The different scenarios given in the question are categorized as legitimate variables or not as given below.
What is a variable?
A variable is a symbol used to denote a mathematical object in mathematics. Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable. A variable is a letter that stands in for an unknown; it always represents a number but can take on several meanings when used in an expression.
a) Numer of states that have a female governor has only one value and it cannot be varied. So it is not a legitimate variable(N).
b) The percentage of state's residents over 65 years of age is a legitimate variable (L) because the number will vary for different states.
c) The highest speed limit in the state is a legitimate variable(L) as the limits are different for different states.
d) Whether or not the state's name consists of one word is a legitimate variable(L) as it varies for different states.
Therefore the different scenarios are categorized as legitimate variables or not.
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scores on a management aptitude examination are normally distributed with a mean of 72 and a standard deviation of 8.we want to find the lowest score that will place a manager in the top 10% (90th percentile) of the distribution. which of the following is true to solve this problem?
The lowest score for the normally distribution with mean 72 and standard deviation 8 is equal to 82.
Mean of the normally distributed data 'μ' = 72
Standard deviation 'σ ' = 8
Lowest score with 10% ( 90percentile )
z = InvNorm(0.90)
= 1.28
Let 'X' be the lowest score for the normal distribution
z = ( X - μ ) / σ
Substitute the values we get,
⇒ 1.28 = ( X - 72 ) / 8
⇒ X - 72 = 1.28 × 8
⇒ X = 10.24 + 72
⇒ X = 82.24
⇒ X = 82 ( round to an integer )
Therefore, the lowest score for normally distribution which will place manage on 90th percentile with given mean and standard deviation is equal to 82.
The above question is incomplete, the complete question is:
Scores on a management aptitude examination are normally distributed with a mean of 72 and a standard deviation of 8.we want to find the lowest score that will place a manager in the top 10% (90th percentile) of the distribution. Your answer is Please round to an integer number.
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Solve the equations by graphing. Graph the system below and enter the solution set as an ordered pair in the form (x,y).
Hey, for this type of question, go on desmos it a calculator. but I hope this is right. Sorry if wrong
need help with pre calc hw
The factors of the quadratic function p(x) is equal to
(x + 5 + √(65)/2)(x - 5 + √(65)/2).
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, The zeros of the quadratic function p(x) = x² - 5x - 10 are,
(5 + √(65)/2, 5 - √(65)/2).
Therefore, The factors of p(x) = [x + (5 + √(65)/2)][x + (5 - √(65)/2)]
p(x) = (x + 5 + √(65)/2)(x - 5 + √(65)/2).
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Pam expected the new edition of her favorite video game, Solar Y, to sell for $45. Her prediction was 12.5% higher than the game's actual cost. What was the actual cost of the game?
well, the actual cost of it was 12.5% of 45 less, hmmm what's 12.5% of 45?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{12.5\% of 45}}{\left( \cfrac{12.5}{100} \right)45} ~~ \approx ~~ 5.63~\hfill \stackrel{45~~ - ~~5.63}{\approx\text{\LARGE 39.37}}[/tex]
Subtract: 13/15−5/21
Answer:0.628571428571- or 63% and in fraction form it would be 5/8
Step-by-step explanation:
Answer: 22/35 (Result in decimals: 0.62)
Step-by-step explanation:
13/15 - 5/21
= 13 x 7/15 x 7 - 5 x 5/21 x 5
= 91/105 - 25/105
= 91 - 25/105
= 66/105
= 66 divided by 3 / 105 divided by 3
= 22/35
Answer the questions below
JL is MK congruent by CPCT.
What is congruency?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Given that, a figure, in which JK ≅ ML, ∠ JKL ≅ ∠ MLK,
We need to prove, JL ≅ MK,
The proof of the same is follows;
STATEMENT REASON
1) JK ≅ ML Given
2) ∠ JKL ≅ ∠ MLK Given
3) KL ≅ KL Reflexive property
4) Δ JKL ≅ Δ MLK By SSA rule
5) JL ≅ MK By CPCT
Hence, we get JL is MK congruent by CPCT.
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Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cAh 2gh , where c (0 < c < 1) is an empirical constant. A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (Assume the removed apex of the cone is of negligible height and volume.) (a) Suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. The differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . In this model, friction and contraction of the water at the hole are taken into account with c = 0.6, and g is taken to be 32 ft/s2. See the figure below. If the tank is initially full, how long will it take the tank to empty? (Round your answer to two decimal places.) 14.31 Correct: Your answer is correct. minutes (b) Suppose the tank has a vertex angle of 60° and the circular hole has radius 2 inches. Determine the differential equation governing the height h of water. Use c = 0.6 and g = 32 ft/s2. dh dt = If the height of the water is initially 10 feet, how long will it take the tank to empty? (Round your answer to two decimal places.) min
a) If the tank is initially full, it will take 14.31 min. long to tank to empty
b) If the height of the water is initially 10 feet, it will take 1.67 min for the tank to empty.
For the first case, we have the differential equation governing the height of the water, where the volume of a cone is V= 1/3 πr^2h by the similar triangles we can conclude that what the value will be for the height, the cone shape will always have the same relation with the radius of the water r/h=8/20⟹r=2/5h⟹r^22=4/25h^2, so V= 4/75πh^3, we will take the derivative of the height of with respect to time t
dV/dt=4/25πh2 dh/dt, now converting into inches we get :
dV/dt=−cAh√2gh=−3/5(π(1/6)^2)√64h=−24π/5⋅36 √h=−2π/15√h.
now adding both the equations of dV/dt,
425πh^2dhdt=−2π15√h⟹dhdt=−56h−3/2.
since the tank is empty m it will happen in at h=0, so for the value of t we will solve for h(t). after solving this differential equation using the separation of variables : dh h^3/2=−5/6dt, after integration of both sides, we get: 25h5/2=−5/6t+C0⟹h5/2=−25/12t+C, since here the intial height is 20 feet , so h(0)=20, Therefore 20^5/2=−25/12(0)+C⟹C=20^5/2, so h(t)=(−25/12t+20^5/2)^2/5.so when h will be 0 , then −25/12t+20^5/2=0⟺25/12t=205/2⟺t=12/25 20^5/2≃858.65 s=14.31 min.
For the second case, the relationship between the height and radius is different, here the angle between the side of the tank and the vertical is 30 degrees, and the ratio of the radius and height of the tank is √3:1, which is also the ratio of height and radius of the water.
1/√3=r/h⟹r=h/√3⟹r^2=h^2/3.
V=1/3πr^2h=π/9h^3, to solve it we need to for dVdt, to find the height and rate of change of height :dV/dt=π/3h^2dhdt here c is 0.6 and Ah=1/9π, dVdt=−35⋅19π⋅8√h, adding up those equations we get dV/dt, we have π/3h^2dh/dt=−8π/15√h⟹dh/dt=−8/5h^−3/2, now apply the separation of variables:
h^3/2dh=−8/5dt⟹2/5h^5/2=−8/5t+C, here the initial was at t=0, h is 11, C will be 2/5 11^5/2, therefore h(t)=−8/5t+2/5 11^5/2, so the time when the tank is empty will be 0=−8/5t+2/5 11^5/2⟺85t=25 11^5/2⟺t=1/4 11^5/2= 100.33 s=1.67 min.
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Suppose water is leaking from a tank through a circular hole of area at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to , where is an empirical constant.
A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom.
a) Suppose the tank is high and has radius and the circular hole has radius . The differential equation governing the height h in feet of water leaking from a tank after t seconds is . In this model, friction and contraction of the water at the hole are taken into account with , and is taken to be . See the figure below. If the tank is initially full, how long will it take the tank to empty? (Round your answer to two decimal places.)
b) Suppose the tank has a vertex angle of and the circular hole has radius . Determine the differential equation governing the height h of water. Use and If the height of the water is initially , how long will it take the tank to empty? (Round your answer to two decimal places.)
Triangle ABC is a right triangle. B What is the length of AC? 20 21 40 58
Answer:
Step-by-step explanation:
58
Find the equation of the surface. The bottom hemisphere of a sphere centered at (4, -3, 0) with radius 10. z=-V75+ 16x – (x2 + y2 + 6y) x
The equation of the surface of the sphere is
z = √(100 - (x - 4)² - (y + 3)²). The solution has been obtained by using equation of sphere.
What is a sphere?
A sphere has a round shape and symmetrical arrangement. This three-dimensional solid's surface points are evenly spaced apart from the centre. It has both a volume and a surface area, depending on the radius. It has no faces, corners, or edges.
We know that general form of an equation of sphere is
(x - a)² + (y - b)² + (z - c)² = r²
where a, b, c are the coordinates and r is the radius.
The equation of the sphere is
(x - 4)²+ (y + 3)² + z² = 10²
So, the equation of the bottom hemisphere of sphere is
z = √(100 - (x - 4)² - (y + 3)²)
Hence, the equation of the surface of the sphere is
z = √(100 - (x - 4)² - (y + 3)²).
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Given that2x - 2 < g(x) < x^2 + 2x - 3, use the Sandwich Theorem to
In this case, 2x - 2 < g(x) < x^2 + 2x - 3 for all x in some interval.
The Sandwich TheoremThe Sandwich Theorem states that if f(x) < g(x) < h(x) for all x in an interval, then g must have a value that is equal to either f or h at some point in that interval.
In this case, 2x - 2 < g(x) < x^2 + 2x - 3 for all x in some interval.
Hence, there exists a constant c such that g(c) = x^2 + 2x - 3.
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Given that2x - 2 < g(x) < x^2 + 2x - 3, use the Sandwich Theorem to prove that there exists a constant c such that g(c) = x^2 + 2x - 3.
the function g is defined by g of x equals 3 over x period what is the instantaneous rate of change at x
The instantaneous rate of change of a function at a point is given by the derivative of the function at that point.
The instantaneous rate of change of a function at a particular point x is equal to its derivative at that point. To find the derivative of the function g(x) = 3/x, we can use differentiation rules.
the function g(x) = 3/x describes the relationship between x and 3/x. The derivative of this function, which is -3/x^2, gives us the instantaneous rate of change at any given value of x.
The derivative of g(x) is given by:
d/dx (3/x) = -3/x^2
The derivative at a given x tells us exactly how quickly the value of the function is increasing at that particular x.
So, the instantaneous rate of change of g(x) at a point x is given by -3/x^2.
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Linear equation that passes through the points of (0,5) and (-5,1)
Answer:
y = 4/5 x + 5
Step-by-step explanation:
Slope
Change in y over the change in x
[tex]\frac{1-5}{-5-0}[/tex] = [tex]\frac{-4}{-5}[/tex] = [tex]\frac{4}{5}[/tex]
The slope is [tex]\frac{4}{5}[/tex]
The y-intercept is 5. It comes from the point (0,5).
Given the problem: Linear equation that passes through the points of (0,5) and (-5,1).
First, whenever you are asked to find a linear equation that passes through two points, remember its going to be slope intercept equation, or y=mx+b. m is the slope, b is the y-intercept.
The y-intercept is where the line crosses the y-axis. The slope can be written as rise/run. Rise and run right is positive, drop and run left is negative.
So in this case, looking at the first point: (0,5), we can see that the y-intercept is 5. Now let's find the slope. We will start at (-5,1) and go to (0,5). Count how many units we rise/drop and how many units we run. Rise 4, run right 5. So the slope is 4/5. Now put all the information into y=mx+b.
Your answer is y=4/5x+5
A video game designer places an anthill at the origin of a coordinate plane. A red ant leaves the anthill and moves along a straight line to (1, 1), while a black ant leaves the anthill and moves along a straight line to (−1, −1). Next, the red ant moves to (2, 2), while the black ant moves to (−2, −2). Then the red ant moves to (3, 3), while the black ant moves to (−3, −3), and so on. Complete the explanation of why the red ant and the black ant are always the same distance from the anthill.
Answer:
In order in which the boxes appear:
[tex]\boxed{a\sqrt{2}}[/tex]
[tex]\boxed{a\sqrt{2}}[/tex]
[tex]\boxed{a\sqrt{2}}[/tex]
Step-by-step explanation:
At any coordinate (x , y) the distance from the origin (0, 0) is computed by the distance (Pythagorean formula) as:
d = [tex]\sqrt{x^2+y^2}[/tex]
Since x = y = a for both ants, the distance is
[tex]d = \sqrt{a^2+a^2}\\\\d = \sqrt{2a^2}\\\\d = \sqrt{a^2}\cdot \sqrt{2}\\\\d = a\sqrt{2}[/tex]
It does not matter whether both coordinates are positive or both negative since we are taking the squares of the coordinates and distance is always positive
Given that someone has $5,000 in debt, the monthly payment is $75, and the interest rate is 16% per year, how long will it take to pay off the debt? Please show as much work as possible. The formula is attached if you need it. I will mark you as brainliest.
Is it possible for two numbers to have a difference of 6,
and also a sum of 6?
Answer:
ksjsvsbsvsdjsjsbwbwbwbwushs
olve each equation for x. Give both an exact value and a decimal approximation, correct to three decimal places. (a) In(5x + 6) = 4 exact value decimal approximation XE (b) e6x - 5 = 15 exact value X decimal approximation Solve each equation for x. Give both an exact value and a decimal approximation, correct to three decimal places. (a) In(In(x)) = 0 exact value X = decimal approximation X = 40 (b) =4 3 + e- exact value X = decimal approximation X =
The exact value of is x [tex]e^{4}[/tex] - 6/5 and the value of x will be 9.720.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
a) In(5x + 6) = 4 exact value decimal approximation XE
ln (5x+6) = [tex]e^{4}[/tex]
5x = [tex]e^{4}[/tex] - 6
x = [tex]e^{4}[/tex] - 6/5
5x = e^-6 x = 5 (r) x = 9.720
Hence, The exact value of is x [tex]e^{4}[/tex] - 6/5 and the value of x will be 9.720.
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Franklin is fishing from a small boat. His fishing hook is 8 meters below him, and a fish is swimming at the same depth as the hook, 6 meters away. How far away is Franklin from the fish?
Answer: x = 15
Step-by-step explanation:
Use the Pythagorean theorem
There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue?
Answer:
5/13 chance of getting blue marble
Step-by-step explanation:
5+6+2=13
5 blue marbles so
5/13
what are the advantages of using a bar chart over a pie chart
The advantages of bar charts over pie charts while graphing the given data are discussed below.
What are the advantages of using a bar chart over a pie chart?A bar chart or bar graph is a visual representation of categorical data that uses rectangular bars with heights or lengths proportional to the values they represent. The possibility of a bar plot, both vertical and horizontal, exists. Vertical bar graphs are also referred to as column charts.
A circular statistical image known as a pie chart uses slices to represent numerical proportions. Each slice's arc length in a pie chart varies depending on the amount it represents.
Any numbers can be chosen for the numeric value axis in a bar chart.
Pie charts can only be used if the sum of the various parts equals a meaningful whole because they are intended to illustrate how each portion contributes to the whole.
Hence bar chart is more advantageous over pie chart when more information is to be presented through charts.
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Find the length of the third side. If necessary, round to the nearest tenth. 7 3
The length of the third side of the given right triangle is 6.32.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”. The formula for the same is;
c² = a² + b², where a, b, c are sides of a right triangle.
Given that, a right triangle, with two sides 7 and 3, since, the figure is unavailable, let us assume that 7 is the hypotenuse and 3 is the other side, let the unknown side be x,
According to the Pythagoras theorem,
7² = 3² + x²
x² = 7² - 3²
x² = 49-9
x² = 40
x = √40
x = 6.32
Hence, the length of the third side of the given right triangle is 6.32.
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Suppose two cards are drawn randomly.
What is the probability of
drawing two blue cards if
the first one IS replaced
before the second draw?
Assume the first card
drawn is blue.
[?]
Show your answer as a
fraction in lowest terms.
Enter the numerato
Enter
The probability of drawing two blue card is 1/16
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space / total outcome
The total number of cards = 12
number of blue cards = 3
Probability of drawing blue card = 3/12
= 1/4
Since the blue card is replaced,
the probability to draw blue card in the second draw is 3/12 = 1/4
probability of drawing two blue cards = 1/4× 1/4
= 1/16
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Isaiah plans to repaint some classroom bookcases. He has 6 gallons of
paint. All of the bookcases are the same size and each requires 1/3 gallon
of paint. How many bookcases will he be able to paint?
3
So Isaiah has a total of 6 gallons of paint and each bookcases takes 1/3 gallon. How many bookcases can he paint?
Alright to solve this problem, we can simply take the total gallons of paint Isaiah has and divide that by 1/3
So 6 divided by 1/3 should give us the answer.
But how do we divide fractions? Remember this useful tip for all throughout your school life when you don't have a calculator: Keep, Change, Flip
Keep the first fraction, change the sign to a multiplication sign, and flip the second fraction.
This should give us 6 x 3/1 or 3, which is 18.
Isiah will be able to paint 18 bookcases.
Hope this helped!
Find the area of $\triangle DEF$ with vertices $D\left(2,\ 5\right)$ , $E\left(3,\ -1\right)$ , and $F\left(-2,\ -1\right)$ . The area of $\triangle DEF$ is
The required area of the given triangle is given as 15 cm².
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
To calculate the area of a triangle with its vertices A(2, 5), B(3, -1), and C(-2, -1),
Evaluate the absolute value of the expression 1/2
= 1/2|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|
Substitute the value in the above expression
= 1/2|2(-1 + 1) + 3(-1 - 5) -2(5 + 1)|
= 1/2[30]
= 15 cm²
Thus, the required area of the given triangle is given as 15 cm².
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convert 720 kilograms into tons. Round to the nearest hundredth
Answer:0.794
Step-by-step explanation:
Answer:
the answer would be 0.794. but hundredths would be 0.79
hope this helped!
Step-by-step explanation:
I need help with this question. I cant figure out how to find revenue with just the cost function.
The equation of the profit function is P(x) = 269x - 4x^2 - 128
How to determine the profit functionThe profit function P(x) can be found by subtracting the cost function C(x) from the revenue function R(x), where R(x) = p * x:
So, we have
P(x) = R(x) - C(x)
Substitute the known values in the above equation, so, we have the following representation
P(x) = (285 - 4x) * x - (128 + 16x)
So, we have
P(x) = 285x - 4x^2 - 128 - 16x
Evaluate the like terms
P(x) = 269x - 4x^2 - 128
To find the profit for making and selling 3 million fans, we substitute x = 3 into the profit function P(x):
P(3) = 269(3) - 4(3)^2 - 128
P(3) = 643
For other number of fans, we have
P(5) = 269(5) - 4(5)^2 - 128
P(5) = 1117
P(9) = 269(9) - 4(9)^2 - 128
P(9) = 1969
P(12) = 269(12) - 4(12)^2 - 128
P(12) = 2524
Hence, the profits are 643, 1117, 1969 and 2524
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Height of vase?
Pre Calculus
The height of the vase is 45 inches. To the nearest tenth of an inch, this is 45.0 inches.
What do you mean by hyperbola?A hyperbola is a type of conic section that is the result of intersecting a right circular cone with a plane that is perpendicular to one of its sides, and is oblique to the other. It is defined by two curves that are mirror images of each other and are each a set of all points such that the difference of their distances from two fixed points, called the foci, is a constant value.
A hyperbola can be represented in standard form as an equation, where the x and y terms are squared and the constant terms have opposite signs. It can also be graphed in the coordinate plane, where it appears as a set of two open curves, each going off to infinity in opposite directions.
The height of the vase can be found by using the formula for the height of a hyperbolic paraboloid, which is given by:
h = e × c × √(1 + (2a/c)²)
where h is the height of the vase, e is the eccentricity, a is the width at the narrowest point (4 inches), and c is the average width of the opening and base (6 inches).
Plugging in the values, we get:
h = 2.5 × 6 × sqrt(1 + (2 × 4 / 6)²)
h = 2.5 × 6 × sqrt(1 + (2 × 2)²)
h = 2.5 × 6 × sqrt(1 + 8)
h = 2.5 × 6 × sqrt(9)
h = 2.5 × 6 × 3
h = 45
The height of the vase is 45 inches. To the nearest tenth of an inch, this is 45.0 inches.
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6s + 17 where s is 1/2
Answer: 20
Step-by-step explanation:
6 (1/2) + 17
3 + 17 = 20
Answer:
20
Step-by-step explanation:
6(1/2) + 17
6(1/2) = 3
3 + 17 = 20
Find the value of x.
Give your answer in degrees.
(hint: form an equation, then solve it to find x)
Answer:x=8
Step-by-step explanation:
The interior angles of a triangle add up to 180 so
2x+39 + 2x+70 + x+31 = 180
2x + 2x +x=180-39-70-31
5x= 40
x=40/5
x=8
x+31 is in there because one of the int angles of the triangles is congruent with the angle of x+31
Solving Linear Equations (px + q = r)
Ava had $28.50 to spend at the farmer's market. After buying 3 pumpkins Ava, has $12 left.
Question 1 Which equation could you use to find the price of one pumpkin (x)? Responses
A 28.50/3 = x
B x + 12 = 28.50
C 3x − 12 = 28.50
D 3x + 12 = 28.50
Question 2 How much did Ava pay for each pumpkin?
Responses
A $5.25
B $5.50
C $6.30
D $4.75
The linear equation that represents the given literal problem is 3x+12= 28.50 (letter D) and Ava pays $5.5 (letter B) for each pumpkin.
Linear EquationAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=9x+5. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=9 and b=5.
The exercise presents two questions, before solving them, you should convert the given text information into equations.
Data question
Total of money= $28.50;Ava bought 3 pumpkins and you do not know the price (x) of the pumpkins;After the bought, Ava has $121) Question 1
Here you should write a linear equation that represents the given problem. Thus, you can write
3x+12= 28.50
Since 3x represents the payment of pumpkins and the value 12 is the difference between the total of Ava´s money and the total cost of pumpkins.
Therefore, the answer to question 1 is the letter D ( 3x+12= 28.50)
2) Question 2
As you know the equation that represents the problem, for solving this question you need to find the value of x.
3x+12= 28.50
3x=28.5-12
3x=16.5
x=16.5/3
x=5.5 (letter B)
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Find the general form of the equation of a hyperbola with vertices at (-2, 5) and (6, 5) and foci at (-3, 5) and (7, 5). A. 16x2 - 9y2 - 160x + 36y - 508 = 0 B. 9x2 - 16y2 - 36x + 160y - 508 = 0 C. none of these D. 3x2 - 16y2 - 12x + 160y - 532 = 0
The general form of the equation of the hyperbola with the given information is [tex]9x^2 - 16y^2 - 36x + 160y - 508 = 0[/tex]. The equation can be determined by first finding the center of the hyperbola, which is (2, 5), and the distance between the foci, which is 4.
The general form of the equation of a hyperbola can be determined from the given information. The vertices of the hyperbola are given as (-2, 5) and (6, 5). The foci of the hyperbola are given as (-3, 5) and (7, 5). The first step in finding the equation of the hyperbola is to determine the center of the hyperbola. The center of the hyperbola can be calculated by taking the average of the x-coordinates of the vertices and then the average of the y-coordinates of the vertices. The center of the hyperbola is then (2, 5). The distance between the foci of the hyperbola is 4. This distance can be calculated by subtracting the x-coordinates of the foci and then subtracting the y-coordinates of the foci. The standard equation for a hyperbola can then be formed by substituting the center coordinates and the distance between the foci into the equation. The resulting equation is [tex]9x^2 - 16y^2 - 36x + 160y - 508 = 0[/tex]. This equation is the general form of the equation of the hyperbola with the given
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