Literal Equations

help asap !!

To find the maximum height that the pumpkin reaches, we can set the derivative of the equation equal to 0 and solve for x. The derivative of y = 12 + 105x - 16x^2 is y' = 105 - 32x. Setting y' = 0, we get:

0 = 105 - 32x

32x = 105

x = 105/32

The maximum height is reached when x = 105/32 seconds. To find the maximum height, we can plug this value of x into the original equation:

y = 12 + 105(105/32) - 16(105/32)^2

= 12 + 1053.28125 - 163.28125^2

= 12 + 342.8125 - 106.25

= 248.5625

The maximum height that the pumpkin reaches is 248.5625 feet.

To find the number of seconds it takes for the pumpkin to hit the ground (when its height is 0), we can set y = 0 in the original equation and solve for x:

0 = 12 + 105x - 16x^2

16x^2 - 105x + 12 = 0

(4x - 3)(4x - 4) = 0

The solutions to this equation are x = 3/4 and x = 4/4. The second solution is extraneous, since it represents the time at which the pumpkin was launched (when x=0, y would be 12 feet, not 0 feet). Therefore, the number of seconds it takes for the pumpkin to hit the ground is x = 3/4 seconds.

The correct part is (d) i.e. 32pq2, -4p2q and 12pq are not constants in the given algebraic expression.

What is a constant?

A constant is a value or number that is consistently the same, regardless of how it is expressed.

The algebraic expression given is 32pq2−4p2q + 12pq−7.

A constant is that term which does not any variable portion or which is fixed.

Here, all terms have variables in the form of p and q but The last term does not have any variable.

So, The terms which have variables are the terms which are not constant.

Hence, 32pq2, -4p2q and 12pq are not constant in the given expression.

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The work done to empty the tank by pumping the water out of the top of the tank is 3.4 * 10^6 .

Given :

a tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. it is filled with water to a height of 8 m. find the work done to empty the tank by pumping the water out of the top of the tank .

Formula :

[tex]W=\int_a^bpA(y)D(y)dy[/tex]

Using the base radius of 4, I found the equation of the line which was y = 5x / 2 and by solving for x gives us x = 2y / 5 .

Work = [tex]9.8*1000\int_0^{8} (\pi(\frac{2y} 5)^2)(10-y)dy[/tex]

= 3.4 * 10^6

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Juliet will have  13 cups mixture of the orange juice and water .

Given :-

Juliet already has 9 cups of orange juice , and she adds 32 fluid ounces of water into the  cup of orange uice syrup.

So, we have to find that how much cups of syrup does Juliet had ,

So, we know that

1 cup = 8 ounces

but she adds 32 ounces of water which means

= No. of ounces added / no. of ounces in a glass

= 32 / 8

= 4

therefore ,

9 + 4 = 13 glasses.

which means she has 13 glasses of the syrup made up of water and orange juice .

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Answer: 7/13 is the y intercept

According to the given statement Liam is incorrect because average speed is 34.28 miles per hour.

The average scores of a body's speed over a duration of time is its average speed. Because a moving body's speed is not constant over time and fluctuates, the average speed formula is required.

The overall distance the thing travels in a given amount of time is its average speed. A scalar value symbolizes the average speed. It has no direction and therefore is indicated by the magnitude.

Distance covered in first three hours = 40 × 3 = 120 miles

Time taking to covered remaining 120 miles = 120/30

                                                                          = 4 hours

Total time = 4 hours + 3 hours = 7 hours

Total distance = 120 miles + 120 miles

                        = 240 miles

Average speed = total distance /  total time

Average speed = 240 miles / 7 hours = 34.28 miles per hour

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The functions f(g(x)) and g(f(x)) are not inverse functions

From the question, we have the following parameters that can be used in our computation:

f(x) = x³

g(x) = 1/3x

Calculate the composite function f(g(x)).

So, we have

f(g(x)) = (1/3x)³

This gives

f(g(x)) = 1/27x³

Calculate the composite function  g(f(x)).

So, we have

g(f(x)) = 1/3(x³)

This gives

g(f(x)) = 1/3x³

The functions f(g(x)) and g(f(x)) are not the same

Hence, they are not inverse functions

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The dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.

In three dimensional space prism is a polyhedron where two ends are similar.

Given that volume of rectangular prism is 168 cubic centimeters.

And the wooden block is 2x cm tall, (x-4) cm wide and (x-3) cm long.

And also given that a wooden block in a set of building blocks is a rectangular prism.

That means,

Volume of wooden block = Volume of rectangular prism = 168 cm³

Volume of wooden block ;

length × width × height = 168 cm³

Substituting given values in above expression,

2x (x-3) (x-4) = 168 cm³

2x (x²-7x + 12) = 168 cm³

2x³ - 14x²+ 24x = 168 cm³

Simplifying the above equation;

2x³ - 14x²+ 24x- 168 = 0

x³ - 7x²+ 12x- 84 = 0

The factor of above cubic equation is x = 7.

Now the 2x = 14 , x-3 = 4, x-4 = 3.

Therefore the dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.

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The inequality that represents this situation is, (1 + x) > 2.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Ava’s pet pig is older than Izzy’s pet pig, which is 2 years old.

Ava adopted her pig when it was 1 year old, and she has had it for x years.

∴ The inequality that represents this situation is,

(1 + x) > 2.

x > 2 - 1.

x > 1.

Ava adopted her pig for more than one year.

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Approximate new height QR of the scaffold would be 11.31 Fee

What is Pythagoras theorem?

The pythagorean theorem or Pythagoras' theorem may be a elementary relation in geometry between the 3 sides of a triangle.

Main Body:

A) Here, We'll use "Pythagoras Theorem" which tells:

a² + b² = c²

So, PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

In short,  approximate length of rod PR would be 16.64 Feet.

B) Again, Use the Pythagoras Theorem,  

c² - a² = b²

18² - 14² = b²

b² = 324 - 196

b = √128

b = 11.31

Hence , approximate new height QR of the scaffold would be 11.31 Feet

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They send 32 coupons to existing members. Option C is correct.

What is a linear equation in two variables?

A Linear equation in two variables x and y is of the form

Ax + By = C.

Given,

They provide 5 times as many to potential members than existing members.

Let, there are y potential members and x existing members.

Therefore, x + 5y = 192

Also, x and y are whole numbers.

Hence, x=32 satisfy the equation.

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Answer: They both meet up at $160

Step-by-step explanation:

40 + 20= 60 + 20 = 80 + 20 = 100 + 20 = 120 + 20 = 140 + 20 = 160

60 + 15 = 75 + 15 = 90 + 15 = 115 + 15 = 130 + 15 = 145+ 15 = 160

Using a graphing calculator to plot the vertices, the points plotted gave a triangle

This can be said to be the location of the endpoints in a given square. The vertices of a square must be equidistant from one another. This is a place in geometry where common endpoints of two or more rays or line segments meet. Thus, in a square, the vertex is the point where two sides meet. It is each corner of a square. Thus, each square has 4 vertices.

In this problem, we have to use a graphing calculator and plot each points

In doing so, we have A(1, 2), B(4, 2) and C(4, -1)

Plotting the points, it gives a triangle instead of a square;

The point A and B are located in the first quadrant and point C is located in the second quadrant.

Kindly find the attached graph below

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Answer:

bom é a soma dos algarismos se for matemática

1.You can find another name for plane P by using any three points in the

plane that are not on the same line. Hence, the another name for plane P is the plane GAC .

2. The line intersects the plane is EF

3. The two rays in the plane are CB , DB

4. A,B,C are three points in the plane p.

Spanned by two linearly independent vectors, a plane is a doubly ruled surface in two dimensions. Hyperplanes are the result of extending the plane to higher dimensions. The dihedral angle is the angle at which two planes intersect.

Using any three points on the plane that are not on the same line, you can come up with another name for plane P. Therefore, another name for plane P is GAC. The plane is intersected by the line at EF. CB and DB are the two rays in the plane. There are three points in the plane p, A, B, and C.

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If a coil of cable ,50m in length has a conductor resistance of 0. 275W,then the value of resistance for 800m of the same cable will be 4.4 ohms.

The opposition to current flow in an electrical circuit is measured by resistance. The Greek letter omega represents the unit of measurement for resistance, known as ohms. Georg Simon Ohm (1784–1854), a German physicist who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance.

the ratio of a conductor's current to potential difference, which measures how well a thing conducts electricity. This is the resistance' inverse, and it is measured in siemens.

as we are given with;

Length=50m

Resistance=0.275W

we got Formula;

Resistance=pL/A

p/A=R/A

p/A=0.275/50

=0.0055

Now for 800m wire

R= p/A(800)

R=0.0055x800

R=4.4 ohms

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Your friend's rate of change in elevation is 0.5 feet per minute more than your rate.

Rate of change in elevation = elevation of distance/time

The elevation of 720 feet to an elevation of 750 feet in 30 minutes.

Your rate of change in elevation = 750 - 720 / 30

Your rate of change in elevation = 30 / 30

Your rate of change in elevation = 1 foot per minute

Your friend in-line skates from an elevation of 600 feet to an elevation of 690 feet in one hour.

Your friend's rate of change in elevation = 690 - 600 / 60

Your friend's rate of change in elevation = 90 / 60

Your friend's rate of change in elevation = 1.5 feet per minute

The difference in rate of change in elevation = 1.5 - 1 = 0.5 feet per minute

Thus, your friend's rate of change in elevation is 0.5 feet per minute more than your rate.

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Answer:

-x+4 [tex]\leq[/tex]y

Step-by-step explanation:

Answer:

Apples are least preferred

75% don’t prefer oranges

40 people prefer bananas

Answer:

Step-by-step explanation:

a) apples
b)
(40+ 20 + 15)

75% do not prefer oranges
c)
20% prefer bananas
20% as decimal is 0.2
0.2 * 200 =
40 people prefer bananas

The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The linear equation is given below.

4x + 6y = 21            ...1

7x - 3y = 3              ...2

From equation 2, then we have

7x - 3y = 3

3y = 7x - 3

y = (7/3)x - 1

Put in equation 1, then we have

4x + 6[(7/3)x - 1] = 21

4x + 14x - 6 =  21

18x = 27

x = 3/2

x = 1.5

Then the value of the variable 'y' is calculated as,

y = (7/3)(3/2) - 1

y = 7/2 - 1

y = 3.5 - 1

y = 2.5

The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).

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Answer:

The price of 5$ worth of apples will be $3.10.

Step-by-step explanation:

5 dollars worth of apples would be 2 and a half apples. So, you would multiply 1.24 by 2.5. that gives you 3.1. Then, change those into change and  you have your answer. Hope this helps!

Answer:

The data given from the graph proves that Catherine and Ana's suspicions were correct and the athletes at their school do indeed have a quicker reaction time than other students at their school. The average reaction time for the athletes ranges from 240 - 300, while the normal student's reaction time ranges from 260 - 330. There still should be more experiments to test this theory to get more detailed and accurate results because there are still athletes that have the same reaction time as normal students and the dot away from the boxes shows that there is a athlete that has a slower reaction rate than all of the  normal students. So it is safe to say there is indeed a difference in reaction times, but not a drastic one.

Answer:

15 ft

Step-by-step explanation:

60 divide by 40 equal 1.5

1.5 x 10 = 15

F(x) is defined by the equation f(x) = 5x² - 9x-12, the effect will multiplying

f(x) by 0.5 have on the graph ,then the graph will be compressed vertically.

A transformation in which all distances on the coordinate plane are shortened by multiplying either all x-coordinates (horizontal compression) or all y-coordinates (vertical compression) of a graph by a common factor less than 1.

Given that;

            f(x) = 5x² - 9x-12

Effect will multiplying f(x) by 0.5 , After the transformation

                             g(x) = (0.5) f(x)

After transformation the graph will be composed vertically.

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We need 8 plates for muffins, 4 plates for breadsticks, and 7 plates for rolls, with this arrangement, all plates will have the same amount of items, 12 per plate.

What are the denominator and numerator?

A fraction's top digit is always referred to as the numerator. It displays the number of our parts. A fraction's numerator—the lowest digit—is referred to as the denominator. It displays the overall number of pieces that something can be broken down into.

we have to divide each item in a way that gives us equal groups on each plate,

we have to find a divisor for each item that gives us the same result.

Muffins.

96/2=48

96/3=32

96/4=24

96/8=12

That is, by dividing all muffins into 8 plates we would have 12 muffins per plate.

Breadsticks.

48/2=24

48/4=12

That is, by dividing all breadsticks into 4 plates we would have 12 breadsticks per plate.

Rolls.

84/2=42

84/3=28

84/4=21

84/6=16

84/7=12

By dividing all rolls in 7 plates, we would have 12 rolls per plate.

Therefore, we need 8 plates for muffins, 4 plates for breadsticks, and 7 plates for rolls, with this arrangement, all plates will have the same amount of items, 12 per plate.

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Answer:

18

Step-by-step explanation:

If n=9, then plug in 9 for n in the equation and solve. You should get 2•9, which is 18 when you simplify. Hope this helps and please mark brainliest!

The correlation coefficient is -7.44, which shows a strong negative correlation.

To calculate the correlation coefficient, you can use the following formula:

r = (n Σ(xy) - Σ(x) Σ(y)) / √((n Σ(x²) - (Σ(x))²) (n Σ(y²) - (Σ(y))²))

Where n is the number of data points, x is the variable on the x-axis, y is the variable on the y-axis, Σ(xy) is the sum of the products of x and y, Σ(x) is the sum of x, Σ(y) is the sum of y, Σ(x²) is the sum of the squares of x, and Σ(y²) is the sum of the squares of y.

Plugging in the values from the data, we get:

r = (5 x 198 - 39 x 91) / √((5 x 114 - 39²) x (5 x 187 - 91²))

Simplifying this equation gives us:

r = (-179) / √((-97) x (-6))

r = (-179) / √(582)

r = (-179) / 24.07

r = -7.44

The correlation coefficient is -7.44, which indicates a strong negative correlation. This means that as the value of x increases, the value of y decreases. Conversely, as the value of x decreases, the value of y increases.

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statisticians have been able to show that the normal bell curve property also occurs when the sample size is 30 observations or fewer: False.

The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean. 

The normal distribution is a continuous probability distribution with symmetry around its mean, a central peak around which the majority of observations cluster, and a tapering off of probabilities in both directions for values that are farther from the mean.

When a result is significant, it simply implies that you may be certain that it is true, not that you merely got fortunate (or unlucky) in the sample selection.

Thus, the statement given in the question is false.

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Any quality that pertains to a certain set is referred to in mathematics as a property. A property p that is rigorously specified for every component of a set X is typically defined as a function p: X → {true, false}.

The four properties of equality addition, subtraction, multiplication, and division can be used to solve an equation. To get the value of an equation's unknown variable, we can easily add, subtract, multiply, or divide the two sides of the equation.

The qualities of equality are those characteristics that have no effect on an equation's truth value, i.e., those characteristics that do not affect the equality of two or more values. These equality-related qualities enable us to define an equivalence relation and solve a number of algebraic equations.

9/2 x - 3 = 1/2 x + 2  Addition property of equality

9/2 x - 1/2 x - 3 = 1/2 x - 1/2 x + 2 Addition property of equality

1/4 * 4x = 1/4 * 5 Multiplication property of equality

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