What are the equations to find this?

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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The inequalities that could be used to solve for x; the number of school buses still needed to transport all of the students is x > 3

The number of students still needing transportation is: 400 - 265 = 135

The number of school buses still needed to transport all of the students:

135 ÷ 45 = 3

Therefore, the principal still needs 3 more school buses to transport all of the students.

The inequality that could be used to solve for x: x > 3

This inequality represents the number of buses needed (x) as being greater than 3

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Answer:

612

Step-by-step explanation:

To find this answer, you can invert the equation:

452.88 = 0.74x

x = 452.88 / 0.74

x = 612

The number 452.88 is 74% percentage of the number 612.

percentage, a relative value indicating hundredth parts of any quantity.

We have to find the number of 452.88 is 74%

Let x be the number

74/100×x=452.88

74x/100 = 452.88

Multiply both sides by 100

74x=45288

Divide both sides by 74

x=45288/74

x=612

Hence, 452.88 is 74% of the number 612.

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Answer:

D

Step-by-step explanation:

Least common denominator of 7 and 8 = 56

\(\frac{-1}{8}=\frac{-1*7}{8*7}=\frac{-7}{56}\\\\\\\frac{1}{8}=\frac{1*7}{8*7}=\frac{7}{56}\\\\\\\frac{-1}{7}=\frac{-1*8}{7*8}=\frac{-8}{56}\\\\\\\frac{1}{7}=\frac{1*8}{7*8}=\frac{8}{56}\)

-8/56   , -7/56 , 7/56 ,   8/56  ,

-1/7 , -1/8 , 1/8 , 1/7

The number of students who liked cake batter frozen yogurt is 135.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

From the given diagram the sum of all the percentages except the Cake batter is (28.5 + 21.5 + 13 + 10)% = 73%.

Therefore, The percentage of students who liked Cake batter is,

= (100 - 73)%.

= 27%.

So, The number of students who liked cake batter is,

(27/100)×500.

= 27×5.

= 135.

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The inverse function is f inverse (x) = 3x / (1-x) The domain is (x) is (-∞, 1) U (1, ∞). The range of f inverse (x) is also all real numbers except for y = 3/2, that is f inverse (x) is (-∞, 3/2) U (3/2, ∞).

The collection of all potential input values—also referred to as the independent variable—for which a function can be defined is known as the domain of the function. In other words, it is the range of numbers that can be used to call the function and get a legitimate result.

The collection of all possible output values—also referred to as the dependent variable—that a function can produce is its range. The collection of values that the function really accepts as the input vary over the domain, in other words, is the input.

To find the inverse replace f(x) with y and then solve for x:

y = 6x/(3-x)

y(3-x) = 6x

3y - yx = 6x

3y = x(1+y)

x = 3y / (1+y)

Therefore, the inverse of the function f(x) is:

f inverse (x) = 3x / (1-x)

The domain of f inverse (x) is all real numbers except for x = 1, that is f inverse (x) is (-∞, 1) U (1, ∞).

The range of f inverse (x) is also all real numbers except for y = 3/2, that is f inverse (x) is (-∞, 3/2) U (3/2, ∞).

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Answer:

928,543,543,300

For function f (x) =3 x²- 5 x +7 a) It turns upward b) The vertex is (5/6, 59/12) c) The axis of symmetry is 5/6.

a) The graph formed in the function is turns upward please refer to image.

b) vertex = (-b/2a , -D/4a)

f (x) =3 x²- 5 x +7

on comparing equation by general equation of parabola ax² + bx +c

a = 3 , b = - 5 , c = 7

D = b² - 4ac

D = (-5)² - 4(3)(7)

D = 25 - 84

D = -59

vertex = (5/6 , 59/12)

c) The axis of symmetry is -b/2a

b = -5 , a = 3

The axis of symmetry = 5/6

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\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.75\% of 9.99}}{\left( \cfrac{6.75}{100} \right)9.99} ~~ \approx ~~ 0.67~\hfill~\underset{ total~cost }{\stackrel{ 9.99~~ + ~~0.67 }{\approx\text{\LARGE 10.66}}}\)

Answer:

47 x  + 28 y  + 74

Step-by-step explanation:

A sensible original hypothesis that suggests a positive relationship between two variables could be: "Hypothesis: Increased physical exercise is positively associated with improved cardiovascular health."

The hypothesis suggests that there is a positive relationship between increased physical exercise and improved cardiovascular health. This means that as the level of physical exercise increases, it is expected to result in an improvement in cardiovascular health.

To explain further, the hypothesis is based on the understanding that physical exercise has various beneficial effects on the cardiovascular system. Regular exercise can lead to improvements in heart function, increased blood flow, lower blood pressure, improved cholesterol levels, and better overall cardiovascular fitness.

By proposing this hypothesis, we are suggesting that individuals who engage in more physical exercise will experience greater improvements in their cardiovascular health compared to those who engage in less or no exercise. This hypothesis can be tested through research studies, where data on exercise habits and cardiovascular health measures are collected and analyzed to determine if a positive relationship exists between the variables.

It is important to note that while the hypothesis suggests a positive relationship, further research is needed to provide concrete evidence and establish a causal link between increased physical exercise and improved cardiovascular health.

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Answer:

Step-by-step explanation:

Distance upstream = (34-c)(39/60) miles

--------------------------

Distance downstream = (34+c)(29/60) miles

-----------------------------------------------

Equation:

distance = rate*time

distance up = distance down

(34-c)(39/60) = (34+c)(29/60)

Multiply both sides by 60 to get:

39(34-c) = 29(34+c)

39*34 - 39c = 29*34 + 29c

68c = 340

c = 5 mph speed of the current

Answer:

a- 130, 130, and 50

b- 7 and 10

Answer:

a- 130, 130, and 50

b- 7 and 10

Step-by-step explanation:

The coordinates of the polygon are given, and then dilated by a factor of 1/2.

Hence the new coordinates would be derived as follows;

The new coordinates therefore are derived as;

A'(1, 2)

B'(-2, -4)

C'(0, 2)

D'(6, 1)

This is a reduction

Answer:

5 hours are the answer long will take her to go the remaining

The global maximum and minimum values of f(x, y) subject to the constraint x^2 + y^2 = 80 are both approximately 15.314, and they occur at the points (2√5, -4√5) and (-2√5, 4√5), respectively.

To use Lagrange multipliers, we need to define the Lagrangian function as follows:

L(x, y, λ) = f(x, y) - λg(x, y)

where g(x, y) is the constraint function, which in this case is g(x, y) = x^2 + y^2 - 80.

So, we have:

L(x, y, λ) = (x - 1)^2 + (y + 2)^2 - λ(x^2 + y^2 - 80)

Next, we need to find the partial derivatives of L with respect to x, y, and λ, and set them equal to 0:

∂L/∂x = 2(x - 1) - 2λx = 0

∂L/∂y = 2(y + 2) - 2λy = 0

∂L/∂λ = x^2 + y^2 - 80 = 0

Simplifying the first two equations, we get:

x(1 - λ) = 1

y(1 - λ) = -2

Dividing these two equations, we get:

x/y = 1/-2 => x = -y/2

Substituting this into the constraint equation, we get:

(y/2)^2 + y^2 = 80 => 5y^2 = 320 => y = ±4√5

Substituting this back into x = -y/2, we get:

x = ∓2√5

So, the critical points are (2√5, -4√5) and (-2√5, 4√5).

To determine whether these are maximum or minimum values, we need to compute the second partial derivatives of L:

∂^2L/∂x^2 = 2 - 2λ

∂^2L/∂y^2 = 2 - 2λ

∂^2L/∂x∂y = 0

At the critical points, we have λ = 1/5, so:

∂^2L/∂x^2 = -2/5 < 0, so (2√5, -4√5) is a local maximum.

∂^2L/∂y^2 = -2/5 < 0, so (-2√5, 4√5) is a local maximum.

To determine whether these are global maximum or minimum values, we need to compare the values of L at these critical points and at the endpoints of the constraint region:

L(2√5, -4√5) ≈ 15.314

L(-2√5, 4√5) ≈ 15.314

L(4√2, 0) = 18

L(-4√2, 0) = 18

So, the global maximum and minimum values of f(x, y) subject to the constraint x^2 + y^2 = 80 are both approximately 15.314, and they occur at the points (2√5, -4√5) and (-2√5, 4√5), respectively.

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Answer:

Step-by-step explanation:

the power house of the midriccondria examples of solutions of the 9+ 10 so the annswer is 11

Answer:

1) The rate of change is constant ($$ 2) The line passes through the origin (0, 0). 3) The equation of the direct variation is $$ y =1 x or simply $$

Answer:

1) The rate of change is constant ($$ 2) The line passes through the origin (0, 0). 3) The equation of the direct variation is $$ y =1 x or simply $$

Step-by-step explanation:

I know this because I done this last week

a=7/2-3/10

Step-by-step explanation:

20a +158+6c= 120+60+48

20a +158+6c=228

20a =228-158-6c

20a =70-6c

a= 7/2 - 3/10

Answer:

120 + 60 + 48 would be the correct answer !

Step-by-step explanation:

The rug will fit on the floor of Lanie's room. The height of the parallelogram is 12 feet.

To determine if the rug will fit in Lanie's room, we need to compare the dimensions of the rug and the room. The room is a parallelogram with a base of 9 feet, and the area is 108 square feet. To find the height, use the formula for the area of a parallelogram: Area = base × height. For Lanie's room, 108 = 9 × h. Divide both sides by 9 to find the height, h = 12 feet. Now, compare the dimensions of the rug (6 feet wide, 10 feet long) with the dimensions of the room (9 feet base, 12 feet height). The length of the rug (10) is less than the height of the parallelogram (12), and the width of the rug (6) is less than the base of the parallelogram (9). Therefore, the rug will fit on the floor of Lanie's room.

Calculation steps:
1. Area of the parallelogram = base × height
2. 108 = 9 × h
3. h = 108 / 9
4. h = 12 feet
5. Compare dimensions: rug (6 feet wide, 10 feet long) vs room (9 feet base, 12 feet height)

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Answer:

the x-intercept is found when 0 is put into the equation for y.  

Because the x-intercept is found when the function passes through the x-axis.

x+2y=5

x=5

So x=5, y=0, the point would be (5,0).

Answer:

(5,0) would be the x-intercept.

Answer:

Me too i cant understand

Step-by-step explanation:

ba bay

Answer:

d is it

Step-by-step explanation:

Answer:

-2 degrees

Step-by-step explanation:

-14 + 12 = -2

Complete Question

Martin painted 255 square feet of his kitchen wall with 2/3 gallon of paint. If he continues coverage at the same rate, how many square feet can he cover with 2 gallons of paint?765 ft2510 ft2382.5 ft21,020 ft

Answer:

765 square ft

Step-by-step explanation:

2/3 gallon of paint = 255 square feet

2 gallons of paint =

Cross Multiply

2 × 255 square feet/2/3 gallon of paint

= 510 ÷ 2/3

= 510 × 3/2

= 765 square feet

According to the information in the graph, the money that was collected was $79.5.

To make a graph of this problem, we must relate the number of units sold of special dinners and lunches and the total price obtained for these sales.

This graph helps us because it allows us to visualize how much money we got from the sale of these.

According to the graph the total price of lunches and dinners would be $79.5.

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Length of the loan in months is 12 months by using formula for simple interest rate.

To find the length of the loan in months, we can use the formula for simple interest rate:

Simple Interest = Principal × Interest Rate × Time

In this case, the principal is $500, the annual interest rate is 13%, and the total amount repaid is $565. We first need to find the simple interest earned during the loan period:

Simple Interest = $565 (repaid) - $500 (principal) = $65

Now, we can rearrange the formula to find the time (in years) by dividing the simple interest by the principal and interest rate:

Time (in years) = Simple Interest / (Principal × Interest Rate)

Time (in years) = $65 / ($500 × 0.13) = 1

Since we want the length of the loan in months, we need to multiply the time in years by the number of months in a year:

Length of the loan (in months) = Time (in years) × 12 months/year

Length of the loan (in months) = 1 × 12 = 12 months

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If each marble is different: 14,348,907 ways.

If each marble is the same: 136 ways.

If each marble is the same and each jar must have at least two marbles: 126 ways.

If each marble is the same but each jar can have at most 6 marbles: 324 ways.

If you have 10 identical red marbles and 5 identical blue marbles: 63,063 ways.

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The ogive is a line graph that plots the cumulative relative frequency distribution.

An ogive, also known as a cumulative frequency polygon, is a line graph that shows the cumulative frequency distribution of a data set. The cumulative frequency is calculated by adding up the frequencies of each value up to a certain point in the data set.

The cumulative relative frequency is calculated by dividing the cumulative frequency by the total number of observations in the data set. The ogive plots these cumulative relative frequencies against the corresponding values in the data set, usually on the x-axis.

By plotting the cumulative relative frequencies, the ogive shows how the data is distributed over the entire range of values. It can be used to identify patterns in the data, such as whether it is skewed or symmetrical. It is also useful for determining percentiles, as the percentile for a given value can be read directly from the ogive.

Overall, the ogive is a helpful tool for summarizing and visualizing the distribution of a data set, particularly when dealing with large data sets or complex distributions.

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we must use trigonometric ratios to solve the right triangle

i will use the cosine

where alpha is the angle, a the adjacent side and H the hipotenuse,

so replacing

now solve for x

so the right option is I