help, and if you could explain how you got your value, domain and your range. thank you.
Answers
Answer: This is a quadratic function in standard form:
f(x) = x^2 - 10x + 9
The vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
where (h, k) is the vertex of the parabola.
To rewrite the given function in vertex form, we need to complete the square:
f(x) = x^2 - 10x + 9
= (x - 5)^2 - 16
Now we can see that the vertex is at (5, -16) and the axis of symmetry is x = 5.
To find the x-intercepts, we set y = 0:
0 = (x - 5)^2 - 16
16 = (x - 5)^2
±4 = x - 5
x = 1 or x = 9
Therefore, the x-intercepts are (1, 0) and (9, 0).
To find the y-intercept, we set x = 0:
f(0) = 9
Therefore, the y-intercept is (0, 9).
The graph of the function is a parabola that opens upward with vertex at (5, -16), x-intercepts at (1, 0) and (9, 0), and y-intercept at (0, 9).
Step-by-step explanation:
the vertex is at (5, -16)
y-intercept is (0, 9).
the x-intercepts are (1, 0) and (9, 0).
axis of symmetry is x = 5
the range of the function is all real numbers greater than or equal to -16. In interval notation, we can write this as [-16, ∞).
the domain of the given function f(x) = x^2 - 10x + 9 is all real numbers.
Related Questions
Money Magic
How did you use the 3 meters and the “Show Earnings Report” throughout the game?
Answers
In the game "Money Magic," the three meters and "Show Earnings Report" are used to track the player's progress and earnings.
The three meters represent the player's three main resources: time, money, and energy. Each of these meters decreases as the player performs certain actions within the game. For example, taking on a job or activity may decrease the time and energy meters, while earning money through completing tasks can increase the money meter.
The "Show Earnings Report" is a feature within the game that allows the player to view their earnings and expenses over a given period of time. This report shows the player how much money they have earned and spent, as well as where their earnings are coming from (such as through jobs or investments).
Overall, the three meters and "Show Earnings Report" are important tools for tracking progress and making strategic decisions within the game. By monitoring their resources and earnings, players can make informed choices about how to allocate their time and money to achieve their goals in the game.
The three meters represent the player's three main resources: time, money, and energy. Each of these meters decreases as the player performs certain actions within the game. For example, taking on a job or activity may decrease the time and energy meters, while earning money through completing tasks can increase the money meter.
The "Show Earnings Report" is a feature within the game that allows the player to view their earnings and expenses over a given period of time. This report shows the player how much money they have earned and spent, as well as where their earnings are coming from (such as through jobs or investments).
Overall, the three meters and "Show Earnings Report" are important tools for tracking progress and making strategic decisions within the game. By monitoring their resources and earnings, players can make informed choices about how to allocate their time and money to achieve their goals in the game.
would this relationship best be described as proportional or non proportional? justify your answer
Answers
the relationship between the diameter of the pizza and its cost per square inch is non-proportional.
The relationship between the diameter of the pizza and its cost per square inch is non-proportional.
If the relationship were proportional, then the cost per square inch of the pizza would remain constant as the diameter changes. However, in this case, we see that as the diameter of the pizza increases, the cost per square inch decreases. This is because the area of a circle increases more rapidly than its diameter, so the cost must be spread out over a larger area, resulting in a lower cost per square inch.
Therefore, the relationship between the diameter of the pizza and its cost per square inch is non-proportional.
the complete question is :
would relationship between the dilation factor k and the resulting volume of a solid best be described as proportional or non proportional? justify your answer
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if A shopkeeper sold a Radio at 336 rs and gain 5 persent profit find c. p
Answers
Answer:
If the shopkeeper sold the radio for 336 rs and gained a 5% profit, then the cost price (c.p.) of the radio can be calculated as follows:
Let x be the cost price of the radio. Since the shopkeeper gained a 5% profit, we can write the equation: x + 0.05x = 336 Solving for x, we get: x(1 + 0.05) = 336 x = 336/1.05 x = 320
So, the cost price (c.p.) of the radio is 320 rs.
Step-by-step explanation:
I need help please!!
Answers
The average rate of change of the function f(x) over the interval [-2, -9] is -6.
What is the average rate of change of the function f(x)?To determine the average rate of change of the function f(x) over the interval [-2, -9], we need to find the slope of the secant line that connects the points (-2, f(-2)) and (-9, f(-9)).
We first find the values of f(-2) and f(-9):
f(-2) = (-2)² + 5(-2) + 14 = 4 - 10 + 14 = 8
f(-9) = (-9)² + 5(-9) + 14 = 81 - 45 + 14 = 50
So, the two points are (-2, 8) and (-9, 50).
The slope of the secant line between these two points is:
slope = (f(-9) - f(-2)) / (-9 - (-2)) = (50 - 8) / (-9 + 2) = 42 / -7 = -6
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A banner is centered between two poles by four ropes of equal length. The dimensions of the banner ground and poles are shown what is the length of one of the ropes x to the nearest foot
Answers
The length of one of the ropes is approximately 10.77 feet when rounded to the nearest foot.
Let's call the distance between the poles "d" and the height of the poles "h". We can use the Pythagorean theorem to find the length of the ropes:
If we draw a diagram, we can see that the four ropes form the hypotenuses of four right triangles. Each right triangle has a base of d/2 and a height of h - (banner height)/2.
Therefore, we have:
[tex]x^2[/tex] = [tex](d/2)^2[/tex] + [tex](h - (banner height)/2)^2[/tex]
Substituting the given values, we get:
[tex]x^{2}[/tex] = [tex](20/2)^2[/tex]+ [tex](16 - (8/2))/2)^2[/tex]
[tex]x^{2}[/tex]= 100 + [tex](8/2)^2[/tex]
[tex]x^{2}[/tex] = 100 + 16
[tex]x^{2}[/tex] = 116
Taking the square root of both sides, we get:
x = [tex]\sqrt{116}[/tex]
x ≈ 10.77
Therefore, the length of one of the ropes is approximately 10.77 feet when rounded to the nearest foot.
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the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing (in mm3/s) when the diameter is 100 mm? (round your answer to two decimal places.)
Answers
The volume of the sphere is increasing at a rate of 209,439.51 mm³/s when the diameter is 100 mm
The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 100 mm? (Round your answer to two decimal places).Formula to calculate the volume of a sphere = (4/3) × π × r³where r = radius of the sphere, π = pi = 3.14, d = diameter of the sphere. The diameter of the sphere, d = 100 mm.So, the radius of the sphere, r = d/2 = 100/2 = 50 mm.
Now, we need to find the rate of change of the volume of the sphere when the radius of the sphere is increasing at a rate of 4 mm/s.We know that the volume of the sphere is given by V = (4/3) × π × r³.We have to differentiate the above formula with respect to time (t).dV/dt = d/dt [(4/3) × π × r³]dV/dt = (4/3) × π × 3r² × dr/dt, substitute r = 50 mm and dr/dt = 4 mm/s in the above equation to find dV/dt.dV/dt = (4/3) × π × 3(50)² × 4dV/dt = 209,439.51 mm³/sTherefore, the volume of the sphere is increasing at a rate of 209,439.51 mm³/s .
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The hour hand of a clock is 4.5 cm long while the minute hand of clock is 5.5 cm long (Take # 3.14) What distance does the tip of the hour hand cover in twelve hours (b) What distance does the tip of the minute hand cover in one (c) Which tip covers a longer distance in (a) and (b) above and by how much
Answers
(a) The distance that the tip of the hour hand covers in twelve hours is 28.29 cm.
(b)The distance that the tip of the minute hand covers in one hour is 34.57 cm.
(c) The tip of the minute hand covers a longer distance than the tip of the hour hand by 6.28 cm.
How to find the distance the tip of the hour hand cover in twelve hours?(a) To find the distance that the tip of the hour hand covers in twelve hours, we need to calculate the circumference of the circle that the tip of the hour hand traces in twelve hours. The circumference is given by:
C = 2πr
where r is the length of the hour hand
C = 2 x 22/7 x 4.5
C = 28.29 cm
(b) Also, the distance that the tip of the minute hand covers in one hour is:
C = 2 x 22/7 x 5.5
C = 34.57 cm
(c) We can see that the distance covered by the minute hand in one hour (34.57 cm) is greater than the distance covered by the hour hand in twelve hours (28.29 cm).
difference = 34.57 cm - 28.29 cm = 6.28 cm
Thus, the tip of the minute hand covers a longer distance than the tip of the hour hand by 6.28 cm.
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The cone and cylinder above have the same radius and height. The volume of the cylinder is 57 cm3. What is the volume of the cone? A. 114 cm3 B. 171 cm3 C. 19 cm3 D. 28.5 cm3
Answers
The cone and cylinder above have the same radius and height and the volume of the cone is 171 cubic inches.
Volume of a three-dimensional shape is the space occupied by the shape.
Given that,
Radius and height of the cylinder and the cone are same.
Let r and h be the radius and height of each of the cylinder and the cone.
Volume of the Cone = 1/3 π r² h
Volume of the cone = We have, volume of the cylinder is 57 cubic inches.
1/3 π r² h = 57
Multiplying both sides by 3,
π r² h = 57 × 3
π r² h = 171 cubic inches π r² h
Hence the volume of the cone is 171 cubic inches
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A worker at an animal shelter recorded data about the adoption of cats in the table shown below.
TIME UNTIL ADOPTION FOR CATS AT SHELTER
Time to Adopt
Age
0000
0
Based on the table, which of these statements are true? Choose all that are correct.
a
Younger than 6 Months
6 Months to 1 Year
1 Year and Older
1 to 7 Days 8 Days to 1 Month More than 1 Month
12
9
4
5
2
6
e
3
6
11
Of all the cats adopted, 34.9% are between 6 months and 1 year old
Of the cats 1 year or older, about 58% took more than 1 month to be adopted.
Of all the cats adopted, about 66% were adopted in a month or less.
C
d Of the cats that took more than a month to adopt, 12.5% were younger than 6 months
Of the cats who took 1 to 7 days to be adopted, 25% were between 6 months and 1 year old.
Answers
Based on the table provided, the statement that is true is of all the cats adopted, about 66% were adopted in a month or less.
How to calculate a percentage?To calculate a percentage, you need to divide a part by the whole and then multiply the result by 100. The formula for calculating a percentage is:
Percentage = (Part / Whole) x 100
Alternatively, if you have the percentage and the whole, you can use the following formula to find the part:
Part = (Percentage / 100) x Whole
Based on this, let's prove the true statement:
Total of animals: 58 cats
Total of cats adopted in a month or less: 38
Percentage = 38/ 58 x 100 = 65.5% which can be rounded as 66%
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Hannah has a cone made of steel and a cone made of granite.
• Each cone has a height of 10 centimeters and a radius of 4 centimeteres.
• The density of steel is approximately 7.75 grams per cubic centimeter.
• The density of granite is approximately 2.75 grams per cubic centimeter.
What is the difference, to the nearest gram of the masses of the cones?
Answers
As a result, the difference is 837 grammes between the cones' respective masses.
Describe density.
Mass per unit volume is measured using density. It is described as a substance's mass per unit volume. The following is the density formula:
Mass / Volume equals density.
So, The formula m = V, where m is the mass, is the density, and V is the volume, can be used to determine each cone's mass.
The formula below can be used to determine each cone's mass:
- The mass of a steel cone weighs 1298.21 grams or 7.75 grams per cubic centimeter.
- The granite cone weighs 460.76 grams, or 2.75 grams per cubic centimeter.
- Mass of steel cone = 7.75 g/cm³ × 167.55 cm³ = 1298.21 grams
- Mass of granite cone = 2.75 g/cm³ × 167.55 cm³ = 460.76 grams
for difference of masses = 1298.2 grams - 460.76 grams = 837 grams
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Drag the expressions into the boxes to correctly complete the table, 25 points
Answers
These are the polynomial equations:
A = x^ (1/4) - ∛x + 4√x - 8x + 16
B = 3x² - 5x⁴ + 2x - 12
C = x³ - 7x² + 9x - 5x⁴ - 20
D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1
These are the non-polynomial equations:
E = 4/x⁴ + 3/x³ - 2/x² - 1
F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1
Describe a polynomial?Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.
Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.
Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.
In the equation, we can solve for other values to obtain:
Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.
A = x^ (1/4) - ∛x + 4√x - 8x + 16
This polynomial exists.
B = 3x² - 5x⁴ + 2x - 12
This polynomial exists.
C = x³ - 7x² + 9x - 5x⁴ - 20
This polynomial exists.
D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1
It is a polynomial.
E = 4/x⁴ + 3/x³ - 2/x² - 1
It is not a polynomial.
F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1
A polynomial is not what it is.
The polynomials are thus resolved.
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Calculate the surface area of the solid
Answers
I remember doing this but I don’t seem to remember sorry
Answer:
220-8pi
Step-by-step explanation:
Monica needs 12 lemons per liter of water, to make lemonade for 4 people. What amount of lemons and water does Monica need to prepare lemonade for 30 friends?
Answers
Step-by-step explanation:
12 lemons / 4 people * 30 people = 90 lemons
1 liter/ 12 lemons * 90 lemons = 7.5 liters of water
A line has a slope of
-5 and includes the points (7,p) and (8,4). What is the value of p?
Answers
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{p})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{p}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{7}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -5 }\implies \cfrac{4-p}{1}=-5 \\\\\\ 4-p=-5\implies 4=-5+p\implies 9=p[/tex]
Step by step
Slope is -5/1 as y/x
Slope can be found with slope formula
y2 - y1 over x2 - x1
We only need to solve for y since “p” is a y value
Y2 - y1 = -5
4 - p = -5
Subtract 4 from both sides to isolate p
4 - 4 - p = -5 -4
-p = -9
p = 9
So now we have ( 7, 9) and ( 8, 4)
y2 - y1 over x2 - x1
4 - 9 over 8 - 7 = -5/1 slope
Problem solved!
An object 60m long is drawn using a scale of 1cm to 10m. What is the length on drawing?
Answers
Using strategy 1 (in your head), divide 60m by 10m to get 6, then multiply that number by one to get 6cm. the length on drawing is 6cm
Procedure 2 (proportions)
Create a proportion first.
We know that 1 cm equals 10 metres, so we place them on a fraction (the operation is unaffected by the denominator or numerator). However, we don't know how many cm equal 10m, so we make that into a variable, in this case x.
1cm x cm
——— ———
100m 60m
Go diagonally to where the variables have already been put in to solve a proportion. You are unable to calculate 60 metres and x centimetres because you are unsure of x. Yet you can travel 60m. Start by multiplying 1 by 30 to reach the number 60. The result of multiplying 60 by 10m is x. This will equal 6.
Thus, your response is 6.
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There are plans to install underground pipeline from the lake to the water level in Apache Durham Park what is the approximate length of pipe needed to the nearest meter
Answers
To determine the approximate length of the underground pipeline needed from the lake to the water level in Apache Durham Park, we would know the distance between the lake and park, as well as the specific path that the pipeline would take from the lake to the park.
Define the term length?Length is a physical or conceptual measurement of the extent of something from one end to the other.
It refers to the distance between two points or the size of an object or entity in the direction of its longest dimension. In mathematics and geometry, length is a fundamental concept used to describe the size and shape of geometric figures and objects.
It is measured in units such as meters, feet, inches, or centimeters
Assuming that we have this information, we can use the distance between the two points as the approximate length of the pipeline. To calculate this distance, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) represents the coordinates of the lake and (x2, y2) represents the coordinates of Apache Durham Park.
Once we have the distance between the two points, we can round it to the nearest meter to get the approximate length of the pipeline needed.
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We would know the distance between the lake and park, as well as the precise route that the pipeline would travel from the lake to the park, if we knew the approximate length of the underground pipeline required from the lake to the water level in Apache Durham Park.
Define the term length?A gauge of length is one that shows how far something extends from one end to the other.
It describes the separation of two points or the size of an item or entity measured along its longest axis. Length is a basic notion in mathematics and geometry that is used to describe the size and shape of geometric figures and objects.
Its dimensions are expressed in terms of meters, feet, inches, or millimeters.
Assuming we have this knowledge, we can use the distance between the two locations to estimate the pipeline's length. We can use the following algorithm to determine this distance:
[tex]d=\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2} }[/tex]
where [tex](x_{1},y_{1} )[/tex] stands for the lake's coordinates and [tex](x_{2} ,y_{2} )[/tex] for Apache Durham Park's coordinates.
Once we know how far apart the two locations are, we can round it to the closest meter to determine how long the pipeline should be roughly.
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The complete question is as follows:
Landon measures the angles of two triangles. Four of the angles in the two triangles measure 52°, 70°, 44°, and 36°. Which two angles cannot be the angle measures for the two triangles? OA. 100° and 58° OB. 84° and 74° OC. 88° and 68° O D. 92° and 66°
Answers
Option D, which has 92° and 66° curves, is the correct choice. The total of these angles is 158°, which is needed for the final two angles.
Are a triangle's edges proportional to 3 to 4 to 5?The triangle with edges in the ratio $3:4:5 is therefore "yes" a right-angled triangle. Note: We can only apply Pythagoras' Theorem to right-angled triangles; it cannot be applied to any other triangles.
Let's add the given angle measures: 52° + 70° + 44° + 36° = 202°. This means that the sum of the measures of the remaining two angles in the two triangles is:
360° - 202° = 158°
As a result, since both options A and B have one angle that is higher than 90 degrees, we can rule them out.
Option C has angles of 88° and 68°, which add up to 156°.
Since the highest sum of two acute angles is 180°, the other two angles would have to have a sum of 204°, which is not feasible.
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The initial amount of money borrowed or deposited?
Answers
Answer:
yes
Step-by-step explanation:
A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the the first arc is 18 feet long and the third arc is 8 feet long, what is the length of the second arc?
Explain step by step.
Geometric Sequence:
In mathematics, a sequence in which each number is multiplied by its previous term is called a geometric sequence.
The standard form of the geometric sequence is:
an=a1×rn−1Where, r = Common ratio a1= First term an=n th term
Answers
The length of the second arc is 8 feet.
The rope is swinging in such a way that the length of the arc is decreasing geometrically.
If the first arc is 18 feet long and the third arc is 8 feet long,
The length of the second arc :
In order to find the second arc length, we need to use the formula of the geometric sequence.
We have to understand what is given and what is required.
Given : First arc = 18 feet
Third arc = 8 feet.
To Find : Length of the second arc.
The formula of the geometric sequence is :
[tex]a_n[/tex] = [tex]a_1[/tex] × rn − 1
where, r = Common ratio [tex]a_1[/tex] = First term [tex]a_n[/tex] = [tex]n^{th}[/tex] term
Here, the length of the first arc is [tex]a_1[/tex] = 18.
The length of the third arc is [tex]a_3[/tex] = 8.
We have to find the length of the second arc, which is [tex]a_2[/tex]
Using the formula of the geometric sequence, we can find the [tex]a_1[/tex]: r= [tex]a_3[/tex] / [tex]a_2[/tex]
We know that [tex]a_1[/tex]= 18 and [tex]a_3[/tex]= 8
Substitute the values: r= 8 / [tex]a_2[/tex]
Now, we can rewrite the formula of the geometric sequence: an=[tex]a_1[/tex]×rn−1an= [tex]a_1[/tex] x r(n-1)
The length of the first arc is [tex]a_1[/tex] = 18 feet.
Substituting the value of r, we get:
8 / [tex]a_2[/tex] = r18 x r(n-1) = [tex]a_2[/tex]
We are given that the length of the third arc is 8 feet,
thus : 8 = 18 x r(3-1)8
= 18 x [tex]r_2[/tex][tex]r_2[/tex]
= 8 / 18[tex]r_2[/tex]
= 4 / 9r
= √(4/9)
Using this value of r, we can find the length of the second arc :
[tex]a_2[/tex] = 18 x (4/9) (2-1) [tex]a_2[/tex]
= 18 x (4/9)[tex]a_2[/tex]
= 8
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Here are four different crescent moons shapes.
1. What do Moons A,B, and C all have in common that Moon D doesn't?
2. Use numbers to describe how moons A,B, and C are different from Moon D.
Answers
The number of horizontal square of D over the number of vertical
squares = 3 : 2
What is square in math?
A planar shape with four equal sides and four right (90°) angles is referred to as a square in geometry. An equilateral rectangle is a specific sort of square, while a parallelogram is a special kind of square (an equilateral and equiangular one). All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees apart from each other or at right angles. The square's diagonals are also equal and split at an angle of 90 degrees.
the number of horizontal squares of A, B , and C over the number of vertical square = 2 : 3
the number of horizontal square of D over the number of vertical
squares = 3 : 2
6 : 4 = 3 : 2
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Un vêtements qui coutait initialement 100€ a vu son prix diminuer de 30% une première fois puis une deuxième fois de 20%.Quel pourcentage de réduction correspond à ces deux baisses successives?
Answers
Step-by-step explanation:
La première baisse de prix est de 30%, ce qui signifie que le prix du vêtement est maintenant de 70% de son prix initial :
Prix après la première baisse = 100€ - (30% x 100€) = 70€
Ensuite, le prix est réduit à nouveau de 20%. Cela signifie que le prix final est de 80% du prix après la première baisse :
Prix après la deuxième baisse = 70€ - (20% x 70€) = 56€
Le pourcentage de réduction totale correspond donc à la différence entre le prix initial et le prix final, exprimé en pourcentage du prix initial :
Pourcentage de réduction totale = ((100€ - 56€) / 100€) x 100% = 44%
Le vêtement a donc subi une réduction de 44% au total après les deux baisses successives de prix.
12m ² - 4mn-5n².solve the quadratic equation
Answers
The Solutions to 12m ² - 4mn-5n² are:
m = n/3 or m = -5n/3
How did we get these values?To solve the quadratic equation 12m² - 4mn - 5n² = 0, we can use the quadratic formula:
m = (-b ± √(b^2 - 4ac)) / 2a
where a = 12, b = -4n, and c = -5n².
Substituting these values into the formula, we get:
m = (-(-4n) ± √((-4n)^2 - 4(12)(-5n²))) / 2(12)
Simplifying:
m = (4n ± √(16n² + 240n²)) / 24
m = (4n ± √(256n²)) / 24
m = (4n ± 16n) / 24
So the solutions are:
m = n/3 or m = -5n/3
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One night a theater sold 524 movie tickets. An adult's ticket costs $6.50 and a child's ticket cost $3.50. In all, $2881 was taken in. How many of each kind of ticket were sold?
Answers
196 children's tickets and 328 adult tickets were sold.
What is a system of equations?
A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
Here, we have
Given: One night a theater sold 524 movie tickets. An adult's ticket costs $6.50 and a child's ticket cost $3.50. In all, $2881 was taken in.
Let the amount of the child's ticket be x
Let the amount of adults tickets be y
If the total number of tickets sold is 524 movie tickets, then;
x + y = 524
x = 524 - y...(1)
If an adult ticket cost $6.50 and a child’s ticket cost $3.5 with a total of $2881 in all, then;
3.5x + 6.5 y = 2881
35x + 65y = 28810 ...(2)
Substitute equation 1 into 2:
35x + 65y = 2881
35(542-y) + 65y = 28810
18970 - 35y + 65y = 28810
30y = 9840
y = 328
Put the value of y in equation (1) and we get
x = 524 - 328
x = 196
Hence, 196 children's tickets and 328 adult tickets were sold.
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Factor
F(x)= x^2 + 2x - 35
Answers
Answer:
Step-by-step explanation:
I need some help with this question!
You are building a square table. You put a diagonal support on the underside of the tabletop. The diagonal support is 3 meters long. What is a side length of the square table? Round to the nearest tenth, if necessary.
Answers
Answer:
2.1
Step-by-step explanation:all side lengths are the same (duh) use 4 and 3 (4 bc there is 4 sides). 4 as the diagonal support
4²=16
3²=9
16-9=7 then use square root for 7 the square root of 7 is 2.6457513111 or 2.1
Express the function f(x) = -2(x-4)² + 1 graphically, with a table of values, with a
mapping diagram, and using set notation with integers over the interval 1 ≤x≤7.
Answers
The expression of the function using the specified formats are presented as follows;
Please find attached the required graph of the function f(x) = -2·(x - 4)² + 1 created with MS Excel
The table of values for the function can be presented as follows;
[tex]\begin{tabular}{|c|c|c|} \cline{1-2}x& f(x) \\ \cline{1-2}1 & -17\\ \cline{1-2} 2 & -7 \\ \cline{1-2} 3 & -1 \\ \cline{1-2} 4 & 1 \\ \cline{1-2} 5 & -1\\\cline{1-2} 6 & -7 \\ \cline{1-2} 7 & -17 \\ \cline{1-2}\end{tabular}[/tex]
The mapping diagram can be presented as follows;
x [tex]{}[/tex] f(x)
1 → -17
2 → -7
3 → -1
4 → 1
5 → -1
6 → -7
7 → -17
The function expressed using set notation can be presented as follows;
f(x) = {-17, -7, -1, 1, -1, -7, -17} where x ∈ {1, 2, 3, 4, 5, 6, 7}
What is a function?A function is a rule that assigns a unique value for the output for each input value.
The specified function is; f(x) = -2·(x - 4)² + 1
Please find attached the graph of the parabola, created with MS Excel, which is a parabola that opens downwards, with a vertex of (4, 1)
The table of values can be presented as follows;
x | f(x)
-----|------
1 | -17
2 | -7
3 | -1
4 | 1
5 | -1
6 | -7
7 | -17
Mapping diagram:
A mapping diagram is a diagram that illustrates how an element of a set is paired with elements in another set.
The mapping diagram for the function can be made to show how the x-values are mapped to the f(x) values as follows;
1 → -17
2 → -7
3 → -1
4 → 1
5 → -1
6 → -7
7 → -17
Set notation;
The function, f(x) = -2·(x - 4)² + 1 can be expressed using set notation for the interval 1 ≤ x ≤ 7, which is the set of integers between 1 and 7, inclusive, which is presented as follows;
Set of x-values; {1, 2, 3, 4, 5, 6, 7}
Set of f(x) values is therefore; {-17, -7, -1, 1, -1, -7, -17}
Therefore, we get f(x) = -2·(x - 4)² + 1 expressed using set notation can be presented as follows;
f(x) = {-17, -7, -1, 1, -1, -7, -17}, where, x ∈ {1, 2, 3, 4, 5, 6, 7}
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Which is the cheapest + workings out, PLEASE HELP!!
Answers
The cheaper price for the 12 orchid is the 8.60 pounds for 4 orchid.
How to find the cheaper price for the 12 orchid?The cheaper price for the 12 orchid can be calculated as follows;
Therefore, for the first Orchid:
4 orchid = 8.60 pounds
12 orchid = ?
cross multiply
cost for 12 orchid = 8.60 × 12 / 4
cost for 12 orchid = 103.2 / 4
cost for 12 orchid = 25.8 pounds
For the second orchid:
5.40 pounds for each.
Now, 1 / 3 off,
Therefore,
1 / 3 ×5.40 = 1.8
Therefore,
5.40 - 1.8 = 3.6 pounds for each
Therefore,
12 orchid = 12 × 3.6 = 43.2 pounds
Therefore, the cheaper price is 8.60 pounds for 4 orchid.
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PLEASE PLEASE HELP GIVE ME A WELL EXPLAINED ANSWER AND I WILL GIVE YOU 100 POINTS
Before a renovation, a movie theater had 140 seats. After the renovation, the theater has 171 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
Answers
Difference = New number of seats - Old number of seats
Difference = 171 - 140
Difference = 31
Percentage increase = (Difference / Old number of seats) x 100
Percentage increase = (31 / 140) x 100
Percentage increase ≈ 22.1%
Therefore, the approximate percentage increase of the number of seats in the theater is 22.1%.
Answer:22.1%
Step-by-step explanation:
What property is being used in the following:
5/6 + 7/12 = 7/12 + 5/6
Answers
Answer:
Commutative property of addition
Step-by-step explanation:
The property being used in this equation is the commutative property of addition. This property states that when two numbers are added, the order in which they are added does not change the sum. So, in this case, we can rearrange the terms 5/6 and 7/12 and still get the same result.
Find the Area of the triangle below
Answers
Answer:20.25
Step-by-step explanation: