit is $4 when 8 candles are sold. The x-intercepts are (6,0) and (10,0), indicating zero profit when either 6 or 10 candles are sold.
Explanation:
The function given is a quadratic equation of the form f(x) = ax2 + bx + c, where the constants are a = -1, b = 16, and c = -60. To find the vertex of the parabola, we can use the formula -b/(2a) for the x-coordinate of the vertex.
Calculate the x-coordinate of the vertex: x = -b/(2a) = -16/(2 * -1) = 8.
Substitute x = 8 into the original function to find the y-coordinate: f(8) = -(8)2 + 16(8) - 60 = -64 + 128 - 60 = 4.
The vertex is at the point (8, 4). In the context of the problem, this point represents the maximum daily profit of $4, which occurs when 8 candles are sold.
To determine the x-intercepts, we set f(x) to zero and solve for x, which represents the number of candles sold when the profit is zero.
Set the function equal to zero and solve for x: 0 = -x2 + 16x - 60.
Apply the quadratic formula x = [-b ± sqrt(b2 - 4ac)]/(2a) to find the x-intercepts. In this case, a = -1, b = 16, and c = -60.
Calculate the discriminant, sqrt(162 - 4(-1)(-60)) = sqrt(256 - 240) = sqrt(16) = 4.
Find the two x-intercepts: x = [16 ± 4]/(2 * -1) which yields x = 6 and x = 10.
The x-intercepts (6,0) and (10,0) indicate the number of candles sold at which the profit would be zero, specifically at 6 and at 10 candles sold.
Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?
A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that angle ADC is a right angle and that angle BDC is 32° greater than mangle ADB. Solve an equation to find angle BDC and angle ADB.
Answer:
m∠ADB = 29° and m∠BDC = 61°
Step-by-step explanation:
It is given that m∠ADC = 90°
Since m∠ADB + m∠BDC = 90° [∠ADB and ∠BDC are complimentary]
Since ∠BDC = ∠ADB + 32°
So, m∠ADB + m∠ADB + 32° = 90°
2(m∠ADB) + 32° = 90°
2(m∠ADB) = 90 - 32
2(m∠ADB) = 58°
m∠ADB = 29°
Since m∠ADB + m∠BDC = 90°
So, m∠BDC + 29° = 90°
m∠BDC = 90 - 29
= 61°
Therefore, m∠ADB = 29° and m∠BDC = 61°
m∠ADB = 29° and m∠BDC = 61°
Solving this will just be based on some basic angle theorems in a triangle.
We are given; m∠ADB = 29° and m∠BDC = 61° We are told that m∠ADC is a right angle. This means that; m∠ADC = 90°Now, since m∠ADC = 90°, it means that;m∠ADB + m∠BDC = 90° (because m∠ADB and m∠BDC are complimentary angles due to the fact that angle at point D is 90°)
We are also told that;m∠BDC is 32° greater than angle m∠ADB
This means that we can write as;
m∠BDC = m∠ADB + 32°
From earlier, we saw that;m∠ADB + m∠BDC = 90°
Thus, putting m∠ADB + 32° for m∠BDC, we will have;m∠ADB + m∠ADB + 32° = 90°
2(m∠ADB) + 32° = 90°
Subtract 32° from both sides to get;
2(m∠ADB) = 90° - 32°
2(m∠ADB) = 58°
m∠ADB = 58°/2
m∠ADB = 29°
Puttting 29° for m∠ADB into; m∠ADB + m∠BDC = 90° gives us;29° + m∠BDC= 90°
Subtract 29° from both sides to get;
m∠BDC = 90° - 29°
m∠BDC = 61°
In conclusion, m∠ADB = 29° and m∠BDC = 61°Read more at; brainly.com/question/4687866
4m - 4 = 4m
Please solve and show work
. In the algebraic expression mc034-1.jpg 7, 17, and –10 are _____ terms. operations. coefficients. variables.
Answer:
Coefficient
Step-by-step explanation:
The correct option is A.
In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are coefficients.
A. Coefficients. The numbers 7, 17, and -10 are coefficients in the expression 7a + 17b - 10c because they are the constants that multiply the variables a, b, and c respectively.
B. Incorrect. Operations are mathematical actions like addition, subtraction, multiplication, or division, not the constants themselves.
C. Incorrect. Variables, denoted by a, b, and c, are letters or symbols representing unknown or changing quantities, not the constants.
D. Incorrect. Terms are the individual parts of an expression separated by addition or subtraction, consisting of a coefficient and possibly a variable or variables multiplied together. The numbers 7, 17, and -10 are coefficients within the terms of the expression but are not terms themselves.
So, the correct option is A. Coefficients.
The complete question is here:
In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are ______
A. coefficients.
B. operations.
C. variables.
D. terms.
(50 Points Please help)
Drag the expression that is the most reasonable measurement for each object.
Answer:
A. Length of a Tour Bus ↔ #2. 1.1 × 10¹ meters
B. Width of an apple ↔ #3. 4 × 10⁰ centimeters
C. Distance from Earth to a Satellite ↔ #6. 8 × 10² kilometers
D. Thickness of a human hair ↔ #5. 9 × 10¹ micrometers
Step-by-step explanation:
The length of a tour bus should be measured in meters. It sure is way less than 1 kilometer and way more than a few centimeters. It could be about some meters, more than 5 meters, may be between 10 meters and 15 meters.
The measurement in the box # 2. is 1.1 × 10¹ meters, which is equivalent to 1.1 × 10 meters = 11 meters. Thus, this is a reasonable length.
B. Width of an apple.
The most appropriate unit to measure the width of an apple should be centimeter. It certainly is shorter than 1 meter and bigger than 1 mm.
The width of an apple could be, more or less, around 8 centimeters. The only measurement in the boxes that is in that order is that in the box #3., 4 × 10⁰ centimeters, because 10⁰ = 1, so 4 × 10⁰ = 4 × 1 = 4 centimeters.
C. Distance from Earth to a Satellite
The distance from Earth to a satellite should be measured in kilometers.
You can find in the internet that the distances of the satellites are between 700 kilometers and 36,000 kilometers.
The number in the box #1 is too big, in the order of ten trillions of kilometers, because one trillion is 10¹²; thus that is nonseasonal (too big).
The number in the box #6 is 8 × 10² kilometers, which is equal to 8 × 100 = 800 kilometers.
Thus, 8 × 10² kilometers (box #6) is the most reasonable measurement for the distance from Earth to a Satellite
D. Thickness of a human hair
Of course, kilometers, meters, centimeters and even millimeters are units too big to measure the thickness of a human hair.
One micrometer is 10⁻⁶ meters or 10⁻³ millimeters.
In the internet you can find that diameter of the human hair is in the range from 17 micrometers to 181 micrometers.
The measurement in the box #5. is 9 × 10¹ micrometers, which is equivalent to 9 × 10 = 90 micrometers.
Thus, 9 × 10¹ micrometers is the most reasonable measurement for the thickness of a human hair.
A. Length of a Tour Bus ↔ 2. 1.1 × 10¹ meters
B. Width of an apple ↔ 3. 4 × 10⁰ centimeters
C. Distance from Earth to a Satellite ↔ 6. 8 × 10² kilometers
D. Thickness of a human hair ↔ 5. 9 × 10¹ micrometers
What is Satellite?
A satellite is a moon, planet or machine that orbits a planet or star. For example, Earth is a satellite because it orbits the sun. Likewise, the moon is a satellite because it orbits Earth.
What is expression?
An act, process, or instance of representing in a medium (such as words) : utterance freedom of expression. Something that manifests, embodies, or symbolizes something else this gift is an expression of my admiration for you.
According to question, we have to drag the expression that is the most reasonable measurement for each object.
Length of Tour Bus is generally between 1 meter to 2 meters.
So, Reasonable measurement for Length of a Tour Bus is [tex]1.1[/tex]× [tex]10^{1}[/tex] meters
Width of an apple is generally between [tex]2[/tex] centimeters to [tex]6[/tex] centimeters
So, Reasonable measurement for Width of an apple is [tex]4[/tex]×[tex]10^{0}[/tex] centimeters .
Distance from Earth to a Satellite is generally between [tex]700[/tex] kilometers to [tex]3600[/tex] kilometers.
So, Reasonable measurement for Distance from Earth to a Satellite is
[tex]8[/tex]×[tex]10^{2}[/tex] kilometers.
Thickness of a human hair is generally between 17 micrometers to 181 micrometers.
So, Reasonable measurement for Thickness of a human hair is [tex]9[/tex]×[tex]10^{1}[/tex] micrometers.
Hence, we can conclude that the following expression is the most reasonable measurement for each object.
A. Length of a Tour Bus ↔ 2. 1.1 × 10¹ meters
B. Width of an apple ↔ 3. 4 × 10⁰ centimeters
C. Distance from Earth to a Satellite ↔ 6. 8 × 10² kilometers
D. Thickness of a human hair ↔ 5. 9 × 10¹ micrometers
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If ABCDE is translated 2 units to the right and 4 units up, what will happen to the polygon?
Answer:
A polygon will move but won't change shape or size
Step-by-step explanation:
Given the figure
If ABCDE is translated 2 units to the right and 4 units up, then we have to choose the correct option.
A translation is a geometric transformation that moves every coordinate point of a figure by the same distance.
The result of translation transformation implies
The size, the shape and the orientation of the image after translation are same as that of the original object.
Hence, a polygon will move but won't change shape or size
Option A is correct
Which number is greatest?
a. 3.4 × 10-2
b. 4.3 × 10-3
c. 5.2 × 10-4
d. 6.1 × 10-4
Answer:
the answer is d 6.1x 10-4
Step-by-step explanation:
Four girls and three boys volunteer to represent their class at a school assembly.the teacher selects one name and then another from a bag containing the seven students names.what is the probability that both representatives will be girls
The volume of a sphere with radius r is 4 3 πr 3 . what is the volume of a sphere with radius 5
Final answer:
To find the volume of a sphere with a radius of 5, plug the value into the formula V = (4/3)πr³. The result is approximately 523.6 cm³.
Explanation:
The question asks for the volume of a sphere with a given radius. The formula to calculate the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius of the sphere.
To find the volume of a sphere with radius 5, we substitute r with 5 in the formula:
V = (4/3)π(5)³
V = (4/3)π(125)
V = (4/3)π(125) = 500/3π cm³
The volume of a sphere with radius 5 is therefore 500/3π cubic centimeters, which is approximately 523.6 cm³ when rounded to one decimal place.
How do I find the perimeter and area?
The perimeter of a triangle is 86 inches. The largest side is four inches less than twice the smallest side. The third side is 10 inches longer than the smallest side. What is the length of each side?
The depreciating value of a semi-truck can be modeled by y = Ao(0.87)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 13% per year. What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $67,000?
Answer: 1) The value of truck initially would be $87000.
2) at t = 0 , y-axis would be cut at $67000.
Step-by-step explanation:
Since we have given that
[tex]y=A_0(0.87)^x[/tex]
Here, A₀ is the initial value.
Rate of depreciation = 13%
Number of years = x
So, The value of truck initially would be $87000.
As shown in the given figure.
If the the initial value of truck = $67000
Rate will be same but the y-intercept will change.
As change in initial value does not affect the rate but the y - intercept.
Then at t = 0 , y-axis would be cut at $67000.
Given f(x) = x + 2 and g(x) = x2 – 4, find the function (g/f)(x).
WILL PICK BEST ANSWER IF ITS CORRECT TO ANSWER THESE FEW PROBLEMS
YOU MUST EXPLAIN WHY YOU KNOW
1)Which system of linear inequalities is represented by the graph?
(goes with pic 1)
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y > -1/3x + 2
y > 2/3x + 3 and y >-1/3 x + 2
2)
Which system of linear inequalities is represented by the graph?
(goes with pic 2)
y > 2x – 1 and y < 2x + 2
y > 2x + 2 and y < 2x – 1
y < 2x + 2 and y > 2x – 1
y < 2x + 1 and y > 2x – 2
3)Which linear inequality is represented by the graph?
(goes with pic 3)
y > 2x + 2
y ≥ 1/2x + 1
y > 2x + 1
y ≥ 1/2x + 2
4)
What is the solution to the system of linear equations?
(goes with pic 4)
(–3, 0)
(–3, 3)
(0, 2)
(3, 1)
Part 1)
In this problem we have two lines
The equation of the fist line is
[tex]y=\frac{2}{3}x+3[/tex]
The solution is the shaded area above the dashed line
so
the inequality is
[tex]y>\frac{2}{3}x+3[/tex]
The equation of the second line is
[tex]y=-\frac{1}{3}x+2[/tex]
The solution is the shaded area below the full line
so
the inequality is
[tex]y\leq -\frac{1}{3}x+2[/tex]
therefore
the answer Part 1) is
[tex]y>\frac{2}{3}x+3[/tex] and [tex]y\leq -\frac{1}{3}x+2[/tex]
Part 2)
In this problem we have two lines
The equation of the fist line is
[tex]y=2x+2[/tex]
The solution is the shaded area above the full line
so
the inequality is
[tex]y\geq 2x+2[/tex]
The equation of the second line is
[tex]y=2x-1[/tex]
The solution is the shaded area below the full line
so
the inequality is
[tex]y\leq 2x-1[/tex]
therefore
the answer Part 2) is
[tex]y\geq 2x+2[/tex] and [tex]y\leq 2x-1[/tex]
Part 3)
In this problem we have only one line
The equation of the line is
[tex]y=2x+1[/tex]
The solution is the shaded area above the dashed line
so
the inequality is
[tex]y>2x+1[/tex]
therefore
the answer Part 3) is
[tex]y>2x+1[/tex]
Part 4)
we know that
the solution of the system of linear equations is the intersection both graphs
so
see the graph
the solution point is [tex](0,2)[/tex]
therefore
the answer part 4) is the option
[tex](0,2)[/tex]
In a right triangle angle C measures 40 degrees. The hypotenuse of the triangle is 10in long. What is the approximate length of the side adjacent to angle C?
Sarah decides to take her six-year-old son to the circus the price for the child ticket is $4.75 dollars Less in the price for the adult ticket if we represent the price for the child ticket using the variable X how would you write the algebraic expression for the adult ticket price
You want to buy a new bike, and your parents will contribute $32.50 toward the cost of the bike. If the most expensive bike is $50.00, how much will you have to spend on the bike? Solve the following inequality 50.00 > 32.50 + x and graph its solution.
solve the equation using any method: -2x^2-4x=6
I need to know how to find angle "H"
One-on-one mapping from one plane to the same plane is called:
congruency.
transformation.
isometry.
None of the choices are correct.
Final answer:
Isometry is the term used for a one-on-one mapping from one plane to the same plane. It is key in transformations and geometry studies.
Explanation:
Isometry is the term for a one-on-one mapping from one plane to the same plane. In mathematics, this concept is crucial in the study of transformations and geometry. An isometry preserves distances, angles, and areas in a mapping, making it a significant concept in mathematical modeling.
A 10-foot piece of string is cut into two pieces so that the longer piece is 1 footfoot longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
shorter piece = x
longer piece = 2x+1
3x+1 =10
3x=9
x = 9/3=3
short piece = 3 feet
long piece = 2*3+1 = 7 feet
Meghan works at an ice cream shop and makes $8.25 per hour Lucas works at a landscaper and makes $6.50 per hour how much more does Meghan makes each hour ?
The number of lines that can be drawn perpendicular to a given line at a given point on that line in a plane is
Answer:
I JUST HAD THIS QUESTION 1
Step-by-step explanation:
Sarah is y years old now. How could you represent her age 5 years ago?
y + 5
5 y
y - 5
y ÷ 5
y-5..................................................
Rewrite the equation 8x+6x^2-7=x^2
in standard form and identify a, b, and c.
To rewrite the equation 8x + 6x^2 - 7 = x^2 in standard form, subtract x^2 from both sides and combine like terms. The standard form of the equation is 5x^2 + 8x - 7 = 0. The values of a, b, and c are 5, 8, and -7 respectively.
Explanation:The given equation is 8x + 6x^2 - 7 = x^2.
To rewrite it in standard form, we need to collect like terms. Subtracting x^2 from both sides, we get: 6x^2 + 8x - x^2 - 7 = 0.
Combining like terms, the standard form of the equation is 5x^2 + 8x - 7 = 0.
Here, a = 5, b = 8, and c = -7.
A certain triangle has two 45 angles. What type of triangle is it?
A. Acute scalene
B. Right scalene
c. Right isosceles
D. Acute isosceles
Answer:
C. Right isosceles
Step-by-step explanation:
In Acute scalene triangle, all angles are acute ( less than 90 degrees ) and different,
In Right scalene triangle, two angles are acute and different, while, the third angle is of 90°.
In Right isosceles triangle, two angles are acute and equal, while, the third angle is of 90°.
In Acute isosceles, all angles are acute in which any two angles are equal.
Now, given,
The two angle of the triangles are 45° and 45°,
Let x be the third angle,
⇒ x + 45° + 45° = 180°
⇒ x + 90° = 180°
⇒ x = 90°
Hence, the angles of given triangle are 45°, 45° and 90°,
By the above definitions,
It is clear that, given triangle is right isosceles.
Option C is correct.
Which of the following statements is true?
The number 2 /3 is an irrational number.
The number -4 is a whole number.
The number 9 is a rational number.
The number 5/8 is a natural number.
Find 2 consecutive positive even integers such that the product of the 1st and 2nd is 2 less than 5 times the 3rd. Use an algebraic solution.
What is the reason for the third step in this proof? Corresponding sides of congruent triangles are equal in length. The diagonals of a rectangle bisect each other. SSS criterion for congruence Opposite sides of a parallelogram are congruent.
Answer: D Opposite sides of a parallelogram are congruent.
Step-by-step explanation:
The correct answer is the Opposite sides of a parallelogram are congruent.
What is a parallelogram?A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other.
Consider a parallelogram with diagonals that are congruent and perpendicular.
In triangles Δ AOB and Δ AOD,
OA = OA (common)
OB = OD (Since the diagonals of a parallelogram bisect each other)
∠ AOB = ∠ AOD = 90° (diagonals are perpendicular)
Therefore, Δ AOB ≅ Δ AOD (By SAS postulate)
Since, corresponding parts of congruent triangles are equal,
AB = AD
Similarly, we can prove
BC = CD and CD = DA
So, AB = BC = CD = DA.
Also, it is given that AC = BD.
Therefore the correct answer is the Opposite sides of a parallelogram are congruent.
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2x^3+2x^2-19x+20=0 find the roots of the polynomial equation
Answer:
[tex]\frac{3+i}{2} , \frac{3-i}{2} , -4[/tex]
Step-by-step explanation: